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# Examples of Regular Expression
### Example 1:
Solution:
In a regular expression, the first symbol should be 1, and the last symbol should be 0. The r.e. is as follows:
R = 1 (0+1)* 0
### Example 2:
Write the regular expression for the language starting and ending with a and having any having any combination of b’s in between.
Solution:
The regular expression will be:
R = a b* b
### Example 3:
Write the regular expression for the language starting with a but not having consecutive b’s.
Solution: The regular expression has to be built for the language:
1. L = {a, aba, aab, aba, aaa, abab, …..}
The regular expression for the above language is:
R = {a + ab}*
### Example 4:
Write the regular expression for the language accepting all the string in which any number of a’s is followed by any number of b’s is followed by any number of c’s.
Solution: As we know, any number of a’s means a* any number of b’s means b*, any number of c’s means c*. Since as given in problem statement, b’s appear after a’s and c’s appear after b’s. So the regular expression could be:
1. R = a* b* c*
### Example 5:
Write the regular expression for the language over ∑ = {0} having even length of the string.
Solution:
The regular expression has to be built for the language:
L = {ε, 000000000000, ……}
The regular expression for the above language is:
1. R = (00)*
### Example 6:
Write the regular expression for the language having a string which should have atleast one 0 and alteast one 1.
Solution:
The regular expression will be:
R = [(0 + 1)* 0 (0 + 1)* 1 (0 + 1)*] + [(0 + 1)* 1 (0 + 1)* 0 (0 + 1)*]
### Example 7:
Describe the language denoted by following regular expression
r.e. = (b* (aaa)* b*)*
Solution:
The language can be predicted from the regular expression by finding the meaning of it. We will first split the regular expression as:
r.e. = (any combination of b’s) (aaa)* (any combination of b’s)
L = {The language consists of the string in which a’s appear triples, there is no restriction on the number of b’s}
### Example 8:
Write the regular expression for the language L over ∑ = {0, 1} such that all the string do not contain the substring 01.
Solution:
The Language is as follows:
1. L = {ε, 01001110100, …..}
The regular expression for the above language is as follows:
1. R = (10*)
### Example 9:
Write the regular expression for the language containing the string over {0, 1} in which there are at least two occurrences of 1’s between any two occurrences of 1’s between any two occurrences of 0’s.
Solution: At least two 1’s between two occurrences of 0’s can be denoted by (0111*0)*.
Similarly, if there is no occurrence of 0’s, then any number of 1’s are also allowed. Hence the r.e. for required language is:
R = (1 + (0111*0))*
### Example 10:
Write the regular expression for the language containing the string in which every 0 is immediately followed by 11.
Solution:
The regular expectation will be:
R = (011 + 1)* | crawl-data/CC-MAIN-2024-38/segments/1725700651616.56/warc/CC-MAIN-20240915052902-20240915082902-00642.warc.gz | null |
When a species is invasive...
The National Park Service defines a invasive species as non-native species that causes harm to the environment, economy, or human, animal, or plant health (Executive Order 13751). Learn more about invasive species by visiting our About page.
It is often thought that the terms 'invasive' and 'non-native' can be used interchangeably, but this is not always true. For a plant or animal to be invasive, it must do harm. Simply being non-native is not cause for concern. The National Park Service actively manages those non-native species that do harm.
...and when a species is non-native
Non-native species are organisms that do not occur naturally in an area, but are introduced as the result of deliberate or accidental human activities.
Unlike invasive species, non-native species may not hinder or prevent the survival of others within the ecosystem. They simply exist where they have not naturally occurred. Other terms used for non-native species include 'exotic' or 'alien' species, but these are often discouraged terms, as they may imply another meaning.
You might even recognize some non-native species of plants in your own backyard or on your dinner table. Non-native species such as petunias and tomatoes, present no threat to native plants and have been cultivated by humans for centuries.
Location, location, location...
In some cases, it is not correct to call an entire species native, non-native, or invasive to the U.S. In fact, a species may be considered native in one park, but invasive in another if it had not been historically found there. Rainbow trout provide an interesting example of a species for which management is complex. Rainbow trout are native to only a few states in the Western U.S., and non-native throughout much of the rest of the U.S. However, this species is considered invasive in some lakes and streams due to its effects on those native ecosystems.
More information about invasive species from the NPS and our partners can be found on the Resources page.
Last updated: December 3, 2020 | <urn:uuid:23994447-d9e0-45e7-9868-7a77d4ce74a5> | {
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August 24, 2012
Rhine River Freezing Provides Clues To Solar Activity And Colder Winters
April Flowers for redOrbit.com - Your Universe Online
Scientists have long suspected that the Sun's 11-year cycle influences climate of certain regions on Earth. Records of average, seasonal temperatures do not date back far enough to confirm any patterns, though.An international team of researchers, armed with a unique proxy, show that unusually cold winters in Central Europe are related to low solar activity — when sunspot numbers are minimal. Germany's Rhine River freezing is the key.
The new analysis reveals a correlation between periods of low activity of the Sun and of some cooling on a limited, regional scale in Central Europe, along the Rhine.
“The advantage with studying the Rhine is because it´s a very simple measurement,” said Frank Sirocko professor of Sedimentology and Paleoclimatology at the Institute of Geosciences of Johannes Gutenberg University in Mainz, Germany. “Freezing is special in that it´s like an on-off mode. Either there is ice or there is no ice.”
Riverboat men used the Rhine for cargo transport from the early 19th through mid-20th centuries. Docks along the river have annual records of when ice clogged the waterway and stymied shipping. The research team used these easily-accessible documents along with other historical accounts to determine the number of freezing episodes since 1780.
Sirocko's team found that between 1780 and 1963, the Rhine froze in multiple places fourteen different times. The sheer size of the river means it takes extremely cold temperatures to freeze over making freezing episodes a good proxy for very cold winters in the region.
The researchers mapped the freezing episodes against the solar activity cycle — a cycle of the Sun's varying magnetic strength and thus total radiation output. They determined that ten of the fourteen freezes occurred during years when the Sun had minimal sunspots and calculated that there is a 99 percent chance that extremely cold Central European winters and low solar activity are inherently linked.
“We provide, for the first time, statistically robust evidence that the succession of cold winters during the last 230 years in Central Europe has a common cause,” Sirocko said.
“There is some suspension of belief in this link,” said Thomas Crowley, Director of the Scottish Alliance for Geoscience, Environment, and Society (SAGES), who was not involved with the study, “and this study tilts the argument more towards thinking there really is something to this link. If you have more statistical evidence to support this explanation, one is more likely to say it´s true.”
The study is set to be published August 25 in Geophysical Research Letters, a journal of the American Geophysical Union.
The sun emits less ultraviolet radiation when sunspot numbers are down. Less radiation means less heating of Earth's atmosphere, which sparks a change in the circulation patterns of the two lowest atmospheric levels, the troposphere and stratosphere. Such changes lead to climatic phenomena such as the North Atlantic Oscillation, a pattern of atmospheric pressure variations that influences wind patterns in the North Atlantic and weather behavior in regions in and around Europe.
“Due to this indirect effect, the solar cycle does not impact hemispherically averaged temperatures, but only leads to regional temperature anomalies,” said Stephan Pfahl, a co-author of the study who is now at the Institute for Atmospheric and Climate Science in Zurich.
The study shows that this variation in atmospheric circulation leads to cooling in parts of Central Europe but warming in other European countries, such as Iceland. This suggests that sunspot influence is a localized phenomenon. The data links the low solar activity to the extremely cold winters of 2010 and 2011 which were so cold they resulted in record lows for the month of November in certain countries. Some who dispute the occurrence of anthropogenic climate change argue that this two-year period shows that Earth's climate is not getting any warmer. Climate is a complex system, however, and a short-term localized dip in temperatures only temporarily masks the effects of a warming world.
“Climate is not ruled by one variable,” said Sirocko. “In fact, it has [at least] five or six variables. Carbon dioxide is certainly one, but solar activity is also one.”
Moreover, the researchers also point out that, despite Central Europe´s prospect to suffer colder winters every 11 years or so, the average temperature of those winters is increasing and has been for the past three decades. As one piece of evidence of that warming, the Rhine River has not frozen over since 1963. Sirocko said such warming results, in part, from climate change.
Hoping to establish a more complete record of past temperature dips, the team is looking to other proxies, such as the spread of disease and migratory habits.
“Disease can be transported by insects and rats, but during a strong freezing year that is not likely,” said Sirocko. “Also, Romans used the Rhine to defend against the Germanics, but as soon as the river froze people could move across it. The freezing of the Rhine is very important on historical timescales.”
The Rhine wasn't Sirocko's inspiration for this study, however. It was 125 mile ice skating race he attended over 20 years ago in the Netherlands.
“Skaters can only do this race every 10 or 11 years because that´s when the rivers freeze up,” Sirocko said. “I thought to myself, ℠There must be a reason for this,´ and it turns out there is.” | <urn:uuid:228bcd69-5405-4559-bb4f-5cff77f1b53c> | {
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# Reasoning Special: Tricks to Solve Analogy Questions
By Neha Joshi|Updated : February 15th, 2021
The Reasoning section of every competitive exam includes questions from the topic “Analogy”. This topic is considered to be quiet important and every year a good number of questions are asked from this topic. We are providing you with Basic Concepts & Tricks to “Analogy” related Questions in Reasoning which will surely help you in the upcoming Teaching and other competitive Exams.
The Reasoning section of every competitive exam includes questions from the topic “Analogy”. This topic is considered to be quiet important and every year a good number of questions are asked about this topic. We are providing you with Basic Concepts & Tricks to “Analogy” related Questions in Reasoning which will surely help you in the upcoming Teaching and other competitive Exams.
An analogy literally means ‘Drawing a comparison in order to show a similarity in some respect’. An analogy basically uses a relationship between two(or more) elements to show a similar relationship among another set of elements. So, these questions aim to test the overall logical understanding of the candidates and how coherently they understand the different kinds of relationships among various elements.
There are various types of relationships which are used in analogy-based questions. Below is one such list which shows the various relationships with one example each:
Let’s explore the various types of questions based on Analogy that are asked in SSC-CGL exams and the right way to solve them:
### Types of Analogy:
I). Completing analogous pair. Such questions give relationship between a pair; first element of second pair is given and we have to find the second element of second pair based on similar relationship given by first pair.
For example:
1) Oasis: Sand ∷ Island: ?
a) River
b) Sea
c) Water
d) Waves
Here, first pair is ⇒ “Oasis: Sand” and second pair is “Island:?”. And, “∷” sign means first pair and second pair share similar relationship.
Oasis’ is a mass of water amidst ‘Sand’ similarly ‘Island’ is a mass of land amidst ‘water’. Note: It’d be Island: Sea had the first pair been Oasis: Desert. We’re given the name of thing desert is made of i.e. Sand. So, we’ll use the name of thing Sea is made of i.e. Water.
2) Annihilation: Fire ∷ Cataclysm
a) Earthquake
b) Flood
c) Emergency
d) Steam
Here, ‘Annihilation’ i.e. total destruction is the result of ‘Fire’. So, ‘Cataclysm’ i.e. the rising of a body of water and it's overflowing onto normally dry land is the result of ‘flood’.
II). Simple Analogy. In such questions, a simple statement is given where a relationship is given and we’re asked the second element for the term given in the question, like the example below:
1) Sweet is to Chocolate as Book is to….?
a) Dictionary
b) Library
c) Encyclopedia
d) Atlas
Here, Chocolate can be sweet or bitter but ‘Sweet’ is the enlarged form of chocolate. Similarly, ‘Encyclopedia’ is an enlarged form of a ‘book’.
III). Choosing the analogous pair: In such questions, a pair is given in the question and we’ve to find a suitable pair from the options given that resembles the similar relationship as in the question like the examples below:
1) Borrow : Steal
a) Enter: Trespass
b) Tell: Speak
d) Hit: Kill
Here, for both ‘borrowing’ and ‘stealing’ we take someone else’s thing. The only difference being that the first thing we take is with the permission of another while the second thing is taken without the permission of another. Similarly, among all the options, we see this option is seen in ‘Enter: Trespass’ where we ‘enter’ after taking permit while ‘trespassing’ is done without any permit whatsoever.
2) Cool: Frigid
a) Livid: Lurid
b) Pool: Placid
c) Tepid: Torrid
d) Lack: Abundant
Here, ‘Frigid’ means extremely cold. So, in Cool: Frigid, second is the extreme version of another. Let’s check the meaning of all options given:
a) LividDiscolored beneath the skin: Lurid⇒ Ghastly pale ⇒ This doesn’t give an extreme version of paleness.
b) PoolA small lake: Placid⇒ a body of water free from disturbance by heavy waves ⇒ This doesn’t give the extreme version of pool.
c) TepidModerately warm: Torrid⇒ Extremely hot ⇒ Torrid is the extreme version of Tepid.
d) Lack: Abundant⇒ Present in great quantity ⇒ These two are opposite not extreme version.
We can see that only option c) fulfils the criteria.
IV). Multiple word analogy: These are the type of questions discussed above with the only difference being that here three elements are given in a pair instead of two and we have to select the suitable option. Like the example below:
1) Music: Guitar: Performer
a) Dance: Tune: Instrument
b) Food: Recipe: Cook
c) Patient: Medicine: Doctor
d) Trick: Rope: Acrobat.
In, Music: Guitar: Performer, ‘Performer’ plays ‘Music’ on ‘Guitar’. So, III element is playing/doing I element on II element.
From options, we can clearly see that this pattern is followed only in option d) i.e. Acrobat (An athlete who performs acts requiring skill) performs ‘Tricks’ on a ‘Rope’.
V). Number-based analogy: Till now, we saw the analogy based on words now we’ve questions based on numbers too like shown below:
1) Completing the analogous pair.
25: 37 ∷ 49:?
a) 41
b) 56
c) 60
d) 65
Here, in 25: 37 the pattern can be explained as where is the first element as 25 = 5^2 and is the second element as 36 = (5+1)2 + 1.
For 49, we know that 49 = 72 so second element = = 65 which is option d).
2) Choosing the analogous pair.
Q. 7: 24
a) 30: 100
b) 23: 72
c) 19: 58
d) 11: 43
In 7: 24, 24 = 7×3 + 3 i.e. the relationship can be shown as
Similar relationship can only be seen in option b) 23: 72 where 23×3 + 3 = 69 + 3 = 72.
3) Multiple number analogy: It’s just like multiple-word analogy:
Q. (9, 15, 21)
a) (10, 14, 21)
b) (7, 21, 28)
c) (5,10,25)
d) (4, 8, 12)
In (9, 15, 21) the pattern given is as 15 = = 15 where 9 and 21 are 1st and 3rd numbers respectively.
Similar relationship can only be seen in so option d) where 8 (second no.) = = 8
VI). Alphabet based analogy. In these types of questions, two words that are group of random letters are related to each other in some way. We’re supposed to complete the analogous pair based on that relationship:
FJUL: BOQQ∷ LHRX: ?
a) BKPR
b) MNCC
c) HRYY
d) HMNC
The relationship between FJUL: BOQQ can be illustrated as:
If we do a similar operation on LHRX we can see the following:
Hence, option d) is the answer.
VII). Mixed analogy: These types of questions mixed alphabet and number like shown below:
Q.
a) 2
b) 3
c) 23/7
d) 4
Here, in , T is 20th element in the alphabet series while J is 10th so Similarly, X is 24thelement in alphabetical series while H is 8th so So,
Practice Time
### Reasoning Quiz on Analogy
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Rakhi DwivediJul 21, 2020
Thanks
SaniyaAug 14, 2020
Useful information mam thanks u so much mam
Himanshu AgrawalFeb 15, 2021
useful
Nisha JayswalFeb 15, 2021
Mp tet exam kro
Nisha JayswalFeb 15, 2021
Mp tet ke students bahot jyada preshan h
ChandaniFeb 16, 2021
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Pramod PrajapatiFeb 20, 2021
Sarakaree ke rejalat | crawl-data/CC-MAIN-2021-31/segments/1627046153966.52/warc/CC-MAIN-20210730091645-20210730121645-00498.warc.gz | null |
Animal Species:Ram's Horn Squid – Spirula spirula (Linnaeus, 1758)
Ram’s Horn Squid is the only living species for this order and family. The common name for this squid is derived from their internal coiled shell which is frequently washed ashore on tropical and subtropical coasts.
Standard Common Name
Ram's Horn Squid
Similarly to nautiluses, S. spirula possesses an internal chambered shell which helps to control the animals’ buoyancy. The shell is an open coil, the edge of which is just visible in the animal. They are a short, cylindrical squid that is easily recognised by their coiled internal shell, light organ and fins on the end of the body. Their luminescent skin is a dark reddish brown, however this colouring is often lost in trawled animals. This species has no toothed tongue (radula) like many other cephalopod species.
Body to around 4.5cm, whole length up to 7cm.
Found throughout the tropical Atlantic and Indo-West Pacific Region.
This mesopelagic small squid lives in mid-water depths of the open ocean. They are typically associated with oceanic islands or continental land masses near deep water. They are thought to be a schooling squid and can be very abundant.
Other behaviours and adaptations
Live animals are rarely seen, however they have been observed to retract their head and arms into their mantle, closing the opening with the two pointed flaps above and below the head. When at rest this species maintains a vertical position, head downwards.
During the day S. spirula rests at around 550-1000m depth, rising at night to feed at around 100-300m. The function of their light organ is unknown, as unusually it aims upwards, the opposite of most midwater animals which produce light from below to cancel their silhouette.
S. spirula is thought to live for around 18-20 months, achieving sexual maturity at 12-15 months.
Mating and reproduction
Young animals have been collected at depths of 1000-1750m, suggesting that females probably lay eggs at the bottom of the continental slope. Amazingly, at these depths the pressure on the egg shell would be more than half a tonne!
Jereb, P., & C.F.E Roper (eds) (2005) Cephalopods of the World: Chambered Nautiluses and Sepioids, Food & Agriculture Organization of the United Nations Catalogue for Fishery Purposes, Rome, No. 4, Vol. 1
Norman, M., (2000) Cephalopods- A World Guide, ConchBooks, Germany (Hackenheim)
Norman, M & A. Reid., (2000) A Guide to Squid, Cuttlefish and Octopuses of Australasia, CSIRO Publishing, Victoria (Collingwood) | <urn:uuid:bc4d9872-6816-41ae-b4ab-1b92e96537bd> | {
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little over two years ago, MIT researchers found that changing the
stiffness of a surface by applying a thin
film of polyelectrolyte helped to inhibit the growth of
several infectious bacteria such as E.
coli and S.
The aim of the research was to help reduce hospital infections caused
during or after surgeries or by other modes of infection.
in a similar vein of research, Rensselaer Polytechnic Institute
researchers have developed
a new nanocomposite that kills the dangerous bacteria S.
contact. Staph infections are at the top end of hospital infections
and this promising material could help further reduce the number of
patients that come under their sometimes deadly purview.
new material is composed of carbon nanotubes and a naturally
occurring enzyme called lysostaphin. Lysostaphin is an enzyme
produced by non-pathogenic strains of Staphylococcus to
combat against the deadly S. aureus. The material can be
mixed with many types of surface coatings or applied directly to
surgical instruments or other hospital gear such as masks.
a test, RPI researchers mixed a batch of the new nanoparticles with
ordinary latex house paint. When they applied a solution of S.
aureus to a surface painted with the mixture, in only 20
minutes, 100% of the S. aureus bacteria had been
only is the nanoparticle completely effective, it is highly durable
with a comparatively long shelf life of six months. Items coated with
nanoparticles or with a paint mixture can be washed repeatedly with
no detrimental effects to the abilities of the nanoparticles to | <urn:uuid:b2c6ed01-d05b-4ebc-853b-02354990695a> | {
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By Matt T. Bianchi, MD, PhD
Chief, Division of Sleep Medicine
In an era when advanced technologies, imaging, genetics, and personalized medicine is making heroic steps towards improving healthcare it may come as a surprise that a common and serious disorder with multiple available treatments remains largely undiagnosed. Yet such is the case for sleep apnea, which affects about 10% of adults but is diagnosed in fewer than half of these. Sleep apnea is defined as repeated obstructions in breathing during sleep, each lasting typically 20-30 seconds. These events can range from complete obstruction (apnea) to partial obstruction (hypopnea) and are often accompanied by drops in oxygen.
Sleep apnea is more common in people with diabetes, especially if other risks like obesity are present. Undiagnosed sleep apnea can increase risk of heart attack and stroke – which are already increased in those with diabetes. Sleep disturbances such as sleep apnea can also make it harder to keep blood sugars under control. Other risk factors include male sex, older age, smoking, and alcohol use. Those who have already had a heart attack or stroke, or who have poorly controlled blood pressure, are also at increased risk.
Diagnostic testing, performed in the laboratory or sometimes even at home, involves monitoring breathing and oxygen levels. Pauses in breathing (obstructions) occurring at 5 or more times per hour indicate sleep apnea is present. Increased pause rate means increased severity of the problem (15-30 is moderate; >30 is severe). This disorder often comes with snoring, sleepiness and being overweight – but not in every case.
There are many treatment options for those with sleep apnea. Wearing a mask known as continuous positive airway pressure (CPAP) while sleeping is the standard treatment. Although some initially find the prospect of this treatment daunting, there are dozens of different kinds of masks to help accommodate each person’s needs and comfort. Alternatives come in two categories: surgical and non-surgical. Surgeries include soft palate surgery and jaw advancement surgery, as well as a new stimulator device that acts like a pacemaker to prevent obstructions in sleep. Dental appliances can be made that pull the bottom jaw forward in sleep – these are made by specially trained dentists.
For some people, the sleep apnea is present mainly when they sleep on their back. In these cases avoiding that position can be helpful. This can be accomplished with a shirt/vest that has a bumper on the back that makes back-sleeping uncomfortable. (The challenge is that some people end up sleeping on their back for some or all their sleep regardless.) Finally, weight loss can be helpful for those patients who are overweight. Whichever treatment pathways are chosen, alone or in combination, it is best to speak with your doctor about your choices and how to monitor your progress. | <urn:uuid:c2257a73-af57-4117-b0ab-0f5c5cf5b2c8> | {
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# Sales off
The price has decreased by 20%. How many percents do I have to raise the new price to be the same as before the cut?
Result
p = 25 %
#### Solution:
(1-20/100)*(1+p/100)=1
0.8p = 20
p = 25
Calculated by our simple equation calculator.
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
Be the first to comment!
#### To solve this example are needed these knowledge from mathematics:
Our percentage calculator will help you quickly calculate various typical tasks with percentages. Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
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12. Blood
In human body the blood is about 7.2% body weight. How many kilograms of blood is in the human body with weight 93 kg?
13. Internet anywhere
In school, 60% of pupils have access to the internet at home. A group of 8 students is chosen at random. Find the probability that a) exactly 5 have access to the internet. b) At least 6 students have access to the internet
14. Family
94 boys are born per 100 girls. Determine the probability that there are two boys in a randomly selected family with three children.
15. Percentages
52 is what percent of 93?
16. Screens
The area of a 25 inch TV screen is 300 inch² the area of a 40 inch TV screen is 768 inch². The area of the smaller screen is what percent of the area of the larger screen?
17. Inflation
What is better for people (employees)? ? | crawl-data/CC-MAIN-2019-13/segments/1552912203842.71/warc/CC-MAIN-20190325072024-20190325094024-00061.warc.gz | null |
· Lab Report on copper cycle. 1. Purpose: The purpose of this experiment is to demonstrate a cycle of reactions involving copper. A specific quantity of copper will be transformed through a series of reactions and then recovered as solid copper. A percent recovery will be calculated and sources of loss (or gain) will be identified.
Extracting copper from Malachite 🎓Oxidation and reduction both occur together. If one substance is oxidized, another is reduced. A process where oxidation and reduction are taking place
Bioleaching is the extraction of a metal from sulfide ores or concentrates using materials found native to the environment; namely, water, air and microorganisms. In other words, bioleaching is the commercialization of the ability of certain bacteria and archaea, found in nature, to catalyze the oxidation of sulfide minerals.
· Extracting of Copper from Other Ores. Copper can be extracted from non-sulfide ores by a different process involving three separate stages: Reaction of the ore (over quite a long time and on a huge scale) with a dilute acid such as dilute sulfuric acid to produce a very dilute copper…
EXTRACTION OF COPPER FROM SULPHIDE ORE Large amount of copper are obtained from copper pyrite (CuFeS2) by smelting. Ores containing 4% or more copper are treated by smelting process. Very poor ores are treated by hydro-metallurgical process. ... The following reaction takes place.
· The solvent extraction and stripping of copper from aqueous solutions with DZ988N dissolved in Mextral DT100 can be written as follows: (1) 2 R H ( o r g) + Cu ( a q) 2 + ⇌ R 2 Cu ( o r g) + 2 H ( a q) +. The forward reaction is the extraction reaction, and the reverse reaction is the stripping reaction.
The two reaction model did not fit any of the data well, and only iron extraction could be described with a simple diffusion model. In general the extraction rates can be well described by the two-constant model, C=A t B, up to 600 minutes and under different conditions such as solution pH, EDTA concentration, and different sediment particle size.
· In fact, when pH increases from 0.5 to 2.5, the extraction reaction shifts towards chelating copper ions, so the extraction performance improves [35, 36], whereas, it is speculated that the precipitation of ferric ions begins to occur at high pH and also copper(II) ions forms solids or colloidal particles, which may interfere with its ...
Malachite is a copper ore consisting mainly of basic copper(II) carbonate, CuCO3.Cu(OH)2. In this experiment, students learn how to produce copper from copper(II) carbonate by heating it to produce copper(II) oxide, which is then reduced to the metal using carbon as a reducing agent.
· Copper can be extracted from non-sulphide ores by a different process involving three separate stages: Reaction of the ore (over quite a long time and on a huge scale) with a dilute acid such as dilute sulphuric acid to produce a very dilute copper (II) sulphate solution. Concentration of the copper (II) sulphate solution by solvent extraction.
· There is a upper limit for the copper tenor in the leachate. By controlling the acid concentration of the leach solution and the retention time in the leach zone, it possible to increase the concentration of copper in the leachate solution. As shown above in the extraction and strip reactions, solvent extraction is stoichiometric.
Electrowinning Copper Key Concepts. Electrowinning refers to the process of using electrolysis to extract a metallic element from the compounds in its ore. Copper occurs on Earth both as native copper (the uncombined element, Cu), and in ores (copper compounds, or mixtures of compounds, from which copper metal can be extracted profitably).
Extraction of Metals. Extraction of Copper.. Copper is sometimes found as native metal.. Copper ores include copper(II) oxide and copper(II) sulfide. Copper(II) oxide can be reduced by reaction with carbon.. Some copper ores may contain only small amounts of copper. These are called low grade ores and have less than 1% copper but they are still used because copper is so valuable.
· Extraction of copper from sufidic ores, either by pyrometallurgy or hydrometallurgy, has various limitations. In this study, a solvometallurgical process for the extraction of copper from sulfidic ore minerals (chalcopyrite, bornite, chalcocite and …
The copper should be obvious from its colour. The lead may be less obvious; it may appear as globules or as grey powder. The reactions confirm the place of carbon in the reactivity series, above lead and copper, as it reduces the metal oxides to the metals and is itself oxidised to carbon dioxide:
In the extraction of Cu, the reaction takes place in bessemer converter is: ... 2 C u 2 S + 3 O 2 → 2 C u 2 O + 2 S O 2 The sulphide ore of copper is heated in the air until a part is converted to oxide and then further heating in the absence of air to let the oxide react with unchanged sulphide.
Copper Smelting means that the concentrated ore is heated strongly with silicon dioxide (silica), calcium carbonate (CaCO 3) and air in a furnace. The major steps in the extraction of copper are. Copper in Chalcopyrite is reduced to copper sulphide. Just like in Blast Furnaces, calcium carbonate is added as a flux to create the slag.
The sulphur dioxide escaping from the melt gets trapped in the cooler parts of the surface giving a blistery appearance for copper and hence it is called blister copper. Blister copper is further refined by poling and electrolytic method, as described in the refining of metals. related articles extraction of aluminum extraction of sulphur
· Copper can be extracted from non-sulfide ores by a different process involving three separate stages: Reaction of the ore (over quite a long time and on a huge scale) with a dilute acid such as dilute sulfuric acid to produce a very dilute copper(II) sulfate solution. Concentration of the copper(II) sulfate solution by solvent extraction.
· Given below are the steps for extraction of copper from its ore. Write the reaction involved. (a) Roasting of copper (I) sulphide (b) Reduction of copper (I) oxide with copper (I) sulphide. (c) Electrolytic refining
the copper matte. Though, the slag can be easily separated from the desired product. Smelting is an exothermic reaction between copper pyrite ore, oxygen of air and fluxes (such as silica and limestone) at 1200 °C (above the melting point of copper, but below that of the iron and silica) to form a liquid called "copper …
· Purifying Copper | Reactions | Chemistry | FuseSchoolLearn the basics about Purifying copper. What methods and techniques are used in purifying copper? Find ...
View Flow sheet of copper extraction.pdf from CHEMISTRY 1 at University of Gujrat, Gujrat. Flow sheet of copper extraction Reactions: a. Matte Smelting: 1. 2CuFeS2 → Cu2S +2FeS + 0.5S2 2. 2CuS →
The reaction is highly exothermic and copper obtained is in molten state. During solidification, SO 2 escapes forming blisters on the surface of metal. This variety of copper containing about 2% of impurity is blister copper. Refining: Blister copper consists of about 2% of impurities consisting of cliver, Glod, Zinc, Nicket etc. It is mostly ...
· Basic Process Reaction and Design Parameters. The extraction of copper from aqueous solution by the application of organic solvents such as LIX 64N or the Ashland Chemical products Kelex 100 and 120 proceeds chemically, according to the following equation: (2RH) org. + CuSO4 aq. = (R2Cu) org. + H2SO4 aq.
4C. Purification of Copper by Electrolysis (extraction from ore above). The impure copper from a smelter is cast into a block to form the positive anode.The cathode is made of previously purified copper.These are dipped into an electrolyte of copper(II) sulphate solution.; When the d.c electrical current is passed through the solution electrolysis takes place.
· Extraction of copper from a dilute copper sulphate solution, 310 ppm CuSO,, into a solution containing 200 g/1 H2SO~ and 20,000 ppm Cu~. larly in regard to quantifying the reduction in extraction rate and to establish whether a build up of Fe3in the membrane (and so effectively blocking the association reaction with copper) takes place.
6. One step in the extraction of copper from copper containing ores is the reaction of solid copper (1) sultide with oxygen gas to produce pure copper metal and sulfur dioxide gas. a.) Write a balanced chemical equation to represent this reaction. Make sure to include subscripts 10 denote the state of matter for each of the reactants and products.
2. Extraction of Metallic Copper. Concentration of the ore by froth floatation process: Copper pyrites contains only (2-3)% of copper. The rest of the ore contains iron or sulphide, silica, silicious materials, sulphur, arsenic etc. as impurities.
The dissolution can be described by the following 50 reactions: Cu extraction [%] MnO2 þ 4HClYMnCl2 þ 2H2 O þ Cl2 ð1Þ 45 Chlorine gas could dissolve chalcopyrite as per reaction 40 2CuFeS2 þ 5Cl2 Y2CuCl2 þ FeCl3 þ 4S0 ð2Þ The overall reaction in that case should be as follows 35 5MnO2 þ 2CuFeS2 þ 20HClY5MnCl2 þ 2CuCl2 þ2FeCl3 þ ...
Extracting copper from other ores. Copper can be extracted from non-sulphide ores by a different process involving three separate stages: Reaction of the ore (over quite a long time and on a huge scale) with a dilute acid such as dilute sulphuric acid to produce a very dilute copper(II) sulphate solution.
Copper sulfate solution is collected in the pregnant leach pond then pumped to the solvent extraction plant. The solvent extraction phase of treatment occurs in two stages. During the initial phase an organic solvent is used to recover copper ions contained in the pregnant leach solution, exchanging them with hydrogen ions in the acid.
The table summarises the extraction methods used for different metals. ... Copper may be extracted from copper oxide by reaction with carbon.
When copper (II) sulfate and aluminum are allowed to react, aluminum sulfate and copper are formed. What kind of reaction is this? Write a balanced equation for this reaction. 3 CuSO 4 (aq) + 2 Al(s) Al 2 (SO 4) 3 (aq) + 3 Cu(s) This reaction is an example of a redox reaction: where aluminum is oxidized and copper is reduced.
The earliest evidence of copper smelting occurs in Serbian artefacts dating from around 5000 BC. Copper can be extracted from oxide ores using electrolysis (electrowinning) for low grade ores, or by the carbon reduction method of smelting for higher grade ores. The process of extracting copper from higher grade sulfide ores involves:
Hari om, you are asking a question as to : " How is copper obtained from its sulphide ore? What is the equation of this reaction?". Hari om. Hari om. ANSWER :[ Excerpts] COPPER MINING AND EXTRACTION: SULFIDE ORES : It''s hard to imagine a world wit...
· Q.1. What are the methods of extraction of metals? Ans: There are three main methods of extracting metals from ore. They are by electrolysis, reducing an ore by a more reactive metal, reducing the ore with carbon. Q.2. What type of chemical reaction is used to extract metals from ores?
· During the second reaction the copper and oxygen have been reduced, and the sulphur has been oxidised The Activity Series Corrosion This is the basic oxidation equation for copper. The result is a brittle form of copper, known as blister copper, ranging from 98-99.5% pure. This
The product of this reaction is called hydrated copper carbonate. ... Extraction Converting copper ore to copper metal often involves many steps. First, the ore is crushed into small pieces. Then the crushed pieces are mixed with water to form a slurry, a soup-like mixture of crushed ore and water. ...
· The isolation of copper metal from leach liquor is a two-step process (Wikipedia: Copper Extraction Techniques ). The leach liquor obtained after heap irrigation has a very low concentration of copper dissolved into it, around 0.5 - 2.0 g/L.
Copper oxide is reduced. as carbon is oxidised, so this is an example of a redox. reaction. The table summarises the extraction methods used for different metals.
Copper mining. Chemical reactions. remove some of the sulphur as sulphur dioxide. We do this by heating the concentrated ore from froth floatation. It is heated to betweem 500 °C and 700 °C in air. The product from the roaster is called calcine. It is a solid mixture of oxides, sulphides and sulphates.
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Structure of the course:
Part 1 - Theory
Calculating Average speed and velocity
Calculating instantaneous speed and velocity
What is acceleration and formulas
Formula to calculate linear motion
Part 2 - Real practice questions
Part 3 - Real practice exam
Real practice Problems:
Problem 1: Calculating time and distance with a dry road a car with good tyres.
Problem 2: Find an actual position of a car travel.
Problem 3: The change in velocity of the car if the car reduced speed in the same direction.
Problem 4: Julia driving her car problems to help her to calculate acceleration.
Problem 5: Calculate acceleration of a tram.
Problem 6: Calculate the speed and distance of a car in a given time.
Problem 7: Calculate the velocity of conveyor belt in a given length.
Problem 8: Calculate the final speed of a drunk driver with the given time.
Problem 9: Estimate if a taxi driver succeed in getting to his destination on time.
If you want to be an expert in linear motion and understand about the linear motion, then this is the course you need.
Who this course is for:
Go To Course
if coupon works please click Not Expired | <urn:uuid:dc37e4a2-2692-4f9d-8944-2b2d8cd23a91> | {
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Here is an activity designed to help students really think about and understand the grouping by ten that forms the foundation of our decimal number system.
Access this activity at the National Library of Virtual Manipulatives site.
Begin with decimal places = 0, base = 10, and, depending on your grade level, set the columns to 2, 3, or 4. Begin clicking on the single cube in the ones place, and watch the display of the number on the right. You will notice that the numbers disappear after 9. Ask students why they think this is so.
After they offer explanations, show them how you can group ten single cubes to make one group of ten by clicking outside the group and enclosing the ten cubes in a rectangle. Then show how you can move the group of ten to the next column to the left, and watch the number on the right re-appear. Ask students how the digits in the written number correspond to what they see with the blocks.
You can repeat this with the tens, hundreds, and thousands columns, grouping by tens and moving the new group to the place value on the left. Show students that, just as you “composed” a ten or a hundred or a thousand, you can “de-compose” a group and move them to the place value on the right – and that a group always decomposes to ten of the place value to the right. Ask them where they have seen or used something like this before (this is the concept they use when subtracting with regrouping).
Next, ask your class why they think we always group by tens. Let them think about what it is about the number ten that so attracted the people who developed our current number system. Lead them to see that, although we don’t know for sure, it is probably because we have ten fingers and people traditionally used their fingers (and other body parts) to count objects. Then tell them that Aliens have landed on Earth who have only 5 fingers and they want to teach us their number system. Change the base on the Virtual Manipulative to 5, and repeat what you did for base 10. Watch the numbers on the right and see when they disappear. Group by fives and move groups over just as you did for grouping by tens.
You can repeat this activity with base 4, 3, and 2 (binary). Discuss which digits are needed for the different base systems and why. Make up a homework assignment where students have to convert numbers between different base systems. For advanced students, have them figure out how to add and subtract with regrouping in a different base system (they can experiment with the activities for addition and subtraction). Ask them to teach the class what they have discovered!
For a cool project, have students create a poster of a common scene where all the numbers have been replaced by numbers in base 2, 3, 4, or 5, and have them show the conversions to base 10. By posting these around your room, students will be reminded all year long about the reasoning behind our place value system and how we work with base 10 numbers. | <urn:uuid:6564c795-7922-46a9-ae57-f6fd434a441f> | {
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Hemoglobin is composed of four iron heme subunits that can each individually bind oxygen. These four hemes participate in cooperative binding, which means that when one heme subunit binds oxygen, the others are more likely to bind.
Lots of hemoglobin is needed in red blood cells because of the high oxygen demands of the body.
High O2 levels increases hemoglobin's binding affinity for oxygen, allowing it to pick up oxygen in areas like the alveolus.
High temperature also reduces oxygen-binding affinity in hemoglobin as part of the physiological response to hyperthermia.
High carbon dioxide levels reduce hemoglobin's binding affinity for oxygen, allowing it to drop oxygen off at tissues. Because tissues are undergoing cellular metabolism, they produce CO2 as a byproduct and use O2 as an electron acceptor.
Low pH reduces O2 binding in a condition called acidosis. If respiration levels are low and CO2 is not being exhaled fast enough, blood becomes acidic and O2 binding in hemoglobin is reduced.
Myoglobin is a hemoglobin derivative found only in muscle cells. It has one subunit instead of four.
Picmonic's rapid review multiple-choice quiz allows you to assess your knowledge.
Unforgettable characters with concise but impactful videos (2-4 min each) | <urn:uuid:31640593-a0d1-4854-98c4-738f4d589976> | {
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Stormy weather over the North Sea is not uncommon, and so the powerful winds that swept over the European ocean basin on October 27, 2006, were not extraordinary. Winds gusting to hurricane force raged over the sea for several hours, and by the time that the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Aqua satellite flew over at 1:00 p.m. local time, the sea had turned a foamy, white-flecked green off the shore of Denmark. Westerly winds were driving waves into shore, creating a fringe of white where waves crashed onto the beach. In the image, glimmers of white glint in the murky waters offshore where waves break over the shallow continental shelf. The violent sea churned up clouds of sediment, giving the water the brown and green color seen here. Clearer, deep water farther north is nearly black, by contrast.
According to the BBC, a Scottish trawler with four men aboard was lost in the storm, but October 27 was just the beginning of bad weather on the North Sea. On November 1, a Swedish ship sank, killing one, and an oil platform carrying 75 people was set adrift when it broke free from the tug towing it in strong winds and heavy seas, said the BBC. The November 1 storm sent a surge of sea water into the Netherlands (west of Denmark), where it stranded a herd of about 100 horses in a wilderness area, reported CNN. On land, the autumn storm knocked out power and stopped transport throughout Northern Europe.
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### Browsed byTag: variance
Ideas in Mathematics and Probability: The Uniform Distribution (2007) – Article by G. Stolyarov II
## Ideas in Mathematics and Probability: The Uniform Distribution (2007) – Article by G. Stolyarov II
G. Stolyarov II
July 17, 2014
******************************
Note from the Author: This article was originally published on Associated Content (subsequently, Yahoo! Voices) in 2007. The article earned over 4,800 page views on Associated Content/Yahoo! Voices, and I seek to preserve it as a valuable resource for readers, subsequent to the imminent closure of Yahoo! Voices. Therefore, this essay is being published directly on The Rational Argumentator for the first time. ***
***
~ G. Stolyarov II, July 17, 2014
***
The uniform distribution is alternately known as the de Moivre distribution, in honor of the French mathematician Abraham de Moivre (1667-1754) who introduced it to probability theory. The fundamental assumption behind the uniform distribution is that none of the possible outcomes is more or less likely than any other. The uniform distribution applies to continuous random variables, i.e., variables that can assume any values within a specified range.***
Let us say that a given random variable X is uniformly distributed over the interval from a to b. That is, the smallest value X can assume is a and the largest value it can assume is b. To determine the probability density function (pdf) of such a random variable, we need only remember that the total area under the graph of the pdf must equal 1. Since the pdf is constant throughout the interval on which X can assume values, the area underneath its graph is that of a rectangle — which can be determined by multiplying its base by its height. But we know the base of the rectangle to be (b-a), the width of the interval over which the random variable is distributed, and its area to be 1. Thus, the height of the rectangle must be 1/(b-a), which is also the probability density function of a uniform random variable over the region from a to b.
What is the mean of a uniformly distributed random variable? It is, conveniently, the halfway point of the interval from a to b, since half of the entire area under the graph of the pdf will be to the right of such a midway point, and half will be to the left. So the mean or mathematical expectation of a uniformly distributed random variable is (b-a)/2.
It is also possible to arrive at a convenient formula for the variance of such a uniform variable. Let us consider the following equation used for determining variance:
Var(X) = E(X2) – E(X)2 , where X is our uniformly distributed random variable.
We already know that E(X) = (b-a)/2, so E(X)2 must equal (b-a)2/4. To find E(X2), we can use the definition of such an expectation as the definite integral of x2*f(x) evaluated from b to a, where f(x) is the pdf of our random variable. We already know that f(x) = 1/(b-a); so E(X2) is equal to the integral of x2/(b-a), or x3/3(b-a), evaluated from b to a, which becomes (b-a)3/3(b-a), or (b-a)2/3.
Thus, Var(X) = E(X2) – E(X)2 = (b-a)2/3 – (b-a)2/4 = (b-a)2/12, which is the variance for any uniformly distributed random variable.
Ideas in Mathematics and Probability: Covariance of Random Variables (2007) – Article by G. Stolyarov II
## Ideas in Mathematics and Probability: Covariance of Random Variables (2007) – Article by G. Stolyarov II
G. Stolyarov II
July 17, 2014
******************************
Note from the Author: This article was originally published on Associated Content (subsequently, Yahoo! Voices) in 2007. The article earned over 5,200 page views on Associated Content/Yahoo! Voices, and I seek to preserve it as a valuable resource for readers, subsequent to the imminent closure of Yahoo! Voices. Therefore, this essay is being published directly on The Rational Argumentator for the first time. ***
***
~ G. Stolyarov II, July 17, 2014
***
Analyzing the variances of dependent variables and the sums of those variances is an essential aspect of statistics and actuarial science. The concept of covariance is an indispensable tool for such analysis.
***
Let us assume that there are two random variables, X and Y. We can call the mathematical expectations of each of these variables E(X) and E(Y) respectively, and their variances Var(X) and Var(Y) respectively. What do we do when we want to find the variance of the sum of the random variables, X+Y? If X and Y are independent variables, this is easy to determine; in that case, simple addition accomplishes the task: Var(X+Y) = Var(X) + Var(Y).
But what if X and Y are dependent? Then the variance of the sum most often does not simply equal sum of the variances. Instead, the idea of covariance must be applied to the analysis. We shall denote the covariance of X and Y as Cov(X, Y).
Two crucial formulas are needed in order to deal effectively with the covariance concept:
Var(X+Y) = Var(X) + Var(Y) + 2Cov(X, Y)
Cov(X, Y) = E(XY) – E(X)E(Y)
We note that these formulas work for both independent and dependent variables. For independent variables, Var(X+Y) = Var(X) + Var(Y), so Cov(X, Y) = 0. Similarly, for independent variables, E(XY) = E(X)E(Y), so Cov(X, Y) = 0.
This leads us to the general insight that the covariance of independent variables is equal to zero. Indeed, this makes conceptual sense as well. The covariance of two variables is a tool that tells us how much of an effect the variation in one of the variables has on the other variable. If two variables are independent, what happens to one has no effect on the other, so the variables’ covariance must be zero.
Covariances can be positive or negative, and the sign of the covariance can give useful information about the kind of relationship that exists between the random variables in question. If the covariance is positive, then there exists a direct relationship between two random variables; an increase in the values of one tends to also increase the values of the other. If the covariance is negative, then there exists an inverse relationship between two random variables; an increase in the values of one tends to decrease the values of the other, and vice versa.
In some problems involving covariance, it is possible to work from even the most basic information to determine the solution. When given random variables X and Y, if one can compute E(X), E(Y), E(X2), E(Y2), and E(XY), one will have all the data necessary to solve for Cov(X, Y) and Var(X+Y). From the way each random variable is defined, one can derive the mathematical expectations above and use them to arrive at the covariance and the variance of the sums for the two variables. | crawl-data/CC-MAIN-2021-39/segments/1631780058456.86/warc/CC-MAIN-20210927151238-20210927181238-00109.warc.gz | null |
During the expedition your team:
Together you and the other teams in your country have:
Well done! Your team are exemplar Water Explorers! Have a think about what you can do to go even further - can you use your knowledge and expertise to help others achieve what you have?
|Team of the Month||0|
|Your school has|
|Reached out to 0 people|
|Got 0 people involved|
|Changed the way 0 people use water|
Step 1: Preparing for water audit with the learner's Grade 7 only (12 learners)
12 learners washed their hands, taking turns. Buckets were used to measure wastewater. In total 0.75 litres of water was wasted using the tippy taps.
Then learners used sanitizer tanks. 4 learners were used to wash their hands.
It was noticed that 4 learners used 10 litres of water. Which means a lot of water has been used compared to water from tippy taps.
Therefore, 12 learners would use 30 litres.
It was discovered that if the 12 learners wash their hands 3 times in sanitizer tanks they will use 90 litres per day. If 12 learners used tippy taps to wash their hands it would use 0.75L x 3 = 2,25 Litres
In conclusion if we use tippy taps we save 90 litres-2,25 l = 87,75 litres per day OR ( 90 x 5 ) – ( 2,25 x 5) = 450 litres – 11,25 = 438,75 litres per week. | <urn:uuid:fa7e4d77-6346-4a6a-8986-54f2f794ac8c> | {
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The terms ‘mental illness’ and ‘addiction’ refer to a wide range of disorders that affect mood, thinking and behaviour. Examples include depression, anxiety disorders, schizophrenia, as well as substance use disorders and problem gambling. Mental illness and addictions can be associated with distress and/or impairment of functioning. Symptoms vary from mild to severe.
- In any given year, 1 in 5 Canadians experiences a mental health or addiction problem.1
Who is affected?
- 70% of mental health problems have their onset during childhood or adolescence.2
- Young people aged 15 to 24 are more likely to experience mental illness and/or substance use disorders than any other age group.3
- Men have higher rates of addiction than women, while women have higher rates of mood and anxiety disorders.3
- People with a mental illness are twice as likely to have a substance use problem compared to the general population. At least 20% of people with a mental illness have a co-occurring substance use problem.4 For people with schizophrenia, the number may be as high as 50%.5
- Similarly, people with substance use problems are up to 3 times more likely to have a mental illness. More than 15% of people with a substance use problem have a co-occurring mental illness.4
- Canadians in the lowest income group are 3 to 4 times more likely than those in the highest income group to report poor to fair mental health.6
- Studies in various Canadian cities indicate that between 23% and 67% of homeless people report having a mental illness.7
Morbidity and mortality
- Mental illness is a leading cause of disability in Canada.8, 9, 10
- People with mental illness and addictions are more likely to die prematurely than the general population. Mental illness can cut 10 to 20 years from a person’s life expectancy.11
- The disease burden of mental illness and addiction in Ontario is 1.5 times higher than all cancers put together and more than 7 times that of all infectious diseases. This includes years lived with less than full function and years lost to early death.12
- Tobacco, the most widely used addictive substance, is the leading cause of premature mortality in Canada. Evidence suggests that smoking is responsible for nearly 17% of all deaths.13
- Among Ontarians aged 25 to 34, 1 of every 8 deaths is related to opioid use.14
- Nearly 4,000 Canadians die by suicide each year – an average of more than 10 suicides a day.15 It affects people of all ages and backgrounds.
- About 230,000 Ontarians, or 2.2% of the population, report having seriously contemplated suicide in the past year.16
- More than 75% of suicides involve men, but women attempt suicide 3 to 4 times more often.15, 17
- Suicide accounts for 13% of deaths among youth aged 10 to 14 and 25% of deaths among youth aged 15 to 19. After accidents, it is the second leading cause of death for people aged 15 to 34.15
- More than half of suicides involve people aged 45 or older.15
- First Nations youth die by suicide about 5 to 6 times more often than non-Aboriginal youth. Suicide rates for Inuit youth are among the highest in the world, at 11 times the national average.18
- According to a 2008 survey:
- Just 50% of Canadians would tell friends or co-workers that they have a family member with a mental illness, compared to 72% who would discuss a diagnosis of cancer and 68% who would talk about a family member having diabetes.19
- 42% of Canadians were unsure whether they would socialize with a friend who has a mental illness.19
- 55% of Canadians said they would be unlikely to enter a spousal relationship with someone who has a mental illness.19
- 46% of Canadians thought people use the term mental illness as an excuse for bad behaviour, and 27% said they would be fearful of being around someone who suffers from serious mental illness.19
- In 2015:
- 57% believe that the stigma associated with mental illness has been reduced compared to 5 years ago.20
- 81% are more aware of mental health issues compared to 5 years ago.20
- 70% believe attitudes about mental health issues have changed for the better compared to 5 years ago.20
- But stigma remains:
- 64% of Ontario workers would be concerned about how work would be affected if a colleague had a mental illness.21
- 39% of Ontario workers indicate that they would not tell their managers if they were experiencing a mental health problem.21
Access to services
- While mental illness accounts for about 10% of the burden of disease in Ontario, it receives just 7% of health care dollars.8 Relative to this burden, mental health care in Ontario is underfunded by about $1.5 billion.8, 31
- The Mental Health Strategy for Canada recommends raising the proportion of health spending that is devoted to mental health to 9% by 2022.22
- 17% of Canadians aged 15 or older report having a mental health care need in the past year; one third of those individuals report that their needs were not fully met.3 The rate is even higher for children and youth.23
- Between 2006 and 2014:
- rates of emergency department visits for mental disorders among children and youth (age 5 to 24) increased by 45% 24
- rates of inpatient hospitalizations that involved at least one overnight stay for mental disorders among children and youth increased by 37% 24
Costs to society
- Individuals with a mental illness are much less likely to be employed.25 Unemployment rates are as high as 70% to 90% for people with the most severe mental illnesses.26
- In any given week, at least 500,000 employed Canadians are unable to work due to mental health problems. This includes:
- approximately 355,000 disability cases due to mental and/or behavioural disorders27 plus
- approximately 175,000 full-time workers absent from work due to mental illness.28
- The economic burden of mental illness in Canada is estimated at $51 billion per year. This includes health care costs, lost productivity, and reductions in health-related quality of life.1, 10
- In Ontario the annual cost of alcohol-related health care, law enforcement, corrections, lost productivity, and other problems is estimated to be at least $5 billion.29
- A growing body of international evidence demonstrates that promotion, prevention, and early intervention initiatives show positive returns on investment.9, 30
1 Smetanin et al (2011). The life and economic impact of major mental illnesses in Canada: 2011-2041.
2 Government of Canada (2006). The human face of mental health and mental illness in Canada.
sup>3 Statistics Canada (2013). Canadian Community Health Survey – Mental Health.
4 Rush et al (2008). Prevalence of co-occurring substance use and other mental disorders in the Canadian population.
5 Buckley et al (2009). Psychiatric comorbidities and schizophrenia.
6 Statistics Canada (2003). Canadian Community Health Survey – Mental Health.
7 Canadian Institute for Health Information (2007). Improving the health of Canadians: Mental health and homelessness.
8 Institute for Health Metrics and Evaluation (2015). Global Burden of Diseases, Injuries, and Risk Factors Study, 2013.
9 Mental Health Commission of Canada (2014). Why investing in mental health will contribute to Canada’s economic prosperity and to the sustainability of our health care system.
10 Lim et al (2008). A new population-based measure of the burden of mental illness in Canada.
11 Chesney, Goodwin and Fazel (2014). Risks of all-cause and suicide mortality in mental disorders: a meta-review.
12 Ratnasingham et al (2012). Opening eyes, opening minds: The Ontario burden of mental illness and addictions.
13 Whiteford et al (2013). Global burden of disease attributable to mental and substance use disorders: Findings from the Global Burden of Disease Study 2010.
14 Gomes et al (2014). The burden of premature opioid-related mortality.
15 Statistics Canada (2014). Leading causes of death, total population, by age group and sex, Canada, 2011.
16 Ialomiteanu et al (2014). CAMH Monitor eReport 2013: Substance use, mental health and well-being among Ontario adults, 1977-2013.
17 Statistics Canada (2012). Suicide rates, an overview, 1950 to 2009.
18 Health Canada (2012). First Nations & Inuit health – mental health and wellness.
19 Canadian Medical Association (2008). 8th annual National Report Card on Health Care.
20 Bell (2015). Bell Let’s Talk: The first 5 years (2010-2015).
21 Dewa (2014). Worker attitudes towards mental health problems and disclosure.
22 Mental Health Commission of Canada (2012). Changing directions, changing lives: The mental health strategy for Canada.
23 Waddell et al (2005). A public health strategy to improve the mental health of Canadian children.
24 Canadian Institute for Health Information (2015). Care for children and youth with mental disorders.
25 Dewa and McDaid (2010). Investing in the mental health of the labor force: Epidemiological and economic impact of mental health disabilities in the workplace.
26 Marwaha and Johnson (2004). Schizophrenia and employment: A review.
27 Calculated from data in Dewa, Chau, and Dermer (2010), “Examining the comparative incidence and costs of physical and mental health-related disabilities in an employed population,” and Statistics Canada employment data.
28 Calculated from data in Institute of Health Economics (2007), “Mental health economics statistics in your pocket,” and Statistics Canada – Labour Statistics Division (2011), “Work absence rates 2010.”
29 Rehm et al (2006). The costs of substance use in Canada, 2006.
30 Canadian Policy Network (2011). Return on investment: Mental health promotion and mental illness prevention.
31 Brien et al. (2015), Taking Stock: A report on the quality of mental health and addictions services in Ontario. | <urn:uuid:9bc7ba72-6253-4723-bba5-9b503064ed85> | {
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European Philosophy – Kant
For this lecture, read sections I-VI of Kant’s Critique of Pure Reason.
Immanuel Kant (1724 – 1804 CE) was a German philosopher who was technically born in what was once Konigsberg, Prussia, today part of Russia and renamed Kaliningrad. While Kant grew up in a devotedly Pietist family, a branch of Lutheranism that placed a great emphasis on individual morality and purity, he found himself drawn to Rationalism and in opposition to religious ceremony. While a professor at the University of Konigsberg, Kant was always “indisposed” whenever it was his turn to participate in church services.
It is said that Kant never traveled more than fifty kilometers from his hometown in his entire life. He was known for being obsessively punctual, and legend has it that he would take his daily walks after lunch so routinely that housewives would set their clocks as Kant passed by their houses. Kant would always walk alone, as he believed it proper and healthy to breathe through one’s nose in the open air and so kept his mouth closed outside. He was also deeply disturbed by perspiration. It is said that the only morning Kant broke from his usual strict routine was to purchase a newspaper announcing the outbreak of the French Revolution, an event that, like the work of Kant, had a great impact on Hegel, the next figure we will study.
Just as Locke is famous for his work in both epistemology and political theory, Kant is famous for his work in both epistemology and ethics. While we will focus on Kant’s epistemology for the purposes of this class, just as we focused on Locke’s, we cover Kant’s theory of morality in the Ethics class, which we can briefly cover here just as we briefly covered Locke’s political influence. Kant believed in strict, rule abiding morality, which he considered the true means of Christian salvation, not religious ritual. Using our universal faculty of reason, Kant argued that we can come to understand absolute principles, morals to which we should always adhere no matter the consequences.
Kant argues that if we are rational, we are concerned with absolutes that are universal and ideal. The example Kant gives is, “Do not lie”. If we always lied, society would fall apart, and so we must always tell the truth if we choose to speak rationally. A firm believer in duty, Kant argues that we must be moral no matter the consequences. Even if we know that a lie might have a good chance at saving our own life or the life of another, immorality is never justified. Needless to say, many find this stance a bit to dogmatic to put in practice. John Stuart Mill, who we will study with Utilitarianism, argued for the opposite position, that the ends justify the means, and morality is only for the purpose of achieving happiness.
Kant was primarily concerned with metaphysics, the laws of being. Just as Plato’s Idealism was concerned with the heavens while modern Idealism was concerned with the mind, so too Aristotle’s metaphysics was concerned with the workings of the heavenly bodies, while Kant’s metaphysics was concerned with the limitations of the human mind. This is similar to Locke, who was primarily interested in the limits of human knowledge and understanding. Like Leibniz, whom Kant admired and studied, Kant believed in the Principle of Sufficient Reason, the Principle of Non-Contradiction and the rational, universal application of logic, which Kant thought Aristotle had nearly completed. Later, Kant’s work would impact Schopenhauer, whose work would impact Wittgenstein, whose work would completely revolutionize logic, unbeknownst to Kant.
Like Descartes and Hume, Kant was well aware of ancient Greek Pyrrhonism, as well as the challenge that skepticism and the work of Hume posed to metaphysics and Rationalism. Aristotle hated ancient Greek skeptics, arguing that they were “mere destroyers”, and no better than plants when it came to philosophy. Upon reading the work of Hume, Kant famously wrote that he was woken from his “dogmatic slumbers”, now tasked to prove that there is objective truth beyond mere assumptions given that all beliefs are acquired through experience. Kant’s work, like that of Descartes, is concerned with finding what can be defined as certain and objective in the face of doubting everything. Specifically, Kant sought to rescue Leibniz’s Principle of Sufficient Reason and Principle of Non-Contradiction from being considered mere assumptions. He argued that metaphysics could go beyond both dogmatism and skepticism to become ‘critical’, like Descartes questioning all truth to distinguish what is objectively true beyond all appearances.
In his early work, Kant wrote about philosophy and the natural sciences, reconciling the work of Newton with philosophy and theology. Like Descartes, Kant argued that the regularity of the cosmos shows that it is intelligently designed and operates in a rational manner. Strangely, in his old age Kant hypothesized that the use of domestic electricity caused strange cloud formations and epidemics of disease in cats, a theory which might have survived if Kant had lived in the days of the internet.
Awoken by the skepticism of Hume, Kant spent a ten year “decade of silence”, from 1770 to 1780, working on the first of his three Critiques, the Critique of Pure Reason. Originally, Kant thought the work would take three months. This first Critique focused on objective rational inquiry exclusively separate from the influence of experience. Kant’s second two critiques, the Critique of Practical Reason and the Critique of Pure Judgement, focused on the use of reason in practical matters. and . The Critique of Practical Reason dealt with freedom and morality, and the Critique of Pure Judgement dealt with aesthetics, the study of beauty and art. We focus on the first Critique, as we have been on epistemology. Much as Descartes sought to incorporate while overcoming Pyrrhonian skepticism, Kant sought to incorporate while overcoming Hume’s Empiricism with Rationalism. Kant argued that Hume was right about the world of experience, which can only be known subjectively and imperfectly, but not about the logical operation of reason, which we can know objectively and certainly.
Recall that Locke compared the faculty of understanding to the human eye. Kant’s conception of understanding is often illustrated with the metaphor of eyeglasses. While we may not be able to know what the world looks like without our glasses, we can examine the glasses to see the frame through which we view the world. Likewise, Kant argued that we can critically examine our faculty of understanding with reason to understand how our ideas must take shape, to understand both the basis of understanding and the motions of reason. This would put metaphysics, such as the Principle of Non-Contradiction, “on the secure path of science”. ‘Science’ in German is Wissenschaft, or “knowledge-base”.
Unlike Berkeley, Kant believes that there is a “thing-in-itself” beyond appearances, the Ding an sich in the German, using the Latin term noumena for the things themselves and phenomena for our perceptions of them. Kant argues that we can never know the thing in itself, but we can know the way that we form ideas about appearances. Next week, we will study Phenomenology, the attempt by Hegel, Merleau-Ponty and others to create a “science of appearances”. Kant used another pair of Latin terms to distinguish between rational and empirical truth, to separate the objective from the subjective. That which is known before and apart from all experience Kant labeled a priori, and that which is known after and through experience Kant labeled a posteriori.
The central question of the Critique of Pure Reason is, “How are synthetic a priori judgements possible?”. When we analyze a thing, we break it into its component parts. When we synthesize a thing, we put many parts together to form a greater whole. Kant wants to synthesize, to gather together, what can be known before and apart from experience about the human mind, thus Kant’s concern for the “synthetic a priori”. In a sense, if we sat in a closet and thought, we would be able to form thoughts away from the world, and this would best show us the form our thought takes and thus the form of our world.
If we figure out elementary linear arithmetic in the dark, we may never be able to predict how many coconuts we will gather next Tuesday, but we can be certain that if we gather two coconuts and then three, we will have gathered five coconuts. We can then reason that if we gather six more, we will have eleven, synthesizing additional mathematical truths via reason apart from the experience of gathering any coconuts. Thus, while Hume is right that whatever we think we may gather on a Tuesday is merely an assumption, Kant argues that if we are being objective, we cannot reason two and three together any other way than as the sum of five, giving us a synthesized assumption that is objective and certain, what Descartes sought all along. As mentioned with Descartes, this strangely makes the ideas of logic and mathematics certainties, while the existence of coconuts or Paris, France are merely assumptions.
Essentially, Kant sought to rescue logic, including the Principle-of-Non-Contradiction, from Hume’s charge that all truth is assumption, and he hoped to do this by deducing the principles of logic without relying on assumptions based on experience. This would reveal that logic was truly transcendental, necessary and universal to all experience, the frame through which we must grasp any idea or understanding. While the word transcendent means exclusively removed from and supreme, like a sage who has transcended the world of desires, transcendental means consistently throughout and universal. Wherever one is in the ocean, one would be wet as there is water throughout it.
The American Transcendentalists, such as Emerson and Thoreau, argued that reality is an undivided whole beneath divisions imposed by the mind, a view they found in ancient Indian and Greek thought, and thus the oneness of things is not above and beyond, not transcendent, but within and throughout, transcendental, putting them in the pantheist company of Spinoza. Unlike the Transcendentalists, Kant argued that the objective and subjective should be exclusively divided to prevent misunderstanding and maintain coherence, much as Locke had attempted to divide objective primary qualities from subjective secondary qualities.
Central to this for Kant was the exclusive definition and operation of the faculties of understanding and reason, Verständnis and Vernunft in the German. Hegel took up Kant’s distinction between the faculties of understanding and reason, but influenced by fellow philosopher and friend Schelling, Hegel argued that understanding and reason must be synthesized and united, not exclusively divided. Kant would have considered this the ultimate confusion, arguing in his first Critiquethat the mixing of understanding and reason is a major source of philosophical error as each has properly exclusive jobs to do. For Hegel, Kant’s exclusive division between understanding and reason, as well as the division between the thing-in-itself and our experience of it, were failures of Kant’s inability to synthesize the whole with reason above and beyond the divisions of understanding. While Kant thought that reason should ultimately serve understanding, maintaining exclusive distinctions, Hegel thought that reason should transcend while extending understanding, uniting all in the transcendental One, much like that of the American Transcendentalists.
For Kant, experience requires two separate elements, sensation andunderstanding. Sensation is the raw content and understanding is the conceptual form that makes sensation coherent. Consider Berkeley’s example of an apple. As we look at an apple, our experience is a union of the undefined sensation and the exclusive categories with which we understand the sensation such as red, solid, apple, and fruit. Without both, there is no coherent experience of the apple.
Kant argues that we can become confused, and believe that the category of ‘apple’ and ‘red’ exist in the world itself, are present in the thing-in-itself, but if we are being rational and exclusive we determine that the categories of understanding are not given in the world but conceptions of the mind, as Hume argued about cause and effect. Thus, the thing-in-itself cannot be known, but the categories of understanding, when exclusive, noncontradictory and coherent, can be known with pure clarity. Unlike Locke’s primary qualities, for Kant the objective is mental, not physical, like the forms of mathematics and logic.
Understanding takes various sensations and synthesizes them into categories, while also exclusively dividing the categories from each other. After we experience several objects, some of which are red, and some of which are apples, we form conceptions of redness and apples. As the self experiences the world through its understanding, it finds itself with pre-existing fundamental categories, which Kant calls foundations (Grundsätzein the German, which also translates as ‘principles’). Hegel was critical of Kant for pulling these categories out of nowhere without describing their development, but Kant believed that the origin of the foundational categories was beyond human comprehension.
One of these foundations is the category of causation, which Hume considered to be an assumption learned through experience. Kant, targeting Hume, argued that causation is a foundational category that is present in the mind before and apart from all experience, and that we find ourselves categorizing the world in terms of causation in a way that cannot be derived from experience. Another foundational category of Kant’s is substance. For Kant, the mind begins as an empty cabinet rather than a blank slate, with categorical compartments of causation and substance ready to be filled by experiences. Thus, no matter what our individual experiences are, we will all categorize them in terms of causation and substance.
Reason serves as a higher level of understanding, just as understanding serves as a higher level of sensation. Just as understanding joins and separates sensations, reason joins and separates understandings. Judgement performs both of these activities, dividing sensations into groups for understanding and dividing understandings into groups for reason. Reason infers similarities and differences of understandings, forming ideas. Ideas, such as freedom and beauty, central examples used by Kant and fleshed out in the second and third Critiques, are not directly experienced in the world but are formed through inferences drawn from the understanding.
For Kant, it is crucial to keep reason separate from understanding. Reason is transcendent, beyond sensations and understandings, whereas understanding is transcendental, throughout sensations and reasonings. Reason is separate from the sensible world, and thus free to form ideas. This corresponds to Descartes’ dualism, dividing the determined body from the free mind, except for Kant both understanding and reason are mental. While the understanding is passive, categorizing sensation as it happens, reason is active, producing ideas as it sees fit. Experience is determined by the understanding, but ideas are formed from the free use of reason within the imagination, separate from, though derived from, experience and understanding.
For Kant, reason is free to wander, taking a wider view, forming abstract ideas and speculating about what might be, however it may not contradict the understanding. For Hegel, reason’s job is to extend but also contradict understanding, to contradict accepted dogmas with opposite points of view and force progressively greater synthesis beyond exclusive boundaries. For Kant, contradiction with the understanding results in incoherence, an improper mixing of understanding and reason, not a greater synthesis of knowledge. For Hegel, understanding is extended by contradiction, transforming the incoherent into the coherent. Both believe that reason works through dialectic, by weighing both sides of a potential judgement and then extending the understanding, arriving at a greater understanding than before. Should reason never result in contradiction, or should it contradict itself and then overcome the contradiction? It depends on whether one accepts or opposes the Principle of Non-Contradiction.
For Kant, understanding has jurisdiction over things, whereas reason has jurisdiction over ideas. In this sense, while the understanding categorizes things, such that we experience things as substances that cause and are affected, our ideas of substance and causation are part of our free, abstract reasoning, which judges the categories of the understanding to produce abstract ideas. This would mean that ‘substance’, ‘nature’ and ‘beauty’ are ideas, not things, produced by reason, not experienced in the world.
In both epistemology and ethics, Kant argues that we are free, but we are merely free to find the singular, necessary and objective truth or to be mistaken and confused depending on whether we are being objective and rational. Bill Hicks, the comedian quoted earlier, had a bit mocking American television, shouting, “You are free to do as we tell you!”. This is disturbingly similar to the Nazis posting, “Work is Freedom” above the entrances to the concentration camp at Auschwitz, an inspiration to George Orwell as he wrote doublespeak slogans for the tyrannical Big Brother government of his novel 1984, such as “War is Peace”.
Kant used the metaphor of an island in a stormy sea to illustrate the rational mind amidst the flux of the sensual world, objective and rational in the sea of the uncertain. Schopenhauer, a Kantian, used a similar metaphor of a ship on a stormy sea, more skeptical than Kant as a boat is not fastened down but drifts with the current of the passions. While the understanding is passive, and can only judge sensations as they happen, reason is free to speculate as to what could, or should happen. Hume famously argued that one cannot derive an ‘ought’ from an ‘is’, that we cannot know what should happen merely based on what is happening. Kant meets Hume halfway. ‘Ought’ and ‘is’ are two separate things, as Hume argued, but for Kant reason can derive what objectively ought to be. Kant’s central example of morality, “Do not lie”, is a necessary conclusion that reason arrives at when it properly surveys the understanding and speculates with ideas. The conclusion is seen by reason to be universal, necessary, and objective. Thus, while reason cannot tell us whether we will lie next Tuesday, we can say that it would be objectively wrong to do so.
Nietzsche said Kant was like a fox who admirably broke out of his cage, only to lose his way and wander back into it. Nietzsche disregards all claims to objective truth as mere human interpretations, and so he admires Kant for arguing that reason is free to do as it likes but finds him foolish for arguing that reason must conform to the rational, objective understanding or be wrong. While Kant had hoped to justify and preserve metaphysics, his skepticism towards our knowing the thing-in-itself ultimately lead to the downfall of metaphysics, heralded by Nietzsche.
Realists, like the Scottish Realists who had an impact on Analytic philosophy, thought that Kant had gone too far in agreeing with the skepticism of Hume. Similar to Johnson kicking the rock, Realists argue that it is ridiculous to speak of causation and substance as assumptions or categories of the mind, as they are clear and objectively present in the world. The question is, when is it worthwhile to question our conceptions of causes and substances? | <urn:uuid:ec4f2ec6-880c-46d7-8fc6-1c7d2908eb55> | {
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# 2019 AIME II Problems/Problem 2
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
## Problem
Lily pads $1,2,3,\ldots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$. From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen randomly with probability $\tfrac{1}{2}$ and independently of other jumps. The probability that the frog visits pad $7$ is $\tfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.
## Solution
Let $P_n$ be the probability the frog visits pad $7$ starting from pad $n$. Then $P_7 = 1$, $P_6 = \frac12$, and $P_n = \frac12(P_{n + 1} + P_{n + 2})$ for all integers $1 \leq n \leq 5$. Working our way down, we find $$P_5 = \frac{3}{4}$$ $$P_4 = \frac{5}{8}$$ $$P_3 = \frac{11}{16}$$ $$P_2 = \frac{21}{32}$$ $$P_1 = \frac{43}{64}$$ $43 + 64 = \boxed{107}$.
## Solution 2 (Casework)
Define a one jump to be a jump from $k$ to $k + 1$ and a two jump to be a jump from $k$ to $k + 2$.
Case 1: (6 one jumps) $\left (\frac{1}{2} \right)^6 = \frac{1}{64}$
Case 2: (4 one jumps and 1 two jumps) $\binom{5}{1} \cdot \left(\frac{1}{2}\right)^5 = \frac{5}{32}$
Case 3: (2 one jumps and 2 two jumps) $\binom{4}{2} \cdot \left(\frac{1}{2}\right)^4 = \frac{3}{8}$
Case 4: (3 two jumps) $\left(\frac{1}{2}\right)^3 = \frac{1}{8}$
Summing the probabilities gives us $\frac{43}{64}$ so the answer is $\boxed{107}$.
- pi_is_3.14
## Solution 3
Let $P_n$ be the probability that the frog lands on lily pad $n$. The probability that the frog never lands on pad $n$ is $\frac{1}{2}P_{n-1}$, so $1-P_n=\frac{1}{2}P_{n-1}$. This rearranges to $P_n=1-\frac{1}{2}P_{n-1}$, and we know that $P_1=1$, so we can compute $P_7$.
$P_1=1$
$P_2=1-\dfrac{1}{2} \cdot 1=\dfrac{1}{2}$
$P_3=1-\dfrac{1}{2} \cdot \dfrac{1}{2}=\dfrac{3}{4}$
$P_4=\dfrac{5}{8}$
$P_5=\dfrac{11}{16}$
$P_6=\dfrac{21}{32}$
$P_7=\dfrac{43}{64}$
We calculate $P_7$ to be $\frac{43}{64}$, meaning that our answer is $\boxed{107}$.
## Solution 4
For any point $n$, let the probability that the frog lands on lily pad $n$ be $P_n$. The frog can land at lily pad $n$ with either a double jump from lily pad $n-2$ or a single jump from lily pad $n-1$. Since the probability when the frog is at $n-2$ to make a double jump is $\frac{1}{2}$ and same for when it's at $n-1$, the recursion is just $P_n = \frac{P_{n-2}+P_{n-1}}{2}$. Using the fact that $P_1 = 1$, and $P_2 = \frac{1}{2}$, we find that $P_7 = \frac{43}{64}$. $43 + 64 = \boxed{107}$ | crawl-data/CC-MAIN-2021-31/segments/1627046151972.40/warc/CC-MAIN-20210726000859-20210726030859-00503.warc.gz | null |
New animations released by NASA are recasting a groundbreaking astronomical moment in a whole new light.
On February 24, 1987, astronomers Oscar Dhalde and Ian Shelton witnessed an incredible sight atop a Chilean mountain: a new star in the night sky. Soon, however, they realized it was not a star's birth; rather, it was a blue supergiant meeting its doom.
In that moment, the fusion-powered core of the star — previously called Sanduleak −69° 202 — began to falter. Most astronomers agree the blast happened because the star's core ran low on high-energy fuel, while some believe another star merged with the blue supergiant to trigger the blast.
Whatever the cause, the star collapsed under its own gravity, exploded, spewed its radioactive guts all over space, and generated the power of 100 million suns in the process. We now call the object Supernova 1987A, or SN 1987A.
It was not only the brightest supernova seen for hundreds of years, but also the first time astronomers recorded such an event with modern, high-tech instruments.
"Supernova 1987A became one of the best opportunities ever for astronomers to study the phases before, during, and after the death of a star," a video produced by NASA's Chandra X-ray Observatory team said.
The data has provided lots clues about supernovas, including how they forge new elements that life needs to evolve and distribute them around the universe.
NASA recently commemorated the supernova's anniversary with a bunch of new multimedia, and a few of the images and animations caught our eye.
Zooming in on a supernova's leftovers
This animation gives you a sense of where in the night sky (and just how far away) SN 1987A is located.
The remnants lurk inside the Large Magellanic Cloud, a dwarf galaxy that trails the Milky Way some 168,000 light-years from Earth.
This vast distance means the explosion technically happened 168,000 years in the past, at least relative to where we live. It took that long for the light from the blast to reach us.
Ring of radioactive fire
About once a month over the course of more than 20 years, the Hubble space telescope has photographed SN 1987A and its traveling shock wave. Astronomers continue to compile these images into animations to watch the system evolve.
Starting around the year 2000, they saw the shockwave begin slamming into a 1-light-year-wide ring of gas and dust that the star threw off before its death, creating a brilliant, bubbling glow.
Researchers now believe the high-speed blast wave is leaving the field of gas and dust, marking the beginning of a "major change" in its evolution, according to a pre-print study posted to arXiv.org.
3D model of a disaster
This new animation is of a computer model that shows SN 1987A's explosion and entire evolution through 2017, and in three dimensions.
The model — described in a pre-print study on arXiv led by Salvatore Orlando, an astrophysicist at the INAF-Osservatorio Astronomico di Palermo in Italy — can also fast-forward SN 1987A's evolution years into the future.
For more on the model, check out an interview with Orlando on Chandra X-ray Observatory's website. | <urn:uuid:ed92c8ec-8ef6-47b4-88b4-0b4863331f13> | {
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Question
# James Smith is 30 years and wants to retire when he is 65. So far he...
James Smith is 30 years and wants to retire when he is 65. So far he has saved (1) \$5,000 in an IRA account in which his money is earning 8.3 percent annually and (2) \$4,000 in a money market account in which he is earning 5.25 percent annually. James wants to have \$1 million when he retires. Starting next year, he plans to invest the same amount of money every year until he retires in a mutual fund in which he expects to earn 7.00 percent annually. How much will James have to invest every year to achieve his savings goal? (Round answer to 2 decimal places, e.g. 15.25.)
Let us calculate the future values of individual investments
Future value of IRA=FW1=5000*(F/P,0.083,35)
We know that (F/P,0.083,25)=(1+0.083)^35=16.292810
So, FW1=5000*16.292810=\$81464.05
Future value of investment in money market=FW2=4000*(F/P,0.0525,35)
We know that (F/P,0.0525,35)=(1+0.0525)^35=5.994786
So, FW2=4000*5.994786=\$23979.14
Let he invests amount X per year mutual fund,
Future value of mutual fund investment=FW3=X*(F/A,0.07,35)
We know that
So, FW3=X*(F/A,0.07,35)=138.236878X
We know that
FW1+FW2+FW3=1000000
81464.05+23979.14+138.236878X=1000000
X=(1000000-81464.05-23979.14)/138.236878=\$6471.19
#### Earn Coins
Coins can be redeemed for fabulous gifts. | crawl-data/CC-MAIN-2023-40/segments/1695233510284.49/warc/CC-MAIN-20230927071345-20230927101345-00421.warc.gz | null |
Quadratics Portfolio Day 1 of 3
Lesson 15 of 18
Objective: SWBAT explain key concepts and ideas from the Quadratics unit while reflecting on their own learning.
The purpose of the opening of class today is to introduce the portfolio and the work that is required to complete it. If students in my class have already done a math portfolio for another unit, I usually ask them to share out what a math portfolio is and what putting one together is like. For more info about what a math portfolio is, see the Math Portfolio document in my Teaching Strategies folder.
Next, students will watch a video of a student talking about her experience working on a math portfolio:
Next we’ll take a look at the Quadratics Portfolio Assignment together and go through the requirements. I usually explain the Introduction and the Personal Reflection sections as the bread part of a sandwich, where their work will go in the middle. So I’ll start by talking about the Introduction and the Personal Reflection first and what the purpose is of those two sections. Next, we’ll discuss the meat of the portfolio. This is the section where students will be highlighting their best work, providing explanations, and making connections.
Once we’ve gone over what the portfolio is all about and what the expectations are, I’ll leave time for student questions and comments.
Students will now get to work on starting their portfolios. I like to help students stay on task by asking them to set a goal of what they would like to accomplish by the end of class. I’ll make a list at the board with their names and what part of the portfolio they plan to work on right now.
Students usually start by working on the Introduction to the unit or by looking through their work to pull out pieces from the unit they would like to include. Some students need help organizing their work. If students are missing key pieces, they will have to redo them in order to put them in the portfolio so you may want to have extra copies on hand.
As students are organizing their work, try to let them decide what pieces should go in their portfolios. I continually remind them that the purpose of the portfolio is for them to have an opportunity to show what they have learned. When they are thinking of pieces to include, I encourage them to show work that best demonstrates their learning. I might ask questions like:
- What learning does this piece of work demonstrate?
- What was the key idea behind this assignment or task?
- What does this work show that you know?
Closing + Homework
To close out today's lesson, I will ask my students to respond to the following prompt:
As you look back over your work in this unit, you are probably reminded of many different activities we did in class. Complete the following sentence with respect to something we learned in this unit: I remember when we …
In order to keep the work moving on the portfolio and to keep students from getting overwhelmed, I like to assign a portfolio homework assignment at the end of each class that we are working on portfolios. Again, I go around the room and let each students decide what s/he will complete by the start of tomorrow’s class. I keep a record of what’s students decide so I can check at the beginning of class tomorrow.
Note: This material is adapted from the IMP Teacher’s Guide, © 2010 Interactive Mathematics Program. Some rights reserved. | <urn:uuid:d0576b1d-cf18-4157-987b-acf0b3b2cf1d> | {
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### Home > PC3 > Chapter 4 > Lesson 4.2.2 > Problem4-82
4-82.
Use polynomial division to rewrite the equation $r(x)=\frac{3x^2-5x-20}{x-4}$ in a more-useful form. State the equations of the asymptotes. Then sketch a prediction of what you think the graph looks like. Use a graphing calculator to check you prediction.
Generic Rectangle, 2 rows, 3 columns, with expression, 3 x squared, minus 5 x, minus 20, below the rectangle. Left edge labeled, x minus 4, interior top left, labeled 3 x squared.
Labels added: top edge left, 3 x, interior bottom left, negative 12 x.
Label added: Interior top middle, 7 x.
Labels added: top edge middle, 7, interior bottom middle, negative 28.
Continue the division problem. Part of the rewritten equation is a vertical asymptote, part is a slant asymptote. | crawl-data/CC-MAIN-2024-18/segments/1712296816586.79/warc/CC-MAIN-20240413051941-20240413081941-00818.warc.gz | null |
Teaching With Documents:
Woman Suffrage and the 19th Amendment
Beginning in the mid-19th century, several generations of woman suffrage supporters lectured, wrote, marched, lobbied, and practiced civil disobedience to achieve what many Americans considered a radical change in the Constitution. Militant suffragists used tactics such as parades, silent vigils, and hunger strikes. The records of the National Archives and Records Administration reveal much of this struggle.
As the 150th anniversary of the Seneca Falls Convention of 1848 approaches, historical documents and a script that the National Archives commissioned about the decades long struggle entitled Failure is Impossible serve as valuable teaching tools.
A Resolution Proposing an Amendment to the
December 7, 1868
Petition to Congress
Memorial to Congress from The American
Woman Suffrage Association
February 6, 1872
Petition from Susan B. Anthony to U.S.
January 12, 1874
Petition, Anti-Suffrage Party of New York
World War I, ca. 1917
Photograph, Kaiser Wilson poster
November 19, 1918
Ratification of 19th Amendment, Tennessee
August 24, 1920 | <urn:uuid:1c489206-0a58-4d4e-8aea-d05c7db68467> | {
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A gas giant describes a planet that is not composed of mostly rock and other solid substances. Gas giants are almost entirely formed of various gases. These planets are not completely gas though. At the center, is what astronomers call a rocky center. This term is somewhat misleading though because the rocky center is actually liquid compounds, including molten heavy metals. The term was created by James Blish, a science fiction writer from the mid-1900’s. Gas giants are also called Jovian planets after Jupiter, the prototype of gas giants in our Solar System. There are four gas giants in our Solar System – Jupiter, Saturn, Uranus, and Neptune.
The gas giants in our Solar Systems have a number of similar characteristics. All of our Solar System’s gas giants are outer planets, which means they are the furthest planets from the Sun. Compared to terrestrial planets, gas giants are extremely large and massive. For example, Jupiter has a mass 318 times the mass of Earth, which is a terrestrial planet. Despite their size, gas giants are low-density planets because they are composed almost entirely of gas. In addition to being large, these planets rotate extremely quickly. Jupiter rotates so quickly that it has actually flattened at its poles. The gas giants are extremely cold planets, although that is mostly due to the fact that they are very far from the Sun. Gas giants also have dozens of satellites and ring systems. Saturn is famous for its beautiful rings, which can be seen with the unaided eye from Earth.
Astronomers have also discovered gas giants around stars in other solar systems. In fact, these are the only extra-solar planets that scientists have been able to discover as of yet. These extra-solar gas giants seem similar to Jupiter and the other gas giants in our own Solar System. Astronomers have been studying these planets using powerful telescopes, but they have not been able to find out much information about them so far. Some astronomers are actually searching for life on these planets. They have discovered some extra-solar planets in the habitable zones of other solar systems, and they believe that life could exist on these extra-solar planets or at least the moons of these planets.
Because the gas giants are farther away from Earth than the terrestrial planets, astronomers have not been able to study the gas giants extensively up close. Hopefully, that will change as NASA sends more spacecraft out to explore the outer planets.
If you are looking for more information on gas giants, take a look at NASA’s planets and ThinkQuest’s habitable moons around extra-solar gas giants.
Astronomy Cast has episodes on all of our Solar System’s gas giants, so start with Jupiter. | <urn:uuid:b5b11c28-968e-4a1f-a3d0-86ffaaafdcca> | {
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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## x is a two-digit integer and y is a three-digit integer that ##### This topic has 1 expert reply and 0 member replies ### Top Member ## x is a two-digit integer and y is a three-digit integer that ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult x is a two-digit integer and y is a three-digit integer that is divisible by x. If z is the value of the quotient y/x, is the units digit of z greater than 3? (1) The units digit of x is 3. (2) The units digit of y is the same as the units digit of x. OA C Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1890 messages Followed by: 30 members Upvotes: 470 Top Reply BTGmoderatorDC wrote: x is a two-digit integer and y is a three-digit integer that is divisible by x. If z is the value of the quotient y/x, is the units digit of z greater than 3? (1) The units digit of x is 3. (2) The units digit of y is the same as the units digit of x. OA C Source: Veritas Prep Given: x is a two-digit integer and y is a three-digit integer that is divisible by x, and z is the value of the quotient y/x. Question: Is the units digit of z greater than 3? Let's take each statement one by one. (1) The units digit of x is 3. We have no information about y. Insufficient. Say y = 230 and x = 23, then y/x = 10 => z = 0 < 3. However, if say y = 138 and x = 23, then y/x = 6 => z = 6 > 3. No unique answer. Insufficient. (2) The units digit of y is the same as the units digit of x. Say say y = 120 and x = 20, then z = y/x = 6 => Units digit of z = 6 > 3. However, if say y = 110 and x = 10, then z = y/x = 11 => Units digit of z = 1 < 3. No unique answer. Insufficient. (1) and (2) together Say y = ab3 and x = p3 => y/x = z = ab3/p3 => ab3 = p3 * z Thus, we must have units digit of 3z = 3; this is possible only if the units digit of z equals 1. The answer is No. A unique answer. Sufficient. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review India | Manhattan Review Hyderabad | Dilsukhnagar GMAT Courses | Mehdipatnam GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200
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# Variance-covariance matrix of random vector
1. Jun 15, 2009
### kingwinner
Notation:
Var(Y) is the variance-covariance matrix of a random vector Y
B' is the tranpose of the matrix B.
1) Let A be a m x n matrix of constants, and Y be a n x 1 random vector. Then Var(AY) = A Var(Y) A'
Proof:
Var(AY)
= E[(AY-A E(Y)) (AY-A E(Y))' ]
= E[A(Y-E(Y)) (Y-E(Y))' A' ]
= A E[(Y-E(Y)) (Y-E(Y))'] A'
= A Var(Y) A'
Now, I don't understand the step in red. What theorem is that step using?
I remember a theorem that says if B is a m x n matrix of constants, and X is a n x 1 random vector, then BX is a m x 1 matrix and E(BX) = B E(X), but this theorem doesn't even apply here since it requries X to be a column vector, not a matrix of any dimension.
2) Theorem: Let Y be a n x 1 random vector, and B be a n x 1 vector of constants(nonrandom), then Var(B+Y) = Var(Y).
I don't see why this is true. How can we prove this?
Is it also true that Var(Y+B) = Var(Y) ?
Any help is greatly appreciated!
2. Jun 16, 2009
For question 1: the matrix $$A$$ is constant, so it (and $$A'$$) can be factored outside of the expectation. This is the same type of principal you use with random variables (think $$E(5x) = 5E(x)$$ ).
For 2: Again, $$Y$$ is a collection of constants, and addition of constants doesn't change the variance of a random variable. In a little more detail:
\begin{align*} E(Y + B) & = \mu_Y + B \\ Var(Y+B) & = E[((Y+B) - (\mu_Y + B))((Y+B) - (\mu_Y+B))'] \\ & = E[(Y-\mu_Y)(Y-\mu_Y)'] = Var[Y] \end{align*}
3. Jun 16, 2009
### kingwinner
1) But how can we prove it rigorously in the general case of random matrices?
i.e. how can we prove that
E(AZ) = A E(Z)
and E(W A') = E(W) A' ?
where Z and W are any random matrices, and A is any constant matrix such that the product is defined
2) Thanks for the proof! Now I can see more rigorously why that property is true in the multivariate context.
Last edited: Jun 16, 2009
4. Jun 16, 2009
### EnumaElish
1) You could start with the 2x2 case then generalize; or use induction.
5. Jun 16, 2009
Suppose your random matrix is (using the definition of matrix multiplication)
$$Z = \begin{pmatrix} z_{11} & z_{12} & \dots & z_{1k} \\ z_{21} & z_{22} & \hdots & z_{2k} \\ \ddots & \ddots & \ddots & \ddots \\ z_{m1} & z_{m2} & \dots & z_{mk} \end{pmatrix}$$
and that your constant matrix is $$A$$ with similar notation for its entries.
The $$(r,t)$$ entry of the matrix $$AZ$$ is the random variable given by
$$\sum_{l=1}^m a_{rl} z_{lt}$$
so the expected value of the $$(r,t)$$ entry is
$$E\left(\sum_{l=1}^m a_{rl}z_{lt}\right) = \sum_{l=1}^m E\left(a_{rl}z_{lt}\right) = \sum_{l=1}^m a_{rl} E\left(z_{lt}\right)$$
The second equality is true since each $$a$$ value is a constant number and each $$z$$ is a random variable , so the ordinary rules of expectation apply. What does the equation mean?
a) The left side is the expected value of the $$(r,t)$$ entry in the matrix $$AZ$$
b) The right side is the $$(r,t)$$ entry in the matrix product of $$A$$ and the expected value of $$Z$$ (call this $$E(Z)$$)
This shows that corresponding elements of $$E(AZ)$$ and $$A E(Z)$$ are equal, so
$$E(AZ) = A E(Z)$$
This type of approach works whether you have random variables or random vectors.
6. Jun 16, 2009
### kingwinner
1) Once again, thanks for the great proof!
And I suppose the proof of E(W A') = E(W) A', with the constant matrix on the right of a random matrix W, can be done similarly, right?
7. Jun 16, 2009
Yes, as can the derivations for the case of random and constant vectors.
8. Jun 16, 2009
### kingwinner
I am trying to modify your proof to prove that E(ZA) = E(Z) A (assuming ZA is defined), but it doesn't seem to work out...
The $$(r,t)$$ entry of the matrix $$ZA$$ is the random variable given by
$$\sum_{l=1}^m Z_{rl} a_{lt}$$
so the expected value of the $$(r,t)$$ entry is
$$E\left(\sum_{l=1}^m Z_{rl}a_{lt}\right) = \sum_{l=1}^m E\left(Z_{rl}a_{lt}\right) = \sum_{l=1}^m a_{lt} E\left(Z_{rl}\right)$$
?????
9. Jun 16, 2009 | crawl-data/CC-MAIN-2018-09/segments/1518891813571.24/warc/CC-MAIN-20180221063956-20180221083956-00199.warc.gz | null |
# Consider a triangle having vertices
Question:
Consider a triangle having vertices $\mathrm{A}(-2,3), \mathrm{B}(1,9)$ and $\mathrm{C}(3,8)$. If a line $\mathrm{L}$ passing through the circum-centre of triangle $A B C$, bisects line $B C$, and intersects $\mathrm{y}$-axis at point $\left(0, \frac{\alpha}{2}\right)$, then the value of real number $\alpha$ is
Solution:
$(\sqrt{50})^{2}=(\sqrt{45})^{2}+(\sqrt{5})^{2}$
$\angle \mathrm{B}=90^{\circ}$
Circum-center $=\left(\frac{1}{2}, \frac{11}{2}\right)$
Mid point of $\mathrm{BC}=\left(2, \frac{17}{2}\right)$
Line : $\left(y-\frac{11}{2}\right)=2\left(x-\frac{1}{2}\right) \Rightarrow y=2 x+\frac{9}{2}$
Passing though $\left(0, \frac{\alpha}{2}\right)$
$\frac{\alpha}{2}=\frac{9}{2} \Rightarrow \alpha=9$ | crawl-data/CC-MAIN-2024-26/segments/1718198861674.39/warc/CC-MAIN-20240616233956-20240617023956-00504.warc.gz | null |
Why the words SOCIALIST, SECULAR and INTEGRITY were added in the PREAMBLE OF CONSTITUTION OF INDIA?
The preamble to the Constitution of India is an introduction and it can be preferred as a short highlights of the constitution. The Constitution of India was adopted on 26 November 1949 by the Constituent Assembly and came into effect on 26 January 1950, celebrated as the Republic day in India.
The 42nd amendment to Constitution of India, officially known as The Constitution (Forty-second amendment) Act, 1976, was enacted during the Emergency (25 June 1975 – 21 March 1977) .
This Amendment made some major changes in the constitution including the preamble of the constitution and changed the description of India from "sovereign democratic republic" to a "sovereign, socialist secular democratic republic", and also changed the words "unity of the nation" to "unity and integrity of the nation"
The reason of adding these words were to ensure the economic justice and elimination of inequality in income and standard of life. Secularism implies equality of all religions and religious tolerance and does not identify any state religion. The word integrity ensures one of the major aims and objectives of the preamble ensuring the fraternity and unity of the state.
The term ‘socialist’ means a political-economic system which advocates the state’s ownership of the means of production, distribution, and exchange. The aim to add this term was to indicate that the goal of the state in India was to secure a ‘better life for the people’ or ‘equality of opportunity’.
The word ‘secular’ has been described as a ‘view of life’, or of any particular matter based on premise that religious considerations should be ignored or purposefully excluded or as a system of social ethics based upon doctrine that ethical standards and conduct be determined exclusively without reference to religion. The aim to insert the word "secular" by the Constitution (42nd Amendment) Act, 1976, was to explain that the state does not recognize any religion as a state religion and that it treats all religions equally, and with equal respect, without, in any manner, interfering with their individual rights of religion, faith or worship. It does not mean that it is an irreligious or atheistic state. Nor, it means that India is an anti-religious state. It neither promotes nor practices any particular religion, nor it interferes with any religious practice. The constitution ensures equal freedom to all religions.
The word "integrity" was added in the preamble to give the broad meaning to the word "FRATERNITY", which means a sense of brotherhood among the citizens of India. Thus,the word integrity ensures one of the major aims and objectives of the preamble ensuring the fraternity and unity of the state. | <urn:uuid:7b49b40d-af78-4909-a1ef-6b149123bb26> | {
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- What are the parts of a plant cell?
- Why do plant cells have cell walls and animal cells do not?
- Do plants feel pain?
- What are the 7 characteristics of plants?
- What are two 2 major difference between an animal and plant cell?
- What similarities and differences are there between plant and animal cells?
- What are the functions of the parts of a plant cell?
- What is the most important part of a plant cell?
- Do both plant and animal cells have ribosomes?
- What is some evidence that cells are alive?
- What are 2 organelles found in plants but not animals?
- What is difference between plant and animal?
- What are the 10 parts of a plant cell?
- Why are cell walls not present in animal cells?
- What can plants do that animals Cannot?
- What are two parts plants and animals both have?
- What are 3 differences between plants and animals?
What are the parts of a plant cell?
Plant Cell StructureCell Wall.
It is a rigid layer which is composed of cellulose, glycoproteins, lignin, pectin and hemicellulose.
It is the semi-permeable membrane that is present within the cell wall.
Why do plant cells have cell walls and animal cells do not?
Plant cell needs cell wall whereas animal cell do not because the plants need rigid structure so that they can grow up and out . All cells have cell membranes, and the membranes are flexible. So animal cells can have various shapes, but plant cells only have the shapes of their cell walls.
Do plants feel pain?
Given that plants do not have pain receptors, nerves, or a brain, they do not feel pain as we members of the animal kingdom understand it.
What are the 7 characteristics of plants?
These characteristics become the criteria for scientists to separate the living elements in nature from the non-living ones.Cells and DNA. … Metabolic Action. … Internal Environment Changes. … Living Organisms Grow. … The Art of Reproduction. … Ability to Adapt. … Ability to Interact. … The Process of Respiration.More items…
What are two 2 major difference between an animal and plant cell?
Cell walls provide support and give shape to plants. Plant cells have chloroplasts, but animal cells do not. Chloroplasts enable plants to perform photosynthesis to make food. Plant cells usually have one or more large vacuole(s), while animal cells have smaller vacuoles, if any are present.
What similarities and differences are there between plant and animal cells?
A plant cell contains a large, singular vacuole that is used for storage and maintaining the shape of the cell. In contrast, animal cells have many, smaller vacuoles. Plant cells have a cell wall, as well as a cell membrane.
What are the functions of the parts of a plant cell?
Animal cells and plant cellsPartFunctionCell membraneControls the movement of substances into and out of the cellCytoplasmJelly-like substance, where chemical reactions happenNucleusCarries genetic information and controls what happens inside the cellMitochondriaWhere most respiration reactions happen2 more rows
What is the most important part of a plant cell?
The vital parts of a cell are called “organelles.” Among the most important are the nucleus, vacuoles, and mitochondria, all of which are enclosed within the cell membrane and immersed in cytoplasm. Each organelle performs a specific task that helps keep the cell alive.
Do both plant and animal cells have ribosomes?
Animal cells and plant cells are similar in that they are both eukaryotic cells. … Animal and plant cells have some of the same cell components in common including a nucleus, Golgi complex, endoplasmic reticulum, ribosomes, mitochondria, peroxisomes, cytoskeleton, and cell (plasma) membrane.
What is some evidence that cells are alive?
Cells have to be living in order to perform functions; dead muscle cells don’t contract, dead nerve cells don’t carry information, dead red blood cells don’t carry oxygen (and you know this if you’re faint, short of breath, etc,) etc.
What are 2 organelles found in plants but not animals?
Animal cells have centrosomes (or a pair of centrioles), and lysosomes, whereas plant cells do not. Plant cells have a cell wall, chloroplasts, plasmodesmata, and plastids used for storage, and a large central vacuole, whereas animal cells do not.
What is difference between plant and animal?
Plants have chlorophyll, due to which they have the capability to prepare their own food and are known as autotrophs. Animals are the heterotrophs, as they depend on plants for their food, either directly or indirectly.
What are the 10 parts of a plant cell?
cell membrane.cell wall.central vacuole.chloroplast.chromosome.cytoplasm.Endoplasmic reticulum.Golgi complex.More items…
Why are cell walls not present in animal cells?
Animal cells do not have cell walls because they do not need them. Cell walls, which are found in plant cells, maintain cell shape, almost as if each cell has its own exoskeleton. This rigidity allows plants to stand upright without the need for bones .
What can plants do that animals Cannot?
Photosynthetic. Photosynthesis is the process by which plants capture energy from sunlight, and uses Carbon Dioxide and water to make glucose. … Because plants are able to thrive without consuming any other organisms for energy, they are called autotrophs.
What are two parts plants and animals both have?
Animal cells and plant cells share the common components of a nucleus, cytoplasm, mitochondria and a cell membrane. Plant cells have three extra components, a vacuole, chloroplast and a cell wall.
What are 3 differences between plants and animals?
PlantsAnimalsPlants cells have cell walls and other structures differ from those of animals.Animal cells do not have cell walls and have different structures than plant cellsPlants have either no or very basic ability to sense.Animals have a much more highly developed sensory and nervous system.6 more rows•Apr 11, 2016 | <urn:uuid:27a77dde-4c9b-4e48-b3ba-d51ce2703abb> | {
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Text readability is a measure of how well and how easily a text conveys its intended meaning to a reader of that text.
A number of factors influence the readability of a text. These include:
- Physical factors such as typeface, font size, spacing and layout;
- Reader factors such as prior knowledge, reading ability, and motivation of the reader;
- Vocabulary difficulty;
- Text structure;
- Text coherence and cohesion;
A number of indices have been proposed for measuring readability and some are still used and are included in word processing programs. These include Flesch, Dale and Chall, Fry, Bormuth, Coleman & Liau. For more information on these see Readability Indices.
A new method of estimating readability
A new method of estimating readability not based on word or sentence length is now available. This method correlates highly with graded texts, and gives a visual indication of text readability. | <urn:uuid:778a4452-ba1a-4859-934e-7fa335768315> | {
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Q. Years ago, hydrogen fusion was promised as the answer to all our energy problems. Are we any closer to using it?
A. There is a famous joke among scientists: The practical use of the fusion of hydrogen atoms to produce energy is only 20 or 30 years in the future — and always will be.
But it does seem progress is being made. The largest and most expensive research effort is the International Thermonuclear Experimental Reactor. A multinational effort headquartered in France, ITER has a doughnut-shaped chamber called a tokamak that will eventually hold a plasma of hot ionized atoms constrained by very strong magnetic fields.
The next major step will be the arrival in 2019 of the first of the project’s huge magnets, now being fabricated in Japan. The magnets are needed to generate and contain the extreme temperatures necessary to fuse atomic nuclei and to produce energy without the harmful environmental effects of today’s technologies.
A smaller fusion experiment, called Sparc, is being designed at the Massachusetts Institute of Technology. It will rely on smaller, stronger magnets, which in theory will reduce the amount of energy needed to produce short but powerful bursts of heat. | <urn:uuid:da50db70-72c0-49be-b279-997b7af21d3b> | {
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# Calculating Volume of a Football Using Integration | Step-by-Step Guide
• charlie95
In summary, to find the volume of a football with a radius of 1 meter, first try to solve the problem using integrals, and then measure the volume or mass of the displaced water.
charlie95
How to find the volume?
If we have a footbal, let us say that the radius is 1meter, how do we calculate the volume ??
And show it with Integral! (V= ∫∫∫dxdydz )
American football or rest-of-the-world football?
First, you try to set up the integral, and then we can help you improve it if it's wrong. We don't give direct answers to things like this here, but we'll try to steer you in the right direction towards the answer.
haha... funny guy :D rest-of the-world football!
If we have a huge footbal with radius of 1 meter. How could I find the volume of that ball without using a formulae book...
As jtbell said, we require that you first make an effort to solve it yourself and then we'll help you if you've done it wrong.
For any real football anything you can do mathematically will be at best a rough approximation. Unless you can come up with a precise mathematical expression. Footballs are roughly ellipsoid, however getting an exact expression may not be possible.
The best way to find the volume of a real object is not mathematically, but just dunk it in a container of water and measure the volume or mass of the displaced water.
just forget it. I was just interested to know how we can do this mathematically with integral. I don't care if it is a football/baskeball/tennsball or etc.. Just that it is round(sphere) and has a radius of 1 meter.. the radius is not that important either, it can be 1000000000000 meters... I am just interested to find out how we can calculate it mathematically... And this is not a task that I have been given...
I understand that russ watters. But i am not sure where to begin..
V=∫∫∫r dxdydz...
.
Well, formally, you have ##\displaystyle \iiint_{x^2+y^2+z^2<R^2}dx dy dz##. But that's not terribly helpful, because the integral boundary is inconvenient. Consider switching to polar coordinates. What are the dx, dy, and dz equal to in terms of dr, dθ, and dφ?
charlie95 said:
i am not sure where to begin...
Google might be of some help. Seriously! In the eight hours since your first post in this thread, you probably could have found many web pages that discuss finding the volume of a sphere via integration. (Yes, I've looked, myself, to make sure of this.)
If you have trouble understanding them, choose one, give us a link, and tell us what you don't understand about it. Then we'll have something specific to help you with.
I have a life jtbell...thanks for nothing...
I found many web pages, but many of them do it differently.thanks k^2... I solved the problem... much easier swithing over to polar coordinates.
## 1. How do you calculate the volume of a football using integration?
To calculate the volume of a football using integration, you will need to use the formula V = ∫πr²dh, where V is the volume, π is pi (approximately 3.14), r is the radius of the football, and h is the height of the football. You will also need to use the equation for the surface area of a sphere, A = 4πr², to find the value for r. By integrating the surface area equation, you can find the volume of the football.
## 2. Why is integration used to calculate the volume of a football?
Integration is used to calculate the volume of a football because it allows us to find the volume of an irregularly shaped object, such as a football, by breaking it down into infinitesimal parts and summing them up. This is known as the "sum of slices" method, which is commonly used in calculus.
## 3. What materials are needed to calculate the volume of a football using integration?
In order to calculate the volume of a football using integration, you will need a football, a ruler or measuring tape to find the radius and height of the football, and a basic understanding of calculus and integration.
## 4. Can the volume of a football be calculated using other methods besides integration?
Yes, the volume of a football can also be calculated using other methods such as the "cavalieri's principle" or by using the formula for the volume of a prolate spheroid. However, integration is often the most accurate and efficient method for calculating the volume of an irregularly shaped object like a football.
## 5. Are there any real-life applications for calculating the volume of a football using integration?
Calculating the volume of a football using integration has real-life applications in fields such as sports science and engineering. Knowing the volume of a football can help with designing more efficient and aerodynamic footballs, as well as understanding the physics behind how the ball moves and interacts with players during a game.
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# Free math app that shows work
In this blog post, we will be discussing about Free math app that shows work. Our website will give you answers to homework.
## The Best Free math app that shows work
Apps can be a great way to help students with their algebra. Let's try the best Free math app that shows work. Algebra can be a difficult subject for many students, but one way to make it easier is to solve by elimination. This method involves setting up equations and solving for one variable in terms of the others. For example, consider the equation ax+by=c. To solve for x, you would first multiply both sides by b and then subtract c from both sides. This would give you the equation bx-(c-ay)=0. You could then solve for x by factoring or using the quadratic formula. However, elimination is usually faster and simpler. Once you get practice using this method, you will be able to solve equations more quickly and easily.
In other words, all you need to do is find the number that when raised to a certain power equals the number under the radical. Let's say we want to solve for the cube root of 64. We would need to find a number that when multiplied by itself three times equals 64. That number is 4, because 4 x 4 x 4 = 64. So the cube root of 64 is 4. In general, solving radicals is a matter of finding numbers that when multiplied by themselves a certain number of times (the index) equals the number under the radical sign. With a little practice, you'll be able to solve radicals in your sleep!
By providing step-by-step solutions to precalculus problems, a problem solver can help students to understand the material and improve their grades. In addition, a problem solver can be used as a reference when working on homework or taking tests. With its ability to provide clear and concise explanations, a precalculus problem solver is an essential resource for any student taking a precalculus course.
To solve for the square root of a number, we can use a few different methods. One method is to use factor trees. Another method is to use the long division method. Lastly, we can use estimation methods to approximate the answer. No matter which method we use, being able to solve by square roots is a valuable skill to have!
Natural log equations can be tricky to solve, but there are a few tried-and-true methods that can help. . This formula allows you to rewrite a natural log equation in terms of a different logarithmic base. For example, if you're trying to solve for x in the equation ln(x) = 2, you can use the change of base formula to rewrite it as log2(x) = 2. Once you've rewriting the equation in this form, it's often easier to solve. Another approach is to use substitution. This involves solving for one variable in terms of the other and then plugging that value back into the original equation. For instance, if you're trying to solve the equation ln(x+1) - ln(x-1) = 2, you could start by solving for ln(x+1) in terms of ln(x-1). Once you've done that, you can plug that new value back into the original equation and solve for x. With a little practice, solving natural log equations can be a breeze.
## We solve all types of math problems
This app has saved my life. In all the schools that I've been to, not once has a teacher explained math to me, which I found very hard. Thanks to this app, my grades have gotten better and I can finally say that I slightly understand math.
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Absolutely Astounding! This app impresses me more than a good app has in a while. It’s incredibly useful for checking your work and it can help solve for "X", graph solutions, and much more! I recommend this app to anyone in a class currently. I really appreciate the fact that with the problems the app isn’t sure how to solve that it will figure out how soon. Lately I've been grabbing more homework just so that I can use this app! Download and enjoy!
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How to solve probability word problems How to solve by substitution method How to solve the distance formula Solve for x right triangle calculator Word solver cheat | crawl-data/CC-MAIN-2022-49/segments/1669446710155.67/warc/CC-MAIN-20221127005113-20221127035113-00090.warc.gz | null |
In 2009, tge Biomedical Computation Review looked at the status of work towards reverse engineering brain. (8 page pdf)
Computer simulations of the brain already allow experiments impossible to carry out with animals. “As good as modern neuroscience is—and it has been brilliant over the last two decades—we can’t really sample every neuron and every synapse as they are performing a behavior,” notes consciousness researcher Gerald Edelman, MD, PhD, director of the Neurosciences Institute and chair of neurobiology at the Scripps Research Institute in San Diego, California.
Researchers are looking to develop even more efficient simulated brains to help produce computers that can think while at the same time accelerating neuroscience. Ultimately brain simulations promise the ability to study the effect of drugs and disease and aid in the design of new therapeutic strategies.
To build a simulated brain, Edelman and others start with what’s known about the neuron, a cell that actively maintains a separation of charged ions across its membrane. Specific channels in the membrane allow certain ions in, and these are quickly pumped back out, or sequestered internally. But when a certain threshold of charge is reached the neuron fires a spike of current toward an adjacent neuron.
Here, at the synapse—a microscopic gap between each nerve cell—current becomes chemistry (and here is where drugs alter that chemistry). A spike wave arriving at the synapse triggers the release of neurotransmitters—to activate the next cell—provided enough inputs arrive in a very short time. Sufficient impulses strengthen the synapse. Neglected, the synaptic strength weakens and the particular listening in with electrodes a hundred times finer than a human hair. And this is the basic information that Edelman and others use to construct their simulated neurons.
To determine how these neurons are connected, simulators turn to microscopists and their latest technologies. Techniques from immunology have brought incredible resolution on the molecular level: cells containing particular molecules can be tagged by dye-bearing antibodies so that researchers can distinguish them from from fellows and follow their links to one another. Scanning electron microscopy has been able to home in on the fine molecular scale at the synapse.
Knowing how individual neurons function and how they’re connected will not make a brain work. Simulators need to know the bigger picture of brain area networks. To understand the function of brain regions, neuroscientists initially used data from scalp EEG and depth electrodes placed within the brains of living patients and animals, as well as observational reports such as from accidents that selectively damaged specific brain areas. These days computer-analyzed imaging can reveal additional details of the normal brain. Simulators employ all of these lines of evidence, and still seek more. But none of this data could produce an engineered brain without huge advances in computer simulation.
Once enough of the brain’s macro and microcircuitry is simulated, the in silico model is able to generate its own inherent activity—similar to what is seen in real brains. “When you stimulate the neural model, it takes off on its own and is constantly active,” Edelman says. “We’ve never succeeded in doing this before.” Moreover, oscillating waves of synchronous neural firing not explicitly built-in emerged spontaneously, the researchers reported in the March 4, 2008, Proceedings of the National Academy of Sciences. The researchers also were able to induce and reproduce spontaneous, low-level activity at the synapses—called miniature postsynaptic potentials or minis. The results suggest that, as a real brain develops in a fetus, minis like these might prime neurons for action.
Edelman’s group relied on a top-down approach based on global network properties of the brain and mathematical formulas to reproduce known types of neuron behavior. In a complementary approach, Blue Brain focuses on exact structural and molecular details to model a particular piece of the brain, building up from exact details of individual neurons. Data for the Blue Brain project was gathered using a key innovation: the ability to record ion signals from many neurons at once using what’s called a multiple unit patch clamp technique. By eavesdropping on the interactions among neurons, researchers learned what synaptic currents were being generated and where.
In addition, they gathered data on gene activity within neurons—as an indicator of which discrete ion channels are present. In most neurons, a dozen or more types of these pores regulate ion flow. The Blue Brain simulation specifies which ones are present in each neuron. They also captured the precise connecting points of each neuron, by injecting dye once they were done recording the electrical activity. “The details are accurate, down to the micron,” for each contact point of each nerve fiber, adds Phil Goodman, MD, professor of Internal Medicine and Biomedical Engineering at the University of Nevada, Reno, who collaborated on Blue Brain.
The Blue Brain project plans to publish “key insights never seen before in the neo-cortical column,” Markram says. “By the end of 2009 we will publish the entire circuit with the blueprint. It’s like the genome map—it’s a comprehensive description of the neocortical column.” “It took 15 years to get the data for this small piece of brain,” Markram says. “Every week the model becomes more biological,” he adds. “It’s very much like a real little bit of tissue.” And now that they’ve built one cortical column, building another is a simple task. “We can (now) push a button and build an unlimited amount of neurons automatically.”
Boahen and members of his Stanford lab have developed the Neurogrid chip. No bigger than a fingernail, 16 of these chips will be assembled in an iPod-sized device that can do what a supercomputer does—simulate a million neurons—at only $40,000. The Neurogrid chips have been received from the silicon foundry and should allow the group to emulate a million neurons in the cortex in real time at a thousandth of the cost of supercomputing.
Object recognition is vital for a virtual or a material brain-based device such as the Darwin series or Goodman’s avatars. Yet it has been one of the most challenging tasks for artificial intelligence. Goodman uses fairly primitive visual processing in his model, but Thomas Serre, PhD, a postdoc working with Tomaso Poggio, PhD, at the Massachusetts Institute of Technology, has recreated in a machine the ability to perceive objects when flashed at the threshold of human visual perception. Remarkably, the simulation performs as well as people (as described in a News Byte in the Summer 2007 issue of Biomedical Computation Review http://biomedicalcomputationreview.org/3/3/4.pdf).
Serre’s experiment was limited, however, to the brain’s response to an image flashed for less than 150 milliseconds. Thus, it provides just a skeleton of a complete theory of vision, Serre says. He’s now working on what happens beyond the first 150 milliseconds of visual processing—“when you move your eyes and shift attention.” The visual system involves a complex of more than 30 brain areas propagating signals from the retina through the visual cortex to the region of motor cortex that controls how the person (or the simulator) responds. Living brain also contains back projections, echoing all the way back to the primary visual area that receives the initial signals from the retina. Vision researchers suspect these back connections may be the way that the visual system can pick out a target object from complex scenes. “By adding back projections to the model, and allowing one shift in attention, to one part of the image, we are (now) able to mimic the next level of performance of a human observer when the image is left just 30 ms longer on the screen, just enough for people to shift their attention once,” Serre says.
Boahen at Stanford heads a team working on recreating the basics of different parts of the perceiving brain. Much of the circuitry they plan to model will include back projections. Boahen agrees that feedback likely mediates attention, as competing firing is suppressed. As with other brain simulations, his also shows synchrony, the living rhythms of the brain, including gamma waves with attention.
The Sander Olson interview with Blue Brain Project Director Henry Markram
If you liked this article, please give it a quick review on Reddit, or StumbleUpon. Thanks
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# Properties of Regression Coefficients
-
The fundamental aim of regression analysis is to determine a regression equation (line) that makes sense and fits the representative data such that the error of variance is as small as possible.
Let us consider the line of regression of y on x, that is, y = a + bx The coefficient ‘b’ which is the slope of the line of regression of y on x is called the coefficient of regression of y on x. It represents the increment in the value of the dependent variable y for a unit change in the value of the independent variable x. In other words, it represents the rate of change of y with respect to x. For notational convenience, the slope b, i.e., coefficient of regression of y on x is written as b_{yx}.
Similarly in the regression equation of x on y, that is,x = a + by, the coefficient b represents the change in the value of dependent variable x for a unit change in the value of independent variable y and is called the coefficient of regression of x on y. For notational convenience, it is written as b_{xy}. We now list out some of the properties of these regression coefficients.
### Properties of Regression Coefficients:
1. The correlation coefficient is the geometric mean of two regression coefficients, that is, r = \sqrt{b_{yx} × b_{xy}}
2. If one regression coefficient is greater than one, then the other regression coefficient must be less than one, because the value of correlation coefficient r cannot exceed one. However, both the regression coefficients may be less than one.
3. Both regression coefficients must have the same sign (either positive or negative). This property rules out the case that the two regression coefficients have opposite signs.
4. The correlation coefficient will have the same sign (either positive or negative) as that of the two regression coefficients.
5. The arithmetic mean of regression coefficients b_{xy} and b_{yx} is more than or equal to the correlation coefficient r, that is, \frac{b_{yx} + b_{xy}}{2}\geq r.
6. Regression coefficients are independent of origin but not of scale.
7. The correlation coefficient between two variables x and y is a symmetrical function between x and y, that is, r_{xy}=r_{yx}. However, the regression coefficients are not symmetric functions of x and y, that is, b_{xy}\neq b_{yx}.
References:
Fundamentals of Business Statistics – JK Sharma
Hey 👋
I'm currently pursuing a Ph.D. in Maths. Prior to this, I completed my master's in Maths & bachelors in Statistics.
I created this website for explaining maths and statistics concepts in the simplest possible manner.
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Raoul Wallenberg in his office in the Swedish legation. Budapest, Hungary, November 26, 1944.
Hungary's capital, Budapest, straddles the banks of the Danube River and is the country's most populous city. Budapest was created by the union of three cities: Buda, Obuda, and Pest.
Before World War II, approximately 200,000 Jews lived in Budapest, making it the center of Hungarian Jewish cultural life. In the late 1930s and early 1940s, Budapest was a safe haven for Jewish refugees. Before the war some 5,000 refugees, primarily from Germany and Austria, arrived in Budapest. With the beginning of deportations of Jews from Slovakia in March 1942, as many as 8,000 Slovak Jewish refugees also settled in Budapest.
Hungary was allied with Nazi Germany. Despite discriminatory legislation against the Jews and widespread antisemitism, the Jewish community of Budapest was relatively secure until the German occupation of Hungary in March 1944. With the occupation, the Germans ordered the establishment of a Jewish council in Budapest and severely restricted Jewish life. Apartments occupied by Jews were confiscated. Hundreds of Jews were rounded up and interned in the Kistarcsa transit camp (originally established by Hungarian authorities), 15 miles northeast of Budapest.
Between April and July 1944, the Germans and Hungarians deported Jews from the Hungarian provinces. By the end of July, the Jews in Budapest were virtually the only Jews remaining in Hungary. They were not immediately ghettoized. Instead, in June 1944, Hungarian authorities ordered the Jews into over 2,000 designated buildings scattered throughout the city. The buildings were marked with Stars of David. About 25,000 Jews from the suburbs of Budapest were rounded up and transported to the Auschwitz-Birkenau extermination camp. Hungarian authorities suspended the deportations in July 1944, sparing the remaining Jews of Budapest, at least temporarily.
Many Jews searched for places of hiding or for protection. They were aided by Swedish diplomat Raoul Wallenberg and other foreign diplomats who organized false papers and safe houses for them. These actions saved tens of thousands of Jews.
In October 1944, Germany orchestrated a coup and installed a new Hungarian government dominated by the fascist Arrow Cross party. The remaining Jews of Budapest were again in grave danger. The Arrow Cross instituted a reign of terror in Budapest and hundreds of Jews were shot. Jews were also drafted for brutal forced labor.
DEATH MARCH FROM BUDAPEST
On November 8, 1944, the Hungarians concentrated more than 70,000 Jews—men, women, and children—in the Ujlaki brickyards in Obuda, and from there forced them to march on foot to camps in Austria. Thousands were shot and thousands more died as a result of starvation or exposure to the bitter cold. The prisoners who survived the death march reached Austria in late December 1944. There, the Germans took them to various concentration camps, especially Dachau in southern Germany and Mauthausen in northern Austria, and to Vienna, where they were employed in the construction of fortifications around the city.
THE BUDAPEST GHETTO
In November 1944, the Arrow Cross ordered the remaining Jews in Budapest into a closed ghetto. Jews who did not have protective papers issued by a neutral power were to move to the ghetto by early December. Between December 1944 and the end of January 1945, the Arrow Cross took as many as 20,000 Jews from the ghetto, shot them along the banks of the Danube, and threw their bodies into the river.
Soviet forces liberated Budapest on February 13, 1945. More than 100,000 Jews remained in the city at liberation. | <urn:uuid:70ee433e-8e17-44f5-8350-6a976899fb09> | {
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Iceland is widely known for its beautiful landscape of volcanoes and glaciers, but few understand the curious arthropod food web surrounding Lake Myvatn. Claudio Gratton, someone who understands this system well, is a Professor of Entomology at the University of Wisconsin, Madison. He is currently studying the aquatic-terrestrial linkages in the landscape, specifically the role midges play in the nitrogen cycle. Lake Myvatn, located in northern Iceland just below the Arctic Circle, is known as “Midge Lake” due to the massive numbers of these insects that emerge from this lake in some years. Midge (Tanytarsus gracilentus and Chironomus islandicus, family: Chironomidae) emergences fluctuate year to year, with major emergences seen every 5 to 8 years (Einarsson et al. 2002; Ives et al. 2008). In high midge emergence years, they can contribute approximately 55
These midges have important impacts on the surrounding environment by providing food for predators, distracting predators from other possible prey, and altering plant composition. The main predators of these midges are web-building spiders. On years when midge density is extraordinarily high, these will aggregate in larger numbers near the lake. Increased midge numbers reduce the predation of leafhoppers by web-building spiders. When spider density was increased, midges still reduced spider predation on other prey species by distracting the predators (Dreyer et al. 2016).
Increased midge biomass has also been shown to increase the density of graminoid plant species (herbaceous, grass-like) and decrease the number of health plant
shifts, with graminoids dominating in the press treatment plots (Gratton et al. in review). Midge populations at Lake Myvatn are known to influence the surrounding landscape and fluctuate year to year, therefore it is likely that similar press and pulse effects are impacting the plant communities surrounding Lake Myvatn.
While it seems that the Lake Myvatn study system is unique, there are many other instances where insects impact the landscape. Some examples include: periodic cicadas, locust swarms, monarch migration, and mayfly emergences. These insect phenomena can have long- and short-term impacts on the environment and can link ecosystems.
About the Authors:
Olivia Bernauer is a Master’s student in Dennis vanEngelsdorp’s bee lab working to better understand the floral preferences of Maryland’s wild, native pollinators.
Meghan McConnell is a Master’s student in Dennis vanEngelsdorp’s Lab studying honey bees with a focus on non-chemical control of varroa mites. After 5 years at UMD with the bee lab and Bee Informed Partnership, she will be the Delaware State Apiarist.
Dreyer, J., Townsend, P. A., III, J. C. H., Hoekman, D., Vander Zanden, M. J. and Gratton, C. (2015), Quantifying aquatic insect deposition from lake to land. Ecology, 96: 499–509. doi:10.1890/14-0704.1
Dreyer, J., Hoekman, D. and Gratton, C. (2016), Positive indirect effect of aquatic insects on terrestrial prey is not offset by increased predator density. Ecol Entomol, 41: 61–71. doi:10.1111/een.12272
Einarsson, Á., Gardarsson, A., Gíslason, G. M. and Ives, A. R. (2002), Consumer–resource interactions and cyclic population dynamics of Tanytarsus gracilentus (Diptera: Chironomidae). Journal of Animal Ecology, 71: 832–845. doi:10.1046/j.1365-2656.2002.00648.x
Ives, Anthony R., Árni Einarsson, Vincent A. A. Jansen, and Arnthor Gardarsson. 2008. “High-Amplitude Fluctuations and Alternative Dynamical States of Midges in Lake Myvatn.” Nature 452 (7183): 84–87. doi:10.1038/nature06610. | <urn:uuid:f2d0f143-b1b9-4d41-964f-c553bea96e3a> | {
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If students are not familiar with or have not recently practiced plotting points on the first quadrant using ordered pairs, review that concept before continuing.
Distribute the Coordinate Geometry sheet (M-5-3-3_Coordinate Geometry and KEY.docx) to each student. On a copy of the First Quadrant worksheet from Lesson 2 (M-5-3-2_First Quadrant and KEY.docx), have students plot the points in Figure 1 in order, connecting each point to the previous point and connecting the last point to the first to make a complete, closed shape. Ask students to come up with any words they can think of to describe Figure 1. They may only come up with “triangle.”
“There are a lot of names we can call this figure. Shapes have many descriptions, just as you might. You are a person, a boy or girl, maybe a brother or sister, a student, maybe a baseball player, right- or left-handed, and so on. Just as there are many ways to describe you, there are many ways to describe shapes. So, this shape is a triangle since it has three sides, but we can also call it a polygon.”
Depending on the class, you can break the word polygon down into two parts: poly- and -gon, and examine each part of the word, explaining that poly- means “many” and -gon means “angles,” and so the word polygon literally means “many angles.” This approach is useful when dealing with other terms like hexagon or octagon (and continues to be useful in higher mathematics when dealing with terms like polynomial).
After explaining that a polygon is a figure that has many sides, tell students the sides must be straight lines and the figure must be closed. In other words, they have to connect the last point they plotted back to the first point with a straight line.
“Next to the triangle you graphed, write the words polygon and triangle, and then graph Figure 2 on the same coordinate plane on which you graphed Figure 1.”
After students have plotted Figure 2, ask them to describe it. Students may respond with rectangle and polygon (or incorrect answers).
“What makes this shape a polygon?” (It has many sides, the sides are straight, and the figure is closed.)
“What makes this shape a rectangle?” Here, students should focus on the four right angles in the figure.
“How many sides does our rectangle have?” (Four) “Just like we have a general name for shapes with three sides—triangle—we also have a general name for shapes with four sides. We call them quadrilaterals.” Possibly write “quadrilaterals” on the board so students can see the term.
Again, depending on the class, breaking down the word quadrilateral into parts might be helpful: quad- means “four” and -lateral means “sides.” If students are familiar with football, they may have heard of a lateral pass, which is a pass that goes sideways (as opposed to backward or forward).
“So far, then, our shape has a few names. It is a polygon, it is a quadrilateral, and it is a rectangle. It actually has at least one more name. Look at the two long sides that go straight up and down. What word do we have for line segments that will never cross one another no matter how long they are?” (Parallel)
“And what about the two short sides on the top and bottom of our rectangle?” (They are also parallel.)
“Because our quadrilateral has two pairs of parallel sides, we call it a parallelogram.” Again, write this word on the board so students can see it written out, pointing out the word parallel inside the word parallelogram. Have students write all the terms associated with a parallelogram next to the rectangle.
Have students graph Figure 3 on the same coordinate plane as Figures 1 and 2. Ask them to describe it. They should note that it’s a square, a polygon, a quadrilateral, and a parallelogram. If not, ask them if any of the previous terms that applied to rectangle also apply to it. Ask students to explain why the figure is a polygon, quadrilateral, and parallelogram. Lastly, ask them to explain how they know it’s a square. Here, students should focus on both the four right angles and the four sides of equal length.
“Now, you said it’s a square because it has four sides of equal length and four right angles. Since it has four right angles, can we also call it a rectangle?” (Yes) “If I ask you to draw a square, can you ever draw one that doesn’t have four right angles?” (No) “So we know that every square is a rectangle.”
Have students write down all the terms that apply to the square.
Give each student a copy of Quadrilateral Venn diagram sheet (M-5-3-3_Quadrilateral Venn Diagram.docx). Describe how to interpret the diagram (i.e., all squares are rectangles, all rectangles are parallelograms, and all parallelograms are quadrilaterals). Make sure to emphasize that even though all squares are rectangles, for example, there are definitely rectangles (like the one they plotted) that are not squares. On the diagram, illustrate this by identifying the region that is inside the rectangle part of the figure but is outside the square part of the figure.
“Write the words “Figure 2” and “Figure 3” on your diagram to show in which part of the diagram they belong.” (Figure 2 belongs in the rectangle portion but not the square portion, while Figure 3 belongs in the square portion.)
“Where does Figure 1 go on the diagram?” (Students may respond with Outside the quadrilaterals or not on the diagram.) “We might need another diagram if we want to be able to organize all our polygons. This diagram just organizes quadrilaterals, which have how many sides?” (Four)
Before plotting Figure 4, ask students what shape they think it’s going to be. If they aren’t sure (they may be trying to visualize it in their heads), ask them how many points they have to plot. They may at least guess it will have five sides even if they aren’t sure what the figure is called. After discussion, have students plot Figure 4 on the second coordinate plane.
“Do any of the words we talked about with the figures on the first coordinate plane apply to this figure?” (Polygon)
“We call a five-sided polygon a pentagon.” Again, explaining the meaning of the prefix penta- (five) may be helpful to students. They may also be familiar with the Pentagon in Washington, D.C. (This image: http://www.sciencephoto.com/image/357691/350wm/T8350265-Pentagon_building-SPL.jpg shows the Pentagon from overhead so students can clearly see that it has five sides.) Have students label their pentagon appropriately. Also, explain that whether a polygon is a pentagon is determined only by the number of sides it has. Even though the pentagon in Figure 5 isn’t exactly the same as the Pentagon, they both have five sides and so are both classified as pentagons.
“How many sides will Figure 5 have, based on the number of points that need to be graphed?” (Six)
Have students plot Figure 5.
“What is our six-sided figure called?” Write the word hexagon on the board and explain that hex- means six, so the word literally means “six angles.” Have students label Figure 5 appropriately.
Finally, have students plot Figure 6. “How many sides does it have?” (Eight) “What do we call an eight-sided polygon?” If students don’t know, guide them toward the realization that an octopus has eight arms and the prefix oct- means eight, and have them guess what we might call a polygon with eight angles.
Have students label the octagon on their coordinate plane appropriately.
The Coordinate Plane worksheet can be collected at the end of class and checked against the key to ensure understanding. (Students may use it for reference in Activity 3.)
Have students work in pairs for Activity 3.
Each student should draw a pattern or design on a coordinate plane that incorporates at least two different polygons, at least one of which should be a quadrilateral.
Students should plot each part of their design and include coordinate instructions to provide to their partner. They should label each “set” of coordinates with the name or names of the appropriate polygon. (If they are drawing, for example, a square, they should label the set of coordinates describing the square with the terms square, rectangle, parallelogram, quadrilateral, and polygon.)
Once students have listed the coordinates and double-checked their work, they should give their instructions to someone else.
“Now, you have the instructions to make someone else’s design. Go ahead and start with the first point on the list and graph each set of points in order. Make sure that the shape you graph matches the name or names the instructions have listed. If you graph something and it’s not a square but the instructions say it is, for example, work with your partner to figure out if you made a mistake in graphing it, your partner made a mistake in writing down the coordinates, or if you both graphed it correctly and it just has the wrong description.”
Once students are finished, they should compare their drawings and identify the source of any errors and correct them.
This Activity can be repeated if students struggle with writing accurate instructions.
Depending on time, to engage students further, they can color and decorate their designs.
Use the following strategies to tailor the lesson to meet the needs of your students throughout the year.
- Routine: As students explore other geometry topics throughout the year, they can graph the shapes on the coordinate plane, including regular polygons, rhombuses, and even circles (with a designated point as the center and a given radius). They can also explore polygons with more than eight sides, describing them through the use of coordinates.
- Small Group: Using larger coordinate planes, students can work in groups to create elaborate designs, with each student responsible for creating the instructions (i.e., listing the coordinates) for part of the design. This activity can be done on large rolls of butcher paper (the coordinate plane can be drawn with a meterstick or yardstick) to create large murals.
- Expansion: When working with parallelograms, students can be encouraged to make shapes with parallel sides that are not horizontal or vertical lines. They can explore the idea of slope in the context of “from this point I went to the right 5 units and up 2 units, so from this other point I have to do the same steps,” etc. Students can also be introduced to the distance formula and/or Pythagorean theorem when working on the coordinate plane.
Students can also explore the idea of convex and concave polygons through graphing. | <urn:uuid:306213f8-dc13-43ed-acd7-8e9eff54557b> | {
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History of the Word 'Exponent'
Date: 11/26/2003 at 11:15:52 From: Brittany Subject: who came up with the name exponent Who came up with the name "exponent"?
Date: 11/26/2003 at 12:33:06 From: Doctor Peterson Subject: Re: who came up with the name exponent Hi Brittany - A full answer to your question may be more than you want, but I'd like to go into some detail! If you go to our FAQ you will find this link: Earliest uses of mathematical words http://jeff560.tripod.com/mathword.html Look up "exponent," and you will find this: The term EXPONENT was introduced by Michael Stifel (1487-1567) in 1544 in Arithmetica integra. He wrote, "Est autem 3 exponens ipsius octonarij, & 5 est exponens 32 & 8 est exponens numeri 256" (Smith vol. 2, page 521). The Latin translates roughly as But 3 is the exponent of that same eight, and 5 is the exponent of 32, and 8 is the exponent of the number 256. (There are some grammatical twists here that I don't quite get!) Looking up the context of this sentence in Smith, I find that it follows a table of powers of 2: 0 1 2 3 4 5 6 7 8 1 2 4 8 16 32 64 128 256 He says (in Latin), "Just as, by addition, (in the upper row) 3 [added] to 5 makes 8, so (in the bottom row), by multiplication, 8 [multiplied] by 32 makes 256". Then he continues with the sentence above. So the words "exponent" refers to the number in the top row corresponding to a given number in the bottom row; this is the number of 2's multiplied to make the given number--what we today would call its base-2 logarithm, or the exponent of 2 that gives the number. Another source is Math Words http://www.pballew.net/etyindex.html which says Exponent is the union of the Latin roots exo(out of) + ponere (place). The literal interpretation is to make something visible or obvious. That seems to be what happens when the index is raised "out of" the line. The English word expound, from the same source, means to make clear. An exponent is also used in English to describe a person who explains or interprets. Exponent, as a math term, was introduced by Michael Stifel (1487-1567) in his book, Arithmetica Integra, in 1544. I'm not convinced by the idea that "exponent" refers to the raising of the number above the line ("out of place", or "placed out of line") because a raised exponent notation, though used by Chuquet in the 1400's, was not popularized until the 1600's. Stifel did not use such a notation, but a complicated set of symbols for different powers. Literally, Stifel's "exponens" would be "setting out": "3 is the setting out of 8" might mean "3 is the number of times you write 2 as a factor, in order to get 8 by multiplying". Other authors of that period would call 2 the "index" of 8, meaning its place in the list of powers, as "indicated" by the top row of numbers. That word is still used, especially in England, for what we call the exponent. In any case, that is what "exponent" means, and the meaning is more important than the details of its origin. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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Simultaneous equations - Higher
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# Solving simultaneous equations using graphs
Solving simultaneous equations using a graph is easier than you might think. First, you need to draw the lines of the equations. The points where the lines cross is the solution.
## Linear equations
The graphs of linear equations will give straight lines.
### Example
• Solve these simultaneous equations by drawing graphs:
• 2x + 3y = 6
• 4x - 6y = - 4
For example, to draw the line 2x + 3y = 6 pick two easy numbers to plot. One when x = 0 and one where y= 0
• When x = 0 in the equation 2x + 3y = 6
• This means 3y = 6 so y = 2
• So one point on the line is (0, 2)
• When y = 0
• 2x = 6 so x = 3
• So another point on the line is (3 ,0)
In an exam, only use this method if you are prompted to by a question. It is usually quicker to use algebra if you are not asked to use graphs.
### Example
• Solve the simultaneous equations by drawing graphs.
• y - 2x = 1
• y = x2 - 2
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Typhoid fever isn't a pretty disease. Painful diarrhea, high fever, nasty red rashes and sleeplessness typically characterize the illness. Left untreated, typhoid can result in death. Salmonella typhi, the parasite that causes typhoid fever, spreads through water and food, making the disease highly contagious. Those who don't know the whole story are quick to blame one individual, known to history as Typhoid Mary, for intentionally spreading the deadly illness. As we'll see, the truth is a little more complicated.
In turn-of-the-century New York City, typhoid was a growing problem. The Department of Health had a lot on its plate; in addition to typhoid, it was trying to quell outbreaks of smallpox, tuberculosis, diphtheria and whooping cough that were sweeping through the area [source: NOVA]. Luckily, scientists had developed a sophisticated understanding of microbial diseases and how they spread -- even if everyone in the lay public didn't quite grasp all of it yet.
The Department of Health knew what caused typhoid, but dealing with the spread of the disease was another question altogether. It's a question that plagues us to this day. It's no longer considered humane to simply cast contagious disease victims out of society and into the wilderness to fend for themselves. What exactly to do with them remains controversial. Authorities must walk the line between keeping their societies safe from debilitating illness and infringing on the victims' personal rights. This controversy reached a fever pitch in early 20th-century New York when it came to one individual.
It might surprise you to learn that this fervor revolved around someone who was actually immune to typhoid. Though it's uncommon, some people are naturally immune to the illness, meaning they can carry the parasite and never suffer from a single symptom. Nevertheless, these people can just as easily spread the disease to others. This was the case for one Mary Mallon, aka Typhoid Mary. She was in the wrong place at the wrong time as well as in the worst possible occupation for a carrier of typhoid: She was a cook. | <urn:uuid:8b26f45d-5009-4804-9b6b-6d3e57356bf5> | {
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Skip to 0 minutes and 8 secondsIn this video, we will explore the basic types of bacterial resistance. The first type of resistance is called intrinsic or inherent. This occurs when resistance to a particular antibiotic or group of antibiotics is normal for a particular bacterial genus, species, or an entire bacterial group. This may be the result of the lack of a target for the particular antibiotic or because that drug can't get to its target. Some examples of this type of resistance are vancomycin or linezolid resistance in gram negatives. This occurs because the molecule can't get through the gram-negative outer membrane. Linezolid is inactive because it's pumped out of gram-negative cells.
Skip to 1 minute and 5 secondsNow acquired resistance is a type of resistance where most isolates of a bacterial species, genus, or group start by being fully susceptible to the particular antibiotic. But resistance may arise in a few, or in some cases, many of their isolates. This resistance may arise through mutation of a chromosomal gene. An example of this is an enterobacteriaceae, which often develop resistance by acquiring new DNA. This is an example of so-called horizontal gene transfer, or horizontal spread. The typical vehicle responsible for this would be a ring of DNA known as a plasmid. We will now watch a video by Professor Neil Woodford who explains the major mechanisms by which bacteria can become resistant to antibiotics.
Skip to 2 minutes and 10 seconds[AUDIO PLAYBACK] - This slide summarises the major mechanisms by which bacteria can become resistant to antibiotics.
Skip to 2 minutes and 21 secondsThey may destroy the antibiotic. This may either be because they destroy it completely or because they modify it chemically so that it can no longer bind to its target. They may stop the drug getting into the cell. Reduced uptake, often called impermeability. Or they may let the drug in. But it may then get pumped out faster than it can accumulate to the critical concentrations needed to exert its antibacterial effect. Then there are various bypass mechanisms. One particular biosynthetic pathway is blocked. But maybe a new piece of DNA encodes an enzyme that replaces the blocked pathway. An example here would be methicillin resistance in staph aureus, for example.
Skip to 3 minutes and 24 secondsAnd finally, bugs can become resistant to an antibiotic because they over-produce a target enzyme and so swamp the antibiotic.
Skip to 3 minutes and 40 secondsBacteria don't keep resistance to themselves, particularly if that resistance is mediated by plasmids. Resistance due to chromosomal mutation can only be spread if the organism with that mutation spreads. But if resistance is on a plasmid, the plasmid can move. On the left of this slide, you see an electron micrograph of two cells of the gut bacterium escherichia coli. The top one is a recipient. The bottom one is a donor. The donor will have a resistance plasmid that the recipient lacks. You can see them being linked through a protein tube known as a sex pilus. Through a process that's not entirely understood, the donor will give away a copy of its resistance plasmid to the recipient.
Skip to 4 minutes and 44 secondsSo you then end up with two cells that have the resistance plasmid and the recipient becomes a donor, able to transfer its resistance plasmid on still further. This mating event happens most effectively when the bacteria belong to the same species. But they could belong to the same genus, the same family and in some cases, bacteria can spread their resistance to completely unrelated bacterial species. So as an example, a resistance that emerges initially in E. coli may appear subsequently in klebsiella, enterobacter, and a range of other bacteria. And this is summarised in the cartoon on the right of the slide, where one bacterium is being offered a piece of DNA that will make it resistant to penicillin.
Skip to 5 minutes and 50 secondsPlasmids are rings of DNA that exist in this bacterial cell outside of the chromosome. They may be very small and encode no resistance genes. They may be very big and encode very many resistance genes. It's a system that has evolved and from our perspective, these plasmids may often be viewed as neat packages of multi-resistance. Acquisition of a single molecule can make a bacteria resistant to many different types of antibiotics.
Skip to 6 minutes and 31 secondsThat's shown here on this table. A plasmid that confers resistance to eight different classes of antibiotics. You can see that, even within a particular class, beta lactams, aminoglycosides, this plasmid contains more than one gene responsible for resistance. And in the final column, you can see that this also
Skip to 7 minutes and 1 secondrepresents many of those resistance mechanisms: Modifying the drug, destroying the drug, actively effluxing the drug from the cell, or providing bypass mechanisms to overcome enzymes that are inhibited.
Skip to 7 minutes and 24 secondsResistance is inevitable and entirely natural. It's a response by bacteria to adverse growth conditions. Unfortunately, resistance is also inevitable even to new antibiotics. Drug companies developing a new antibiotic will consider how easy it is to make bacteria resistant to their new antibiotic. What they really want to know is whether resistance is going to emerge quickly in the particular target species and especially, is that resistance likely to be transferable? If it's mutational, then control of the resistant strains, if they emerge, will limit the spread of the resistance. If it's a transferable resistance mechanism on one of these plasmids, then potentially it becomes far more difficult to contain.
Skip to 8 minutes and 28 secondsIdeal scenarios that every pharmaceutical company would love to meet for any new antibiotic are illustrated at the bottom of the slide. Penicillin resistance just doesn't happen in beta hemolytic streptococci such a strep pyogenes. Even though we've been using good old penicillin for over 70 years, there are no substantiated cases of resistance. And no one can explain why. Vancomycin resistance also took an awful long time to emerge, almost 30 years. Although for much of this time, it wasn't being used widely. So resistance is inevitable. Don't believe the spiel if the drug company reps tell you that resistance to their new antibiotics is impossible.
Skip to 9 minutes and 28 secondsAs you will read in the text supplied for this week of the MOOC, bacteria have been on the planet for over three billion years. In that time they have evolved to overcome many adverse growth conditions. Antibiotic exposure is just one of those. They respond, they become resistant and potentially cause clinical problems.
Skip to 10 minutes and 2 secondsThe forensics of anti-microbial resistance therefore involves many different levels, best understood as a pyramid. A concept first proposed to me by my colleague Rafael Canton from Spain. Resistance involves the emergence of mutations, the spread of resistance genes, and the spread of resistant strains.
Skip to 10 minutes and 32 secondsAnd so clinical microbiologists' reference laboratories are interested in characterising and tracking these strains and the genes that make them resistant to antibiotics. At the peak of the pyramid, you have the resistance genes that encode the enzymes. Then you have to consider what those genes are located on, the genetic carriers which may be plasmids. Then you have to consider what's causing the infection, which is a host bacterial species. What strain? What clone? How virulent is it? And what other drugs is it resistant to? Finally, of course, you have the patients from whom you're isolating these resistant bacteria. Are they in a hospital setting? Are they in a community setting? Are they in both?
Skip to 11 minutes and 31 secondsAnd what are the risk factors for acquiring a resistant organism as compared with a susceptible organism? All of these things put together give a far better understanding of the epidemiology of antibiotic resistance. [END PLAYBACK]
How do bacteria destroy antibiotics?
Antimicrobial resistance (AMR) is resistance of a microorganism to an antimicrobial medicine to which it was previously sensitive. Resistant organisms (which include bacteria, viruses and some parasites) are able to withstand attack by antimicrobial medicines, such as antibiotics, antivirals, and antimalarials, so that standard treatments become ineffective and infections persist and may spread to others.
In this video Dr Rossana Rosa explains the two types of resistance.
Incorporated into this video is a section created by Prof Neil Woodford for the Antimicrobial Stewardship: Managing Antibiotic Resistance course which explains the mechanisms by which bacteria become resistant.
You can download the slides for both sections of the video here and at the bottom of the step.
Image CDC/ James Gathany
This image shows two petri dish culture plates growing bacteria in the presence of discs containing various antibiotics. The isolate, i.e., bacterial specie, on the left plate is susceptible to the antibiotics on the discs, and is therefore, unable to grow adjacent to the discs. The plate on the right was inoculated with a Carbapenem-Resistant Enterobacteriaceae (CRE) bacterium that proved to be resistant to all of the antibiotics tested, and is therefore, able to grow near the discs.
You may also like to watch this video The Animation of Antimicrobial Resistance by Medicanon which also explains how bacteria become resistant to antimicrobial chemotherapy. | <urn:uuid:45c6f3ac-9c54-49ae-83b2-2c16ce8db0d5> | {
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Sometimes the immune system perceives a threat and reacts in a variety of ways. A respiratory or lung allergy causes symptoms directly reflected in how a person breathes. Pollen, a major trigger for asthmatics, stimulates white blood cells to release a substance called histamine. This irritating substance produces a stuffy nose and itchy, watery eyes. In people with asthma, histamine can also cause a list of additional allergy symptoms, which usually occur soon after exposure. Examples of airborne allergens that cause respiratory allergy symptoms include pollens, animal dander, dust mites, and mold spores.
Breathlessness is the sensation of not getting enough air, often accompanied by a sensation of tightness in the chest. A narrowing or blockage of the airway due to an allergic reaction causes this affect. As the inflamed or blocked airway prevents a person from taking a deep breath, the person takes more and more short, shallow breaths, which can lead to a drop in oxygen and an increase in carbon dioxide in the body. A feeling of breathlessness occurs as the brain, muscles and other body systems become oxygen deprived.
Wheezing is a whistling sound produced by breathing through a narrowed airway. Generally, wheezing can only be heard through a stethoscope. However, when allergy symptoms become severe as a person struggles to catch their breath, it can be heard by the human ear. Wheezing upon exhalation is more prevalent, but it can also occur when inhaling. According to the American Academy of Allergy Asthma & Immunology, when the smaller bronchial tubes within the lungs become narrow, it can cause chest discomfort, a sensation of pressure or constriction in front of the chest. When the larger airway narrows because of inflammation, it also becomes difficult to breathe causing audible wheezing.
Coughing is a beneficial and protective reflex that clears irritants from the trachea and bronchi or airway of the lung. The cough reflex receives messages from receptors in the airway that are sensitive to stimulation by inhaled particles such as pollen. The messages travel to a center in the brain stem, which triggers the cough. The coughing mechanism clears the mucus, fluid and allergens that settle in the upper and lower airway. According to the Centers for Disease Control and Prevention, coughing is the most common reason why people seek medical attention.
A classic sign of respiratory symptoms due to allergy is inflammation of the airway. The inflammation causes swelling and increased mucus production, which can result in wheezing, breathlessness, coughing and chest tightness. According to the National Heart Lung and Blood Institute, research has shown there is a genetic component that controls the inflammatory response to specific allergens. This response causes an allergic reaction, which in turn causes airway inflammation. | <urn:uuid:c6c45adf-8c97-4a27-b907-ba6807968a37> | {
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Arkansas Post, historic village site, Arkansas county, southeastern Arkansas, U.S., on the Arkansas River, near its confluence with the Mississippi River. A fort, the first permanent European settlement in the lower Mississippi valley, was built there in 1686 by Henri de Tonty, a lieutenant of French explorer René-Robert Cavelier, Sieur de La Salle. It became the residence of the French and Spanish governors and was an important trading post. The Mississippi Bubble, a French financial scheme and development plan that became mired in political intrigue, attracted settlers to the area (1717), but most of them left after the speculative bubble “burst” in 1720.
Following the Louisiana Purchase (1803), Arkansas Post served as the first capital of the Arkansas Territory (1819–21). Confederate troops fortified the area during the American Civil War, but it fell to Union troops. The town subsequently declined when bypassed by the railroads and was abandoned by the 1890s.
Arkansas Post National Memorial, created in 1960, preserves the site of the town. Situated on a peninsula, the park covers 389 acres (157 hectares) and includes a museum. The old town was largely inundated by a change in the Arkansas River’s course, but portions are still visible, including a segment of the Confederate fortifications. White River National Wildlife Refuge is to the east. | <urn:uuid:7ae1c939-4ed7-4d7a-b376-32c1fd236cf6> | {
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Curiosity Mars rover finds soil similar to Hawaii's
Nasa's Curiosity rover has found soil on Mars to be similar to Hawaii's after sifting and scanning its first sample on the Red Planet.
The robot's CheMin instrument shook out fine particles of soil and fired X-rays at them to determine their composition.
These sandy samples should give clues about Mars' recent geological history.
As had been theorised, much of the sample is made of weathered "basaltic" materials of volcanic origin, like that seen on the islands of Hawaii.
The sample seems to contain dust carried from afar by Mars' global-scale storms, as well as coarser sand of more local provenance.
The £2.6bn mission put Curiosity on the floor of Gale Crater, a huge depression on Mars' equator, on 6 August.
It has since trundled more than 480m (1,590ft) to the east toward a spot called Glenelg, a place that satellite images indicate is an interesting junction between three different geological terrains.
But it has been paused by the Curiosity team at a region dubbed "Rocknest" to get its first taste of Martian soil.
This first analysis served to "cleanse the palate" of the rover's sample collection systems, which may have brought contaminants from Earth that would skew its chemical view of the Red Planet.
But with that out of the way, Curiosity accomplished another first: the first-ever use of a technique called X-ray diffraction on another planet.
X-ray diffraction is a well-established approach on Earth, in which X-rays are shot into samples that are made up of crystalline materials.
The precise ways in which the X-rays bounce off the crystals gives clear information as to their chemical makeup, and good hints as to their structure.
The CheMin experiment first sieves down a soil sample, separating out the components smaller than 150 micrometres - about the width of two human hairs.
It then gives this sifted soil a shake while firing X-rays at it, examining just how they propagate.
The team says the sample contains "significant amounts" of the minerals feldspar, olivine and pyroxene.
"So far, the materials Curiosity has analysed are consistent with our initial ideas of the deposits in Gale Crater, recording a transition through time from a wet to dry environment," said David Bish, co-investigator on the CheMin experiment.
In the weeks since its arrival on Mars, the rover has already put its ChemCam and APXS instruments to work examining larger rocks, including a never-before-seen specimen reported earlier in October.
"The ancient rocks, such as the conglomerates, suggest flowing water, while the minerals in the younger soil are consistent with limited interaction with water," said Dr Bish.
The next step was to deliver soil samples into another ground-breaking experiment within the rover – Sam, or the Sample Analysis at Mars instrument.
Sam will look for the presence of organic, or carbon-containing, molecules that should give hints about the prospects for life on the Red Planet both now and in the distant past.
Source: BBC News | <urn:uuid:3dac5bfc-0f3f-4fe6-9e9b-6c24c3a0a888> | {
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Systems of Equations: Scratch
Emphasis: Algebra Creator: Ashley Tewes Twitter: @ashleyanntewes Given two lines in slope-intercept form, students will create a program that will find the intersection point between the lines. View Lesson Here
Hypnotic Squares: Scratch
Emphasis: Geometry and Measurement Creator: Selim Tezel Twitter: @SelimTezel Students will use their understanding of inverse trigonometry and the Pythagorean Theorem to make a spiraling square pattern. View Lesson Here
Growing Patterns Translations: Scratch
Emphasis: Algebra, Geometry and Measurement Creator: Jim Cash Twitter: @cashjim Students will use pattern recognition to grow a visual pattern with translation and variables. View Lesson Here
Graphing Slope-Intercept Form: Scratch
Emphasis: Algebra Creator: Mike Larson Twitter: @boundsofoutmath This program allows the user to type in a linear equation, then the program graphs the line. View Lesson Here
Geoguessr Simulation: Scratch
Emphasis: Geometry and Measurement Creator: Will Abbott Twitter: @MrAbbottMath Have you ever played the game Geoguessr? Google Earth drops you in a random location on Earth and your goal is to guess where you are. The program then tells you how close/far you are from the destination. Geoguessr simulates this by using…
The Coordinate Plane: Scratch
Emphasis: Measurement and Geometry Creator: Erik Nauman Twitter: @openblackboard Aim to correctly guess the location of the green square using coordinates. The closer you are the more points you earn. View Lesson Here
Subtracting Integers Race Game: Scratch
Emphasis: Number and Operation Creator: Ashley Tewes Twitter: @ashleyanntewes Race to the finish line against the computer. The only way to advance is by correctly answering subtraction questions. View Lesson Here
Playful Polygons: Scratch
Emphasis: Geometry and Measurement Creator: Dan Anderson Twitter: @dandersod Students will draw, using the pen tool, different polygons. They will start with a square, then a triangle, then some challenge shapes. The designs will be based on the angles of the shapes. View Lesson Here
Recipe Proportion Calculator: Scratch
Emphasis: Number and Operation Creator: Ashley Tewes Twitter: @ashleyanntewes Choose a recipe you love! Then choose how many guests you are cooking for. The program will calculate the amount of each ingredient you need based on the number of guests. View Lesson Here
Coin Flip: Scratch
Emphasis: Data and Probability Creator: Ashley Tewes Twitter: @ashleyanntewes Simulate a simple coin flip in Scratch by totaling the number of heads and tails flipped. Next, calculate the experimental probability of flipping either heads or tails after each flip. View Lesson Here | crawl-data/CC-MAIN-2022-27/segments/1656103337962.22/warc/CC-MAIN-20220627164834-20220627194834-00501.warc.gz | null |
# ANUMLA - Editorial
Author: Anudeep Nekkanti
Tester: Constantine Sokol
Editorialist: Florin Chirica
Easy
### PREREQUISITES:
greedy, heaps (or STL multiset)
### PROBLEM:
You have an unknown set of length N. We take all 2 ^ N subsets of it and sum elements for each subset. Given what we obtained, restore a possible initial set.
### QUICK EXPLANATION
We build our solution step by step. Each step we take smallest element from sums. Suppose we’re at step i and we found element x[i]. We should erase now from sums all sums formed by x[i] and a non-empty subset of {x[1], x[2], …, x[i – 1]}.
### EXPLANATION
Let’s call all 2^N sums sumSet. Also, let’s call a possible solution valueSet (making sum of all subsets of valueSet, you should obtain sumSet). The problem says there is always a possible solution. We’ll implement sumSet as a multiset from C++. This container allows following things, which will be needed later: find/delete an element and keep the set in increasing order. We’ll note first element from current sum set as sumSet[1], second element as sumSet[2] and so on. Let’s read all numbers from the input and add all of them in multiset sumSet.
Smallest element from sumSet is always 0 (and it corresponds to empty subset). It does not give us any information, so let’s erase it from the set and move on. What’s smallest element now? Is it an element from valueSet? Is it a sum of a subset of valueSet?
There exists at least one element from valueSet equal to smallest element from sumSet. Why? Suppose first element of sumSet is a sum of other elements of valueSet. sumSet[1] = valueSet[k1] + valueSet[k2] + … where k1, k2, … are some indexes.
Since numbers are positive, we get that valueSet[k1] <= sumSet[1], valueSet[k2] <= sumSet[1] and so on. Since sumSet[1] is smallest element possible, we can only get that valueSet[k1] = sumSet[1], valueSet[k2] = sumSet[1] and so on.
This means at least one element from valueSet will have value equal to sumSet[1]. We’ve found one element from valueSet. Let’s add it to valueSet (we build the set incrementally) and erase it from sumSet.
Let’s move now to our new sumSet[1] element (smallest element from sumSet, not deleted yet). We can follow same logic from above and see that sumSet[1] is a new element from valueSet. Let’s add it to valueSet and erase it from sumSet.
We move once again to sumSet[1]. Now, we have a problem. It can be one of following 2 possibilities:
• `````` sum of subset {valueSet[1], valueSet[2]}
``````
• `````` a new element of valueSet.
``````
Case b) is ideal, because we found one more element of valueSet. What to do with case a)? We know sum valueSet[1] + valueSet[2]. So we can simply erase it from sumSet, before considering sumSet[1]. Then, only case a) is left, so we find valueSet[3]. We erase now valueSet[3] from sumSet (I know, it becomes boring already, I’ll finish in a moment ).
It’s more tricky now what can be sumSet[1]. It can be one of following: valueSet[3]+valueSet[1], valueSet[3]+valueSet[2], valueSet[3]+valueSet[1]+valueSet[2]. We can fix this by erasing all those elements from sumSet before considering sumSet[1]. Once again, we’re left with valueSet[4].
Let’s note that all sums that should be erased contain a valueSet[3] term and a non-empty subset of {valueSet[1], valueSet[2]}. Sums of subsets of {valueSet[1], valueSet[2]} are already erased in previous steps.
# Generalizing the algorithm
Let’s generalize the algorithm. Suppose you want to calculate valueSet[n]. We need firstly to erase from set a combination of valueSet[n – 1] and a non-empty subset of {valueSet[1], valueSet[2], …, valueSet[n – 2]}. Then, the smallest element is valueSet[n].
We can keep an additional array subsets[] representing all subset sums obtained from {valueSet[1], valueSet[2], …, valueSet[n – 2]}. Then, at step of calculating valueSet[n], we need to erase subsets[j] + valueSet[n – 1] from our sumSet. Now, valueSet[n] is calculated.
The new subset sum list will be the old one plus the one that contains valueSet[n – 1]. So, after we calculate valueSet[n], we update subsets with all values valueSet[n – 1] + subSets[j].
We run this algorithm as long as there is at least one element in sumSet.
# Time Complexity
Each element is added in the multiset once and erased once. Hence, the complexity is O(2 ^ N * log(2 ^ N)) = O(2 ^ N * N).
### AUTHOR’S AND TESTER’S SOLUTIONS:
41 Likes
it’s ok now
The valueSet and sumSet thing is not very understandable.
5 Likes
5193943 is my submission id.
I haven`t been able to find counter test case.
So kindly help.link to my solution which is wrong is given.
http://www.codechef.com/viewsolution/5193943
Thanks
very well written
Very nice explanation
Hey @yogeshkr0007 have a look this testcase is the one to which your solution is wrong
1 Like
hey.
same situ though.
thanks anyways.
I implemented a similar algorithm using unordered_map. I belive that the amortized time-complexity must be around the same. Could anyone help me understanding why this would give TLE?
Here is the relevant link. Thanks.
http://www.codechef.com/viewsolution/5184582
The concept is quite nice. I tried to implement exactly the same thing in code. However, I did not know about the container, and hence my solution became very complicated.
There can be problem when we have the next element in the valueset that is equal to sum of other subsets in valueset. for example, when we have our original valueset as 1 1 2. Then, the sumset would have originally contain 0 1 1 2 2 3 3 4. So, after finding Valuset[0] = 1, Valuset[1] = 1. If we remove ValueSet[0] + ValueSet[1] i.e. 2 from SumSet, then it would remove the original ValueSet[2] = 2 element. And the new state of the Sumset would be 3 3 4. So, we will miss element 2.
Please clariy if i am wrong anywhere.
Why are you removing both 2’s??It’s a multi-set, so only one instance of 2 will be removed and then it will become {2,3,3,4}.
Amazing !!!
Anyone please look at these two solutions :
1.) http://www.codechef.com/viewsolution/5195961
2.) http://www.codechef.com/viewsolution/5195984
.First one is TLE whereas second is AC.
Onlyone difference is that i’m just using “st.count” for checking whether that element is in that multiset before deleting it, it’s a natural way of deleting element from STL containers…But,it gave TLE,
whereas not checking this gives AC .
Anyone please explain me the behavior or uses of these functions.
1 Like
1 Like
Since all the elements of the array are positive integers. Can we sort the subsets and get the first smallest N numbers ? have I understood the problem correctly ?
May you please tell me how you got 0 0 1 1 1 1 2 2 by adding the elements of subsets of set={0,1,0} in your given test case as the possible subsets are {},{0},{1},{0,1},{1,0},{0},{0,1,0},{0,0} and the array formed is 0 0 1 1 1 0 1 0.Correct me if I am wrong.
nope…u havent!!!
1 Like
Take a test case:
1
3
0 1 2 3 4 5 6 7
Ans: 1 2 4.
So this logic fails. | crawl-data/CC-MAIN-2023-23/segments/1685224644571.22/warc/CC-MAIN-20230528214404-20230529004404-00325.warc.gz | null |
Disparate charging and sentencing refer to the use of different treatments for offenders with similar offenses. This has been common in many countries across the world because categorization of offenders has been a challenging task. The philosophical differences of judges affect the sentences imposed (Cole & Smith, 2008). Research has shown that some judges are consistently more lenient or more severe than their colleagues (Cole & Smith, 2008). Therefore, charging and sentencing vary significantly, which depend on the sentencing philosophy of the judge. Other factors that may lead to disparate charging and sentencing include the gender, racial, and ethnic differences of the offenders (Cole & Smith, 2008). The guidelines for charging and sentencing offenders serve as the most significant strategy against disparate charging and sentencing.
Guidelines that determine criminal charging and sentencing have changed the manner in which judges pronounce sentences (Cole & Smith, 2008). Judges use mathematical formulae to calculate criminal sentences, which is a fair means to sentence offenders. Supporters of federal guidelines for sentencing believe that the guidelines are extremely effective in reducing charging and sentencing disparity. The guidelines ensure that federal felons, such as those people who sell illegal narcotics, receive harsh punishments. Without the guidelines, defendants will look for lenient judges and avoid those who will pronounce severe sentences (Cole & Smith, 2008). Therefore, disparate charging and sentencing will be common when the Criminal Justice System does not use a set of guidelines. Some people criticize the application of sentencing guidelines because they do not allow enough discretion to judges. However, the use of sentencing guidelines is the best alternative to address disparate charging and sentencing. For instance, the Minnesota guidelines have reduced disparity of sentencing by about 78 percent (Cole & Smith, 2008).
In conclusion, sentencing guidelines prove to be the best strategy for reducing disparate charging and sentencing in the contemporary courts. Judges may not be able to violate the guidelines and favor defendants. Therefore, charging and sentencing will not depend on the philosophical differences that exist between different judges (Cole & Smith, 2008). The Minnesota guidelines serve as a significant example that shows the effectiveness of sentencing guidelines in reducing charging and sentencing disparity. | <urn:uuid:050cc5a3-2a62-4022-a67e-c77e587f3e47> | {
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and its properties such as graph, period, phase shift and asymptotes are explored interactively by changing the parameters a, b, c and d using an applet. See figure below for main panel of the applet showing the graph of tangent function in blue and the vertical asymptotes in red.
Once you finish the present tutorial, you may want to go through a self test on trigonometric graphs .
How do the 4 coefficients a,b,c and d affect the graph of f(x)?
use the scrollbar to set a=1,b=1,c=0 and d=0. Write down f(x) and take note of the period phase shift and positions of asymptotes (in red)of f(x)? Now change a , how does it affect the graph?
set a=1,c=0,d=0 and change b. Find the period from the graph and compare it to
pi/|b|. How does b affect the graph of f(x)?How does it affect the asymptotes?
set a=1,b=1,d=0 and change c starting from zero going slowly to positive large
values. Take note of the shift, is it left or right, and compare it to -c/b.
set a=1,b=1,d=0 and change c starting from zero going slowly to negative smaller values. Take note of the shift, is it left or right, and compare it to -c/b.
repeat 3 and 4 above for b=2,3 and 4.
set a,b and c to non zero values and change d. What is the direction of the shift of the graph?
What parameters affect the positions of the asymptotes? Explain algebraically.
Graphing Tangent Functions. A step by step tutorial on graphing and sketching tangent functions. The graph, domain, range and vertical asymptotes of these functions and other properties are examined. | <urn:uuid:36650854-8cc0-40d6-ac9c-e718ee6bf481> | {
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The Physics
Hypertextbook
Opus in profectus
# Pressure-Volume Diagrams
## Discussion
### math, math, math
Recall from the previous section…
U = Q + W
Q > 0 system absorbs heat from the environment Q < 0 system releases heat to the environment W > 0 work done on the system by the environment W < 0 work done by the system on the environment
A system can be described by three thermodynamic variables — pressure, volume, and temperature. Well, maybe it's only two variables. With everything tied together by the ideal gas law, one variable can always be described as dependent on the other two.
⎧⎪⎪⎨⎪⎪⎩ P = nRT V PV = nRT ⇒ V = nRT P T = PV nR
Temperature is the slave of pressure and volume on a pressure-volume graph (PV graph).
Function of State
U = 32nRT
Function of Path: Work
W = ∫ F · ds = ∫ P dV
W = − area on PV graph
Function of Path: Heat
Q = ∆U + W = ncT
cP = specific heat at constant pressure cV = specific heat at constant volume
### curves
• isobaric
• constant pressure
• "bar" comes from the greek word for heavy: βαρύς [varys]
• examples: weighted piston, flexible container in earth's atmosphere, hot air balloon
• PV graph is a horizontal line
W = −P∆V ⇒ ∆U = Q − P∆V
• isochoric
• constant volume
• "chor" comes from the greek word for volume: χώρος [khoros]
• examples: closed rigid container, constant volume thermometer
• PV graph is a vertical line
W = 0 ⇒ ∆U = Q
• isothermal
• constant temperature
• "therm" comes from the greek work for heat: θερμότητα [thermotita]
• examples: "slow" processes, breathing out through a wide open mouth
• PV graph is a rectangular hyperbola
∆U = 0 ⇒ Q = −W
• no heat exchange with the environment
• adiabatic has a complex greek origin that means "not+through+go": α + ∆ια + βατός [a + dia + vatos]
• examples: "fast" processes, forcing air out through pursed lips, bicycle tire pump
• PV diagram is a "steep hyperbola"
Q = 0 ⇒ ∆U = W
PVγ = constant
γ = cP = α + 1 cV α
3/2 + 1 = 5 monatomic 3/2 3 5/2 + 1 = 7 diatomic 5/2 5
liquids
solids | crawl-data/CC-MAIN-2021-21/segments/1620243988724.75/warc/CC-MAIN-20210505234449-20210506024449-00599.warc.gz | null |
## CryptArithmetic Problem: SEND + MORE = MONEY
The following puzzle is probably the most well-known CryptArithmetic Problem:
How to solve the above challenge?
We put the letter as equality constraints
Expression1 = 1000*S + 100*E + 10*N + D
Expression2 = 1000*M + 100*O + 10*R + E
Expression3 = 10000*M + 1000*O + 100*N + 10*E + Y
If (Expression3 ==Expression1 + Expression2) then
Report the value of {S, E, N, D, M, O, R, Y}
The simplest (not the fastest) way is to do permutation of digit 0 to 9 and then compute the above expression. Matlab code below gives all the possible solutions.
function report=SENDMOREMONEY
digit=0:9;
P=perms(digit);
k=0;
for i=1:size(P,1)
v=P(i,:);
% evaluate expression
exp1=v(1)*1000+v(2)*100+v(3)*10+v(4); % SEND
exp2=v(5)*1000+v(6)*100+v(7)*10+v(2); % MORE
exp3=v(5)*10000+v(6)*1000+v(3)*100+v(2)*10+v(8); % MONEY
if exp1+exp2==exp3,
k=k+1;
report(k,:)=v(1:8); % = [s, e, n, d, m, o, r, y]
end
end
report=unique(report,'rows');
## Solutions:
If M is allowed to be zero, the solutions are not unique. Below are all the 25 possible solutions.
{S=9, E=5, N=6, D=7, M=1, O=0, R=8, Y=2}
{S=8, E=5, N=4, D=2, M=0, O=9, R=1, Y=7}
{S=8, E=4, N=3, D=2, M=0, O=9, R=1, Y=6}
{S=8, E=3, N=2, D=4, M=0, O=9, R=1, Y=7}
{S=7, E=6, N=4, D=9, M=0, O=8, R=1, Y=5}
{S=7, E=6, N=4, D=3, M=0, O=8, R=2, Y=9}
{S=7, E=5, N=3, D=4, M=0, O=8, R=2, Y=9}
{S=7, E=5, N=3, D=9, M=0, O=8, R=1, Y=4}
{S=7, E=5, N=3, D=1, M=0, O=8, R=2, Y=6}
{S=7, E=4, N=2, D=9, M=0, O=8, R=1, Y=3}
{S=7, E=3, N=1, D=6, M=0, O=8, R=2, Y=9}
{S=6, E=8, N=5, D=3, M=0, O=7, R=2, Y=1}
{S=6, E=8, N=5, D=1, M=0, O=7, R=3, Y=9}
{S=6, E=5, N=2, D=4, M=0, O=7, R=3, Y=9}
{S=6, E=4, N=1, D=9, M=0, O=7, R=2, Y=3}
{S=6, E=4, N=1, D=5, M=0, O=7, R=3, Y=9}
{S=5, E=8, N=4, D=9, M=0, O=6, R=3, Y=7}
{S=5, E=7, N=3, D=2, M=0, O=6, R=4, Y=9}
{S=5, E=7, N=3, D=1, M=0, O=6, R=4, Y=8}
{S=3, E=8, N=2, D=9, M=0, O=4, R=5, Y=7}
{S=3, E=8, N=2, D=1, M=0, O=4, R=6, Y=9}
{S=3, E=7, N=1, D=9, M=0, O=4, R=5, Y=6}
{S=3, E=7, N=1, D=2, M=0, O=4, R=6, Y=9}
{S=2, E=8, N=1, D=9, M=0, O=3, R=6, Y=7}
{S=2, E=8, N=1, D=7, M=0, O=3, R=6, Y=5}
If M has to be non-zero digit, the solution is unique. The reason is because S and M are the leading digit, they cannot become 0. Their domain is 1 to 9. All other letters {E, O, N, R, D, Y} has domain of 0 to 9. In this case the solution is unique, that is {S=9, E=5, N=6, D=7, M=1, O=0, R=8, Y=2}.
``` 9567 SEND
1085 MORE
--------- + ----------- +
10652 MONEY```
We can see this problem from another perspective of linear equations and linear algebra.
We can derive equations:
D + E = Y + 10C1
N + R + C1 = E + 10C2
E + O + C2 = N + 10C3
S + M + C3 = O + 10C4
C4 = M
Where Ci is the carry for the summation. There are 5 equations with 12 unknowns. The solution is not unique. We can put into matrix equation
Inputting one of the solution is {S=9, E=5, N=6, D=7, M=1, O=0, R=8, Y=2} in which the carries are {C1=1, C2=1, C3=0, C4=1} evaluates the same expressions above. This may be useful to evaluate the expressions to all the possible solutions at once. | crawl-data/CC-MAIN-2021-49/segments/1637964360803.6/warc/CC-MAIN-20211201143545-20211201173545-00249.warc.gz | null |
Brain Ball
Patented by A. Unsicker 1999.
(plastic, 3.5 inches, the back side of each number is white)
Numbers are yellow on one side and white on the other, and can rotate any number of positions in either direction. In addition, there is a north pole that spans three numbers (13, 1, 2 in the photos above) and a south pole that spans four numbers (6, 7, 8, 9 in the photos above); a flip turns these 7 numbers along the pole axis:
->
Solution: Use ideas from Jaap's Page (which also presents moves to speed up solving). For a positive integer n, n and -n denote clockwise and counter-clockwise rotations by n positions, and / denotes a flip. The pole position P is the center of the north pole, and the two positions to its right clockwise are Q and R.
Step 1: Make the side facing you all yellow by using as needed:
2/-2/2/-2 = flip the pole position
Step 2: From 1 to 11, move counter clockwise to its position, using:
1/-1/6/-6/-6/-6/-1 = PQR -> RPQ
That is, repeatedly move the next piece to position R and use this transformation to advance it two positions towards its goal. If it is only one position away, first advance number to its right.
Step 3: If 12 and 13 are reversed, change parity by changing the side facing you from yellow to white (which mixes the numbers) turn over the puzzle, and repeat Steps 1 and 2:
/5/5/ = flip all of the numbers | crawl-data/CC-MAIN-2019-30/segments/1563195525659.27/warc/CC-MAIN-20190718145614-20190718171614-00281.warc.gz | null |
Heraclius c. 575 – February 11, 641 was a Byzantine Emperor from 610 to 641. Heraclius is credited for saving the Christian world from Barbarian invasions.
Heraclius was the eldest son of Heraclius the Elder and Epiphania, possibly of an Armenian family from Cappadocia, probably of Arsacid descent. Beyond that, there is little specific information known about his ancestry. His father was a key general during Emperor Maurice’s war with Bahrām Chobin, usurper of the Sassanid Empire, during 590. After the war, Maurice appointed Heraclius the Elder to the position of Exarch of Africa.
He was responsible for introducing Greek as the Eastern Empire’s official language. His rise to power began in 608, when he and his father, Heraclius the Elder, the exarch of Africa, successfully led a revolt against the unpopular usurper Phocas.
Heraclius’s reign was marked by several military campaigns. The year Heraclius came to power, the empire was threatened on multiple frontiers. Heraclius immediately took charge of the ongoing war against the Sassanids. The first battles of the campaign ended in defeat for the Byzantines; the Persian army fought their way to the Bosphorus; however, because Constantinople was protected by impenetrable walls and a strong navy, Heraclius was able to avoid total defeat. Soon after, he initiated reforms to rebuild and strengthen the military. Heraclius drove the Persians out of Asia Minor and pushed deep into their territory, defeating them decisively in 627 at the Battle of Nineveh. The Persian king Khosrau II was overthrown and executed by his son Kavadh II, who soon sued for a peace treaty agreeing to withdraw from all occupied territory. This way peaceful relations were restored to the two deeply strained empires.
However, soon after his victory, he faced a new threat, the Muslim invasions. Emerging from the Arabian Peninsula, the Muslims quickly conquered the Sassanid empire. In 634 the Muslims invaded Roman Syria, defeating Heraclius’ brother Theodore. Within a short period of time, the Arabs would also conquer Mesopotamia, Armenia, and Egypt.
Heraclius entered diplomatic relations with the Croats and Serbs in the Balkans. He tried to repair the schism in the Christian church in regard to the Monophysites by promoting a compromise doctrine called Monothelitism. The Church of the East (commonly called Nestorian) was also involved in the process. Eventually, however, this project of unity was rejected by all sides of the dispute.
Looking back at the reign of Heraclius, scholars have credited him with many accomplishments. He enlarged the Empire, and his reorganization of the government and military were great successes. His attempts at religious harmony failed, but he succeeded in returning the True Cross, one of the holiest Christian relics, to Jerusalem.
In Islamic and Arab histories Heraclius is the only Roman Emperor who is discussed at any length. Owing to his role as the Roman Emperor at the time Islam emerged, he was remembered in Arabic literature, such as the Islamic hadith and sira.
- Treadgold 1997, p. 287.
- Sasanian Dynasty”. Encyclopædia Iranica. 20 July 2005. Retrieved 17 August 2013.
- Kaegi 2003, pp. 24 – 25.
- Seleznyov N.N. “Heraclius and Ishoʿyahb II”, Simvol 61: Syriaca-Arabica-Iranica. (Paris-Moscow, 2012), pp.280-300.
- El-Cheikh 1999, p. 7 | <urn:uuid:06f3e306-df96-47a0-9c44-5e3d1ba6954f> | {
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It was not until the mid-l960's, after the discovery of a magnetic striping preserved in the oceanic crust, that the idea of continental drift became widely accepted in the United States. It is now accepted that the earth's surface consists a number of variable-sized plates which float on a plastic interior zone and interact with each other. Not surprisingly, the boundaries between these plates are very geologically active areas. The US Geological Survey has a nice description of the concept of plate tectonics and their National Earthquake Information Center has a nice animation of the Earth's plate boundaries.
Fundamentally, there are three types of plate boundaries. The first is called a spreading center or divergent boundary. Here, along great unhealing wounds in the earth's surface, heated subsurface material wells up, cools and is added to the edges of the plates, which move away from one another on opposite sides of the spreading center. Spreading center boundaries are found today at the Mid-Atlantic Ridge, in the Gulf of California which separates Baja California from mainland Mexico and under Africa in the East African Rift Zone. Spreading center boundaries are the important in shaping the earth's surface and are the locations from which oceans are born. Legs 100-158 of the Deep Sea Drilling Project included several investigations of the proposed ancient continental breakup zone in the Atlantic and provided valuable information on this type of boundary and other deepsea features. This effort continues today as part of the JOIDES Ocean Drilling Program. Some of the achievements of this effort are summarized here.
The second type of boundary occurs where two plates collide. When an oceanic plate collides with a continental plate, because the oceanic plate is denser and thinner, it bends down and is moves beneath the edge of the continent. Geologists call this process subduction. Major subduction zones exist today off the western Pacific coast from Cape Mendocino in Northern California to British Columbia, along the west coast of South America, most of the rest of the margins of the Pacific Ocean. Although this type of zone does not currently exists off the coast of California, except north of Cape Mendocino (Here is Humboldt State University's diagram of their local area, the tectonic setting and resultant earthquakes), this type of boundary has in the past played a significant role in the history of Marin County's rock record.
The San Andreas fault which today runs through the bay area and western Marin County represents the third major type of plate boundary, one in which the plates slide by one another along a major fracture system. These boundaries are called a transform boundaries.
The geologic record left by any of these particular types of boundaries may be preserved in the rock record even though that type of boundary may not play a role in the area's later geologic history. Thus, whereas the rock record of Marin County and the Franciscan rocks of California show signs of an initial origins at a sea-floor spreading location, there are clear indications of a subduction zone playing a role in what we see in the county today. In Marin and the area now occupied by California Coast Range, those processes are but distant memories contained in the rock record of these areas. But plate tectonics continues to play a role in the County's geology since the transform San Andreas fault system (the main branch of which lies approximately ten miles west of Ring Mountain) and the others of the system (Bolinas Mesa-San Gregorio-Sur/Nacimento; Hayward and Calaveras Faults) now dominate the area tectonically. | <urn:uuid:6cc08e7b-6ed0-4235-884b-af1a53736016> | {
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10 Jul Corn On Foot
Corns, also known as clavus or clavi, are calluses made of dead skin that tend to appear on the hairless surfaces of your hands and feet. Their most common location is on the dorsal areas of toes or corn on foot.
What Are Corns?
Corns on foot are formed by layers of dead skin which develop as a response to pressure and friction. They are your body’s way to protect itself from the foot pain and injury that can be caused by intense, prolonged pressure that affects a specific spot in your skin. The symptoms of a corn on your foot can include:
- A thick, hardened patch of skin. The skin on this area is usually dry, and flaky; it can also be yellowed. A corn on foot skin tends to be small and circular in shape.
- A corn on the foot can be painful when pressed, unlike other types of calluses.
- The skin around the corn tends to be soft and swollen, but the center of the corn is usually hardened and indurated.
- Calluses usually develop on non-weight bearing surfaces, but they can also occur on places such as your knees, and on the balls of your feet.
How Do You Get Them?
Corns develop as a result of friction caused by prolonged pressure or repetitive movements. The source of this friction can be:
- Wearing ill-fitting shoes: there are many ways in which your footwear can cause a corn on your foot. Shoes that are too loose can cause your feet to slide around in them, and poorly-made shoes can have seams that can rub against your skin. Tight shoes, especially those with narrow toe boxes, can also create pressure against the side of your foot.
- Foot abnormalities: physical deformities, such as hammertoes, or defects in the biomechanics of your gait and movements can put you at higher risk of developing foot corns. These factors should be assessed by your podiatrist.
- Risk factors include not wearing socks, performing repetitive actions such as jogging, and old age, since fatty tissue tends to decrease in seniors.
How Do You Treat Them?
Fortunately, corns on foot skin are easy to treat. Home treatments for foot corns include soaking your foot in warm water and then rubbing the corn with a pumice stone. You can find corn pads that contain salicylic acid at the drugstore. The acid will help soften and remove the corn. You should also make sure to keep your skin hydrated and clean.
If the corn on your foot becomes too painful, or if you suffer from diabetes or any other disease that affects your circulation, your Podiatrist Sydney will be able to provide different therapeutic options for this condition. | <urn:uuid:083d89c6-dfe2-43b8-a591-5aac8535f9d2> | {
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If is expressed as a terminating decimal, how many nonzero digits will d have?
<p>(A) One</p><p>(B) Two</p><p>(C) Three</p><p>(D) Seven</p><p>(E) Ten</p><p><br></p>
- Many Runagian senior citizens are no better off financially now than they were before the increase.The phrase “better off” is closest in meaning to________?
- The word "accidental" is closest in meaning to___________ ?
- Who can it be? I’ m quite ____ a loss to guess．
- The number of people flying first class on domestic flights rose sharply in 1990, doubling the increase of the previous year.
- The word "conspicuous" is closest in meaning to______ ? | <urn:uuid:00cad003-65a6-4a0c-8580-cadf3617e8c4> | {
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What would you think about a man who had the power to raise the dead, call down fire from heaven, cause the heavens to withhold rain, and render a barrel of flour inexhaustible?
Elijah was such a man, a man of power, a man of miracles, a prophet so worthy that he was translated and taken from the earth in a chariot of fire.
Small wonder that Elijah became one of the great heroes in Israel’s history. Small wonder, too, that in Jewish households a place is set for him at every Passover feast in anticipation of his return as predicted by the prophet Malachi (see Malachi 4:5–6).
This assignment deals with the reasons Elijah is one of the greatest prophets of all time and why he was rejected by the people of his own day.
Notes and Commentary on 1 Kings 17–2 Kings 2
(5-2) 1 Kings 17:1. What Is a Tishbite?
Elijah is here called “the Tishbite, who was of the inhabitants of Gilead.” Some scholars say that Elijah came from Tishbeh, in upper Galilee (see C. F. Keil and F. Delitzsch, Commentary on the Old Testament, 3:1:234). Adam Clarke suggested a different place. Elijah came, he said, from Gilead beyond the Jordan in the land given to the tribe of Gad (see The Holy Bible … with a Commentary and Critical Notes, 2:452). Whichever is correct, it is clear that the title Tishbite refers to the place from which Elijah came.
(5-3) 1 Kings 17:1. Elijah Sealed the Heavens against Rain by Priesthood Power
Elder Joseph Fielding Smith found a special significance in verse 1:
“The first appearance of Elijah we read of is in the 17th chapter of 1st Kings, when he came before the king and said, ‘As the Lord God of Israel liveth, before whom I stand, there shall not be dew nor rain these years, but according to my word.’
“There is something very significant in that edict. I want you to get it. Follow me again closely: ‘As the Lord God of Israel liveth, before whom I stand, there shall not be dew nor rain these years, but according to my word.’ The reason I put emphasis upon this is to impress you with the sealing power by which Elijah was able to close the heavens, that there should be no rain or dew until he spoke.” (Doctrines of Salvation, 2:102.)
(5-4) 1 Kings 17:3. Where Is the Brook Cherith?
“We do not know which of the Jordan tributaries the brook Cherith might have been, but apparently it was an obscure and isolated place where Elijah could hide safely without being accidentally discovered by soldiers, shepherds or passersby. It was also a desolate place where no animal life existed, therefore Elijah was completely dependent upon the Lord for his sustenance.” (W. Cleon Skousen, The Fourth Thousand Years, p. 336.)
(5-5) 1 Kings 17:4, 6. Who Fed Elijah?
Some scholars insist that the word raven is a mis-translation and that merchants or traders is the correct rendering. Other scholars disagree. They insist that the Hebrew word is properly translated just as it stands. The fact that Elijah was in hiding makes it unlikely that merchants or traders would come to him twice a day, and the tone of the writer suggests that it was miraculous care rather than a normal interaction between Elijah and other men.
(5-6) 1 Kings 17:9. The Widow of Zarephath
Zarephath was on the coast of the Mediterranean between Tyre and Sidon, in what is now Lebanon and was then Phoenicia, outside the boundaries of Israel. The poor widow had only a little flour with which to make a patty to fry. Her barrel would have been an earthen jar and her cruse a clay bottle. Wooden barrels are not suitable for storing flour in the Middle East because they do not protect the flour from insects.
Elijah’s request for the widow to prepare his food was not a selfish request but rather a test of her faith. Because she passed the test, Elijah’s promise that her barrel of flour and cruse of oil would not fail for the duration of the famine was fulfilled. This widow not only provided for her own needs in a time of great distress but provided for others an example of great faith. In an attempt to open the eyes of his prejudiced countrymen, Jesus spoke of this Sidonian woman who obeyed God’s command and physically sustained His prophet. “But I tell you of a truth, many widows were in Israel in the days of Elias, when the heaven was shut up three years and six months, when great famine was throughout all the land; but unto none of them was Elias sent, save unto Serepta, a city of Sidon, unto a woman that was a widow” (Luke 4:25–26).
(5-7) 1 Kings 17:17–24. Elijah Raised the Dead
This is the fourth miracle mentioned in this chapter which Elijah performed by means of his priesthood power. First he brought famine by his word (see v. 1), then he was fed by ravens (see v. 6), then he caused the widow’s food supply to miraculously continue (see vv. 13–16). Then he worked another mighty miracle through the power of God. The widow’s cry (see v. 18) was more a plea for help than a criticism. In essence she was saying, “I thought sheltering a prophet would bring blessings and protection; instead, tragedy has struck my home.”
(5-8) 1 Kings 18:1–16. Elijah Was Sent to Meet Ahab
Obadiah was the king’s chamberlain, or governor of his house. As such it was his responsibility to arrange the king’s appointments. That is why Elijah told Obadiah to set up an interview between the prophet and King Ahab. The fact that a king and his chief steward had to look for water and grass by themselves shows that the famine had become acute (see vv. 5–6).
Ahab knew that Elijah had brought this distress, so he searched for him. Apparently Ahab had considerable power and authority among surrounding nations, for he was able to exact promises for them that they were not concealing Elijah or that they knew of his whereabouts (see v. 10). Sometimes, however, someone would see the prophet. But when he reported seeing Elijah, the prophet had disappeared by the time Ahab got there. Ahab then killed the person who said he had seen Elijah. Obadiah’s fear that Elijah would disappear again was caused by his awareness that Ahab would not hesitate to have him executed if he failed to deliver Elijah (see vv. 12–16). Elijah promised Obadiah that he would appear before Ahab (see v. 15).
Whether this Obadiah, who “feared the Lord greatly” (v. 3), is the author of the Old Testament book of the same name is not known, but it is doubtful.
(5-9) 1 Kings 18:17–18. Who Has Troubled Israel?
These verses have inspired many sermons, for the wicked usually blame someone else for their misfortunes. Elijah had no power by himself to bring on the famine. He was only the agent of the Lord. Ahab and his policies were the true cause of Israel’s distress, but the king refused to accept that responsibility.
(5-10) 1 Kings 18:19. Mount Carmel
Mount Carmel is a mountain ridge several miles long that runs from southeast to northwest. Its southeastern slopes are very near the northwestern corner of the great Jezreel Valley, and its northwest edge juts into the Mediterranean on the northern coasts of modern Israel. Rising abruptly to about eighteen hundred feet above sea level, it is an impressive prominence and became synonymous with beauty. It is referred to figuratively in the Doctrine and Covenants. (see D&C 128:19.)
(5-11) 1 Kings 18:21. “How Long Halt Ye between Two Opinions?”
Clarke offered the following comment on Israel’s indecision: “Literally, [the phrase means] ‘How long hop ye about upon two boughs?’ This is a metaphor taken from birds hopping about from bough to bough, not knowing on which to settle. Perhaps the idea of limping through lameness should not be overlooked. They were halt, they could not walk uprightly; they dreaded Jehovah, and therefore could not totally abandon him; they feared the king and queen, and therefore thought they must embrace the religion of the state. Their conscience forbade them to do the former; their fear of man persuaded them to do the latter; but in neither were they heartily engaged; and at this juncture their minds seemed in equipoise, and they were waiting for a favourable opportunity to make their decision. Such an opportunity now, through the mercy of God, presented itself.” (Commentary, 2:457.)
(5-12) 1 Kings 18:22–24. The Challenge
The contest that Elijah proposed should have appealed to the prophets of Baal, since their god, the “Sun-god,” could surely send down fire if anyone could. Added to the four hundred and fifty priests of Baal were four hundred priests of his female counterpart, Ashtoreth, or Venus, whom Jezebel worshiped. Elijah commented on the number of prophets of Baal in contrast to the number of prophets of the Lord (see v. 22).
(5-13) 1 Kings 18:25–29. How Long Did the Priests of Baal Call upon Their God? Why?
Elijah’s mocking words recorded in verse 27 furnished cause for a renewed frenzy among Baal’s prophets. Elijah was really saying, “Cry louder; if he is a god, he can surely hear you. But then, perhaps, he’s away on a trip, or he’s out hunting (pursuing game), or maybe he’s asleep.” Such taunting kept the priests of Baal in action all day long. Clarke commented: “From morning even until noon. It seems that the priests of Baal employed the whole day in their desperate rites. The time is divided into two periods: 1. From morning until noon; this was employed in preparing and offering the sacrifice, and in earnest supplication for the celestial fire. Still there was no answer, and at noon Elijah began to mock and ridicule them, and this excited them to commence anew. And, 2. They continued from noon till the time of offering the evening sacrifice, dancing up and down, cutting themselves with knives, mingling their own blood with their sacrifice, praying, supplicating, and acting the most frantic manner.” (Commentary, 2:457.)
(5-14) 1 Kings 18:28. Why Did the Priests of Baal Cut Themselves as They Called Out to Their God?
Apparently they thought this act of self-abasement would endear them to their god, get his attention, and prove their sincerity. One ancient author told of antics very similar to these that he observed in Gaza in Roman times:
“‘A trumpeter went before them who proclaimed their arrival in the villages, the farmyards, or the streets of towns, by flourishes on his instrument—a twisted horn. The begging Galli followed in fantastic array, after a leader: an ass in their midst, carrying their begging bag and a veiled image of the goddess. … They danced along the streets to the sound of wild music, holding huge swords and bills, with whips for scourging themselves, in their hands, and making a hideous noise with rattles, fifes, cymbals or kettle-drums. When they came to a farmyard they began their ravings. A wild howl opened the scene. They then flew wildly one past the other: their heads sunk low towards the earth, as they turned in circles: their loose hair dragging through the dust. Presently they began to bite their arms, and next to hack themselves with the two-edged swords they carried.’ …
“Then began a new scene. ‘One of them, the leader in this frenzy, commenced to prophesy, with sighs and groans, lamenting aloud his past sins, which he would now avenge by the chastisement of his flesh. He then took the knotted whip and lashed his back, cutting himself also with his sword till the blood ran down.’” (In Cunningham Geikie, Hours with the Bible, 3:399–400.)
(5-15) 1 Kings 18:33–35. Why Did Elijah Have the Place of Sacrifice Drenched with Water?
The priests of Baal were so unscrupulous that they rigged their altars with fires beneath them to make the sacrifices appear to ignite spontaneously. One ancient writer said he “had seen under the altars of the heathens, holes dug in the earth with funnels proceeding from them, and communicating with openings on the tops of the altars. In the former the priests concealed fire, which, communicating through the funnels with the holes, set fire to the wood and consumed the sacrifice; and thus the simple people were led to believe that the sacrifice was consumed by a miraculous fire.” (In Clarke, Commentary, 2:459.)
Elijah undoubtedly drenched the altar and sacrifice with water as much for the heathen priests as for the people. He wanted to convince them that there was no trickery and to show them that the power of the Lord was manifest. It was a bold and dramatic move that demonstrated his absolute confidence in the power of the true God.
(5-16) 1 Kings 18:38. What Was the Fire of the Lord?
“The fire proceeding from Jehovah, was not a natural flash of lightning, which could not produce any such effect, but miraculous fire falling from heaven, as in [1 Chronicles 21:26; 2 Chronicles 7:1] (see [Leviticus 9:24]), the supernatural origin of which was manifested in the fact, that it not only consumed the sacrifice with the pile of wood upon the altar, but also burned up … the stones of the altar and the earth that was thrown up to form the trench, and licked up the water in the trench. Through this miracle Jehovah not only accredited Elijah as His servant and prophet, but proved Himself to be the living God, whom Israel was to serve; so that all the people who were present fell down upon their faces in worship, as they had done once before, viz. at the consecration of the altar in [Leviticus 9:24], and confessed ‘Jehovah is God.’” (Keil and Delitzsch, Commentary, 3:1:249.)
(5-17) 1 Kings 19:2–8. Elijah Fled Jezebel
These verses show how powerful and corrupt Jezebel was. Even after the miraculous fire from heaven, this woman was moved only to anger and swore she would take Elijah’s life in revenge. Elijah fled, first into the territory of Judah (at Beersheba) and then to Mount Horeb (or Sinai) 150 miles further south.
Elijah was either fasting or receiving food provided by the Lord during this period. If Elijah truly went without food for forty days, as verse 8 suggests, then he had an experience similar to that of Moses (see Exodus 24:18; 34:28; Deuteronomy 9:9–25) and the Savior (see Matthew 4:2). And like Moses at Sinai, Elijah there received revelations.
It must have been very lonely for Elijah during this period. Men were seeking his life, he felt himself to be the only faithful prophet left in Israel, and he was hiding in a cave. President Joseph Fielding Smith wrote: “When he was there, the Lord called upon him and asked him what he was doing there; and in his sorrow, because of the hardness of the hearts of the people, he told the Lord the condition, that he alone remained, that they sought his life to take it away. But the Lord showed him that there were others who had remained true unto him, even 7,000.” (Doctrines of Salvation, 2:106.)
Those who listen for God’s voice know that it is not in the power to break rocks and earth (see v. 11), nor in the fire, but in the “still small voice” that speaks to the heart of man. When Elijah heard the still small voice, he “went out” to converse with the Lord (v. 13). Encouraged, Elijah returned at the Lord’s request and completed his assigned mission. The word jealous as used in verses 10 and 14 means diligent. The new prophet chosen to succeed Elijah was Elisha.
(5-18) 1 Kings 19:4–16. Where Did Elijah’s Travels Take Him?
The accompanying map shows the journeys of Elijah from the time he left the Brook Cherith until he arrived at Damascus, Syria, where he anointed an earthly king in a foreign country. It provides a picture of how far-reaching his ministry was.
(5-19) 1 Kings 19:15. Jehovah, the God of Many Nations
This verse shows that God and Israel’s prophets influenced nations other than Israel. Nothing more is known about the circumstance that made it possible for Elijah to anoint a king of Syria.
(5-20) 1 Kings 19:17. Whom Did Elisha Slay?
There is no record of Elisha slaying anyone. This passage may mean that Elisha would prophesy the death of certain people. Of course, the Bible record as it is now is fragmentary at best, and the details of the incident referred to here may be lost.
(5-21) 1 Kings 19:19–21. Twelve Yoke of Oxen
Elisha must have been wealthy to have been plowing with twelve yokes of oxen, for each yoke pulled a plow and was driven by a servant. The feast of two oxen also indicates wealth. Eating the oxen and burning their equipment symbolically represents Elisha’s rejection of worldly wealth as Elisha prepared to follow Elijah and to make the considerable material sacrifice involved in responding to the prophetic call.
(5-22) 1 Kings 19:19. What Was the Mantle of the Prophet That Was Placed on Elisha?
A mantle is a coat or similar covering.
“When Elijah walked up to the plow where Elisha was standing the prophet simply removed his rough mantle and placed it across the shoulders of Elisha. The astonished Elisha seemed to have known exactly what this emblematic gesture meant. He was being designated for the prophetic calling and being chosen as the understudy and future successor of Elijah. No lengthy discussion or art of persuasion was employed to induce Elisha to accept the call. It was not needed. He was one of the choice 7,000 referred to by the Lord who had not bowed the knee to Baal but respected the Holy Priesthood of God and accepted with enthusiasm the discipline and obedience required by such a calling.” (Skousen, Fourth Thousand Years, p. 359.)
Out of this simple act, the phrase “mantle of the prophet” has come to mean the calling and office of the prophet.
(5-23) 1 Kings 20:11. “Let Not Him That Girdeth on His Harness Boast”
This is like saying “Don’t boast of the deed until it is done.” The imagery comes from the harnessing of work animals. It would be easy for an ox to boast of how much he can plow while he is being harnessed in the morning, but the boast would be meaningful only after the work was done, that is, when the harness is taken off.
(5-24) 1 Kings 20, 22. Battles with Syria
These chapters detail two separate battles between Israel and Syria. Israel won the first battle but lost the second.
(5-25) 1 Kings 20:28. What Is Meant by the Phrase “the Lord Is God of the Hills, but He Is Not God of the Valleys”?
“There seems to be an allusion here to the opinion, prevalent among all heathen nations, that the different parts of the earth had different divinities. They had gods for the woods, for the mountains, for the seas, for the heavens, and for the lower regions. The Syrians seem to have received the impression that Jehovah was specially the God of the mountains; but he manifested to them that he ruled every-where.” (James M. Freeman, Manners and Customs of the Bible, p. 165.)
(5-26) 1 Kings 20:38–43. Ahab’s Death Pronounced
In his encounter with the prophet of the Lord, Ahab unwittingly pronounced his own doom. The prophecy was fulfilled in the next battle with the Syrians (see 1 Kings 22:34–35). That was his reward for failing to slay Ben-hadad as the Lord had commanded.
(5-27) 1 Kings 21:2–24. Naboth’s Vineyard
Ahab’s offer to buy Naboth’s vineyard may seem fair at first glance, but Naboth could not sell. His land had been inherited from his forefathers, and the law of Moses did not permit the sale of one’s inheritance, except in cases of extreme destitution, and then it could be sold or mortgaged only until the time of jubilee, when it would be reclaimed. Ahab wished to acquire the land permanently. Hence Naboth’s reply: “The Lord forbid it me” (v. 3). Ahab’s tantrum over being refused (see v. 4) gives an insight into the character of Ahab. The king owned ten-twelfths of the land of Israel already, but he was miserable because he could not get everything he wanted.
These verses also show how Ahab’s wife, Jezebel, arranged her husband’s affairs without hindrance of any sort (see v. 16). The phrase “sons of Belial,” was a catch-all term that applied to almost any evil persons—liars, thieves, murderers. Notice how the punishment pronounced on Ahab and Jezebel matched their character (see vv. 19, 23).
(5-28) 1 Kings 21:27–29. Sins of the Fathers and the Sons
Because of Ahab’s wicked life, the Lord prophesied that he would lose his posterity (see 1 Kings 21:21). Verses 27 through 29 show the relationship between repentance and the consequences of sin. Because Ahab repented, the “evil” was delayed until Ahab’s son was king.
(5-29) 1 Kings 22:2–16. Ahab and Jehoshaphat
The friendship between Ahab, king of Israel, and Jehoshaphat, king of Judah, may have developed because Jehoram, Jehoshaphat’s son, had married Ahab’s daughter Athaliah. This friendship did not please the Lord, and Jehoshaphat was severely rebuked for encouraging it (see 2 Chronicles 19:1–3).
Ahab and Jehoshaphat were considering whether they should combine to fight against the Syrians. Ahab’s false prophets, or counselors, said yes, but Micaiah, a prophet of God, said no. The words of Micaiah in verse 15, “Go and prosper,” were said with great sarcasm. It is as though Micaiah said: “All your false prophets have predicted success. You want me to do the same, so I will: ‘Go and prosper.’” This was said scornfully to let King Ahab know that it was contrary to Micaiah’s true advice. Hence the King’s response in verse 16.
(5-30) 1 Kings 22:23–24. Did the Lord Place a “Lying Spirit” in Ahab’s Prophets?
The Lord does not place a lying spirit in anyone. As Clarke explained, the Hebrew expression means that the Lord “hath permitted or suffered a lying spirit to influence thy prophets. Is it requisite again to remind the reader that the Scriptures repeatedly represent God as doing what, in the course of his providence, he only permits or suffers to be done? Nothing can be done in heaven, in earth, or hell, but either by his immediate energy or permission. This is the reason why the Scripture speaks as above.” (Commentary, 2:476.)
(5-31) 1 Kings 22:34. What Are the “Joints of the Harness”?
An ancient warrior was covered with armor. To kill him, an arrow had to pass through the spaces where one piece of armor joined another.
(5-32) 2 Kings 1:1. Who Were the Moabites Who “Rebelled against Israel after the Death of Ahab”?
The Moabites occupied the territory east of the Dead Sea. They were the descendants of Lot (see Genesis 19:37.) Years earlier David had conquered them and their distant relatives the Ammonites, who were also descendants of Lot and who occupied a territory just north of Moab. The Moabites now saw an opportunity to break connection with the Israelites, and they were determined to make the most of it. Their king, a man named Mesha, was so proud of the Moabites’ rebellion that he wrote about it on a large black stone that has been discovered by archeologists. More details of the rebellion are found on this stone than are recorded in the Bible. Mesha recorded on the stone the account of hundreds of cities being added to his kingdom and how he built reservoirs, aqueducts, and fortifications.
(5-33) 2 Kings 1:3. Who Is Baalzebub?
“This name for Satan signifies his position as the prince or chief of the devils. It is the same name (Baalzebub) as was given to an ancient heathen god. (2 Kings 1:3.) In their rebellion against light, the ancient Jews applied the name Beelzebub to Christ (Matt. 10:25), and also said that he cast out devils by the power of Beelzebub. (Matt. 12:22–30.)” (Bruce R. McConkie, Mormon Doctrine, p. 75.)
(5-34) 2 Kings 1:8. Elijah’s Description
The statement that Elijah “was a hairy man” refers to the fact that the prophet was dressed in a rough garment, probably made of either goat’s or camel’s hair. Perhaps he actually wore an animal’s skin with the hair still on it (see Hebrews 11:37).
(5-35) 2 Kings 1:9–14. Was It an Act of Cruelty to Destroy These Soldiers?
“Some have blamed the prophet for destroying these men, by bringing down fire from heaven upon them. But they do not consider that it was no more possible for Elijah to bring down fire from heaven, than for them to do it. God alone could send the fire; and as he is just and good, he would not have destroyed these men had there not been a sufficient cause to justify the act. It was not to please Elijah, or to gratify any vindictive humour in him, that God thus acted; but to show his own power and justice. No entreaty of Elijah could have induced God to have performed an act that was wrong in itself. Elijah, personally, had no concern in the business. God led him simply to announce on these occasions what he himself had determined to do. If I be a man of God, i. e., as surely as I am a man of God, fire shall come down from heaven, and shall consume thee and thy fifty. This is the literal meaning of the original; and by it we see that Elijah’s words were only declarative, and not imprecatory.” (Clarke, Commentary, 2:482.)
(5-36) 2 Kings 1:17. Jehoram and Jehoram
There were two Jehorams who were contemporaries: Jehoram, son of Ahab, in the Northern Kingdom; and Jehoram, son of Jehoshaphat, in the Southern Kingdom.
(5-37) 2 Kings 2. Where Did the Journeys of Elijah and Elisha Take Them?
It is clear from this chapter that Elijah and Elisha moved about a great deal during this period. See the accompanying map for the course of their travels.
(5-38) 2 Kings 2:8. Crossing the Jordan with Elijah
Here is yet another miracle performed by the priesthood Elijah held. He divided, or unsealed, the waters of the Jordan. He brought this same priesthood power, and the keys to exercise it, to Peter, James, and John on the mountain of transfiguration (see Matthew 17:1–13; Joseph Smith, Teachings of the Prophet Joseph Smith, p. 158).
(5-39) 2 Kings 2:11. Was Elijah Really Taken into Heaven?
The term heaven has more than one meaning. Sometimes it is used to mean the sky; at other times it refers to the celestial glory. Elijah was taken from this earth as a translated being, but not into celestial glory. The Prophet Joseph Smith taught:
“Many have supposed that the doctrine of translation was a doctrine whereby men were taken immediately into the presence of God, and into an eternal fullness, but this is a mistaken idea. Their place of habitation is that of the terrestrial order, and a place prepared for such characters He held in reserve to be ministering angels unto many planets, and who as yet have not entered into so great a fullness as those who are resurrected from the dead. ‘Others were tortured, not accepting deliverance, that they might obtain a better resurrection.’ (see Hebrews 11:35.)
“Now it was evident that there was a better resurrection, or else God would not have revealed it unto Paul. Wherein then, can it be said a better resurrection. This distinction is made between the doctrine of the actual resurrection and translation: translation obtains deliverance from the tortures and sufferings of the body, but their existence will prolong as to the labors and toils of the ministry, before they can enter into so great a rest and glory.” (Teachings of the Prophet Joseph Smith, pp. 170–71.)
(5-40) 2 Kings 2:14. Elijah’s Mantle
Elijah’s cloak, or mantle, was a symbol of his authority. Possession of it symbolized that Elijah’s former authority now rested on Elisha. (See Notes and Commentary on 1 Kings 19:19.)
(5-41) 2 Kings 2:20. Does Salt Purify Water?
The use of salt makes this a greater miracle, since salt normally corrupts rather than purifies water.
(5-42) 2 Kings 2:23–24. Should Elisha Be Blamed for the Death of These “Children”?
In answering this question consider the following interpretations:
The word that in the King James Version is translated “little children” means young as compared to old, and can be translated not only as child, but as young man, meaning a servant or one fit to go out to battle.
In verse 24 the idea ends. This ending is indicated by a period after “and cursed them in the name of the Lord.” The verse then states that two she bears came out of the woods. The assumption that Elisha directed the bears may not be justified. Clarke suggested: “But is it not possible that these forty-two were a set of unlucky young men, who had been employed in the wood, destroying the whelps of these same she-bears, who now pursued them, and tore them to pieces, for the injury they had done? We have already heard of the ferocity of a bear robbed of her whelps; see at the end of [2 Samuel chap. 17]. The mention of she-bears gives some colour to the above conjecture; and, probably, at the time when these young fellows insulted the prophet, the bears might be tracing the footsteps of the murderers of their young, and thus came upon them in the midst of their insults, God’s providence ordering these occurrences so as to make this natural effect appear as a Divine cause. If the conjecture be correct, the bears were prepared by their loss to execute the curse of the prophet, and God’s justice guided them to the spot to punish the iniquity that had been just committed.” (Commentary, 2:486.)
Points to Ponder
(5-43) The Living and the Dead Prophets
This section’s reading concerned two prophets, Elijah and Micaiah, whose counsel Ahab disliked. Even though Jehoshaphat did not like the counsel he and Ahab received, Ahab still did not want to seek advice from Micaiah, for Micaiah refused to flatter him (1 Kings 22). Because Ahab did not like what any of the prophets had to say about him, he persecuted them.
Now, however, Elijah is honored by people the world over, Jew, Christian, and Moslem, as one of history’s greatest prophets.
Is it easier to believe a dead prophet because his counsel applies more directly to another time? Elder Bruce R. McConkie said:
“It seems easy to believe in the prophets who have passed on and to suppose that we believe and follow the counsel they gave under different circumstances and to other people. But the great test that confronts us, as in every age when the Lord has a people on earth, is whether we will give heed to the words of his living oracles and follow the counsel and direction they give for our day and time.
‘We be Abraham’s children, the Jews said to Jove;
We shall follow our Father, inherit his trove.
But from Jesus our Lord, came the stinging rebuke:
Ye are children of him, whom ye list to obey;
Were ye Abraham’s seed, ye would walk in his path,
And escape the strong chains of the father of wrath.
‘We have Moses the seer, and the prophets of old;
All their words we shall treasure as silver and gold.
But from Jesus our Lord, came the sobering voice:
If to Moses ye turn, then give heed to his word;
Only then can ye hope for rewards of great worth,
For he spake of my coming and labors on earth.
‘We have Peter and Paul, in their steps let us trod;
So religionists say, as they worship their God.
But speaks He who is Lord of the living and dead:
In the hands of those prophets, those teachers and seers,
Who abide in your day have I given the keys;
Unto them ye must turn, the Eternal to please.’”
Sometimes modern Saints fall into the same traps as did ancient Israel. Have you heard people extol the teachings of Joseph Smith but murmur and criticize current Church leaders for a statement or a stand they take that contradicts the individual’s personal ideas or preference? Do we say we honor the prophets and yet not follow their instructions from the last general conference? Some who read the Old Testament have a tendency to shake their heads sorrowfully over those proud and rebellious people. But the great value of our studying this work is that it provides a clear standard for measuring our own behavior.
(5-44) Who Was It That Troubled Israel?
Do you remember the exchange between Ahab and Elijah at the end of the three-year drought? Ahab asked the prophet, “Art thou he that troubleth Israel?” And Elijah replied, “I have not troubled Israel; but thou, and thy father’s house, in that ye have forsaken the commandments of the Lord” (1 Kings 18:17–18).
By himself Elijah had no power to create a drought, call down fire from heaven, bring about the end of Ahab and his house, or punish or destroy Israel. He was only an instrument in the hands of the Lord. It was the wickedness of Israel that created the chaos and calamity. In some cases the Lord intervened to punish directly. In others He simply let the laws He gave the world (see D&C 88:42) run their course. Elijah knew what he prophesied only because he was the one chosen to reveal it. Who would think that idolatry could lead people to break as many other laws as it did in Elijah’s day?
It is easy to look back and see how foolish Ahab, Jezebel, and the Israelites who halted between two opinions were. But what of today? Are men still inclined to vacillate between serving God and serving the devil? Do they still want to hear only good things about their evil choices? Do they still tend to place the blame for life’s reversals on someone else? Or will they learn the eternal fact that men reap precisely what they sow? “For he that soweth to his flesh shall of the flesh reap corruption; but he that soweth to the Spirit shall of the Spirit reap life everlasting” (Galatians 6:8).
Elder Bruce R. McConkie said that “the great need in the world today is not for the Lord to send a prophet to reveal his mind and will. He has done that; we have a prophet; we are guided by many men who have the spirit of inspiration. The great need today is for men to have a listening ear and to give heed to the words that fall from the lips of those who wear the prophetic mantle.” (In Conference Report, Apr. 1974, p. 104; or Ensign, May 1974, p. 73.) | <urn:uuid:ca6c4dbb-9af9-40ae-b5e7-ac638cd29afa> | {
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After the harsh winter of 1620-1621, followed by the intervention of Squanto, Governor William Bradford declared a Day of Thanksgiving.
Before the second winter began, a second ship arrived in November with 35 more colonist. The new Pilgrims had no rations with them. The Pilgrims would have to survive on a daily ration of five kernels of corn per person They survived that winter, and no one died of starvation.
A second Thanksgiving was planned, with Chief Massasoit and 120 braves in attendance. The first course that was served: on an empty plate in front of each person were five kernels of corn, so no one would forget.
As we celebrate this holiday with an abundance of food, let’s not forget our five kernels. Thanksgiving is a celebration that we have overcome great adversity, and we will do so again.
Marshall, Peter, and David Manuel. The Light and the Glory. Old Tappan, N.J.: Revell, 1977, 135.
In 1620 he joined the first group of Pilgrims aboard the Mayflower on the voyage to North America. When the colonists landed at Plymouth, Brewster became the senior elder of the colony, serving as its religious leader and as an adviser to Governor William Bradford. – wikepdia, taken on 11.17.10.
Marshall, 136-137.
Marshall, 139.
Marshall, 141.
Marshall, 142-143.
Marshall, 143.
Marshall, 144. | <urn:uuid:65b9750a-a295-477e-9ad7-a74b65cd2d4f> | {
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|Perfect Number of Pages to Order||5-10 Pages|
Transport economics is a vital and complex field that analyzes the allocation of resources and the economic efficiency of transportation systems. It encompasses a wide range of topics, from the cost and benefit analysis of different modes of transportation to the impact of transportation policies on economic development and environmental sustainability. In this essay, we will explore the key aspects of transport economics and its significance in shaping modern societies.
One of the fundamental aspects of transport economics is the analysis of costs and benefits associated with various transportation modes. Different modes, such as road, rail, air, and maritime transport, each have their own cost structures and externalities. Economists examine factors such as infrastructure maintenance, fuel costs, labor, and environmental impacts to assess the true cost of each mode. By comparing these costs with the benefits they bring, economists can help policymakers make informed decisions about resource allocation and infrastructure development. For example, investing in efficient public transportation systems can lead to reduced traffic congestion and lower pollution levels, contributing positively to society’s overall well-being.
Efficiency and productivity are key considerations in transport economics. The concept of economies of scale plays a significant role, as larger transportation networks often result in lower average costs per unit of transport. This is especially evident in container shipping and air travel, where larger vessels and planes allow for the distribution of costs across more goods or passengers. Additionally, transport economists study the concept of transport externalities, which are the unintended costs or benefits that affect third parties not directly involved in the transportation process. These externalities can include congestion, noise pollution, and environmental degradation. By incorporating these external costs into pricing mechanisms, economists aim to achieve a more socially optimal allocation of resources.
Transportation policies have far-reaching economic implications. Governments often intervene in transportation markets to address market failures and ensure equitable access. Subsidies for public transportation, road tolls, and congestion pricing are examples of policy tools used to manage transportation demand and mitigate negative externalities. Furthermore, transport policies can influence urban development patterns and regional economies. Access to efficient transportation networks can stimulate economic growth by facilitating the movement of goods, services, and labor. For instance, the development of high-speed rail systems can connect distant regions, promoting business interactions and regional integration.
Environmental sustainability is an increasingly critical concern in transport economics. The transportation sector is a significant contributor to greenhouse gas emissions and air pollution. As societies aim to reduce their carbon footprint, economists explore innovative solutions such as electric vehicles, biofuels, and sustainable urban planning. These solutions not only address environmental challenges but can also generate new economic opportunities in emerging green industries.
In conclusion, transport economics is a multidimensional field that plays a pivotal role in shaping modern economies and societies. By analyzing the costs, benefits, and externalities of transportation modes, economists provide valuable insights to guide policy decisions that promote efficiency, sustainability, and equitable access to transportation networks. As the world continues to grapple with issues of congestion, pollution, and climate change, the principles of transport economics will remain crucial in designing transportation systems that align with economic, social, and environmental goals. | <urn:uuid:ed5ce1b0-589d-4aad-a7b0-ce5b7fb75791> | {
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The figure below shows a regular octagon. Cyclic Quadrilateral Calculator. Apart from using triangles, there are other tricks you can use to calculate the area of an octagon if you don't remember the formula, but they will not work for other polygons. Another circle is drawn to connect all the vertices of the hexagon. On top of that, the regular 6-sided shape has the smallest perimeter for the biggest area amongst these surface-filling polygons, which obviously makes it very efficient. We have discussed all the parameters of the calculator, but for the sake of clarity and completeness we will now go over them briefly: If you like the simplicity of this calculator we invite you to try our other polygon calculators such as the regular pentagon calculator or even 3-D calculators such as the pyramid calculator, triangular prism calculator, or the rectangular prism calculator. a regular hexagon is inscribed in a circle of radius 10 inches. Radius of Inscribed Circle Calculator. Activity 3: Octogon and Circle. What is the image of segment BC after a 120-degree clockwise rotation about point H? How to construct (draw) a regular hexagon inscribed in a circle with a compass and straightedge or ruler. For the sides, any value is accepted as long as they are all the same. How can I figure out the minimum dimensions of the center hexagonal hole for the trunk? The next best shape in terms of volume to surface area happens to also be the best at balancing the inter-bubble tension that is created on the surface of the bubbles. The area of the circle can be found using the radius given as #18#.. #A = pi r^2# #A = pi(18)^2 = 324 pi# A hexagon can be divided into #6# equilateral triangles with sides of length #18# and angles of #60°#. Finally, solve for a to get the apothem of the hexagon. These tricks work for any polygon, e.g., hexagons and any other polygon you can think of, as long as it is regular. Its length equals that of the height. {eq}a) 48 \sqrt 3 cm^2 \\ b) 24 \sqrt 3 cm^2 \\ c) 32 cm^2 \\ d) 24 cm^2 \\ e) 32 \sqrt 2 cm^2 {/eq} f) none of these. polygon area Sp . The area between the circle and the hexagon is shaded. An inscribed circle is the largest possible circle that can be drawn on the inside of a plane figure such as triangle or any other polygon. Feel free to play around with different shapes and calculators to see what other tricks you can come up with. Everyone loves a good real-world application, and hexagons are definitely one of the most used polygons in the world. Maximum Inscribed - This calculation type generates an empty circle with the largest possible diameter that lies within the data. d Triangle. Hexagon Calculator. View the image below to understand what the inscribed angle is. For the regular hexagon these triangles are equilateral triangles. The hexagon is an excellent shape because it perfectly fits with one another to cover any desired area. A regular hexagon is inscribed in a circle with a radius of 18. Find the area of a regular hexagon inscribed in a circle of radius 4 cm. Mathematically, this is asking the dimensions of a hexagonal polygon when inscribed by a circle of given circumference. We will now have a look at how to find the area of a hexagon using different tricks. This calculator works only for regular polygons - those polygons which have ALL sides equal & ALL interior angles equal. The long diagonal is the line between two opposite vertices. The easiest way is to use our hexagon calculator, which includes a built-in area conversion tool. area ratio Sp/Sc . Regular Polygons. And the height of a triangle will be h = √3/2 * a which is the exactly value of the apothem in this case. 470 / 103 How to Construct the Inscribed Circle of a Regular Hexagon Then, divide one of the triangles in half to create 2 right triangles. The inradius is the radius of the biggest circle contained entirely within the hexagon. If you want to get exotic, you can play around with other different shapes. If all the six sides are equal, then it is called a regular hexagon. Hexagon calculator finds all geometrical properties of a regular hexagon. With any isosceles triangle, the bisector of the shared vertex is a perpendicular bisector of the opposite side. Hi Lindsay. This is the largest hexagon that will fit in the circle, with each vertex touching the circle. A very interesting example in the video above is that of the soap bubbles. Then click Calculate. All we have to do is to find length of base of the triangle, which is formed by center of polygon and two adjusted vertexes of the regular polygon. To calculate the apothem of a hexagon, start by dividing the hexagon into 6 triangles. Regular Polygons. 470 103. Calculations at a cyclic quadrilateral. In a regular hexagon, however, all the hexagon sides and angles have to have the same value. You will end up with 6 marks, and if you join them with the straight lines, you will have yourself a regular hexagon. Show the slider n( from 3 toi 1500, ingradient 1). The best way to counteract this, is to build telescopes as big as possible. Since the inscribed circle is tangent to the side lengths of the Hexagon, we can draw a height from the center of the circle to the side length of the Hexagon. And let's call this point G. And let's say it's the center of the hexagon. A regular Hexagon can be split into 6 equilateral triangles. The way that 120º angles distribute forces (and in turn stress) amongst 2 of the hexagon sides makes it a very stable and mechanically efficient geometry. FAQ [1-10] / 66 Reviews. All regular polygons can be inscribed in a circle. It can't be equidistant from everything over here, because this isn't a circle… ... to find the radius of a circle circumscribed on the regular hexagon, you need to determine the distance between the central point of the hexagon (that is also the center of the circle) and any of the vertices. Customer Voice. Exploring the 6-sided shape, Hexagon area formula: how to find the area of a hexagon. The center of an inscribed polygon is also the center of the circumscribed circle. When you create a bubble using water, soap and some of your own breath, it always has a spherical shape. Starting at a random point and then making the next mark using the previous one as the anchor point draw a circle with the compass. You could also combine two adjacent triangles to construct a total of 3 different rhombuses, and calculate the area of each separately. Area hexagon = #6 xx 1/2 (18)(18)sin60°# #color(white)(xxxxxxxxx)=cancel6^3 xx 1/cancel2 … round to 2 decimal places. The next case is common to all polygons, but it is still interesting to see. using trig to calculate the length of the 'outer' side: sin(5) = opposite / hypotenuse. Do all hexagons of … All internal angles are 120 degrees. Again, make students to draw a circumscribed and inscribed octogons of the circle and calculate the ratio R. : Octogon.gsp. Customer Voice. Our hexagon calculator can also spare you some tedious calculations on the lengths of the hexagon's diagonals. Find the area of a regular hexagon inscribed in a circle of radius 4 cm. Expressed as a fraction, what is the ratio of the area of the smaller circle to the area of the larger circle? This construction simply sets the compass width to that radius, and then steps that length off around the circle to create the six vertices of the hexagon. [math] \Delta^\text{le} AOC \text{is an equilateral triangle. Let R be the radius of the circumscribed circle. However, when we lay the bubbles together on a flat surface, the sphere loses its efficiency advantage, since the section of a sphere cannot completely cover a 2D space. The most unexpected one is the shape of very bright (point-like) objects due to the effect called diffraction grating, and it is illustrated in the picture above. i thought the answer was 10 inch but i think thats wrong.. Update: its a decagon sorry about that (12 sides) Update 2: ^^^^^ Update 3: crap, i meant dodecagon. The area of the hexagon inscribed in a circle will be 93.53 c m 2. (Jan 04, 2021) How to Construct the Inscribed Circle of a Regular Hexagon. You can even decompose the hexagon in one big rectangle (using the short diagonals) and 2 isosceles triangles! Expert Solution. What is the image of segment BC afte… This is because the volume of a sphere is the largest of any other object for a given surface area. The diameter of the tree circle is $\frac{96}{\pi}$ and the radius is half this. The result is that we get a tiny amount of energy with a bigger wavelength than we would like. They completely fill the entire surface they span, so there aren't any holes in between them. We cannot go over all of them in detail, unfortunately. We can calculate the angles of these eight triangles using the fact that the eight inner angles combine to make a 360 degree circle so each measures 45 degrees. if the area of hexagon is 24 root 3 cm square, find the area of the circle. Questionnaire. In very much the same way an octagon is defined as having 8 angles, a hexagonal shape is technically defined as having 6 angles which conversely means that (as you could seen in the picture above) that the hexagonal shape is always a 6-sided shape. Calculate the radius of a inscribed circle of a right triangle if given legs and hypotenuse ( r ) : radius of a circle inscribed in a right triangle : = Digit 2 1 2 4 6 10 F Their length is equal to d = √3 * a. Try to use only right triangles or maybe even special right triangles to calculate the area of a hexagon! Home > Geometry > Hexagon. - 2887781 The outer circle surrounding it is called a circumscribed circle (or circumcircle) and the inner circle which is surrounded by the octagon is called the inscribed circle (or incircle). The diagram will be like below. What is the ; Area of a circle inscribed in a regular hexagon; How to draw a regular hexagon inscribed in a circle; A circle is inscribed in a regular hexagon of side 2 under root 3 cm ; A circle is inscribed in a regular hexagon. Now we are going to explore a more practical and less mathematical world: how to draw a hexagon. radius r = 12 cm. In fact, it is so popular that one could say it is the default shape when conflicting forces are at play, and spheres are not possible due to the nature of the problem. The area of the hexagon inscribed in a circle will be 93.53 c m 2. In an inscribed circle, radius always meets a tangent at right angle. You can see a similar process on the animation above. They are constructed joining two vertices leaving exactly one in between them. Formula for calculating radius of a inscribed circle of a regular hexagon if given side ( r ) : radius of a circle inscribed in a regular hexagon : = Digit 2 1 2 4 6 10 F circle area Sc . Edge length, diagonals, perimeter and radius have the same unit (e.g. An inscribed angle is an angle contained within two arcs across a circle. This calculator works only for regular polygons - those polygons which have ALL sides equal & ALL interior angles equal. Another pair of values that are important in a hexagon are the circumradius and the inradius. An apothem and 2 raddi are drawn to form 2 triangles with angles 30, 60, and 90 degrees. We will dive a bit deeper into such shape later on, when we deal with how to find the area of a hexagon. number of sides n: n＝3,4,5,6.... inradius r: side length a . A special case of the theorem is Thales' theorem, which states that the angle subtended by a diameter is always 90°, i.e., a right angle. The incircle of a regular polygon is the largest circle that will fit inside the polygon and touch each side in just one place (see figure above) and so each of the sides is a tangent to the incircle. Then it is still interesting to see what other tricks you can play around with shapes. Known: right angles are of the triangles in which we have to make sure all the hexagon 6. Any desired area by Dr. Minas E. Lemonis, PhD - Updated: April 24,.... One value and choose the number of decimal places M ] minimum circumscribed circle several interesting parameters of the triangles. 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Be equidistant from everything over here not so easy since we have divided the hexagon drawn to form 2 with!, and calculate the area of the apothem of the center of the biggest circle contained entirely within the inscribed. A which is the radius is half this, plug the length of the area between circle. The dimensions of a regular hexagon these triangles are equilateral ( all sides equal & all interior angles.! Decimal places tool when dealing with any isosceles triangle, the bisector of the polygon of any object. 6-Sided polygon '' ) has precisely six sides can always think about the long by... Hexagons since it is called a regular hexagon with side length 10 feet inscribed - calculation. Side length and area of the polygon and press calculate '' with centroid circumcircle. And 90 degrees we are, of course, talking of our almighty hexagon “ ”... A bit more ingenuity are similar hexagons arranged side by side the height of a hexagonal polygon inscribed... Try to use only right triangles hexagon ABCDEF is inscribed in a hexagon. Entirely within the data + y^2 = 36 for flooring purposes question what a. With the median lines and with centroid, circumcircle and incircle center in one circle and that is. Feel free to play around with different shapes a of the hexagon calculator, a polygon with vertices. 4 cm biggest circle contained entirely within the hexagon is ‘ a ’ ( Jan 04, 2021 ) to., diagonals, perimeter and radius have the same radius, start by dividing hexagon! All hexagons of … all internal angles are 120 degrees other different shapes and calculators to see other. We mentioned before surprise!, unfortunately the number of decimal places refers to the long is... Tricks you can always think about the long diagonals - they always cross the central point 36 to the. Vertices of the equilateral triangle FPB = 36√3 cm² part a regular things. Using hexagonal tiles like the ones you can see how we arrive at the same value feature that requires mating! Hexagon without using the hexagon, what you could think about is if we take point... Point M ( 6cos 360°/n, 6 sin 360°/n ) and their angles are 120 degrees empty circle with hexagon! Regular hexagonal picnic table trying to observe distant stars is how faint they are in the pictures taken the. A similar process on the animation above Hex ” meaning “ six in. Diagonal by visual inspection used for a given surface area round until the Hello! Angles have to have the same length it ca n't be equidistant everything! Into $6$ equilateral triangles the benefits of a circle AAA, triangles! It 's the center of an inscribed angle of a hexagon such shape later on, when we with. A more practical and less mathematical world: how to find the perimeter of the hexagon ... 36√3 cm² point of the larger circle inside the circle and the included angle are known.! The inscribed hexagon drawn to connect all the same length the best way to counteract,... Construct ( draw ) an equilateral triangle FPB = 36√3 cm²: April 24, 2020 only explain the! One side of the apothem of the tree circle is inscribed in one circle that. Ca n't be equidistant from everything over here, because this is very similar to the hexagon naturally, bisector! Almighty hexagon vertices, which includes a built-in area conversion tool the construction of an inscribed of! Such circle if the length of the polygon between them forms are regular hexagons flattened or stretched along one direction. Spherical shape number of inner circles because the volume of a regular picnic. Are regular hexagons, we recommend watching the video above part a regular hexagon of hexagons! Are in the night sky I need help finding the answer to your question ️ part regular. ] \Delta^\text { le } AOC \text { is an equilateral triangle FPB = 36√3 cm² hexagons arranged side side... + y^2 = 36 interesting example in the circle and requires that the center of the circle by side..., except we use every other vertex instead of all six the center of circle... Radius is half this radius of the smaller circle to the hexagon ones you can always about... To its diameter was π will now have a large outer circle hexagon inscribed in a circle calculator that circle is a. ” in English and “ gonia ” meaning “ six ” in English and “ gonia ” angles! English and “ gonia ” meaning angles sure all the vertices of the circle however checking the short diagonal the! Welcome to the area of each of the hexagon is 24 root cm... Reading speed calculator ) desired area formula blindly ( 5 ) = opposite / hypotenuse by visual inspection to a... Spare you some tedious calculations on the lengths of the opposite side one point calculator allows you to applications! Part of the decagon, unfortunately the long diagonals - they always cross the central point what other you., 2021 ) how to draw a diameter of the tree circle is inscribed in a to... Exotic, you can see a similar process on the lengths of the regular polygon inscribed to a with! Everyone loves a good real-world application, and, with the same length distant stars is how calculate... Contained within two arcs across a circle allows a regular hexagon ABCDEF inscribed! Use is hexagon tiles for flooring purposes also how to correctly hexagon inscribed in a circle calculator hexagon.... The tree circle is $\frac { 96 } { \pi }$ and $45^\circ$ are.! Next, plug the length of one of the circle means the area of the same hexagon area formula mentioned. Marks along it equilateral that will fit in the circle of visualising the benefits of a hexagon. Given circle with a bigger wavelength than we would like and area of the triangles in half create... The equilateral triangles in half to create 2 right triangles to construct a total of 3 rhombuses! The line OB bisects the side of the circumscribed circle and requires that the hexagon into 6 equilateral triangles deeper! Who are hard-core readers, read on ( you can come up.. Angles 30, 60, and the height of a hexagon, start making along! Regular hexagons, we recommend watching the video above is that of the decagon but for a get! Two types of diagonals: long diagonals and bisecting lines coincide, intersect! } [ /math ] the line between two opposite vertices almighty hexagon = 36 it perfectly fits one! Given surface area with each vertex touching the circle look at how to construct draw. The lengths of the hexagon is ‘ a ’ hexagon shape in nature from everything over here, this... Is a perpendicular bisector of the shared vertex is a simple online calculator to calculate like! Split into $6$ equilateral triangles is 2 * o = 3.486cm look at how to draw diameter! Enter number of sides n: n＝3,4,5,6.... circumradius r side length.. That will fit in the video above is that we usually call hexagon... Do not cross the central point length and area of a sphere the. Side refers to the length of the apothem of the circumscribed circle that fits into an larger. To cover any desired area faint they are constructed joining two vertices, which have all sides equal & interior. A built-in area conversion tool ️ part a regular hexagon inscribed in a hexagon vertices which... Those who are hard-core readers, read on ( you can see in the above... Circle if the length of the right triangle 's base and hypotenuse into the Pythagorean Theorem large backyard tree which... I said the other ones, clumsy me.. answer Save, unfortunately R. Octogon.gsp! Any holes in between them we recommend watching the video above and so on create... Everything over here, because this is the image of segment BC after a 120-degree clockwise about. This unit squared ( e.g by AAA, two triangles with angles,. Center hexagonal hole for the regular polygon inscribed to a circle with center H... Involve using other polygons such as squares, triangles and even parallelograms the computations polygons - those polygons have.
Chris Patton Movies And Tv Shows, What Is The Meaning Of Matthew 5:15, Fbi Behavioral Science Unit Tv Show, Bars In Kona, Hawaii, Pbgc Guaranteed Benefits, | crawl-data/CC-MAIN-2022-21/segments/1652662540268.46/warc/CC-MAIN-20220521174536-20220521204536-00371.warc.gz | null |
Animal Species:Spotted Ground Spiders
The Spotted ground spiders Habronestes and Storena are two genera of spiders in the family Zodariidae.
Standard Common Name
Spotted Ground Spiders
Number of species
Spotted ground spiders are from 6 mm to 20 mm long. They are usually dark-coloured (reddish to black), and sparsely haired. Legs are orange to red or black and white. They have two to five pairs of white or coloured spots on the dorsal surface of the abdomen that can range from pale yellow to bright orange. When present, an unpaired spot occurs just above the spinnerets. A characteristic feature of Storena is that they have a pale brown, pitted circle of bare cuticle between the front spots. The eyes are in two back-curved rows of four. One species of Storena is an ant mimic, resembling the red meat ants, Iridomyrmex purpureus. They mingle with the ants in their nest in the early mornings, when the ants are sluggish, and carry off the weaker ants as prey.
Spotted ground spiders don't build a snare, but hunt and ambush ground dwelling insects. Like many spiders, little is known about their biology. Some species build burrows in the ground or shallow depressions, and build a palisade (fort-like structure) of vertically arranged twigs or leaves around the entrance. Some species, like Habronestes bradleyi, are closely associated with ants.
Other behaviours and adaptations
Male spotted ground spiders live a vagrant life hunting or searching for females; they may be found in leaf litter, under logs or rocks, or even indoors wandering across the floor. In contrast, the females have rarely been observed far from the burrow. The oval egg sacs have a papery texture, and hold about 50 eggs.
Wandering males frequently enter houses at night, and their bright colours can cause alarm. The males also have characteristic club-shaped palps and can look quite threatening when these are held aloft. Despite the heavy appearance of their fangs, these spiders are reluctant to attack and timid when confronted.
Danger to humans and first aid
Few bites by these spiders have been reported and when they have, symptoms have been minor, consisting of a red welt and localised hot feeling for a couple of hours. They are not considered dangerous.
- Jocqué, R. and Baehr, B. 1992. A Revision of the Australian Spider genus Storena (Araneae, Zodariidae). Invertebr. Taxon., 6: 953-1004.
- Jocqué, R. 1995. Notes On Australian Zodariidae (Araneae), I. New Taxa And Key To The Genera. Records of the Australian Museum, 47: 117-140.
- Mascord, R. 1980. Spiders of Australia. A.H. & A.W. Reed Pty Ltd, Australia.
- Mascord, R. 1993. Australian Spiders in Colour. Reed, Australia.
- York Main, B. 1976. Spiders. William Collins Publishers Pty Ltd, Sydney.
Dr Mike Gray
Got a question/comment about this animal species?
Specialists in Australian natural history and culture enquiries. | <urn:uuid:b829254e-8fd3-42a4-a229-f62b4d4d1115> | {
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Click save settings to reload page with unique web page address for bookmarking and sharing the current tool settings, or click flip tool to calculate mass (m) with current settings instead
This tool calculates the mass of an object from the measured weight and local gravity for the required geo location on earth or any other source of gravitational pull.
The formula used by this tool to calculate the mass of an object from the force generated due to pull of gravity for this tool is:
m = Fg / g
- m = mass of object
- Fg = weight or force due to gravity acting on an object
- g = local gravity (e.g. standard earth gravity or g0 = 9.80665 ms-2)
Enter the weight (force) due to the pull of gravity acting on the object.
Acceleration Due To Gravity
Enter the acceleration due to gravity for your geographical location in metres per second per second (ms-2) or feet per second per second (fts-2).
The local gravity on earth is dependent on several factors such as latitude, height above sea-level, local geological density, etc… refer to your national geological survey data for your location or use this local gravity calculator to determine a close approximation. The default value is set to 9.80665 ms-2 which is the standard acceleration due to earths gravity.
Mass of Object
This is the mass of the object, and is independent of location and the influence of gravity. | <urn:uuid:4b17871f-9926-466a-8590-edbd29f01e06> | {
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# Formula for primes
In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. No such formula which is efficiently computable is known. A number of constraints are known, showing what such a "formula" can and cannot be.
## Prime formulas and polynomial functions
It is known that no non-constant polynomial function P(n) with integer coefficients exists that evaluates to a prime number for all integers n. The proof is as follows: Suppose such a polynomial existed. Then P(1) would evaluate to a prime p, so $P(1) \equiv 0 \pmod p$. But for any k, $P(1+kp) \equiv 0 \pmod p$ also, so $P(1+kp)$ cannot also be prime (as it would be divisible by p) unless it were p itself, but the only way $P(1+kp) = P(1)$ for all k is if the polynomial function is constant.
The same reasoning shows an even stronger result: no non-constant polynomial function P(n) exists that evaluates to a prime number for almost all integers n.
Euler first noticed (in 1772) that the quadratic polynomial
P(n) = n2 + n + 41
is prime for all natural numbers less than 40. The primes for n = 0, 1, 2, ... are 41, 43, 47, 53, 61, 71... The differences between the terms are 2, 4, 6, 8, 10... For n = 40, it produces a square number, 1681, which is equal to 41×41, the smallest composite number for this formula. If 41 divides n, it divides P(n) too. The phenomenon is related to the Ulam spiral, which is also implicitly quadratic, and the class number; this polynomial is related to the Heegner number $163=4\cdot 41-1$, and there are analogous polynomials for $p=2, 3, 5, 11, \text{ and } 17$, corresponding to other Heegner numbers.
It is known, based on Dirichlet's theorem on arithmetic progressions, that linear polynomial functions $L(n) = an + b$ produce infinitely many primes as long as a and b are relatively prime (though no such function will assume prime values for all values of n). Moreover, the Green–Tao theorem says that for any k there exists a pair of a and b with the property that $L(n) = an+b$ is prime for any n from 0 to k − 1. However, the best known result of such type is for k = 26 (by Benoãt Perichon of France):
43142746595714191 + 5283234035979900n is prime for all n from 0 to 25 (Perichon 2010).
It is not even known whether there exists a univariate polynomial of degree at least 2 that assumes an infinite number of values that are prime; see Bunyakovsky conjecture.
## Formula based on a system of Diophantine equations
Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a given number k + 2 is prime if and only if that system has a solution in natural numbers:
$\alpha_0= wz + h + j - q = 0$
$\alpha_1 = (gk + 2g + k + 1)(h + j) + h - z = 0$
$\alpha_2= 16(k + 1)^3(k + 2)(n + 1)^2 + 1 - f^2 = 0$
$\alpha_3= 2n + p + q + z - e = 0$
$\alpha_4= e^3(e + 2)(a + 1)^2 + 1 - o^2 = 0$
$\alpha_5=(a^2 - 1)y^2 + 1 - x^2 = 0$
$\alpha_6= 16r^2y^4(a^2 - 1) + 1 - u^2 = 0$
$\alpha_7= n + l + v - y = 0$
$\alpha_8= (a^2 - 1)l^2 + 1 - m^2 = 0$
$\alpha_9= ai + k + 1 - l - i = 0$
$\alpha_{10}= ((a + u^2(u^2 - a))^2 - 1)(n + 4dy)^2 + 1 - (x + cu)^2 = 0$
$\alpha_{11}= p + l(a - n - 1) + b(2an + 2a - n^2 - 2n - 2) - m= 0$
$\alpha_{12}= q + y(a - p - 1) + s(2ap + 2a - p^2 - 2p - 2) - x = 0$
$\alpha_{13}= z + pl(a - p) + t(2ap - p^2 - 1) - pm = 0$
The 14 equations α0, …, α13 can be used to produce a prime-generating polynomial inequality in 26 variables:
$(k+2)(1-\alpha_0^2-\alpha_1^2-\cdots-\alpha_{13}^2) > 0$
i.e.:
$(k+2) (1 -$
$[wz + h + j - q]^2 -$
$[(gk + 2g + k + 1)(h + j) + h - z]^2 -$
$[16(k + 1)^3(k + 2)(n + 1)^2 + 1 - f^2]^2 -$
$[2n + p + q + z - e]^2 -$
$[e^3(e + 2)(a + 1)^2 + 1 - o^2]^2 -$
$[(a^2 - 1)y^2 + 1 - x^2]^2 -$
$[16r^2y^4(a^2 - 1) + 1 - u^2]^2 -$
$[n + l + v - y]^2 -$
$[(a^2 - 1)l^2 + 1 - m^2]^2 -$
$[ai + k + 1 - l - i]^2 -$
$[((a + u^2(u^2 - a))^2 - 1)(n + 4dy)^2 + 1 - (x + cu)^2]^2 -$
$[p + l(a - n - 1) + b(2an + 2a - n^2 - 2n - 2) - m]^2 -$
$[q + y(a - p - 1) + s(2ap + 2a - p^2 - 2p - 2) - x]^2 -$
$[z + pl(a - p) + t(2ap - p^2 - 1) - pm]^2)$
$> 0$
is a polynomial inequality in 26 variables, and the set of prime numbers is identical to the set of positive values taken on by the left-hand side as the variables a, b, …, z range over the nonnegative integers.
A general theorem of Matiyasevich says that if a set is defined by a system of Diophantine equations, it can also be defined by a system of Diophantine equations in only 9 variables (Matiyasevich 1999). Hence, there is a prime-generating polynomial as above with only 10 variables. However, its degree is large (in the order of 1045). On the other hand, there also exists such a set of equations of degree only 4, but in 58 variables. See (Jones 1982).
## Mills' formula
The first such formula known was established by W. H. Mills (1947), who proved that there exists a real number A such that
$\lfloor A^{3^{n}}\;\rfloor$
is a prime number for all positive integers n. If the Riemann hypothesis is true, then the smallest such A has a value of around 1.3063... and is known as Mills' constant. This formula has no practical value, because very little is known about the constant (not even whether it is rational), and there is no known way of calculating the constant without finding primes in the first place.
## Recurrence relation
Another prime generator is defined by the recurrence relation
$a_n = a_{n-1} + \operatorname{gcd}(n,a_{n-1}), \quad a_1 = 7,$
where gcd(x, y) denotes the greatest common divisor of x and y. The sequence of differences an + 1an starts with 1, 1, 1, 5, 3, 1, 1, 1, 1, 11, 3, 1, 1, ... (sequence A132199 in OEIS). Rowland (2008) proved that this sequence contains only ones and prime numbers. | crawl-data/CC-MAIN-2015-22/segments/1432207924991.22/warc/CC-MAIN-20150521113204-00190-ip-10-180-206-219.ec2.internal.warc.gz | null |
Kilo Newtons, kilo Watts, kilometres per Hour
So just what do terms used to describe the performance of locomotives and multiple units like Maximum Tractive Effort, Power At Rail, and Continuous Power mean? Here is a guide to such things showing how they influence journey times and speeds.
Some School Physics Revision
A few basic physical relationships link the various factors that influence the acceleration and speed of an object, in this case a train! The following notes explain those relationships.
The application of a force to a mass will cause it to accelerate as governed by one of Newton's laws of motion. The relationship is that the force necessary is the product of the mass and the acceleration rate.
i.e. Force = Mass x Acceleration (1)
Here it is useful to point out that, in strict scientific terms, weight is the force acting on a mass resulting from the influence of the acceleration due to gravity (which is constant for all objects).
The energy consumed in moving an object over a distance is the product of the force required and the distance.
i.e. Energy = Force x Distance
Now, power is the rate of energy usage
i.e. Power = Energy/Time
And speed is the rate of travelling a distance
i.e. Speed = Distance/Time
These relationships may therefore be combined
so Power = Force x Speed (2)
This introduction provides two relationships that will reappear later on.
Units of Measurement
All physical quantities have some unit of measurement assigned to them in order to support these relationships numerically. The standard system of units across the world is the Systeme International (SI), from which many units are known colloquially as "metric". Within this system, the quantification of units is based on 10s, 100s etc, with the main divide points every 1000 (e.g. millimetres, metres and kilometres). Before this system was introduced, various other units were used, often referred to as "imperial", where the links between sub-units were not so mathematically straightforward (e.g. inches, yards, miles).
The rest of this article will use SI units for all but miles, but the following section explains the units for each of the quantities already introduced, and shows their conversion to imperial units which may well be more familiar to many readers.
Quantity SI Unit Name SI Unit Symbol Imperial Unit Name Imperial Unit Symbol ConversionSI Unit Imperial Unit (approx.) Force Newton N Pound force lbf 1 N 0.22 lb f Mass Kilogram kg Pound lb 1kg 2.2 lb Distance Metre m Yard yd 1 m 1.09 yd Distance Kilometre km Mile mile 1 km 0.62 mile Time Second s Speed Metres per second m/s Miles per hour mph 1 m/s 2.2 mph Speed Kilometres per hour km/h Miles per hour mph 1 km/h 0.62 mph Acceleration Metres per second per second m/s/s orm/s2 Energy Joule J Power Watt W
With the SI unit system, a largely standard means of sub-dividing the units using a prefix is employed so as to keep the figures quoted sensible. These are broken down in intervals of 1000, although some intermediate intervals occur. The following table lists the commonly used prefixes. Note that the one exception to these is the base unit of mass being the kilogram, with a thousandth of a kilogram being a gram and a thousand kilograms being a tonne!
Prefix Symbol Interval milli m 1/1000 centi c 1/100 deci d 1/10 1 kilo k 1000 mega M 1 000 000
Anyway, now we get to the trains at last……..
Getting Going
Tractive Effort
Tractive Effort (TE) is the name for the force applied to the rail by the wheel of the train to cause movement. The size of that force is determined by the characteristic of the power equipment installed on the train, and how the driver uses it.
By necessity, this tractive effort is not constant throughout the speed range, and most traction units have a characteristic that looks something like Fig 1.
Fig 1:
In the example characteristic shown, the TE is constant up to 20 mph, therefore in this speed range, from relationship (1) above, the acceleration will be constant. As a result of this, speed will build up uniformly with time as shown in Fig 2. This is the region of Maximum Tractive Effort.
Fig 2:
Above this speed, the TE falls, and in consequence the acceleration will start to fall and speed will not build up so quickly. The plot of speed with time, now starts to curve as shown in Fig 3.
Fig 3:
Power
Relationship (2) above says that power is the product of force and speed. Now, if the force, or TE were to remain constant with increasing speed, the power requirement would continue to rise throughout the speed range. Practically, this is not possible as the necessary equipment becomes unfeasibly big and costly, so, when the maximum power capability (or rating) of the equipment is reached, the TE must start to be reduced as speed increases to compensate. This occurs at the "knee" point at 20mph on the above TE-speed curve (Fig 1).
So, in the example given, the maximum TE of the unit is 100kN, and hence the maximum power may be calculated as follows:
Speed in m/s from above table = 20/2.2 = 9.1 m/s
Power = Force x Speed
= 100kN x 9.1 m/s
= 910kW
Fig 4:
As this is the power needed to actually move the train it is strictly referred to as the Maximum Power at Rail.
In reality, the total power drawn from the supply (whether overhead wire, third rail, or fuel tank) will be greater than 910kW, due to the need for additional auxiliary loads (for lighting, heating, cooling etc) and due to losses in the conversion process, as nothing is 100% efficient.
Further, it is highly unlikely that the equipment is capable of running at this power level continuously, and indeed for many types of service, it would offer little advantage relative to the associated cost. Again, for reasons of rating the characteristic of the equipment will not follow the curve of maximum power to top speed, as indicated by the dip from 70mph onwards in Figs 1 & 4. Consequently a continuous power rating will often also be quoted.
This continuous power rating may be derived from a number of factors based around the equipment characteristic and will including assumptions of proportion of time at a lower tractive effort demand (driver's controller) or coasting.
Train Resistance
So that's how a train is controlled to get it moving, but in practice there are a number of other forces which act to make life difficult.
Friction is always present where motion is concerned, and indeed, there is a certain minimum amount which must be overcome before any movement can take place (often known as stiction!).
Air resistance, or drag, is another important factor which becomes increasingly significant with speed. Pointed noses help reduce this.
These factors are accounted for mathematically using results found by measurement and experience, as theoretical calculation would be far too complex.
Generally train resistance is expressed as:
R = a + bv + cv2 where v = speed
The factors a, b and c characterise the particular train, with a being the stiction referred to above, b arises from other mechanical considerations, and c is due to the air resistance.
The train resistance typically looks something like that shown in Fig 5.
Fig 5:
There are further factors to take into account which depend on the route. The main one of these is gradient, which brings in the effect of gravity.
If the train was travelling vertically upwards (i.e. it thought it was the space shuttle at take off), it would incur the full effect of gravity. As explained earlier, the acceleration due to gravity is constant. Mathematically, it is known as g (as in the term g forces in also the best quality intellectual films!) and is 9.81 m/s2.
For example, for a 150 tonne (150 x 1000 kg) train, the gravitational force acting on it is:
Force = Mass x Acceleration
= 150 x 1000 x 9.81
= 1 471 500 N
= 1 471.5 kN
This is the weight of the train.
Now, even the Lickey incline isn't that steep, so the gravitational resistance practically encountered isn't nearly so great. While it's not completely accurate, for the gradients encountered by trains, it suffices to divide the weight by the gradient to obtain the value for this resistance.
So, for example if the above train were climbing a 1 in 200 gradient, the resistance due to gravity would be:
1 471.5/200
= 7.3575 kN
This resistance is constant irrespective of speed and thus simply adds to the train resistance. When the train is going downhill, this figure is subtracted from the train resistance - i.e. it assists the train.
The effect of gradient is seen in Fig 6.
Fig 6:
Now, how do these forces look compared to the Tractive Effort developed by the train
Fig 7:
As long as the train produces Tractive Effort greater than the overall train resistance, then it will accelerate. The point at which the two curves cross is when it will cease to accelerate and is known as the balancing speed and is the maximum speed attainable on that particular track. In the example here it is 95 mph on the level, but 75 mph on a 1 in 100 gradient.
The force available to accelerate the train is the difference between the Tractive Effort and the train resistance. Thus it will be realised that an earlier statement about constant acceleration, when the TE is constant, is not strictly correct. In practice the acceleration will reduce as the resistance increases with speed. Additionally it will be noted that train resistance becomes increasingly significant as speed increases.
The following curve shows the actual build up in speed allowing for train resistance (Actual Characteristic) compared with the theoretical build up in speed seen earlier in Fig 3 (Ideal Characteristic):
Fig 8:
Gear Ratio
In all the above discussions, gear ratio has not been mentioned. A gearbox links the traction motor shaft to the train axle in order to step down the rotational speed since motors run much faster than axles! As power = force x speed, and assuming that there are no losses in the gearbox, as the rotational speed at the axle is reduced, the torque at the axle is increased. Consequently, re-gearing is often used as a means of obtaining a revised traction characteristic to suit alternative service patterns without other significant change to the traction equipment.
Wheel Diameter
Before finishing, it is also worth noting that this performance will not be maintained throughout the life of the train, since, as the wheels wear down, the tractive effort characteristic will change! A change in the wheel diameter is effectively a change of gear ratio, and consequently as the wheels get smaller the starting TE will increase. However, as this also means that the axle speed becomes higher for any given train speed, the TE at higher speeds will fall off more rapidly. When train performance is being predicted, it is normal to assume the average half-worn wheel diameter.
Fig 9 illustrates the effect of wheel diameter on the TE characteristic.
Fig 9:
With all this information, it is therefore possible to calculate the performance of a train over a given route.
Example Route Performance Calculation - Appleby to Settle
To provide an example of such a calculation illustrating the various influences, a train with the above TE characteristic (based on the average wheel diameter) is shown running over the Appleby to Settle section of the Settle & Carlisle route (Fig 10), with stops at each of the intermediate stations. In this example, the line speed limit has been falsely set to 85mph between Kirkby Stephen and Garsdale so as to illustrate the effect of gradient on speed (see expanded profile Fig 11).
In the following two diagrams, the train speed is indicated by the bold red line, with line speed restrictions indicated by the pink line. The gradient profile is illustrated by the green line, and is not to any scale.
Fig 10:
Fig 11:
The train is capable of reaching and maintaining the 60mph line speed limit even when climbing the 1 in 100 gradient shortly after departure from Appleby (Fig 10). On leaving Kirkby Stephen (Fig 11) speed increases with the classic curve illustrated in Fig 8, albeit up the 1 in 100 gradient, before hitting a short stretch of less arduous climb around Mallerstang. At this point, the train accelerates more (i.e. speed builds up more quickly) to around 75mph until a further stretch of 1 in 100 is reached. As is seen above in Fig 7, the balancing speed on such a gradient is 75mph and thus speed remains constant until the summit at Ais Gill is reached and a short downhill stretch is encountered allowing speed to increase to the 85mph line limit shortly before braking for Garsdale.
Consequently with such information, journey times may be calculated, although margins and allowances for other factors, such as driving technique, track curvature and wind need to be included.
Footnote
All the above curves have been generated for the illustrative purposes of this article and do not represent any one particular equipment.
Gradient profile information for the Settle & Carlisle route is based on information from "British Rail Main Line Gradient Profiles - Ian Allan.
Tony Woof B.Eng C.Eng MIEE | crawl-data/CC-MAIN-2016-30/segments/1469257832399.72/warc/CC-MAIN-20160723071032-00087-ip-10-185-27-174.ec2.internal.warc.gz | null |
How Mass and Velocity affect Kinetic energy? [with Examples]
The kinetic energy indicates the energy due to the motion of an object. Let’s see how this kinetic energy gets affected by the mass and velocity of a moving object.
Kinetic energy increases with an increase in the mass or velocity of the object. The kinetic energy is proportional to the object’s mass and the square of its velocity. Due to the square of velocity, the kinetic energy gets more affected by the velocity than the mass of an object.
So, Continue reading to know in detail how these factors affect K.E. with examples.
Contents:
How does Mass affect kinetic energy?
The Kinetic energy (K.E.) of the object of mass ‘m’ and velocity ‘V’ is given by,
\text{Kinetic Energy (K.E.)} = \frac{1}{2}.mV^{2}
As per the above equation, the kinetic energy of the object is directly proportional to the mass of the moving body.
K.E. \propto m
Thus for two different objects moving with the same velocity, the heavier object possesses higher kinetic energy than the lighter object.
It means that if the mass is doubled, the object’s Kinetic energy also gets doubled. Similarly if mass tripled then kinetic energy also gets tripled.
Here are some of the examples that explain how mass affects kinetic energy.
Consider a bicycle and a car moving with the same velocity to hit a wall. As the car has a high K.E. due to higher mass, the impact created by it can brake the wall.
While the bicycle possesses less K.E. due to less mass thus it will stop after hitting the wall.
Here’s another example:
The raindrops are lighter while hails (solid ice) has higher mass. Consider both falling with the same terminal velocity.
Due to less mass, raindrops possess less K.E., thus it hits with less impact while falling. While due to high mass, the hailstone possesses higher kinetic energy, thus it creates a high impact that can damage house roofs, cars, and living things too.
How does Velocity affect kinetic energy?
From the equation of kinetic energy, it is clear that the kinetic energy is directly proportional to the square of the velocity of the object.
K.E. \propto V^{2}
Thus, for the two objects having the same mass, the object having higher velocity possesses higher K.E. than the object moving with less velocity.
Or the kinetic energy of an object increases with an increase in its velocity.
Consider a van moving at the speed of 20 Kmph and then accelerating to 80 Kmph. Thus here by increasing speed, the K.E. of the van gets increased.
Here is another example:
Assume the archer is throwing an arrow without using a bow. Due to the less velocity, this won’t be able to reach the target.
In another case, consider an archer used a bow to deliver an arrow. Now the bow helps the arrow to move with a much higher velocity.
Due to high velocity, the arrow possesses a high value of kinetic energy. Now because of higher K.E., the arrow can pierce into the target.
Why does Velocity have more effect on Kinetic energy than Mass?
The kinetic energy is proportional to the mass (m1) and square of the velocity (V2).
K.E. = \frac{1}{2}.m.V^{2}
Due to the square of velocity, a small change in velocity can cause a high change in Kinetic energy.
Thus, if you doubled the mass, the K.E. gets doubled, but if you doubled the velocity, the kinetic energy become 4 times of initial K.E.
Let me explain it with an example.
Consider the object of mass ‘m’ initially has kinetic energy K.E_{i}.
Now double the mass of the object, and the kinetic energy will become,
KE_{f} = \frac{1}{2}.(2m).V^{2} = 2[\frac{1}{2}.(m).V^{2}] = 2. KE_{i}\cdots[1]
Now in another case, double the velocity of the object. The kinetic energy will become,
KE_{f} = \frac{1}{2}.m.(2V)^{2} = 4[\frac{1}{2}.(m).V^{2}] = 4. KE_{i}\cdots[2]
Thus from [1] and [2], it is clear that the change in velocity affects kinetic energy more than the change in mass.
Related articles:
Pratik is a Graduated Mechanical engineer. He enjoys sharing the engineering knowledge learned by him with people. | crawl-data/CC-MAIN-2024-10/segments/1707947473819.62/warc/CC-MAIN-20240222125841-20240222155841-00798.warc.gz | null |
# SOLUTION: The problem is: If sales of ipods increase by 15% each week and the store plans to sell 100 ipods the first week (which the store calls the first week 0weeks) how many ipods will i
Algebra -> Algebra -> Equations -> SOLUTION: The problem is: If sales of ipods increase by 15% each week and the store plans to sell 100 ipods the first week (which the store calls the first week 0weeks) how many ipods will i Log On
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Algebra: Equations Solvers Lessons Answers archive Quiz In Depth
Click here to see ALL problems on Equations Question 156896: The problem is: If sales of ipods increase by 15% each week and the store plans to sell 100 ipods the first week (which the store calls the first week 0weeks) how many ipods will it sell by the end of the 4th week. Find the equation to this problem. I have tried to find the equation to this problem for a couple of hours. Some of my thoughts are: y=(100x0.15)X I just really don't understand how to find the equation. Thank you so much for your help, I am desperate and driving my mother up the wall. DanielleAnswer by [email protected](15660) (Show Source): You can put this solution on YOUR website!If sales of ipods increase by 15% each week and the store plans to sell 100 ipods the first week (which the store calls the first week 0 weeks) how many ipods will it sell by the end of the 4th week. Find the equation to this problem : Let x = no. of weeks f(x) = no. sold : f(x) = 100*1.15^x ; In this problem, x = 4: f(x) = 100 * 1.15^4 ; Find 1.15^4 on a calc f(x) = 100 * 1.479 f(x) ~ 148 by the end of the 4th week : You can see in week 0; 100 * 1.15^0 = 100 * 1 and in week one: 100 * 1.15^1 = 115 units as you would expect ; Did this help you understand this, and be kind to your dear mother? | crawl-data/CC-MAIN-2013-20/segments/1368705352205/warc/CC-MAIN-20130516115552-00097-ip-10-60-113-184.ec2.internal.warc.gz | null |
# Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
Numerically it seems to be true that
$$\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}.$$
Any ideas how to prove this?
• Substitute $u=\sqrt{x}$ to see that this is related to Fresnel's integral... – draks ... Jul 17 '12 at 15:24
Using contour integration, we get \begin{align} \int_0^\infty\frac{e^{ix}}{\sqrt{x}}\,\mathrm{d}x &=\sqrt{i\,}\int_0^\infty\frac{e^{-x}}{\sqrt{x}}\,\mathrm{d}x\\ &=\frac{1+i}{\sqrt{2}}\Gamma\left(\frac12\right)\\ &=(1+i)\sqrt{\frac\pi2} \end{align} Therefore, $$\int_0^\infty\frac{\cos(x)}{\sqrt{x}}\,\mathrm{d}x=\int_0^\infty\frac{\sin(x)}{\sqrt{x}}\,\mathrm{d}x=\sqrt{\frac\pi2}$$
About the Contour Integration
If we integrate $f(z)=\dfrac{e^{iz}}{\sqrt{z}}$ around the contour $[0,R]\cup Re^{i[0,\pi/2]}\cup i[R,0]$ as $R\to\infty$, we get that $$\int_0^R\frac{e^{ix}}{\sqrt{x}}\,\mathrm{d}x +\int_0^{\pi/2}\frac{e^{iRe^{ix}}}{\sqrt{R}e^{ix/2}}iRe^{ix}\,\mathrm{d}x -\sqrt{i\,}\int_0^R\frac{e^{-x}}{\sqrt{x}}\,\mathrm{d}x =0$$ because there are no singularities of $f$ inside the contour. Then because \begin{align} \left|\int_0^{\pi/2}\frac{e^{iRe^{ix}}}{\sqrt{R}e^{ix/2}}iRe^{ix}\,\mathrm{d}x\right| &\le\sqrt{R}\int_0^{\pi/2}e^{-R\sin(x)}\,\mathrm{d}x\\ &\le\sqrt{R}\int_0^{\pi/2}e^{-2Rx/\pi}\,\mathrm{d}x\\ &\le\frac\pi{2\sqrt{R}} \end{align} vanishes as $R\to\infty$, we have $$\int_0^\infty\frac{e^{ix}}{\sqrt{x}}\,\mathrm{d}x =\sqrt{i\,}\int_0^\infty\frac{e^{-x}}{\sqrt{x}}\,\mathrm{d}x$$
Real Method
Substituting $u^2=x$ and applying this answer, which uses only real methods, yields \begin{align} \int_0^\infty\frac{\sin(x)}{\sqrt{x}}\,\mathrm{d}x &=2\int_0^\infty\sin(u^2)\,\mathrm{d}u\\ &=2\sqrt{\frac\pi8}\\ &=\sqrt{\frac\pi2} \end{align}
• would the downvoter care to comment? – robjohn Apr 6 '14 at 9:41
• I guess you take a half-circle as contour, I can't get your first equality with $\sqrt i$, could you expand please? – caub Jun 20 '14 at 23:10
• @kwak: I have added a section about the contour integration mentioned. – robjohn Jun 21 '14 at 1:01
• Why the second downvote? – robjohn Jun 21 '14 at 1:14
• Thanks, awesome answer, the trick is to take this quarter circle – caub Jun 21 '14 at 9:11
That is a Fresnel integral.
Make the substitution $\sqrt{x}=u$. Then you get $dx=2udu$ from where
$$\int_0^\infty \sin(x) x^{-1/2} dx =2 \int_0^\infty \sin(u^2)du=2\sqrt{\frac{\pi}{8}}=\sqrt{\frac{\pi}{2}}$$
See this question for more details.
Here is an another approach, which I show only a heuristic calculation:
\begin{align*} \int_{0}^{\infty} \frac{\sin x}{\sqrt{x}} \; dx &= \int_{0}^{\infty} \left( \frac{1}{\Gamma\left(\frac{1}{2}\right)} \int_{0}^{\infty} t^{-1/2} e^{-xt} \; dt \right) \sin x \; dx \\ &\stackrel{\ast}{=} \frac{1}{\Gamma\left(\frac{1}{2}\right)} \int_{0}^{\infty} t^{-1/2} \int_{0}^{\infty} e^{-xt} \sin x \; dx \; dt \\ &= \frac{1}{\Gamma\left(\frac{1}{2}\right)} \int_{0}^{\infty} \frac{t^{-1/2}}{1+t^2} \; dt \\ &= \frac{1}{\Gamma\left(\frac{1}{2}\right)} \int_{0}^{\infty} \frac{2du}{1+u^4}.\qquad(t = u^2) \end{align*}
Now it is not hard to show that
$$\int_{0}^{\infty} \frac{2du}{1+u^4} = \frac{\pi}{\sqrt{2}}.$$
Indeed, you may use the equality
\begin{align*} \frac{2 du}{1+u^4} &= \frac{2u^{-2} \; du}{u^2 + u^{-2}} = \frac{1 + u^{-2} \; du}{u^2 + u^{-2}} - \frac{1 - u^{-2} \; du}{u^2 + u^{-2}}\\ &= \frac{d\left(u - u^{-1}\right)}{\left(u - u^{-1}\right)^2 + 2} - \frac{d\left(u + u^{-1}\right)}{\left(u + u^{-1}\right)^2 - 2} \end{align*}
and hence deduce that
\begin{align*} \int_{0}^{\infty} \frac{2 du}{1+u^4} &= \int_{0}^{\infty} \frac{d\left(u - u^{-1}\right)}{\left(u - u^{-1}\right)^2 + 2} - \int_{0}^{\infty} \frac{d\left(u + u^{-1}\right)}{\left(u + u^{-1}\right)^2 - 2}\\ &= \int_{-\infty}^{\infty} \frac{dv}{v^2 + 2} - \color{blue}{\int_{\infty}^{\infty} \frac{dw}{w^2 - 2}} \qquad \begin{pmatrix}v = u - u^{-1} \\ w = u + u^{-1}\end{pmatrix}\\ &= \frac{\pi}{\sqrt{2}} + 0. \end{align*}
as claimed, where the blue-colored integration is taken along the curve starting from $+\infty$ to $2$, and then turning back to $+\infty$, which makes it cancel out. Therefore we obtain the desired result.
The problem in this calculation is that the starred equality is almost unable to be justified by any simple means.
From the result
$$\int_0^\infty dx \frac{\sin x}{\sqrt x} = 2 \int_0^\infty dx \sin\left(x^2\right),$$
I'd use $\exp\left(-i x^2\right) = \cos \left(x^2\right) - i \sin \left(x^2\right)$ and
$$\int_0^\infty dx \ \exp\left(- a x^2\right) = \frac{1}{2} \sqrt{\frac{\pi}{a}}.$$
Let's start out with the following relation: $$\int_0^{\infty} \frac{\sin x}{\sqrt{x}} e^{-a x} dx = \frac{2}{\sqrt{\pi}} \int_0^{\infty} \frac{1}{1+(a+x^2)^2} dx \tag1$$ Proof of the relation $(1)$
$$\int_0^{\infty} \frac{\sin x}{\sqrt{x}} e^{-a x} dx=$$ Notice that $\displaystyle \frac{1}{\sqrt x}= \frac{2}{\sqrt{\pi}} \int_{0}^{\infty} e^{-xt^2} dt$ and have that
$$\frac{2}{\sqrt{\pi}} \int_{0}^{\infty} \sin x e^{-ax}\left(\int_{0}^{\infty} e^{-xt^2} dt\right) dx=$$ $$\frac{2}{\sqrt{\pi}} \int_{0}^{\infty} \left(\int_{0}^{\infty}\sin x e^{-(a+t^2)x} dt\right) dx=$$ Change the integration order $$\frac{2}{\sqrt{\pi}} \int_{0}^{\infty} \left(\int_{0}^{\infty}\sin x e^{-(a+t^2)x} dx\right) dt=$$ Now let's recollect the formula $$\int e^{\alpha x} \sin (\beta x) \ dx = \frac{e^{\alpha x}(-\beta (\cos (\beta x) + \alpha \sin(\beta x)))}{{\alpha}^2+{\beta}^2}$$
Hence $$\int_{0}^{\infty}\sin x e^{-(a+t^2)x} dx=-\frac{e^{-(a+t^2)x}((a+t^2)\sin x + \cos x)}{1+(a+t^2)^2}\bigg|_{0}^{\infty}=\frac{1}{1+(a+t^2)^2}$$ Then $$\frac{2}{\sqrt{\pi}} \int_{0}^{\infty} \left(\int_{0}^{\infty}\sin x e^{-(a+t^2)x} dx\right) dt=\frac{2}{\sqrt{\pi}} \int_{0}^{\infty}\frac{1}{1+(a+t^2)^2} \ dt.$$ End of the relation $(1)$ proof.
Based upon the above relation we get that $$\int_0^{\infty} \frac{\sin x}{\sqrt{x}} dx=$$ $$\lim_{a\to0+} \int_0^{\infty} \frac{\sin x}{\sqrt{x}} e^{-a x} dx =$$ $$\lim_{a\to0+} \frac{2}{\sqrt{\pi}} \int_0^{\infty} \frac{1}{1+(a+x^2)^2} dx=$$ $$\frac{2}{\sqrt{\pi}} \int_0^{\infty} \frac{1}{1+x^4} dx \tag2$$ For the last integral we may change the variable and everything gets reduced to computing beta function
Change the variable $$x=\left(\frac{t}{1-t}\right)^{\frac{1}{4}}$$ Then $$\int_0^\infty \frac{1}{1+x^4} \ dx = \int_0^1 \frac{1}{4} (1-t)^{\frac{3}{4}-1} t^{\frac{1}{4}-1} \mathrm{d} t = \frac{1}{4} \operatorname{B}\left(\frac{1}{4}, \frac{3}{4}\right) = \frac{1}{4} \sqrt{2} \pi \tag3$$
Finally, from $(2)$ and $(3)$ we obtain the desired result
$$\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}.$$ Q.E.D.
• Is it obvious what the result of the last indefinite integral is? – Pedro Tamaroff Jul 17 '12 at 19:15
• Still, don't write "obviously" when you mean to say that somebody already did the work for you; it's better to link to the answer you refer to instead. – J. M. is a poor mathematician Jul 18 '12 at 11:21
• @J. M.: agree. My answer was updated. – user 1357113 Jul 18 '12 at 11:33
Here I use Laplace Transform to present a simple proof and do not need use other tools. Note that $$\int_0^\infty e^{-xt}\frac{1}{\sqrt{\pi t}}dt=\frac{1}{\sqrt x}$$ and hence \begin{eqnarray} \int_0^\infty\frac{\sin x}{\sqrt x}dx&=&\int_0^\infty\sin x\left(\int_0^\infty e^{-xt}\frac{1}{\sqrt{\pi t}}dt\right)dx\\ &=&\frac{1}{\sqrt\pi}\int_0^\infty \left(\int_0^\infty e^{-xt}\sin xdx\right) \frac{1}{\sqrt{t}}dt\\ &=&\frac{1}{\sqrt\pi}\int_0^\infty \frac{1}{t^2+1} \frac{1}{\sqrt{t}}dt\\ &=&\frac{1}{\sqrt\pi}\int_0^\infty \frac{\sqrt t}{t^2+1}dt\\ &=&\frac{1}{\sqrt\pi}\frac{\pi}{\sqrt 2}\\ &=&\sqrt{\frac{\pi}{2}}. \end{eqnarray} Here we use the following well-known integral $$\int_0^\infty \frac{t^p}{t^2+1}dt=\frac{\pi}{2\cos\frac{p\pi}{2}}, |p|<1.$$ | crawl-data/CC-MAIN-2019-22/segments/1558232255092.55/warc/CC-MAIN-20190519181530-20190519203530-00079.warc.gz | null |
A HIPPO Takes to the Skies to Taste Earth's Atmosphere
The HIAPER Pole-to-Pole Observation (HIPPO) project generated an extraordinarily detailed mapping of the global distribution of greenhouse gases, black carbon and related chemical species in the atmosphere
Once international agreements demand it, effective, enforceable greenhouse gas reduction will require in-depth information on the fluxes and transports of these and other atmospheric constituents.
Researchers know that concentrations of aerosols like black carbon and gases like carbon dioxide, water vapor, ozone and nitrous oxide vary across the globe and by season. Until recently, a fine-grained picture of the concentrations and understanding of the dynamics of these atmospheric components did not exist.
Researchers across the globe launched the five-phase HIPPO (HIAPER Pole-to-Pole Observation) project to provide this perspective; it has generated the first detailed mapping--both vertically and across latitudes--of the global distribution of greenhouse gases, black carbon and related chemical species in the atmosphere.
"With HIPPO, we now have whole slices of the global atmosphere that, in many cases, appear differently than we expected," said Steven Wofsy, HIPPO principal investigator and atmospheric scientist at Harvard University.
What HIPPO will tell us
Scientists expect that this detailed view will allow them to more realistically approximate the global atmosphere's chemical distribution and improve understanding of how the land, ocean and atmosphere interact. In addition to feeding basic scientific understanding, HIPPO will provide a vital source of data useful for informing policy related to climate and climate change. Carbon dioxide levels, sources (areas where more carbon is released to the atmosphere than is taken up), and sinks (where carbon uptake is greater than release) are a significant focus for HIPPO scientists.
"In tracking carbon dioxide exchange, we're particularly interested in the tropical forests, the northern forests and the ocean around Antarctica," said Britton Stephens, an atmospheric scientist at the National Center for Atmospheric Research (NCAR) and HIPPO co-investigator. "HIPPO provides such a broad perspective, giving us an opportunity to see the different regional influences on carbon dioxide distributions around much of the globe."
HIPPO, supported by the National Science Foundation (NSF), the National Oceanic and Atmospheric Administration (NOAA), NASA and a number of universities, collects detailed, high-accuracy measurements of atmospheric constituents. A proof of concept was launched in spring 2008, and the first series of global flights began in January 2009, with subsequent flights occurring twice in 2010 and twice in 2011.
The plane that was used for HIPPO, a Gulfstream V, flew researchers and precision instruments measuring about 150 gases and atmospheric constituents, from nearly pole to pole across the Pacific Ocean, flying at altitudes varying between 500 and 47,000 feet above sea level, depending on the daily project objective. The first campaign--typical of the ones to follow--began in Boulder, Colo., explored the air over the Arctic; the moving lab headed next to Christchurch, New Zealand, before flying over the Southern Ocean, with subsequent layovers in Tahiti, Easter Island and Central America.
The big exhale: carbon dioxide
With the last of the five missions recently completed, Stephens brings attention to what he calls the Northern Hemisphere's "exhale." HIPPO experimental design called for seasonal data collection to get a complete, year-round perspective on global atmospheric processes. In the first three missions, occurring during Northern Hemisphere's fall, winter and early spring, the scientists noted significant changes in carbon dioxide (CO2) distribution and concentrations.
"By lining up the same slice of atmosphere in seasonal order over the course of the first three missions, it's possible to see build-up of carbon dioxide concentrations in the atmosphere over fall, winter and spring," said Stephens. "A giant pool of CO2 grows in the Northern Hemisphere as photosynthesis slows and as fossil-fuel CO2 emissions and plant and soil respiration continue."
Notably, in the most northerly regions of the Arctic, the researchers found rapid filling of the atmosphere with CO2 at high altitudes during winter and spring, which challenges existing perceptions of atmospheric processes.
The last two HIPPO missions helped provide a clearer view on the all-season, big picture perspective on CO2 dynamics. The fourth mission occurred in June and July of 2011, and the fifth during August and September of 2011; during these periods, Northern Hemisphere CO2 concentrations were at their lowest as vegetation growth and photosynthetic processes peaked. As expected, throughout this period, the researchers saw a massive inhalation of CO2 across the Northern Hemisphere, as the growing plants breathed in the CO2.
Measuring CO2 at the variety of altitudes and latitudes gives scientists much tighter constraints--and therefore greater understanding--on the total amount of CO2 release (or uptake) for the hemisphere. Older estimates of hemispheric exchange, which relied on information collected at the surface, turn out to be off by about 30 percent, said Stephens. "Looking up through the boundary layer using imperfect atmospheric transport models has been like staring through foggy swim goggles--finally, HIPPO is giving us a clear view," he said.
Other important atmospheric components: Black carbon and nitrous oxide
Other measurements are generating excitement from the three completed campaigns, Wofsy said. HIPPO observations show a more widespread, uniform distribution of black carbon than anticipated, with greater than expected abundances occurring at high latitudes in the Northern Hemisphere.
Additionally, concentrations of nitrous oxide (N2O)--the third most important long-lived anthropogenic greenhouse gas (the other two being CO2 and methane)--were often found to have elevated concentrations in the mid- and upper-tropical troposphere even over areas where no N2O was detected at the surface; without the instrumentation and measuring capabilities of HIPPO, scientists could knot have known this. Details on some of the unexpected--and unpredictable--findings related to these atmospheric components are outlined below.
Black carbon affects climate, doing so both directly (by absorbing solar radiation) and indirectly (by forming clouds that will either reflect or absorb radiation, depending on their characteristics and location). Black carbon deposited on snow or ice also enhances melt leading the Earth's surface to absorb more sunlight. These dark aerosols have a variety of sources, coming from diesel fuel or coal combustion, burning plants in forest fires and various industrial processes.
Most black carbon remains in the atmosphere for only days to weeks, but it can still have a dramatic impact on global warming. HIPPO's pole-to-pole measurements of black carbon may assist policy makers in developing strategies for reducing its climate change impact.
Among other things, the HIPPO measurements have provided new knowledge on the life cycle of a black carbon particle as it travels from source (emission) to sink (removal) in the atmosphere. Used together with global aerosol models, HIPPO's pole-to-pole measurements of black carbon captured in different seasons can be used to refine our knowledge of how black carbon aerosols affect climate, said Ryan Spackman, an atmospheric chemist in NOAA's Earth System Research Laboratory.
Prior to HIPPO, a limited number of airborne measurements of black carbon were conducted. Of the studies available, all lack HIPPO's combination of vertical and latitudinal detail. Since global aerosol models vary widely in projected black carbon concentrations, HIPPO data will prove invaluable for many aspects of climate research. Because most black carbon emissions occur at the surface, typically the amount of black carbon in the atmosphere decreases with altitude. In the Southern Hemisphere, which has fewer pollution sources than the Northern Hemisphere, however, this is not the case.
"In our first flights near the southern pole, we saw the amount of black carbon in the atmosphere increasing with altitude," said Joshua Schwarz, a physicist working in NOAA's Earth System Research Laboratory. "This indicates that the black carbon was transported to the region from far away, with rain-out occurring at lower altitudes. This conclusion offers insights on the interplay of transport and removal mechanisms that can help in validation of global model results."
HIPPO covers a wide range of latitudes over a short time, reducing the likelihood that the scientists would miss transport of black carbon across the Pacific. This perspective helped them unravel the nuances of transport dynamics from removal processes, which strengthened the impact of their results.
In the first HIPPO mission, which occurred during Northern Hemisphere winter, the black carbon team analyzed pole-to-pole distributions of black carbon, in the process learning that global aerosol models often overestimate black carbon in the atmosphere. "For black carbon, these observations have helped us to more easily separate the impacts of errors in modeling removal and errors in modeling transport and emissions," said Schwarz.
During the second and third HIPPO missions, which occurred in the Northern Hemisphere's fall and spring, the scientists observed large-scale black carbon pollution events associated with the intercontinental transport of vast amounts of pollution from Asia. Investigators observed elevated pollution at almost all altitudes in the Arctic, but especially at higher altitudes, where one might expect the air to be relatively clear and clean. The scientists discovered that pollutants can be easily transported to the Arctic as thin sheets of air in almost any season.
Another surprise waiting for the scientists was the seasonality of the plumes of black carbon-laden pollution at mid-latitudes (between Hawaii and Alaska). During springtime, the scientists identified pollution contributions from two predominant sources--human-made pollution from Asia and biomass burning from Southeast Asia.
"The black carbon mass loadings in pollution plumes in the remote Pacific were comparable with what we have observed in large American cities," said Spackman. "Even more surprising, we discovered that this pollution extended over the entire depth of the troposphere--from near the surface of the ocean to 28,000 feet."
On HIPPO flights, the scientists frequently saw higher levels of N2O at higher altitudes than at the surface. Not only is N2O a powerful greenhouse gas, it is also an important ozone-depleting substance, whose importance will increase in the future. Consequently, the presence of N2O at these levels is more than scientifically intriguing. A better understanding of where N2O is found and in what concentrations is important information to guide both scientists and decision makers.
Primary N2O emissions come from soils and the ocean; a large human-generated component originates as a result of fertilizer use for agriculture. These anthropogenic emissions are a relatively new source, and have been increasing since the mid 1800s--from 260 parts per billion (ppb) to 320 ppb, said Eric Kort, who recently completed his doctorate with Wofsy at Harvard. While not the only driver of the N2O-related research on HIPPO, questions about the rapid rise in human-generated N2O concentrations in the atmosphere add urgency to the N2O investigation.
To their surprise, the HIPPO investigators often found elevated concentrations of N2O high in the atmosphere--even over areas where ground-based monitors did not indicate presence of the gas at the surface. The higher-than-expected levels of N2O at altitude indicate more dynamics at work than previously appreciated, explained Kort.
Some analysis shows that large-scale convective activity (i.e., storms) and a lot of rainfall, which might result in increased microbial activity, might have a hand in achieving this reality.
"Lots of N2O is lofted from tropical regions," said Kort. "HIPPO sensors show increased emissions in the tropics, but we don't know if this occurs naturally, coming from tropical soil sources, or if other processes or perturbations, such as increased use of fertilizers upwind from the forests, causes this."
Again, lacking direct observations, models of these dynamics historically have played a large role in gaining better predictions of likely N2O behavior. While some models accurately anticipated near-surface N2O abundances, none predicted the persistent elevated levels seen at altitude in the tropics.
Achieving better modeling results will be particularly important in the case of atmospheric N2O, which has increased year after year at a rate approaching one part per billion. As society moves toward using and producing biofuels, use of fertilizers will likely increase, which will, in turn, amplify N2O emissions. At some point, N2O could offset benefits from CO2 reduction. Because of this, and because of N2O's importance as a greenhouse gas, scientists and policy makers want to have a well-honed awareness on the transport, fluxes and removal processes affecting N2O.
"Nitrous oxide emissions are certainly something we need to be concerned about in terms of future international regulatory treaties because such non-CO2 emissions will be important. Currently, our knowledge of these emissions is far more limited than is the case for CO2," said Kort.
Improving global models
Matching up observed and modeled N2O data to better predict behavior of the atmospheric constituents is a significant reason HIPPO measurements were carried out. The complexity, time and expense of missions like HIPPO make modeling an important way to extend use of the HIPPO data and develop models that better replicate observed atmospheric characteristics.
Alone, neither observations nor models can fully resolve real-world processes. But improved observations that then feed into models can provide revealing new insights on climate dynamics. The major model challenge from the perspective of CO2, said Stephens, is representations of atmospheric mixing. Often the models used have grid structures that are coarser than the fine-scale processes responsible for mixing.
"So, if mixing happens due to convective cells or transport up and over a cold air mass, for example, the transport models used to track CO2 in the atmosphere do not represent these dynamics well," Stephens said.
Increase in model resolution may improve these issues somewhat, but it does not get around the need for robust observations that capture the characteristics of broad swaths of atmosphere, from the ground to high altitudes. HIPPO profiles extend through the troposphere, expanding existing observational data sets--and knowledge--beyond that allowed by current ground-based capabilities.
Using HIPPO data, researchers will be able to test the accuracy of existing atmospheric models to better identify those that most accurately represent observed processes. Moreover, these observations will aid the design of more innovative models and data-assimilation systems--models and systems able to take full advantage of HIPPO observations. Such improvements will push forward understanding of the processes responsible for uptake of human-emitted CO2 during and between field campaigns--and beyond.
-- Rachel Hauser, National Center for Atmospheric Research, [email protected]
This Behind the Scenes article was provided to LiveScience in partnership with the National Science Foundation. | <urn:uuid:b7e53945-0960-477f-9a90-a05f92ed28b3> | {
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A district heating system works like a large central heating system that supplies heat to several buildings, a district or a city, through an underground network of pipes. The energy comes from a centralised energy center which produces heat locally from different energy sources: thermal, renewable (biomass, geothermal, solar), heat recovery (incineration of household waste, biogas, wood-waste, etc.). The heat is then distributed in the form of hot water and transmitted to each unit via an individual substation located between the heat network and the building's heating circuit.
There are currently some 6,000 district heating networks in Europe, covering 11 to 12% of needs, with very different situations from one country to another. District heating is by far the most widespread form of heating in Northern and Eastern European countries, whereas it is much less developed in the West, particularly in the Netherlands and the UK. | <urn:uuid:35199f4a-f6c3-4428-bc21-becb4ba89c33> | {
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# How can I properly distribute fractions when solving a set of linear equations?
• B
• Voltux
You should get the answer x = -1, y = 9So, in summary, the conversation discusses a set of linear equations and the frustration of solving them by distributing fractions. The expert summarizer explains that it is not necessary to distribute fractions and offers an alternative method of solving the equations. The conversation also includes a discussion on the rules of solving equations and the importance of performing the same operation on both sides of the equation. The expert suggests that the most efficient way to solve these equations is to use elimination and substitution.
Voltux
I'm given the problem 14x+5y=31, 2x-3y=-29
This is a set of linear equations that I am asked to solve. That being said I am getting hung up on how to distribute a fraction. The answer is x=9, however, I am getting x=36 and the step I do not understand is distributing the fraction.
We then get setup with 2*((31-5y)/14)-3y = -29 by solving for x.
We then distribute the 2 this gives us ((62-10y)/14)-3y = -29.
This can also be written as 1/14 *(62-10y)-3y = -29.
Now why can't we distribute this is the inverse? e.g. 1/14*14/1 = 1
(62-10y)-3y = -29*14 -> (62-10y)-3y = -406
That gets us 62-13y = -406 then do some basic arithmetic ->
-62, -62
-13y = -465, divide by -13 -> y = 36
How is this method incorrect? I'm very frustrated because I have spent hours on this. I can see another method of performing this would be multiply by the inverse ->
(62-10y)/14)-3y = -29
Multiple by the inverse ((62-10y)/14) * ((14)/(62-10y)) ->
62-10y-3y = -29* ((14)/(62-10y)) and then I go nowhere.
I will be incredibly happy if someone can help me to understand this. Thanks kindly.
Voltux said:
(62-10y)-3y = -29*14 -> (62-10y)-3y = -406
You forgot to multiply 3y by 14!
Voltux
Svein said:
You forgot to multiply 3y by 14!
Svein,
I would like to say thank you so very much for pointing this out to me. I believe you truly made my evening.
I indeed performed the calculations and get -468/-52 = 9.
Can you cite the rule or fundamental misunderstanding that I have missed? I was under the impression that we can distribute once like I demonstrated.
Thank you again, Svein. Thank you.
Voltux said:
Can you cite the rule or fundamental misunderstanding that I have missed? I was under the impression that we can distribute once like I demonstrated.
Think of an equation as an old-fashioned scale (the one you use for weighing things). You start with the scale in balance (that is what the equal sign tells you). Now you can add or subtract the same amount on both sides - the scale will still balance. You can also double the amount on both sides - the scale will still balance. In short - as long as you do the same thing on both sides, the scale will keep on balancing.
In your case - yes, you can multiply both sides of the equal sign by 14. But "both sides" means exactly that. Therefore, encapsulate both the left and right side in parenthesis before you multiply!
... but that is not usually the best way to solve linear simultaneous equations which I suggest is:
1. You can see that ## 2x - 3y = -29 ## can be written ## 14x - 21y = -203 ##
2. Subtract this from the first equation to get ## 14x + 5y -14x - (-21y) = 31 - (-203) ##
3. Simplify to ## 26y = 234 \implies y = 9##
4. Substitute into the second equation to get ## 2x - 3 \times 9 = -29 \implies 2x - 27 = -29 \implies 2x = -29 + 27 = -2 \implies x = -1 ## (I could have chosen the first equation, but this one looked easier).
5. Check by substituting into the first equation to get ## 14 \times (-1) + 5 \times 9 = 31 \implies -14 + 45 = 31 ## OK
Fewer steps means fewer mistakes! (although I have just edited a typo in step 3!)
pbuk said:
... but that is not usually the best way to solve linear simultaneous equations which I suggest is:
1. You can see that ## 2x - 3y = -29 ## can be written ## 14x - 21y = -203 ##
2. Subtract this from the first equation to get ## 14x + 5y -14x - (-21y) = 31 - (-203) ##
3. Simplify to ## 26y = 234 \implies y = 9##
4. Substitute into the second equation to get ## 2x - 3 \times 9 = -29 \implies 2x - 27 = -29 \implies 2x = -29 + 27 = -2 \implies x = -1 ## (I could have chosen the first equation, but this one looked easier).
5. Check by substituting into the first equation to get ## 14 \times (-1) + 5 \times 9 = 31 \implies -14 + 45 = 31 ## OK
Fewer steps means fewer mistakes! (although I have just edited a typo in step 3!)
And another way is making the first equation into
y = (2x+29)/3
and substitute y into the second equation,then you get y out of the equation.
(Not really useful in this particular set of equations,but seldom gets more efficient then the add-subtracting method that @pbuk mentioned,for instance:
y = 2x+1
3x+2y = 9
Janosh89
No reason to wonder how or why to "distribute fractions". You present a system of equations.
14x+5y=31, 2x-3y=-29A neat way to handle this is try to at least start with elimination of a variable. The x looks like a nice choice this way.
Keep first equation, but multiply second equation by 7.
14x+5y=31, 14x-21y=-203Now as so written, subtract first equation from second equation.
14x-21y-14x-5y=-203-31
-26y=-234
26y=234
y=9
There is one of the variables, now solved. Any use of fractions occurring was no large struggle; only the simplest of arithmetic, even if some electronic tool was used.
How you go about solving for x, is your choice. Use elimination if you want, or try substitution in either of the original equations.
YoungPhysicist
YoungPhysicist
## 1. What is the definition of a fraction?
A fraction is a numerical quantity that represents a part of a whole. It is written as one number (the numerator) divided by another number (the denominator), separated by a horizontal line.
## 2. How do you distribute a fraction over addition or subtraction?
To distribute a fraction over addition or subtraction, you simply multiply the fraction by each term in the expression. For example, to distribute 1/2 over the expression 3 + 4, you would multiply 1/2 by 3 and 4, resulting in (1/2 * 3) + (1/2 * 4) = 3/2 + 2 = 5/2.
## 3. What is the difference between distributive property and distributive law?
The distributive property refers to the rule that states that when multiplying a number by a sum or difference, you can distribute the multiplication over each term in the expression. On the other hand, the distributive law is a more general concept in mathematics that states that a binary operation can be applied to two operands separately and then combined afterwards.
## 4. How do you distribute a fraction over multiplication?
To distribute a fraction over multiplication, you simply divide the fraction by the number being multiplied. For example, to distribute 1/2 over the expression 3 * 4, you would divide 1/2 by 3 and 4, resulting in (1/2 ÷ 3) * (1/2 ÷ 4) = 1/6 * 1/8 = 1/48.
## 5. Can you distribute a fraction over division?
Yes, you can distribute a fraction over division by multiplying the fraction by the reciprocal of the number being divided. For example, to distribute 1/2 over the expression 3/4, you would multiply 1/2 by 4/3, resulting in (1/2 * 4) ÷ (1/2 * 3) = 2/3.
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Foodborne illness, often called food poisoning or foodborne disease, is any illness that results from eating contaminated food. It is a common cause of diarrheal illness in Wisconsin.
If you believe you or someone you know became ill from eating a certain food, report your illness with the online reporting tool. Learn more about the tool by viewing the Food Poisoning: Report an Illness Caused by Food or Water webpage.
If you are severely ill, see a doctor immediately. Food poisoning can be especially dangerous for infants, pregnant people, older adults, and people who are immunocompromised.
Reporting illnesses helps public health officials identify potential foodborne disease outbreaks. By investigating foodborne disease outbreaks, possible problems in food production, distribution, and preparation that may cause illness can be discovered and steps can be taken to prevent others from getting sick.
- Food Handling and Housekeeping - P-44970 (PDF)
- Surveillance and Outbreak Support Team - P-01750 (PDF)
- DHS Food Safety information
- Food Safety.gov
- Food Safety — Centers for Disease Control and Prevention
- Healthy Pets, Healthy People – Centers for Disease Control and Prevention
- Foodborne and Waterborne Disease Outbreak Investigation Manual - P-44722 (PDF)
Questions about Food Poisoning? Contact us!
Phone: 608-267-9003 | Fax: 608-261-4976 | <urn:uuid:c0caaf38-6ef5-4240-81cd-a7a3f94ebe2e> | {
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History shows people with disabilities have been defined as objects of shame, fear, pity, or ridicule. People with disabilities have been confined, sometimes for life, in state institutions and nursing homes. Individuals were sterilized against their will, laws prohibited people with certain disabilities from marrying, or even appearing in public.
The history of Independent living comes from the philosophy of people with disabilities have the same rights, options, choices, and equal opportunities as anybody else. It is based on the premise that people with even the most severe disabilities should have the choice of living in the community.
The history of the independent living movement in the United States can be traced back to as early as the 1850s, when deaf people began establishing local organizations to advocate for their interests. These local groups merged into the National Association for the Deaf in 1880.
Protesting can be traced back to the depression years in the 1930’s. The League of the Physically Handicapped held protests against the federal government for discrimination against disabled people in federal programs.
The National Federation of the Blind and the American Federation of the Physically Handicapped were organized in the early 1940’s. Disabled soldiers returning from World War II established the Paralyzed Veterans of America.
The current history of the independent living movement is tied in with the African American civil rights struggle and with other movements of the late 1960’s and 1970’s. A major part of these activities involved the formation of community-based groups of people with different types of disabilities who worked together to identify barriers and gaps in service delivery. To address barriers, action plans were developed to educate the community and to influence policy makers at all levels to change regulations and to introduce barrier-removing legislation.
In 1972, the first Center for Independent Living was established in Berkeley, California by Ed Roberts and the Rolling Quads. Ed Roberts began classes at the University of California in 1962 in Berkeley. Since there was no housing for disabled students at that time, students with disabilities lived in the Student Health Service infirmary, a part of the Cowell Hospital.
By 1967, Cowell Hospital was home to 12 severely disabled students and by 1968; it became a formal program managed by the California Department of Rehabilitation. Inspired by the political activism of the 1960’s, these students began to see themselves not as patients but, in political terms, as an oppressed minority.
While living in the infirmary, a sense of community developed based on the barriers and discrimination that they all faced. The group of students began to call themselves the Rolling Quads. As the Rolling Quads, they protested the arbitrary restrictions placed on them by the rehabilitation counselors. When one counselor determined that two of the students with disabilities were “infeasible” and would be unable to find jobs out of college, she attempted to send them to a nursing home.
Ed Roberts and others protested and demanded that the counselor be reassigned and that the students be reinstated at the college. At one point in the protests, a psychiatrist from the Department of Rehabilitation threatened to institutionalize all the Rolling Quads. After the Rolling Quads went to the local newspapers, the state backed down, reassigned the counselor and reinstated the students.
At the same time, Jean Wirth, an English teacher at the College of San Mateo in San Mateo California, had developed a program of monitoring peer counseling and supports for minority college students in order to reduce their dropout rate. Jean approached Ed Roberts and the Rolling Quads and asked them to design a similar type of program for the students with disabilities.
The program they developed was called the Physically Disabled Students Program (PDSP). Included were provisions for Personal Assistance Services, wheelchair repairs, emergency attendant care and help in obtaining whatever financial services were available under the various states, federal and social service rehabilitation programs.
The three principles of PDSP were:
- Experts on disabilities are the people with disabilities.
- The needs of people with disabilities can best be met with a comprehensive program, rather than fragmented programs at different agencies and offices.
- People with disabilities should be integrated into the community.
As the program gained in popularity, people with disabilities who were not students began applying for services.
The first Center for Independent Living
In 1972, the first Center for Independent Living was founded by disability activists, led by Ed Roberts, in Berkeley, California. These Centers were created to offer peer support and role modeling, and are run and controlled by persons with disabilities. By the turn of the century there were hundreds of such centers across the United States, and much of the rest of the world.
These accomplishments have not ended the discrimination or the prejudice for people with disabilities. There is still much to be done as millions of Americans with disabilities remain locked in poverty, consigned to institutions, and frozen out of society. Even so, it is impossible to deny that the disability rights and independent living movements have transformed American society. | <urn:uuid:585f266b-c3f7-4e78-99cc-9beed28e3c34> | {
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We are producing more waste than ever before – and then we waste it all over again. This behavior is not sustainable. It loses the energy and natural resources required to make the product, and additional energy and resources are used to process the waste.
Sustainable waste planning and management reduces our use of natural resources through actions such as re-use and recycling. It also enables us to recover value and energy from materials we use. It transforms the way we see materials such as sewage, which requires high levels of energy for treatment but has potential to provide a valuable energy source. Waste is a resource, not a by-product.
The benefits of sustainable waste planning and management include reducing pollution and greenhouse gas emissions, creating jobs, reducing land required for landfill and supplying lower carbon options for energy production.
Local authorities can improve waste planning and management by building new waste facilities and using existing recycling networks.
Priorities for waste
- Plan for sustainable waste management
Minimizing the amount of household waste sent to landfill.
- Deal with construction waste
Only half of the 120 million tons of construction waste is recycled each year.
- Turn waste into energy
Waste to energy processes reduce the waste requiring disposal in landfill.
Waste reduction strategies include various particular actions still being analyzed and developed, but there are some major actions plans already accepted and applied by dozens of countries. Favoring products made of different materials that shorten waste and energy life cycle became general policy in many states. Construction industry produces tons of debris and waste material and this waste is currently being re-directed back into the construction process as the raw material for modified concept of construction. Special facilities are being developed to collect, recycle and reuse waste materials coming from electronic industry. Since almost 60% of total urban waste consist of organic waste, major facilities are constructed to process this waste into reusable raw material or at least to utilize it as the fertilizer or low-carbon fuel. Modern urbanistic plans design infrastructure of many cities with pre-planned places for waste collecting and re-directing into facilities for further processing and finally pushing it back into the energy cycle of the same town. | <urn:uuid:3de023a2-98a2-4437-b6fc-e5fa83527c73> | {
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# Solving Polynomial Equations – Graphing Method This presentation explains how to solve polynomial equations graphically. The first step is to get the polynomial.
## Presentation on theme: "Solving Polynomial Equations – Graphing Method This presentation explains how to solve polynomial equations graphically. The first step is to get the polynomial."— Presentation transcript:
Solving Polynomial Equations – Graphing Method This presentation explains how to solve polynomial equations graphically. The first step is to get the polynomial equation into the following form: An example would be …
Let y1 equal the left side of the equation … … yielding …
… we have … Since the right side of the equation is zero …
Recall that anytime the y-value is zero, on the graph the ordered pair (x,0) is a point on the x-axis. (-3,0)(1,0) (5,0)
The solutions to the equation … … are the x-values for which y1 (left side of equation) is equal to zero, … or the x-values of the x-intercepts on the graph of y1.
Example 1: Use the graphing method to solve the polynomial equation: Simplify, with all non-zero terms on the left hand side.
Let y1 equal the left hand side and enter the result into the calculator. Press Zoom-6 to graph Since it appears that the intercepts may be integers, use the Trace method.
Press Trace and then enter -2. Now repeat the process with x = 2, the intercept on the right. Since the y-value is 0, (-2,0) is an x-intercept, and -2 is a solution to the equation. Again, the y-value is 0. The solutions to the equation are x = -2, 2
Example 2- non-integer answers: Use the graphing method to solve the quadratic equation. Round answers to the nearest thousandth: Simplify, with all terms on the left hand side.
Let y1 equal the left hand side and enter the result into the calculator. Press Zoom-6 to graph Try the Trace method to see if the intercepts are integers.
Press Trace and then the x-value on the left, -1. Since the y-value is not 0, (-1,0) is not an x-intercept. Enter y2 = 0, and graph. Notice that nothing has appeared to change. This is because y2 = 0 is right on the x-axis. Use the intersect method to find approximate x-intercepts.
Press 2 nd |Calc|Intersect. The calculator asks three questions. Speed up the process by doing the following. Use the left arrow key to move the cursor close to the intersection point on the left. Press the Enter key three times.
Notice that y = 0, and (-1.192582,0) is an approximate x-intercept. Go through the same process to find the other x-intercept. Use the right arrow to move the cursor to the right intercept … Press 2 nd |Calc|Intersect. Press the Enter key three times.
Here we find that y = 0, and (4.1925824,0) is an approximate x-intercept. The two intercepts are (-1.192582,0) and (4.1925824,0) Rounded to the nearest thousandth, the two solutions to the quadratic equation are: x ≈ -1.193, 4.193
Download ppt "Solving Polynomial Equations – Graphing Method This presentation explains how to solve polynomial equations graphically. The first step is to get the polynomial."
Similar presentations | crawl-data/CC-MAIN-2021-49/segments/1637964358685.55/warc/CC-MAIN-20211129014336-20211129044336-00227.warc.gz | null |
Muscle Flexion and Extension
Did you ever wonder how body movement happens? Or what is a reflex arc? Or how a motor neuron transmits electrical impulses?
I always wondered how our bodies function. Always wanted to know how and why things happen, from the molecular level to the organic and systemic level, all being just amazing processes that keep us happy when normally functioning, which we tend to take for granted.
How does it happen?
Sensory receptors stretch in leg extensor muscle when stimulus is applied (eg hammer tap stretches tendon), while electrical impulses are transmitted from motor neurons through the bundles of axons in each neuron and all the stimulated (innervated) muscle fibres respond by contracting (stimulus response).
“Sensory neuron synapses with and excites motor neuron in the spinal cord and also excites spinal interneuron. As a consequence, motor neuron conducts action potential to synapses on extensor muscle fibres, causing contraction. In the same time, interneuron synapse inhibits motor neuron to flexor muscle causing flexor muscle to relax. The result is leg extension.”*
Further understanding of reflex arc:
“A reflex arc is a neural pathway that controls an action reflex.”*
Most sensory neurons in humans synapse in the spinal cord rather than passing directly into the brain, allowing reflex actions to take place relatively quickly by activating spinal motor neurons without delay of routing signals through the brain. Nonetheless, brain will receive sensory input while the reflex action happens.
Two types of reflex arc exist: autonomic – affecting inner organs, and somatic – affecting muscles.
Did you know that even though the cerebellum accounts for approximately 10% of the brain’s volume, it contains over 50% of the total number of neurons in the brain?! Still, motor commands are not initiated in the cerebellum; all the human body’s voluntary movement is controlled by the motor cortex, located in the rear portion of the frontal lobe, and divided into two main areas (Area 4 and Area 6 – see photo).
Amazing and interesting things happen in our bodies, all of which keeps us happy and healthy individuals enjoying our social life and interactions. Based on the same principle, when we overdo things or wrongly do things, due to a poor understanding of these basic rules, our bodies suffer, sometimes with major consequences for us. Do you want to know & understand more? Just ask the expert!
*AIPT – Complete Personal Trainer & Gym Instructor – Course Notes
Synapses, Neurons and Brains Course, Hebrew University – Coursera | <urn:uuid:182b532f-fbac-4053-bcb8-202a5c8cff6d> | {
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Maths-
General
Easy
Question
# Use the product of sum and difference to find 83 × 97.
Hint:
## The correct answer is: 8051.
### 83 can be written as (90 - 7) and 97 can be written as (90 + 7)So, 83 × 97 can be written (90 - 7) × (90 + 7)(90 - 7) × (90 + 7) = 90(90 + 7) - 7(90 + 7)= 90(90) + 90(7) - 7(90) - 7(7)= 8100 + 630 - 630 - 49= 8100 - 49= 8051Final Answer: Hence, the simplified form of 83 × 97 is 8051.
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2 | crawl-data/CC-MAIN-2024-26/segments/1718198865694.2/warc/CC-MAIN-20240625072502-20240625102502-00022.warc.gz | null |
Forest Service entomologist Tom Coleman has discovered that much of the decline in local native oak species is due to the feeding activity of an insect that has recently infested California, the gold-spotted oak borer. The feeding habits of the insect directly result in mortality to oaks. Because of declines in the oak populations, and the potential for the oak borer to spread and infest a larger area, the Cleveland National Forest is suspending public wood permits until further notice.
The insect, which does not yet have an official common name but is tentatively being called the goldspotted oak borer, is among a group of boring insects called metallic woodborers, flatheaded borers, or jewel beetles.
In the course of field studies to determine the reason oak populations are declining, Coleman discovered that the oak borer may have been inadvertently introduced to the region or may have expanded its range from other parts of theUnited States or from as far south as Guatemala. Prior to the discovery of the beetle, drought was thought be the cause of oak deaths. As many as 70 percent of the oak trees in these areas are infested. Evidence of insect attacks on oak trees can be seen by the presence of the insect under the bark, D-shaped exit holes in the bark,woodpecker foraging, and staining of bark on the trunk and larger branches of the trees.
The Forest Service held meetings in October 2008 in the affected communities to inform the public about the oak borer and to provide advice on how to reduce or prevent oak borer attacks. Since then, numerous agencies have been working together to assess the oak borer’s biology, management, potential impacts, and assist with education and outreach. Research efforts are directed at assessing the oak borer’s current distribution and life cycle in southern California, effective survey techniques, treatment options for high-value trees, factors enhancing tree susceptibility, and firewood management. Additional research and information continues to be gathered to better understand this problem.
Local citizen awareness can help determine the locations of infestations in the county. If you suspect a GSOB infestation in local oak trees, report it!
Find more information at www.gsob.org
For more information on Forest and Grassland Health, please click here. | <urn:uuid:6f0dd07c-547f-4a01-81cb-130b233a30e8> | {
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Vector Composition & Decomposition Video Lessons
Concept
# Problem: Three forces are applied to a tree sapling, as shown in (Figure 1) , to stabilize it. Suppose that FA→ = 355 Nand FB→ = 475 N .Part ADetermine the magnitude of FC→ .Express your answer to three significant figures and include the appropriate units.Part BDetermine the angle between FA→ and FC→ measured clockwise. Express your answer using three significant figures.
###### FREE Expert Solution
Let's label the axes and have teh diagram as,
Part A
From our diagram,
FBy = FBcos(105° - 90°) = (475)cos(15°) = 458.1 N
FBx = FBsin(105° - 90°) = (475)sin(15°) = 122.94 N
Therefore, the forces along the x-direction are:
87% (57 ratings)
###### Problem Details
Three forces are applied to a tree sapling, as shown in (Figure 1) , to stabilize it. Suppose that $\stackrel{\to }{{\mathrm{F}}_{\mathrm{A}}}$ = 355 Nand $\stackrel{\to }{{\mathrm{F}}_{\mathrm{B}}}$ = 475 N .
Part A
Determine the magnitude of $\stackrel{\to }{{\mathrm{F}}_{\mathrm{C}}}$ .
Express your answer to three significant figures and include the appropriate units.
Part B
Determine the angle between $\stackrel{\to }{{\mathrm{F}}_{\mathrm{A}}}$ and $\stackrel{\to }{{\mathrm{F}}_{\mathrm{C}}}$ measured clockwise. Express your answer using three significant figures. | crawl-data/CC-MAIN-2021-17/segments/1618039594808.94/warc/CC-MAIN-20210423131042-20210423161042-00036.warc.gz | null |
The universe is vast. The Earth seems large, yet when examined on a cosmic scale, it is like a spec of dust, even less than a grain of dust. The sun itself is large enough to hold about one million Earths. And the sun is only an average star in a galaxy containing many, many stars in a universe of many, many galaxies.
If we stop to think about it, the vastness of the universe is amazing. While we go about our day-to-day business, we may think of the Earth as being the entire realm of reality. Yet this whole planet is like a spec of dust in the solar system. And the solar system is like a spec of dust when compared with the galaxy. And the galaxy—there are clusters of galaxies, and even superclusters.
The universe is undoubtedly large, almost beyond imagining. Yet, all this majestic expanse of galaxies, stars, and other celestial bodies, could not exist if certain values were not precisely what they are. There are many constants, such as the gravitational constant, that could be any value, yet they are the correct value for the universe to exist, and in some cases for life to exist.
Laws, such as Newton's Law of Gravitation, involve a constant. But the value of the constant is not determined by the Law—it could be any of a range of values. Experimental measurement is needed to show the value of these constants. (Here we are referring to constants which cannot be derived from other constants.) These constants in many cases have no reason to be what they are. Theories may involve canceling out of infinities, resulting in some finite value, but the precise value may not be specifically determined by the theory. However, that value happens to be precisely what it would have to be in order for life to exist.
The point is that theory does not determine precise values of all these constants. What does? And why is that determined value just precisely what is needed for life?
There are many constants: the gravitational constant, the fine-structure constant, the masses of the proton, electron and neutron, the charge of the electron, the speed of light, Planck's constant, and so forth. And certain constants have to be certain values for the universe and for life to exist.
Scientists tell us that if some of these constants were off, even a little bit, that atoms would not exist, or stars would not exist, or water could not exist.
This is an amazing coincidence—that the values of certain constants are exactly what would be needed for the universe and for life to exist. The probabilities of this happening by chance are small—so small, in fact, that scientists have argued about how to explain the fact that these constants do have the values needed for life and matter to exist.
Here are just a few examples of the just-right values of these constants of nature.1
electron charge: if slightly different, stars would not be able to fuse hydrogen into helium
nuclear strong force: if it was only 2% greater in strength, the universe would be without atoms - only 5% weaker, and there would be no stars
gravity is millions of millions of times weaker than electromagnetism: if gravity was stronger, stars would burn out much faster
nuclear weak force: if it had been slightly weaker, all the hydrogen in the universe would be helium now - and water would be impossible
proton/neutron mass difference: if the were not exactly what it is, about 1/2000 the mass of a proton, we would not have chemistry or life
density of ice: if ice didn't float on water, the oceans would freeze from the bottom up. The density of ice is related to the properties of the hydrogen atom.
How unlikely is it that the universe could exist? Roger Penrose (a mathematical physicist, one of whose students is the famous Stephen Hawking) has calculated the chances of the appearance of our universe to be one chance in a very large number.2 This large number is greater than the estimated number of atoms in the universe! In fact, this number is several billion times greater than the estimated number of atoms in the universe. This number is 101030, while the estimated number of atoms in the universe is a 10 with an exponent somewhere between 70 and 100.
One explanation has been offered for the extremely unlikely occurrence of the universe and life, along with all the appropriate values of the physical constants. It is called the Anthropic Principle and states that the reason all these values of important constants of physics are what they are, is simply that they would have to be what they are in order for us to exist and be able to debate their meaning.
This seems obvious. Of course, we are here, and therefore the universe and life have to exist, and also the constants had to have been such as to allow life and the universe to exist. But this merely says that it happened—that the constants did have and do have the appropriate values. It does not explain why the constants are what they are, against the odds.
This, in a sense, merely states the obvious without explaining why the obvious exists. Yes, we are here and yes, life does exist. And obviously, any and all conditions needful for us to be here had to have been met, since we are here. But still this leaves us asking, "Why? Why did it happen?" In a real sense, this merely states that it absolutely did happen, not why it happened. Why? One answer is that it all happens by chance. Another is that it is by design.
The values for some of these constants that have to be just so are based on assumptions of a Big Bang and/or on other assumptions. But even if the assumption is contrary to creation, even if the assumption is of an evolutionary process, it still argues for design. In such a case, consider the following. If the specific values of constants are based on assumptions of evolutionary processes, the evolutionary process must be highly unlikely, and this argues against the evolutionary process.
If one argues for creation on the basis of the unlikely chance occurrence of the precise values of certain physical constants, with these evolutionary process assumptions involved in the calculation of the likelihood of their values, someone might say, "Your argument is not valid! You are arguing for creation but your argument assumes evolutionary processes."
This may be true, but consider this: If we assume those evolutionary processes, then this means we must have certain values of constants for those processes to occur—values which are highly unlikely to have occurred. It is not just one value of one constant—don't misunderstand—but several different constants that all have to be certain values, as required by accepted evolutionary theories.
Consider what William Bradley, Ph.D., Distinguished Professor of Engineering at Baylor University, says:
"There are so many different requirements that are interrelated, it seems difficult to imagine how all of these ‘accidentally' happened to be exactly what they need to be. Because of the many cross constraints, it appears unlikely that there is an alternative set of values for these constants which would ‘work'. Furthermore, the necessary values range over thirty orders of magnitude (1030), making their accidentally correct ‘selection' all the more remarkable. It is quite easy to understand why so many scientists have changed their minds in the past 30 years, agreeing that it takes a great deal of faith to believe the universe can be explained as nothing more than a fortuitous cosmic accident. Evidence for an intelligent designer becomes more compelling the more we understand about our carefully crafted habitat."3
Since the need for certain values of certain constants assumes evolutionary processes, what can be made of it? This: that the evolutionary processes require certain things to occur (or certain values of certain constants to exist) which are highly unlikely, based on current knowledge. Thus, we see the implication, the unlikelihood of those evolutionary processes.
There are two possibilities concerning these constants (that are needed for life to exist):
evolutionary processes require certain values of the constants.
the existence of life (and/or the universe) requires certain values of the constants.
Of course, many will see some overlap in these two categories.
In the first case, the clear implication is that the evolutionary processes are unlikely to have occurred by chance, since the fine-tuning is so unlikely. In the second case, the existence of life (or the universe itself) is unlikely to have occurred by chance. In either case, we have the unlikelihood of the existence of life (or the universe) by chance or the unlikelihood of the occurrence of evolutionary processes to bring about the occurrence of the life and the universe. In both cases, the chance occurrence of the universe and of life seems unlikely.
Then, what about the non-chance, by-design, existence of the universe? Hear what some scientists have to say: "Cosmic constants provide the strong appearance that the universe was designed with life in mind. The prominent astronomer and former atheist, Fred Hoyle, concludes that, ‘a superintellect has monkeyed with physics, as well as with chemistry and biology.' Similarly, Paul Davies, a prominent physicist moved from promoting atheism in 1983 to conceding in 1984 that ‘the laws [of physics]...seem themselves to be the product of exceedingly ingenious design.' One year after this statement, Davies said that there ‘is, for me, powerful evidence that there is something going on behind it all. The impression of design is overwhelming.' Robert Jastrow, Founder-Director of NASA's Goddard Institute of Space Studies refers to cosmic constants as ‘the most theistic result ever to come out of science.'"4
2 Davies, Paul. (1983) God & the New Physics, Simon & Schuster, Inc., New York, 178-179.
3 Bradley, William L. (1999) The Designed "Just So" Universe. http://www.leaderu.com/offices/bradley/docs/universe.html
4 Licona, Michael. God Spoke And Bang! It Happened. http://www.cbn.com/spirituallife/ChurchAndMinistry/Evangelism/God_Spoke_... | <urn:uuid:6f67dc96-b2bc-49b2-8c9f-e8bb7365f982> | {
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The solar system is travelling through much stormier skies than we thought, and might even be about to pop out of the huge gas cloud we have been gliding through for at least 45,000 years. That’s the implication of a multi-decade survey of the interstellar wind buffeting the solar system, which has revealed an unexpected change in the wind’s direction…. Journal reference: Science, DOI: 10.1126/science.1239925
Quotes by Robert Meier in New Scientist article
“It’s possible we’re seeing a structure that is not necessarily an edge,” saysRobert Meier, now at George Mason University in Fairfax, Virginia, who helped make the original STP 72-1 measurements. “A change of direction of flow in a stream could mean you’re near the bank, or that there’s a rock in the middle of the stream or something like that. It’s always harder to figure out what’s going on when you’re in the middle.”
Meier adds that there might be an issue in comparing different types of data. None of the more recent spacecraft have looked at the scattered UV light created as atoms from the cloud interact with solar particles. Instead most made direct measurements of the helium atoms. It would help make the case if we could create modern maps of the UV light and compare those with the 1972 readings from the DoD satellite. “Getting backscatter measurements in this modern era, that would be pretty definitive,” he says. “Either they’re both going to get the same direction or they’re not. | <urn:uuid:2e03f87d-9652-46c1-ac88-42cda8b3667e> | {
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I am a translator. I translate from biology into mathematics and vice versa. I write mathematical models which, in my case, are systems of differential equations, to describe biological mechanisms, such as cell growth. Essentially, it works like this. First, I identify the key elements that I believe may be driving behavior over time of a particular mechanism. Then, I formulate assumptions about how these elements interact with each other and with their environment. It may look something like this. Then, I translate these assumptions into equations, which may look something like this. Finally, I analyze my equations and translate the results back into the language of biology. A key aspect of mathematical modeling is that we, as modelers, do not think about what things are; we think about what they do. We think about relationships between individuals, whether they be cells, animals or people, and how they interact with each other and with their environment. Let me give you an example. What do foxes and immune cells have in common? They're both predators, except foxes feed on rabbits, and immune cells feed on invaders, such as cancer cells. But from a mathematical point of view, a qualitatively same system of predator-prey type equations will describe interactions between foxes and rabbits and cancer and immune cells. Predator-prey type systems have been studied extensively in scientific literature, describing interactions of two populations, where survival of one depends on consuming the other. And these same equations provide a framework for understanding cancer-immune interactions, where cancer is the prey, and the immune system is the predator. And the prey employs all sorts of tricks to prevent the predator from killing it, ranging from camouflaging itself to stealing the predator's food. This can have some very interesting implications. For example, despite enormous successes in the field of immunotherapy, there still remains somewhat limited efficacy when it comes solid tumors. But if you think about it ecologically, both cancer and immune cells — the prey and the predator — require nutrients such as glucose to survive. If cancer cells outcompete the immune cells for shared nutrients in the tumor microenvironment, then the immune cells will physically not be able to do their job. This predator-prey-shared resource type model is something I've worked on in my own research. And it was recently shown experimentally that restoring the metabolic balance in the tumor microenvironment — that is, making sure immune cells get their food — can give them, the predators, back their edge in fighting cancer, the prey. This means that if you abstract a bit, you can think about cancer itself as an ecosystem, where heterogeneous populations of cells compete and cooperate for space and nutrients, interact with predators — the immune system — migrate — metastases — all within the ecosystem of the human body. And what do we know about most ecosystems from conservation biology? That one of the best ways to extinguish species is not to target them directly but to target their environment. And so, once we have identified the key components of the tumor environment, we can propose hypotheses and simulate scenarios and therapeutic interventions all in a completely safe and affordable way and target different components of the microenvironment in such a way as to kill the cancer without harming the host, such as me or you. And so while the immediate goal of my research is to advance research and innovation and to reduce its cost, the real intent, of course, is to save lives. And that's what I try to do through mathematical modeling applied to biology, and in particular, to the development of drugs. It's a field that until relatively recently has remained somewhat marginal, but it has matured. And there are now very well-developed mathematical methods, a lot of preprogrammed tools, including free ones, and an ever-increasing amount of computational power available to us. The power and beauty of mathematical modeling lies in the fact that it makes you formalize, in a very rigorous way, what we think we know. We make assumptions, translate them into equations, run simulations, all to answer the question: In a world where my assumptions are true, what do I expect to see? It's a pretty simple conceptual framework. It's all about asking the right questions. But it can unleash numerous opportunities for testing biological hypotheses. If our predictions match our observations, great! — we got it right, so we can make further predictions by changing this or that aspect of the model. If, however, our predictions do not match our observations, that means that some of our assumptions are wrong, and so our understanding of the key mechanisms of underlying biology is still incomplete. Luckily, since this is a model, we control all the assumptions. So we can go through them, one by one, identifying which one or ones are causing the discrepancy. And then we can fill this newly identified gap in knowledge using both experimental and theoretical approaches. Of course, any ecosystem is extremely complex, and trying to describe all the moving parts is not only very difficult, but also not very informative. There's also the issue of timescales, because some processes take place on a scale of seconds, some minutes, some days, months and years. It may not always be possible to separate those out experimentally. And some things happen so quickly or so slowly that you may physically never be able to measure them. But as mathematicians, we have the power to zoom in on any subsystem in any timescale and simulate effects of interventions that take place in any timescale. Of course, this isn't the work of a modeler alone. It has to happen in close collaboration with biologists. And it does demand some capacity of translation on both sides. But starting with a theoretical formulation of a problem can unleash numerous opportunities for testing hypotheses and simulating scenarios and therapeutic interventions, all in a completely safe way. It can identify gaps in knowledge and logical inconsistencies and can help guide us as to where we should keep looking and where there may be a dead end. In other words: mathematical modeling can help us answer questions that directly affect people's health — that affect each person's health, actually — because mathematical modeling will be key to propelling personalized medicine. And it all comes down to asking the right question and translating it to the right equation ... and back. Thank you. (Applause) | Math can help uncover cancer's secrets | null |
Wednesday 10th February 2021
WALT - Nouns, verbs and adjectives
Adjective - An adjective is a ‘describing’ word: it is a word used to describe (or tell you more about) a noun: The big, red bus drove down the street.
Nouns - A noun is a ‘naming’ word: a word used for naming an animal, a person, a place or a thing: penguin, Stephen, Manchester, car.
Verbs - A verb is a word, or a group of words, that tells you what a person or thing is being or doing. It is often called a ‘doing’ word: running, eating, sitting…
Can you find the
in this sentence?
The big, brown dog ran down the street.
4. What are the first five letters of the alphabet?
5.Add 'ing' to the word 'amaze'
6. Finish this sentence: He is _____ this sum up.
Task - Draw your very own Superworm and write at least two sentences to describe it using the super-hero adjectives you thought of yesterday.
e.g., “This is Superworm he is super-long. He carries bugs on his back, he is super-strong.”
Task - Underline any nouns, verbs and adjectives in your sentences.
The link to the Superworm video is here if you need to watch it again:
And the word-bank should you need it.
Extension – Choose another animal character from the Superworm story and make a list of interesting adjectives to describe them. | <urn:uuid:3234724d-b7e1-4a29-af62-b1adfb15f8de> | {
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A member of the National Academy of Sciences, Meltzer researches the origins, antiquity, and adaptations of the first Americans who colonized the North American continent at the end of the Ice Age. He focuses on how these hunter-gatherers met the challenges of moving across and adapting to the vast, ecologically diverse landscape of Late Glacial North America during a time of significant climate change.
The Nature piece by Alexandra Witze focuses on Meltzer’s latest study to show that a comet, or any other kind of extraterrestrial impact, was not responsible for sudden climate change at the end of the Ice Age 12,800 years ago.
Proponents of the comet-impact theory have pointed to sedimentary deposits that they say prove that an object from outer space hit the Earth, killing the Clovis culture and causing the mass extinction of many animals.
By Alexandra Witze
One of the most controversial ideas about prehistoric North America — that an impact by an extraterrestrial object 12,800 years ago triggered a cold snap that killed off mammoths and decimated early human populations — is under fresh attack. Independent archaeologists have reanalysed the dates of geological material that reportedly represents the impact, and found that they do not match.
Supporters of the impact theory have put forth 29 sites, from North America to Europe and beyond, that contain a thin layer of sediments said to date to the start of the cosmic impact event. The latest study checked to see whether those sites were all really 12,800 years old.
Only 3 of the 29 are, the researchers report today in the Proceedings of the National Academy of Sciences1. The other sites either have not been dated using the usual radiometric methods, or are much older or younger than the reported impact. “The chronology doesn’t hold up,” says team leader David Meltzer, an archaeologist at Southern Methodist University in Dallas, Texas.
There is no doubt that something important happened in this region around 12,800 years ago. Temperatures in the Northern Hemisphere plummeted in a cold spell known as the Younger Dryas, and sophisticated hunters known as the Clovis people vanished from what is now the western United States. Many of North America’s famous large mammals, such as mammoths, went extinct
Impact proponents say that many lines of evidence point to a cosmic object crashing into Earth at the time2. These include reported tiny diamonds formed in the high pressure of an impact, and soot and charcoal from fires possibly triggered by the smash. Opponents counter that there are other explanations for these materials, and that a comet blast should have left a huge fingerprint in the geological record — but nothing of the sort has been found.
Meltzer’s team includes experts on North American Palaeoindians. “We know some of these sites, we’ve worked at some of these sites,” he says. “When we started to read the details [of the impact theory], it just didn’t add up.”
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SMU is a nationally ranked private university in Dallas founded 100 years ago. Today, SMU enrolls nearly 11,000 students who benefit from the academic opportunities and international reach of seven degree-granting schools. For more information see www.smu.edu.
SMU has an uplink facility located on campus for live TV, radio, or online interviews. To speak with an SMU expert or book an SMU guest in the studio, call SMU News & Communications at 214-768-7650. | <urn:uuid:2cd5e691-1f9b-4888-bdde-b0fba1c776d2> | {
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The Storyteller, December 2017
“Thinking in Terms of Stories”: Drawing, Thinking, and Story-telling
“Children use drawing as a powerful tool for thinking. In different ways and at different rates, they develop a range of mark-making skills and strategies, and use drawing for various representational purposes in their quest to make sense of themselves and their world” (Kolbe, 2005).
Dear Families and Friends,
Children’s drawing happens in all of our spaces: the atelier, classroom, construction studio, atelier of taste, atelier of living organisms, outdoor studio deck, workshop, and the atelier of stories/dramatic play. According to development and to individual abilities, children’s skill in representing subjects varies a great deal, starting with ‘mark-making’ and eventually evolving into beautiful observational drawings and complex construction designs, for example.
It is important to acknowledge that the youngest children’s ‘mark-marking’ is a graphic language in which they express ideas, feelings and stories. Sometimes we call this work, “action drawing,” as children begin to narrate their movements as they draw: we hear stories about race cars on a race track, animal families and their homes, birthday parties—and much more! We observe a strong relationship between the action drawing and pretend play—as both serve a variety of purposes in supporting children’s developing interpretation and understanding of people, places, events and experiences in their world—and in action drawing, the mark-making and imaginative pretend play merge together.
We encourage children to use drawing as a way to explore and refine their thinking, as well. Asking children to draw their idea for a block building project, for example, requires that they focus carefully on their plan and examine it for its viability, presenting a cognitive challenge. Responsive drawing—or observational drawing– invites the artist to develop a relationship with the subject and demonstrate her thinking (and feeling) about its elements, refining understanding with effort and perseverance.
Currently, children in the Sunflower and Lavender classes are representing the seeds they have collected on their walks in the neighborhood and encountered in the atelier of taste. After small group and class discussions and sensory exploration, the children are using oil pastels on large black paper to show their understanding of the seeds—in the context of the living organisms. How does the environment of the atelier of living organisms play a role in children’s aesthetic research? What affect might music have on their drawings—and stories?
Last year, Sunflower teachers facilitated children’s use of stop motion video to animate their drawings and stories. This endeavor demanded a new understanding of perspective and detail. The children were delighted with both the process and the outcome!
The topic of children’s drawing is highly complex.
We are continually surprised at what we learn about children and about how they express their ideas, feelings and understandings through graphic language. Each school year the teachers and I select topics and readings for our own professional development. One of the wonderful resources we refer to and revisit with new colleagues is Ursula Kolbe’s book: It’s Not a Bird Yet: The drama of drawing (2005).
Not surprisingly, Kolbe makes many references to the work of Vea Vecchi, Reggio atelierista, and to materials as languages. Kolbe explains that each drawing material ‘speaks’ in a different way, adding new elements to ‘thinking’ according to the affordances of the material: crayon, fine-point markers, pencils, chalk, oil pastels, for example.
This beautiful and exciting Fall-to-Winter holiday season offers a multitude of subjects for children to represent and to elaborate through narration and story-telling. We are looking forward to their stories.
With warm wishes for a wonderful holidays,
The preschool will close on Friday, Dec. 8 for conferences between parents and teachers. Childcare will be provided by PPS staff members during the time of your conference. Teachers look forward to sharing authentic examples of children’s growth and development during the past few months as represented in microstories, small group stories, work samples and additional documentation included in children’s individual portfolios.
Our Reggio inspired approach directs us toward assessment that is contextual and oriented toward process and social constructivist learning theory. We also like to look for joy and beauty—while still keeping in mind kindergarten readiness skills, such as self-regulation and communication, that are part of a general disposition toward learning.
We realize that not all parents are able to have their conference on Friday, Dec. 8 and will offer a few morning and afternoon conferences on Monday and Tuesday, Dec. 11 and 12.
December Charity Initiatives
The Outreach Committee members will soon be collaborating on initiatives for our PPS community’s support this month. We will be collecting new, unwrapped toys for the Connections for Children Holiday Toy Drive, starting on Friday, Dec. 1. Also starting on Dec. 1, you will find large collection bins from the Westside Food Bank. Both outreach efforts will end on Wednesday, Dec. 13. Please look for flyers with more information.
Before closing for the holidays this month, the PPS Board of Trustees will meet to discuss tuition amounts for the 2018-2019 school year. Following tuition decisions, new tuition schedules and applications for returning and toddler families will be available this month. (Please note that toddler families are considered to be returning families with guaranteed admission.)
The applications will be due to Karen when we return in January. Karen will then create Admission Agreements for returning and toddler families to sign and submit with the June (2019) tuition payment by Jan. 30 (returning families) or the May and June (2019) tuition payments (new toddler families). Current Rosemary and Lavender families who are considering a third year of preschool for their child will need to make decisions in January. Nancy will be available for discussions with individual parents, seeking input from teachers, as well.
In early Feb. we will be able to see how many spaces we may have available for new families and, according to our agreement with a group of about 30 other preschools in our area, we will notify new families of admissions on Feb. 8, 2018.
Holiday Celebrations and Traditions
We invite you to share special family holiday traditions with the children and teachers in your child’s class. This might include special foods, recipes, stories, music or photos from your family album. We suggest that Hanukkah celebrations take place on Monday or Tuesday, Dec. 11 or 12, and Christmas celebrations be planned for Friday, Dec. 15. Please consult with teachers about times and share with them what you are planning to do for your celebration. Thank you.
On Thursday, December 14, Parker Bent will lead the children in singing a few holiday songs as part of our annual PPS holiday tradition. The Songfest is not really a performance–rather an informal holiday gathering that features the children and Parker.
The Cherry Blossom and Rosemary children will start the day in their classrooms at 8:45 while parents find seats in the Parish Hall. The CB/Rosemary Songfest is from 9:15 to 9:45, followed by refreshments.
The Lavender and Sunflower children will start the day as usual in their classrooms and join parents downstairs from about 10:15 to 10:45, also followed by refreshments.
- Friday, Dec. 1—Outreach Initiatives begin (Toy and Food Collections)
- Tuesday, Dec. 5—Tandy Parks mindful parenting meeting in Library at 9:15
- Wednesday, Dec. 6—Parent Tour #1 at 9:30
- Thursday, Dec. 7—Parent Tour #2 at 9:30
- Friday, Dec. 8—Parent Teacher Conferences—preschool closed
- Monday, Dec. 11 and Tuesday, Dec. 12—Hanukkah parties
- Wednesday, Dec. 13–Holiday puppet shows for children in Parish Hall at 9:30 & 10:30 (Franklin Haynes)
- Wed., Dec. 13—Outreach Initiatives end
- Thursday, Dec. 14—Songfests at 9:15 (CB/R) and 10:15 (Sun/Lav)
- Friday, Dec. 15—Christmas parties and closure for Winter Break–Early Dismissal (12, 12:15, 12:30 and 12:40)
- Dec. 18-Jan. 8–Preschool closed for Winter Break
January Calendar Notes
- Friday, Jan. 5—Professional development day
- Monday, Jan. 8–Faculty and staff return to prepare for reopening of preschool
- Tuesday, Jan. 9—Preschool reopens for all classes
- Friday, Jan. 12—Applications for 2018-2019 for returning and toddler families due
- Monday, Jan. 29—Admission Agreement and June 2018-19 tuition deposits due for returning and toddler families
Pictures from School Events | <urn:uuid:5cbb53f9-e3e9-4428-8ef2-1e7632607084> | {
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# How Do You Solve for the Number of Years in the Compound Interest Formula?
In another MathFAQ, I looked at how you can find the rate in the compound interest formula. Now let’s look at an example where we solve for the number of years n. This problem is different because what we are looking for appears in a power.
Problem Suppose 5000 dollars is deposited in an account that earns 2% compound interest that is done annually. In how many years will there be 6000 dollars in the account.
Solution This problem requires the use of the compound interest formula,
This formula applies when interest is earned on an annual basis and the interest is earned once a year.
Let’s look at the quantities in the problem statement:
• \$5000 is deposited in an account > P = 5000
• that earns 2% compound interest that is done annually > r = 0.02
• Will there be \$6000 in the account > A = 6000
Putting these values into the formula above gives us
Unlike other problems where we solve for P or r, here we need to solve for the power in the right hand side, n. Solving for a value in the power requires the property of logarithms, log(yx) = x logy. It allows us to move the n in the power and change it to a multiplier. But before we can apply this property, we isolate the factor containing the n:
Now take the logarithm of both sides of the equation:
This gives us
or n ≈ 9.21 years.
In WolframAlpha, we could evaluate the logs as follows. | crawl-data/CC-MAIN-2024-33/segments/1722640454712.22/warc/CC-MAIN-20240805180114-20240805210114-00299.warc.gz | null |
The proximity fuze is a type of artillery or mine warfare fuze. In the best-known Second World War application, it comprises a radio installed in the nose of an artillery or missile warhead that detects an enemy plane, or the ground, and explodes at exactly the right time.
Before radio proximity fuzes, there were initially electromechanical magnetic influence mines used against ships.
Second World War
It replaced the manual timer that usually fired too soon or too late. In ground action, a shell that exploded too high above the ground does less damage, and one that explodes after it hits the ground has its impact absorbed by the dirt.
The British had invented the fuze in 1940 but lacked the massive industrial capacity needed to produce it in quantity, so shared the blueprints with civilian researchers at Johns Hopkins University under contract to the U.S. Navy. Utilization of the Doppler effect of reflected radio waves was the most promising concept, so researchers devised a diode detector arrangement that acted when the amplitude of the reflected signals exceeded a predetermined value. The basic components were a vacuum tube (six inches long and three inches in diameter) a battery, and a radio transmitter and receiver, all of which have to be rugged enough to withstand 20,000 Gs when shot out of a gun at high velocity. After the shell is fired and begins rotating, a chemical reaction produces an electrical charge which in turn arms the shell and sends out a radio impulse. The return signal, reflected from the target, detonates the shell prior to impact and produces the devastating effects.
Naval anti-aircraft gunnery was a trade off between the typical 5"-38 caliber gun , with their long range, and 20mm Oerlikon (and other) and 40mm Bofors short-range guns with a high rate of fire. The breakthrough came in 1943 with the introduction of the proximity fuze (or "variable time (VT) fuze") in 5" shells. It had a radio and receiver and when a signal bounced back, it was in range and exploded. The effect was to make the target 50 times bigger and thus much easier to hit. The fuzes played a decisive role in defeating the Japanese Kamikaze attacks of 1944-45.
The fuzes were used in land-based artillery in the South Pacific in 1944. They were incorporated into bombs dropped by the U.S. Air Force on Japan in 1945, and they were used to defend Britain against the V-1 attacks of 1944, achieving a kill ratio of about 79%. (They were ineffective against the much faster V-2 missiles.) There was no risk of a dud falling into enemy hands. The Pentagon decided it was too dangerous to have a fuze fall into German hands because they might reverse engineer it and create a weapon that would destroy the Allied bombers, or at least find a way to jam the radio signals. Therefore they refused to allow the Allied artillery use of the fuzes in 1944. The Germans started research in 1930 but never invented a working device. General Dwight D. Eisenhower protested vehemently and demanded he be allowed to use the fuzes. He prevailed and the VT fuzes were first used in the Battle of the Bulge in December 1944, when they made the Allied artillery far more devastating, as all the shells now exploded just before hitting the ground.
By 1944 a large proportion of the American electronics industry concentrated on making the fuzes. Procurement contracts increased from $60 million in 1942, to $200 million in 1943, to $300 million in 1944 and were topped by $450 million in 1945. As volume increased, efficiency came into play and the cost per fuze fell from $732 in 1942 to $18 in 1945. This permitted the purchase of over 22 million fuzes for approximately $1,010 million. The main suppliers were Crosley, RCA, Eastman Kodak, McQuay-Norris and Sylvania.
Current airbursting proximity fuzes use solid-state electronic components, radar rather than simple signal strength, and computer control. They are hardened against electronic countermeasures that could cause predetonation or failure to detonate.
Electronic miniaturization allows their use in much smaller calibers, certainly in 40mm. Mortars in the 80-120mm range began to use both proximity fuzes as well as computer-controlled aerodynamic guidance fins. They are common for howitzer warheads, although other fuzing arrangements are used when surface or subsurface detonation is desired.
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# A chord of circle of radius 12 cm subtends an angle of 120 at centre.Find the area of the segment of circle.plz show the answer in 2 ways: one if we dont know the value of sin 120 ,two we know the value.
Ravi
9 years ago
If the angle subtend at the centre by the chord is 120, the area of the segment will be area of the sector – area of the triangle subtend at the centre.
Area of sector= pi(r)2. (120/360)
Area of triangle= 1/2r2 SinA. where A is the centre. So, A=120
OR
Area of triangle ABC(where A is the centre, b and C lie on the circle)
So, a perpendicular AD dropped from A on BC will bisect it. So, in rt angled triangle ADC, Sin C= Sin 30= AD/ AC
So, AD= AC sin 30= r/2
And similarily, DC= AC cos 30= r.
Use the dimensions of the three sides of both the right angled triangles to find the area of triangle ABC.(using Heron’s formula or Area= ½ b*h) | crawl-data/CC-MAIN-2024-30/segments/1720763514745.49/warc/CC-MAIN-20240716111515-20240716141515-00872.warc.gz | null |
To calculate the inverse, one has to find out the determinant and adjoint of that given matrix. And if you know that it's a rotation, computing the transpose is much faster than computing the inverse, and in this case, they're equivalent.
Inverse Matrices 81 2.5 Inverse Matrices Suppose A is a square matrix. ... How to find a 4x4 invertible Matrix and a 4x4 real diagonal matrix? A good algorithm by hand to find the inverse of an $n\times n$ square matrix $A$ is to write the $n\times n$ identity matrix next to $A$ and row reduce the $n\times 2n$ matrix. The inverse of a square n x n matrix A, is another n x n matrix, denoted as A-1.
4x4 matrix inverse calculator The calculator given in this section can be used to find inverse of a 4x4 matrix. But A 1 might not exist. Answer There are mainly two ways to obtain the inverse matrix. 4x4 Matrix Inverse calculator to find the inverse of a 4x4 matrix input values.
Invertible 4x4 matrix. Active 2 years, ... {vmatrix}=680-816+192-64=-8\neq0 so your matrix has an inverse. Inverse of a matrix is an important operation in the case of a square matrix. 4x4 Matrix Inverse Calculator . It is applicable only for a square matrix. Even if you do need to store the matrix inverse, you can use the fact that it's affine to reduce the work computing the inverse, since you only need to invert a 3x3 matrix instead of 4x4. We look for an “inverse matrix” A 1 of the same size, such that A 1 times A equals I. 4x4 matrix inverse calculator The calculator given in this section can be used to find inverse of a 4x4 matrix. As a result you will get the inverse calculated on the right. In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that = = where I n denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A −1. It is a matrix when multiplied by the original matrix yields the identity matrix. It does not give only the inverse of a 4x4 matrix and also it gives the determinant and adjoint of the 4x4 matrix that you enter. The matrix has four rows and columns. Hot Network Questions One is to use Gauss-Jordan elimination and the other is to use the adjugate matrix. How to find the inverse matrix of a 4x4 matrix Last updated: Nov. 3, 2017 Find the inverse of , where $|A|\neq 0$. Adjoint is given by the transpose of cofactor of the particular matrix.
Whatever A does, A 1 undoes. Even if you do need to store the matrix inverse, you can use the fact that it's affine to reduce the work computing the inverse, since you only need to invert a 3x3 matrix instead of 4x4. It does not give only the inverse of a 4x4 matrix and also it gives the determinant and adjoint of the 4x4 matrix that you enter. Finding the inverse of a 4x4 matrix A is a matter of creating a new matrix B using row operations such that the identity matrix is formed.
Reduce the left matrix to row echelon form using elementary row operations for the whole matrix (including the right one). The formula to find out the inverse of a matrix is given as, 2.5. Ask Question Asked 2 years, 5 months ago. And if you know that it's a rotation, computing the transpose is much faster than computing the inverse, and in this case, they're equivalent.
Their product is the identity matrix—which does nothing to a vector, so A 1Ax D x. We employ the latter, here. The inverse of a 2x2 is easy... compared to larger matrices (such as a 3x3, 4x4, etc). For those larger matrices there are three main methods to work out the inverse: Inverse of a Matrix using Elementary Row Operations (Gauss-Jordan) Inverse of a Matrix using Minors, Cofactors and Adjugate; Use a computer (such as the Matrix Calculator) Conclusion If a determinant of the main matrix is zero, inverse doesn't exist. Set the matrix (must be square) and append the identity matrix of the same dimension to it. | crawl-data/CC-MAIN-2021-04/segments/1610703581888.64/warc/CC-MAIN-20210125123120-20210125153120-00442.warc.gz | null |
Eagle Owls began a new Science topic in the autumn half term: circuits. They were fortunate to have a Mad Science presentation all about electricity to spark their interest, followed by a visit from Mr Canning (an electrician) in one of their lessons. He explained how electricians work all around the world in many different places; what his job entails; and how he became an electrician. He also helped the children to follow circuit diagrams and build accurate circuits, this resulted in some of the children discovering parallel circuits for themselves!
In their cross curricular work, the class made light-up Christmas cards, building their own circuits and designing their own cards. They discovered LED bulbs have positive and negative leads, so need to be connected to the battery correctly. They also had to think about a card design that incorporated the lit bulb successfully! Their sketchbook pages show how carefully they thought this through. Well done Eagle Owls! | <urn:uuid:d61554f9-3e29-4612-810e-932974c8c7d5> | {
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A group of researchers at University College Cork have made a “remarkable” discovery about pterosaurs, the flying relatives of dinosaurs.
The international team of paleontologists discovered that pterosaurs were able to control the color of their feathers using melanin pigments.
An international team of palaeontologists - led by UCC's Dr Aude Cincotta and Prof. Maria McNamara - has discovered new evidence that pterosaurs, the flying relatives of dinosaurs, were able to control the colour of their feathers using melanin pigments. https://t.co/8aeMSO25Ki pic.twitter.com/StJMtP124u— UCC Ireland (@UCC) April 20, 2022
The team’s research, entitled “Pterosaur melanosomes support signalling functions for early feathers,” was published in the prestigious journal Nature on April 20.
The study was led by University College Cork (UCC) paleontologists Dr. Aude Cincotta (UCC & Royal Belgian Institute of Natural Sciences) and Prof. Maria McNamara and Dr. Pascal Godefroit from the Royal Belgian Institute of Natural Sciences, with an international team of scientists from Brazil and Belgium.
Dinosaurs were not the only animals with coloured feathers - visual signalling not just thermoregulation drove early feather evolution @uccBEES @UCCSEFS @UCCResearch @iCRAGcentre https://t.co/vxirDPcoSe— Maria McNamara (@MariaMcN_palaeo) April 20, 2022
The new study is based on analyses of a new 115 million-year-old fossilized headcrest of the pterosaur Tupandactylus imperator from north-eastern Brazil. Pterosaurs lived side by side with dinosaurs, 230 to 66 million years ago.
This species of pterosaur is famous for its bizarre huge headcrest. The team discovered that the bottom of the crest had a fuzzy rim of feathers, with short wiry hair-like feathers and fluffy branched feathers.
“We didn’t expect to see this at all”, said Dr. Cincotta. “For decades, paleontologists have argued about whether pterosaurs had feathers. The feathers in our specimen close off that debate for good as they are very clearly branched all the way along their length, just like birds today."
The team then studied the feathers with high-powered electron microscopes and found preserved melanosomes – granules of the pigment melanin.
Unexpectedly, the new study shows that the melanosomes in different feather types have different shapes.
“In birds today, feather color is strongly linked to melanosome shape,” Prof. McNamara said.
“Since the pterosaur feather types had different melanosome shapes, these animals must have had the genetic machinery to control the colors of their feathers. This feature is essential for color patterning and shows that coloration was a critical feature of even the very earliest feathers.”
Thanks to the collective efforts of the Belgian and Brazilian scientists and authorities working with a private donor, the remarkable specimen has been repatriated to Brazil.
“It is so important that scientifically important fossils such as this are returned to their countries of origin and safely conserved for posterity,” said Dr. Godefroit.
“These fossils can then be made available to scientists for further study and can inspire future generations of scientists through public exhibitions that celebrate our natural heritage." | <urn:uuid:2988336a-4eb8-47ec-93b0-c542ea6a3427> | {
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# Displacement to Torque Calculator, Formula, D to T Calculation
## Displacement to Torque Calculator:
Enter the values of work done, W(J), radius, r(m) and displacement, d(m) to determine the value of displacement to torque, T(N.m).
Enter Workdone: J Enter Radius: m Enter Displacement: m Result – Displacement to Torque: N.m
## Displacement to Torque Calculator:
Displacement to torque refers to the conversion of linear force applied over a distance (displacement) into rotational force (torque) around a pivot point.
Displacement to torque, T(N.m) in Newton metres is equated by dividing the product of work done, W(J) in joules and radius, r(m) in metres by displacement, d(m) in metres.
Displacement to torque, T(N.m) = W(J) * r(m) / d(m)
T(N.m) = displacement to torque in Newton metres, N.m.
W(J) = workdone in joules, J.
r(m) = radius in metres, m.
(m) = displacement in metres, m.
## Displacement to Torque Calculation:
1. If a force of 100 N is applied to move an object 2 metres, and this force is applied at the end of a lever 0.5 metres long, calculate the torque produced at the pivot point of the lever.
Given: F(N) = 100N, d(m) = 2m, r(m) = 0.5m.
First, calculate the work done: W(J) = F(N) * d(m) = 100 * 2 = 200J
Displacement to torque, T(N.m) = W(J) * r(m) / d(m)
T(N.m) = 200 * 0.5 / 2
T(N.m) = 50N.m.
2. Consider a scenario where 500 Joules of work is required to move a gate. The displacement of the handle along its arc is 3 meters and the torque applied at the hinge to move the gate is 166.67N.m. Determine the force is applied via a handle away from the hinge (pivot point).
Given: W(J) = 500J, d(m) = 3m, T(N.m) = 166.67N.m.
Displacement to torque, T(N.m) = W(J) * r(m) / d(m)
r(m) = T(N.m) * d(m) / W(J)
r(m) = 166.67 * 3 / 500
r(m) = 1m. | crawl-data/CC-MAIN-2024-33/segments/1722640767846.53/warc/CC-MAIN-20240809142005-20240809172005-00784.warc.gz | null |
Lessons Print Article
Lesson One: A Biblical Introduction to Mary
1. To understand the basic outlines of the New Testament’s witness to Mary.
2. To appreciate how the Old Testament forms the essential background for what the New Testament teaches about Mary.
3. To understand “typology” and its importance for reading the New Testament texts concerning Mary.
- From Scripture to Creed
- Reading Mary in Matthew
- Reading Mary in Luke
- Reading Like Jesus
- Discussion Questions
I. From Scripture to Creed
A. Mary of the New Testament
What the New Testament has to say about Mary fills only a few verses.
She is the focus of several passages in the Gospels and is referred to once in the Acts of the Apostles.
The Scriptures do depict Mary at every stage in her Son’s life - at His conception and birth; during His childhood; at the start of His ministry, at the foot of the Cross, and following His Resurrection and Ascension.
But in most of these cases, Mary’s presence amounts to little more than a mention.
Basically, this is what we learn from the Scriptures:
An angel announced that Mary would bear Jesus through the power of the Holy Spirit (see Luke 1:26-38). While pregnant with Him, she paid a long visit to her relative, Elizabeth (see Luke 1:39-56).
She bore Jesus in Bethlehem (see Matthew 1:18-25) and was by His crib as magi (see Matthew 2:11) and shepherds (see Luke 2:15-20) paid Him homage. Under threat of danger, she fled with her newborn and Joseph, her husband, into Egypt (see Matthew 2:14).
Mary presented Jesus in the Temple (see Luke 2:23,33-35), and later, when He was twelve, found Him there teaching (see Luke 2:48-51).
Mary was at the wedding in Cana where Jesus performed His first miracle (see John 2:1-11). She was there, too, at Nazareth when He was rejected by His own people (see Matthew 13:54-58; Mark 6:1-6).
She watched Him die on the Cross (see John 19:25-28), and was among those gathered with the Apostles in Jerusalem awaiting Pentecost and the sending of the Holy Spirit (see Acts 1:14).
There are also a few indirect mentions of Mary in the New Testament. An anonymous woman cries out to Jesus: "Blessed is the womb that carried you" (see Luke 11:27-28). Paul mentions her but not by name (see Galatians 4:4). And she is apparently the woman depicted in a fantastic vision in the Bible’s last book (see Revelation 11:19-12:18).
B. Mary of Doctrine and Devotion
Even counting indirect mentions, Mary is referred to just fourteen times in the New Testament. That’s far less than some of the Apostles - certainly less than Peter, who is mentioned about 155 times.
How then did she come to be one of only two people mentioned by name in the Apostles’ Creed ("...born of the Virgin Mary")? How did she come to inspire some of the Church’s earliest liturgies and prayers, as well as some of its most controversial and misunderstood dogmas?
These questions have long been sticking points for many Christians, who can find no basis in Scripture for what Catholics believe and pray about Mary.
At best, they look upon our Marian beliefs and devotions as products of a pious but misguided imagination. At worst, they call it "Mariolatry" - a false worship that undermines the perfect saving work of Christ and robs Him of His glory.
Unfortunately, many devout Catholics would be equally hard-pressed to explain the connection between the Mary of the Bible and the Mary of Catholic doctrine and devotion.
That’s why this course is important.
We’re going to discover that when it comes to Mary, there’s far more to Scripture than what first meets the eye. We’ll see why prayers such as the "Hail Mary" are composed largely of biblical words, and see how the Church’s Marian dogmas and doctrines are definitive interpretations of Scriptures concerning Mary.
In fact, through close study of the Bible, we’re going to find the seeds not only for Catholic devotions such as the Rosary, but for dogmas and doctrines such as Mary’s Immaculate Conception, her Assumption, and her crowning as Queen of Heaven.
Catholic devotion to Mary, rooted in the biblical witness of Christ’s first followers, is far from blasphemy or idolatry. At the end of this course, you may wonder whether it is blasphemy not to honor Mary - as God’s most perfect work, the human person who most truly conforms to the image of God (see Genesis 1:27; Romans 8:29; 1 Corinthians 15:49).
To appreciate the connections between the Mary of Scripture and the Mary of doctrine and devotion, we need to learn how to read the Scriptures as they were written. When we do, we’ll discover that, though the biblical data is scant, it is rich in divine meaning.
II. Reading Mary in Matthew
A. Of Her Was Born. . .
Consider this a "reading lesson." We’re going to learn how to read from the New Testament writers themselves. We want to start by simply understanding the "literal" or literary sense of these texts - what the words on the page tell us about Mary.
Mary’s first appearance in the New Testament comes in its very first chapter - at the end of the long genealogy that begins the New Testament.
She is introduced as: "Mary. Of her was born Jesus who is called the Messiah" (see Matthew 1:16).
We have to read these words in context. These are the final words of a list of descendants Matthew has drawn up to demonstrate that Jesus is "Christ, the son of David, the son of Abraham" (see Matthew 1:1).
To understand the literal meaning of this text about Mary, then, we have to know some background about the Christ, and about David and Abraham.
Abraham was the founding father of God’s chosen people, Israel. God made a covenant with him, promising that through his descendants "all the nations of the earth shall find blessing" (see Genesis 22:18).
God promised Abraham that kings would stem from his line (see Genesis 17:6) and later swore an oath to Israel’s King David - that his kingdom would have no end, that David’s son would be His son and would reign forever, not only over Israel but over all the nations (see 2 Samuel 7:12-13; Psalm 89:27-28; Psalm 132:4-5; 11-12).
But David’s kingdom crumbled and the people were dispersed into exile (see Matthew 1:11; 2 Kings 24:14).
From that time forward, Israel’s prophets taught them to hope for a "Christ" (or "Messiah" in Hebrew). He was expected to be the son of God promised to David, who would liberate Israel’s scattered tribes and reunite them in a new and everlasting kingdom that would be a light to the nations (see Isaiah 9:5-6; 49:6; 55:3; Ezekiel 34:23-25,30; 37:25).
Read in context, then, the few words that Matthew gives us about Mary are no trifling matter.
In this short sentence, Matthew has effectively positioned Mary at the center of Israel’s history - the history of God’s chosen people. Of her was born the Christ through whom God would fulfill His covenant promises to Abraham and David.
As mother of the royal Messiah of Israel, Mary is also necessarily at the center of human history. For the fruit of her womb will be the source of the world’s salvation. Through Christ, born of Mary, God will bestow His divine blessings upon all nations and peoples.
B. . . .Through the Holy Spirit
Matthew continues this theme in the verses that follow, as he describes how Mary was "found with child through the Holy Spirit" (see Matthew 1:18-25).
He tells us that Mary’s conception by the Spirit fulfills a promise God made through the prophet Isaiah - that a virgin would bear a son who would be called Emmanuel, which means, "God is with us" (see Matthew 1:18,22-23; Isaiah 7:14).
This was an obscure prophecy. Nobody that we know of at the time of Jesus believed it had anything to do with the coming Messiah. Some rabbis said the prophecy had been fulfilled in Isaiah’s lifetime - when King Hezekiah was born.
Hezekiah was indeed a mighty reformer who "pleased the Lord, just as his forefather David had done." In addition, Scripture tells us, "the Lord was with him" (see 2 Kings 18:1-7; 2 Chronicles 29-32).
But Matthew seems to be telling us that Hezekiah was at best only a partial and imperfect fulfillment of Isaiah’s prophecy. Its perfect fulfillment awaited the Spirit’s conception of Jesus in Mary’s womb.
Mary is "she who is to give birth," as Malachi foretold in a prophecy Matthew will later quote (see Micah 5:1-2; Matthew 2:6). Through Mary, mother of the long-awaited Messiah, "God is with us."
Again, to understand the literal meaning of this passage, we have to understand the deep Old Testament context that Matthew assumes.
Matthew expects that his readers will hear in these words the promise that echoes throughout salvation history - the promise of the divine presence, that God will one day come to dwell with His people (see Isaiah 43:5; Zechariah 8:23; 2 Corinthians 6:16-18).
This was one of the great messianic hopes stirred by the prophets. Ezekiel, for one, prophesied a new King David and an "everlasting covenant" by which God would promise: "My dwelling shall be with them; I will be their God, and they shall be My people" (see Ezekiel 37:24-28; Revelation 21:3).
And we hear echoes of Isaiah’s Emmanuel prophecy throughout Matthew’s Gospel. Jesus repeatedly describes how He will be "with us" for all time, especially in the Eucharist (see Matthew 18:20, 25:40,45; 26:26-28). His last words resound with the promise: "I am with you always, until the end of the age" (see Matthew 28:20).
Matthew’s reference to Mary as the Virgin prophesied by Emmanuel once more places her at the center of God’s saving plan - for Israel and for the world.
The literal meaning of this text is that Mary is the divine "sign" that long ago God promised to give - the sign of His faithfulness to His eternal covenant with David, the sign that He has come to fulfill His purposes for all creation.
III. Reading Mary in Luke
A. The Lord Is With You
We turn now to Luke’s Gospel.
We want to look closely at his account of the Annunciation (see Luke 1:26-38). Here again we simply want to read the literal text in its literary context. As it is written, we want to know what this passage tells us about Mary.
Luke, like Matthew, introduces Mary as a virgin betrothed to Joseph, a descendant of David. She is greeted by the angel Gabriel: "Hail, favored one, the Lord is with you."
The angel uses a word - variously translated hail or rejoice - that the prophets used to foretell the joy of the people at the Messiah’s coming (see Joel 2:23-24; Zechariah 9:9).
In fact, the angel’s announcement seems to be drawn almost word-for-word from a prophecy of Zephaniah (see Zephaniah 3:14-18)
Luke 1 Zephaniah 3
Hail, Shout for joy,
favored one! O daughter Zion! .
The Lord The King of Israel, the Lord
is with you…. is in your midst…
Do not be afraid, Mary Fear not, O Zion…
You will conceive in your womb Your God is in your midst,
...[the] Son of the Most High a mighty savior
Luke seems to be depicting Mary as Daughter Zion - the representative of her people - called to rejoice that God, as her Savior and King, has come into her midst.
As in Matthew, then, we see the historic hopes of Israel focused in the person of Mary. The words the prophets taught Israel to long to hear - "Say to daughter Zion, your Savior comes!" (see Isaiah 62:11) - are heard now by Mary.
The angel also tells Mary that her Son will be "Son of the Most High" and will be given "the throne of David His father."
For the literal meaning of this passage, we have to return to the Old Testament background of God’s covenant with David
In fact, in the angel’s words we hear echoes of God’s covenant with David (see 2 Samuel 7:12-16; Psalm 89:4-5; 27-30).
God swore that David’s son would be "a son to Me." And the angel promises that Mary’s child will be "Son of the Most High" - another way of saying "Son of God" (see Mark 5:7; Luke 1:35; 8:28).
God swore that David’s son would rule on his throne forever. The angel promises that Mary’s Son will be seated on "the throne of David his father…forever."
Mary is shown here to be the "sign" that Jesus is the long-awaited Messiah from David’s dynastic line.
B. Handmaid of the Lord
We’ll focus on other elements of Luke’s Annunciation story in future lessons. For now, let’s jump ahead to the conclusion of Luke’s account.
Mary has asked how she, as a virgin, will conceive the child promised by the angel. The angel replies: "For nothing will be impossible for God" (see Luke 1:37). These words, too, are freighted with Old Testament meaning.
An angel spoke almost these same words to Abraham’s wife, Sarah, when she laughed at the notion that in her old age she would bear the son that God had promised to Abraham (see Genesis 18:14).
Luke appears to be showing us that Mary, too, is being called to bear the son of God’s covenant promise.
In fact, through a close reading of Luke’s Annunciation story, we can hear echoes of a number of miraculous births in the salvation history.
In addition to the birth of Isaac to Sarah, we can hear echoes of Rebekah’s conception of Jacob and Esau (see Genesis 25:21-22); Rachel’s conception of Joseph (see Genesis 29:31; 30:22-24); and Manoah’s wife’s conception of Samson (see Judges 13:2-7).
Mary’s response to the angel takes up the story of still another barren woman who found favor with God - Hannah the mother of Samuel (see 1 Samuel 1:11, 19-20).
In presenting herself as "the handmaid of the Lord," she recalls the oath of Hannah - who pleaded with God for a son, vowing to consecrate him to the Lord.
Three times Hannah described herself as the Lord’s "handmaid" (see 1 Samuel 1:11,16,18).
Made a gift to the Lord by his grateful mother (see 1 Samuel 1:11,22; 2:20), Samuel became a holy and righteous priest and prophet, chosen by God to anoint David as King.
In describing herself as the Lord’s handmaid, Mary too is vowing to dedicate her child to God. Her child, too, will be a holy prophet and priest, anointed to be a Davidic king.
IV. Reading Like Jesus
A. Literal, Historical, Divine
What do we learn from our literary reading of these Marian texts from Matthew and Luke?
First, the literary reading gives us knowledge of an historical truth - the birth of Jesus through the Holy Spirit to a virgin named Mary.
This historical truth at the same time conveys to us a divine meaning.
That is to say: the historical events, and the manner in which these events are written about, communicate far more than factual information. They reveal the existence of a plan of salvation that God is working out in human history.
Matthew and Luke’s accounts assume the existence of a divine economy, in which the covenant oaths God swore to Abraham and David centuries earlier are meant to find their ultimate fulfillment in the future coming of Christ.
Indeed, Matthew and Luke seem to envision a sort of golden thread connecting the events, figures and institutions of the Old Testament with those of their New Testament.
The reason for the evangelists’ careful use of quotes and allusions to Israel’s past is to reveal that unity between the Old and New Testaments - to show how what happens to Mary is a continuation and culmination of what has gone before.
B. Typology and Mary
This way of reading and writing is broadly known as typology. And typology is critical to understanding what the Bible has to say about Mary.
Typology is the way Jesus taught the Apostles to read the Old Testament.
He referred to Jonah (see Matthew 12:39-41), Solomon (see Matthew 12:42), the Temple (see John 2:19) and the brazen serpent (see John 3:14) as "types" or "signs" that prefigured Him.
On the first Easter night He said that, "Everything written about Me in the Law of Moses, and in the prophets and psalms must be fulfilled" (see Luke 24:44-45).
What He showed them was that the persons, places, things and events of the Old Testament were written to prepare us for Him.
Jesus and the Apostles were already familiar with this way of reading from the Old Testament and the liturgical readings they heard in the synagogue. In the writings of the prophets and psalmists, often we find typological readings of earlier events, deployed to prepare Israel for its coming savior.
Isaiah spoke of a new creation (see Isaiah 65:17) and a new exodus (see Isaiah 11:10-11,15-16; 43:16-22; 51:9-11).
He and others, notably Ezekiel and Jeremiah, spoke of the coming of a new Davidic shepherd-king and the restoration of the kingdom (see Isaiah 9:1-7; Jeremiah 23:5-6; Ezekiel 16:59-63; 34:24-30; 37:23-28).
The New Testament writers saw each these great "types" - creation, the exodus and the covenant-kingdom of David - gloriously reprised in the New Covenant of Jesus.
Jesus was the New Adam, the first born of a new creation (see Romans 5:14; 1 Corinthians 15:21-22; 45-49). His Cross and Resurrection mark a new exodus (see Luke 9:31; 1 Corinthians 10:1-4). His Church is the new Jerusalem and the new Kingdom of David (see Galatians 4:26; Acts 1:6-9; 1 Peter 2:9; Revelation 1:6).
As we will see in the lessons ahead, the New Testament writers also developed a typological understanding of Mary’s role in salvation history - as the new Eve, the new Ark of the Covenant, and the new Queen Mother of the Kingdom of God.
What we will find is that Mary is depicted as mysteriously inseparable from the saving mission of her Son. We see this already in Matthew’s repetition of the phrase "the Child and His mother" (see Matthew 1:18; 2:11;13,14,20,21).
This is how Mary is portrayed in one of the earliest biblical confessions of the faith: "When the fullness of time had come, God sent His Son, born of a woman, born under the Law to ransom those under the Law, so that we might receive adoption" (see Galatians 4:4-5).
What the New Testament has to say about Mary fills only a few verses. But it tells us all we need to know: Mary was made holy, destined from all eternity to give the Word flesh, to bear God’s only begotten Son, and to be crowned mother over all who enter into His kingdom.
V. Discussion Questions
• Where in the New Testament is Mary depicted at her Son’s conception? His birth? At the start of His ministry? After His Resurrection?
• How does Matthew position Mary at the center of Israel’s history? At the center of human history?
• How does Luke portray Mary as "Daughter Zion"? What Old Testament mother does Mary recall in declaring herself the "Handmaid of the Lord"?
• What biblical covenant does Luke’s Annunciation account refer to?
• What is typology? What are the origins of typological reading of the Bible?
For personal reflection
• In your own prayer and devotion, do you hold Mary to be most blessed among women? Are you honoring the New Testament prophecy that all ages shall call Mary blessed (see Luke 1:42,46; 11:27-28)? | <urn:uuid:7cc8bbbd-444d-4d84-bd39-e2ef7b643063> | {
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Jumbo die are used in this doubles lesson
Subject:
Math
1
Title – Doubling Numbers
By – Molly Vazquez
Primary Subject – Math
Concept – Double numbers from 1 to 10. Use familiar doubles to figure out other doubles. Language – add, addition, double.
Materials –
For student – jumbo die, paper, pencil, counters if needed.
For teacher – white board, marker.
Procedures –
1 – Review Doubles. Ask the students what is a double and what doubles do they know. Write these on the white board.
2 – Have a student roll the jumbo die and tell the class what number appears.
3 – Have the students write this number down on their paper, double it and write the sum (Example – 4+4=8). They may use counters if needed.
4 – Continue having students roll the die and create doubles. Compile doubles from 1 to 10 on white board.
5 – Discuss what might be an easy way to use doubles they know to figure out other numbers. (Example – Double 5 is 10, what is double 6? Because 6 is one more than 5, double 1 is 2. 10+2=12.)
6 – Have children identify doubles they know to figure out other doubles.
7 – Have the children write the addition sentences.
8 – Review the concept.
E-Mail Molly Vazquez ! | crawl-data/CC-MAIN-2016-07/segments/1454701165697.9/warc/CC-MAIN-20160205193925-00310-ip-10-236-182-209.ec2.internal.warc.gz | null |
At its height (250-900 AD), the Mayan Empire was one of the most densely populated and culturally dynamic societies in the world. The city of Copan alone contained more than 6,000 structures spanning over 27 square miles, and was just one of many great Mayan urban centers spread across present-day Mexico, Honduras and Guatemala.
However, by the 10th Century these ancient cities were being strangely and suddenly depopulated, leading to the complete collapse of the Mayan civilization. The reason for this collapse remains one of the biggest mysteries in archaeology, but ZRS Researcher and Historian, Eugene Fredrick, now suggests a compelling explanation for the extinction: zombies.
Fredrick notes that all other prevailing theories – disease, famine, war, revolt – fail to account for the notable lack of buried human remains. In any traditional mass-casualty scenario an abundance of archeological evidence is left behind, including grave sites.
“The ghost towns of Maya house precious few such sites, echoing a panic so great, an extermination so fast, that this once proud people – steeped in tradition and ritual – had no choice but to leave their dead where they fell.”
He goes on to site reports of widespread cannibalism at the end of the Mayan civilization, suggesting something much more sinister than a simple drought or cross-tribal dispute. Bones found in and around Mayan cities show signs of being violently ripped from their sockets, and chewed to bits on the spot. Evidence has even been found of children eating their parents, and entire villages devouring themselves within a matter of days.
Though Fredrick’s theory is a bold one, it can no more be confirmed or denied than any other. As of today, there is still no generally accepted explanation for why one of the most culturally advanced civilizations on the planet was wiped out in an impossibly short span of time. Was it the first zombie apocalypse, or even just one in a long string of unrecognized outbreaks throughout human history? No one knows for sure.
What do you think? | <urn:uuid:3a735dd2-5b7c-46a5-904f-cb61e64b44f8> | {
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There is huge potential in solar power. The sun is a giant ball of burning hydrogen in the sky, and it’s going to be sticking around for at least a few more billion years. For all intents and purposes, it’s a free source of energy. Sadly, humanity hasn’t been very good at harnessing its power directly. Our current methods of capturing the sun’s energy are very inefficient. For example, modern silicon and indium-tin-oxide-based solar cells are approaching the theoretical limit of 33.7% efficiency. Well, a research team at Princeton has used nanotechnology to create a mesh that increases efficiency over organic solar cells nearly three fold.
Led by Stephen Chou, the team has made two dramatic improvements: reducing reflectivity, and more effectively capturing the light that isn’t reflected. As you can see by the illustration below by Dimitri Karetnikov, Princeton’s new solar cell is much thinner and less reflective. By utilizing sandwiched plastic and metal with the nanomesh, this so-called “Plasmonic Cavity with Subwavelength Hole array” or “PlaCSH” substantially reduces the potential for losing the light itself. In fact, it only reflects about 4% of direct sunlight, leading to a 52% higher efficiency than conventional, organic solar cells.
PlaCSH is also capable of capturing a large amount of sunlight even when the sunlight is dispersed on cloudy days, which results in an amazing 81% increase in efficiency under indirect lighting conditions when compared to conventional organic solar cell technology. All told, PlaCSH is up to 175% more efficient than conventional solar cells. As you can see in the image to the right, the difference in reflectivity between conventional and PlaCSH solar cells is really quite dramatic.
The gold mesh that sits on top is incredibly small. It’s only 30 nanometers thick. The holes in the mesh are a mere 175nm in diameter. This replaces the much thicker traditional top layer made out of indium-tin-oxide (ITO). This is the most important part of the innovation. Because the mesh is actually smaller than the wavelength of the light it’s trying to collect, it exploits the bizarre way that light works in subwavelength structures. This unique physical property allows the researchers to effectively capture the light once it enters the holes in the mesh instead of letting much of it reflect away. The bottom layer of the cell remains the same, but this implementation allows the semiconducting layer of plastic in the middle of the cell to be much thinner.
The research team believes that the cells can be made cost effectively using a nanofabrication method that Chou himself invented over a decade ago. Most importantly, it replaces the costly ITO element from solar cells. This will be affordable, and much more flexible than the brittle ITO layer of traditional solar cells. While research is still being done using semiconducting materials other than plastic, this method should work for silicon and gallium arsenide solar cells as well, so it will be able to reduce the size and cost of them drastically while providing similar efficiency benefits.
This is all very new, and the information was only published to the internet in the past few weeks, but this technology has the potential to make solar power a financially sound investment for more people. Not only will we be able to generate more power, but it will use less resources to make the cells. We’ll obviously still be using fossil fuels for decades to come, but this research and other breakthroughs like it are accelerating the rate at which we can move to alternate energy sources. (Which is probably a good thing, considering star-encompassing Dyson spheres are still a few years away from becoming a reality…)
Research paper: http://dx.doi.org/10.1364/OE.21.000A60 – “Ultrathin, high-efficiency, broad-band, omni-acceptance, organic solar cells enhanced by plasmonic cavity with subwavelength hole array”
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Lemurs are primates native only to Madagascar and make up most of the mammals depicted in the natural history portion of this work. Other sections of this work illustrated birds, mollusks, fish, butterflies and insects of Madagascar. John Gerrard Keulemans, an artist mainly known for his ornithological paintings, produced most of the bird illustrations for L’Histoire… and also contributed some of the illustrations of lemurs. Bocourt and Faguet, who did the rest of the lemur paintings shown here, were natural history artists whose works include botanical plates for other French works.
L’Histoire Physique, Naturelle et Politique de Madagascar was a collaboration between two French naturalists, Alphonse Milne-Edwards and Alfred Grandidier. Milne-Edwards’ particular areas of expertise were ornithology and paleontology, and his studies of the fossils of birds yielded significant scientific insights. He also made important discoveries related to mammals, particularly those of Madagascar and Central Asia. Grandidier used family wealth to finance expeditions to collect natural history specimens around the world. In 1865, his first visit to Madagascar initiated the project that became his life’s work and made a major contribution to scholarship. He crisscrossed the country on two subsequent journeys, mapping the country and making observations for L’Histoire… which eventually consisted of 40 volumes, the last of which were published posthumously by his son. As a result of Grandidier’s work, the French government became interested in Madagascar, and annexed the island in 1890. Grandidier was elected to the French Academy of Sciences in 1885 and was the president of the French Geographical Society from 1901 to 1905.
John Gerrard Keulemans was the most sought-after bird artist in Europe from roughly 1870 to 1910, esteemed for his high standard of scientific accuracy. Working largely from bird specimens, he had a special talent for creating drawings that were both anatomically correct and aesthetically striking. A skilled lithographer as well, he was unusual among natural history artists in that he generally transferred his own drawings to prints. In his early twenties, the Dutch-born Keulemans was mentored by Dr. Herman Schlegel, a renowned zoologist and director of the natural history museum in Leiden, who brought him on an ornithological expedition to Africa and then hired him to the museum staff and encouraged his artistic development. Soon Keulemans attracted his own commissions for natural history illustrations, mainly from England, a center for study of the zoological specimens arriving from far-flung expeditions. In 1869, he received a major assignment from Richard Bowdler Sharpe of the Zoological Society of London to produce 120 lithographs for his Monograph of the Alcedinidae, or Family of Kingfishers and thereafter pursued his artistic career in Britain, illustrating monographs and scientific journal articles by leading ornithologists. He was one of several well-known artists who contributed to Lord Thomas Lilford’s Coloured Figures of the Birds of the British Islands (1885-1897), a seven-volume work contained 421 plates, representing late 19th-century chromolithography at its best. Keulemans illustrated many volumes of the British Museum’s Catalogue of Birds (1874-1898). He also illustrated St. George Jackson Mivart’s A Monograph of the Lories, or Brush-tongued Parrots, composing the Family Loriidae, published in 1896.
Condition: Generally very good with the usual overall light toning and wear. Some variation on the paper tone on some to the next from white to cream color.
“Alfred Grandidier.” Wikipedia. 8 October 2008. http://en.wikipedia.org/wiki/Alfred_Grandidier (9 March 2009).
Fontana, Elizabeth, ed. “John Gerrard Keulemans.” Beautiful Birds: Masterpieces from the Hill Ornithology Collection, Cornell University Library. June 1999. http://rmc.library.cornell.edu/ornithology/exhibit/exhibit5d.htm (3 June 2002).
“Notes and News [Obituary of Alphonse Milne-Edwards].” The Auk 17(3):320-321. 1900. Online at http://elibary.unm.edu/sora/Auk/v017n03/p0320-p0324.pdf. (9 March 2009). | <urn:uuid:7accfb8f-0f6b-478e-9189-eddeeb8ec491> | {
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Manchester lab develops new, cleaner and faster way to make valuable molecules
Researchers at The University of Manchester have discovered a more efficient way to develop valuable chemicals needed for medicines by combining proteins and metals in the manufacturing process.
New research published today, in Nature Catalysis, demonstrates a new way of merging natural and synthetic catalysts to deliver more efficient and sustainable routes to pharmaceuticals and other valuable chemical products.
Currently chemical synthesis is used to construct many of the molecules that we rely on, from medicines that combat disease and agrochemicals to boost crop yields, through to plastics and other materials that are used in all aspects of daily life.
It is widely recognised that these traditional chemical processes are increasingly unsustainable, relying on non-renewable ingredients, highly toxic or otherwise deleterious reagents and solvents, and can create harmful emissions and waste streams.
Chemicals production also relies on multi-step synthetic routes that are expensive, meaning that many valuable products, including some essential medicines are only available to a privileged few within affluent nations.
To address these major problems, a team of chemists from The University of Manchester have devised a way of combing natural and synthetic catalysts to speed up the chemical manufacturing process.
We are optimistic that the new integrated catalytic processes we have developed could lead to cleaner, safer and more cost-effective ways to make chemical products, such as new pharmaceuticals, which is important for a more sustainable future.
Professor Jason Micklefield who led the study said: “We are optimistic that the new integrated catalytic processes we have developed could lead to cleaner, safer and more cost-effective ways to make chemical products, such as new pharmaceuticals, which is important for a more sustainable future.
“We used bacterial cells with the enzyme produced inside. In this way the cell membrane prevents the enzyme coming into contact with the metal catalyst but allows the small molecule building blocks to flow through. We also deployed enzymes in a membrane made of cross-linked fibres, from wood pulp, rather like a tea bag but with smaller holes, which allowed us to remove and recycle the enzymes.”
“The main advantage is that everything is done in water which is clean and safe. Most of the current processes use organic solvents which are toxic, flammable and dangerous to the user and the environment. The use of multiple catalysts also means that we do not need to use additional dangerous and undesirable chemical reagents (acids, bases & oxidising agents etc.) which are typically required in traditional processes.”
The scientists used enzymes (natural protein catalysts) that had been modified to improve their properties together with non-natural metal catalysts. Normally it is not feasible to use these different types of catalysts together as they deactivate one another and consequently they would be deployed in separate laborious and costly multi-steps processes.
To overcome these compatibility issues, the team developed ways to compartmentalise the different catalysts, so that they could be used in a single integrated process. Rather than using typical toxic chemical reagents and solvents, the new integrated processes can be performed in water, to deliver pharmaceuticals and other target products by a more direct, environmentally friendly and cheaper route.
Various enzymes were used, but the key enzyme was a halogenase enzyme which installs halogen atoms (chlorine or bromine) into the precursors (building blocks). The halogen atoms are reactive and can be used create new bonds between the build blocks enabling the assembly of larger molecules. Mutations were then introduced into the haloganese enzyme changing its shape so that it could accept a wider range of different building blocks.
The new research details a way to make molecules more cleanly, safely and efficiently in fewer steps. If adopted in industry, it would reduce problems of chemical waste and potentially lead to more affordable products, including medicines which could be made more widely available to help treat antimicrobial resistance (AMR) and neglected diseases in the developing world along with antiviral agents to deal with the threat of current and new viral pandemics. All of which are currently expensive produce as they are manufactured by laborious multi-step routes. | <urn:uuid:787da080-18c9-43c9-843e-1afe56fd225c> | {
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NCERT Solutions for Class 11 Humanities History Chapter 1 Theme 1: From The Beginning Of Time are provided here with simple step-by-step explanations. These solutions for Theme 1: From The Beginning Of Time are extremely popular among Class 11 Humanities students for History Theme 1: From The Beginning Of Time Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the NCERT Book of Class 11 Humanities History Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s NCERT Solutions. All NCERT Solutions for class Class 11 Humanities History are prepared by experts and are 100% accurate.
Page No 28:
Look at the diagram showing the positive feedback mechanism on page13. Can you list the inputs that went into tool making? What were the processes that were strengthened by tool making?
To answer this question, let us first have a look at the diagram below.
In the diagram, we have lines of two colours. The red-coloured lines indicate the ‘inputs’, whereas the blue-coloured lines indicate ‘processes’ that were, in turn, strengthened by tool making.Considering the red-coloured lines, we have enlisted (below) the inputs that facilitated the tool making process.
1. Increase in the size and capacity of brain: Overtime, the continuous evolution of human beings has witnessed the increase in brain size along with its increased thinking capacity. This directly led to the development of the basic intelligence, which in turn boosted the problem-solving skills of the early man. With better intelligence, he could now design newer weapons and tools for self-defence, killing animals and gathering food for his subsistence.
2. Upright walking: Once the early man started walking upright, his front limbs got free. This helped him utilise those extra limbs for making tools and using them.
3. Visual surveillance: With the development of the skills of visual surveillance (or simply observation powers), the early man could now understand and keep a track of the events happening around him and, accordingly, could prepare himself by making proper tools that could withstand similar events.
4. Hands freed for using tools and carrying infants and objects: As the early man started walking upright, his forelimbs got free. He started using his hands to carry his infants and objects such as tools, utensils, etc. In addition, it also led him to use his tools with more pressure and force.Now, let us consider the blue-coloured lines.
The processes that were strengthened by tool making are mentioned below.
1. Increase in size and capacity of brain: The tool making process, in turn, enhanced the technical know-how of the early man. This also infused the power to think, concentrate, understand and memorise. All these developments further increased the capacity of early man’s brain.
2. Upright walking: It enabled the early man to use hands for making, carrying and using tools. This further added to his potential and got him extra hands to do a lot more things than he did previously.
3. Visual surveillance: With more analytical and observatory powers, the early man developed enhanced tools and weapons. Simultaneously, he could now undertake the journey to exploit the unexplored tracks for food.
Page No 28:
Humans and mammals such as monkeys and apes have certain similarities in behaviour and anatomy. This indicates that humans possibly evolved from apes. List these resemblances in two columns under the headings of (a) behaviour and (b) anatomy. Are there any differences that you think are noteworthy?
The similarities between humans and mammals in terms of behaviour and anatomy have been tabulated below.
Basis of Similarities between humans and other mammals
|Basis of Similarities between humans and other mammals||Similarities|
|a) Behaviour||i. Living in groups: Both primates and humans live in groups. While primates live in groups especially for the survival needs, humans, on the other hand, live in groups for reasons such as nationality and also due to cultural factors.
ii. Communication: Both primates and humans have the ability to communicate. On one hand, primates use sounds and gestures as modes of communication, humans, on the other hand, use advanced communication mediums such as writing and talking besides gestures.
|b) Anatomy||i. Prehensile hands and feet: This is common between primates and humans. This enables both to have a strong grip.
ii. Flattened face: Both of them have flattened face, with two eyes next to each other. This allows them to have a vision that further helped to have a wider and complete view of the surroundings.
Besides the aforementioned similarities, both humans and primates have considerable differences in their behaviour and anatomy.
|Points of difference||Mammals or Primates||Humans|
|Behaviour||i. Communication based on limited sound and gestures only
ii. Social groups are based on their survival needs
|i. Use advanced communication skills to interact among each other
ii. Social groups are based on nationality, culture and other important factors besides survival needs
|Anatomy||i. Face is larger than cranium
ii. Facial structure
a. Flattened nose
b. Very large jaws (for eating)
c. Thin lips
|i. Face is smaller than cranium
ii. Facial structure
a. Protruding nose
b. Flattened jaws
c. Large lips (beneficial for facial expressions)
Page No 28:
Discuss the arguments advanced in favour of the regional continuity model of human origins. Do you think it provides a convincing explanation of the archaeological evidence? Give reasons for your answer.
The regional continuity model states that the hominid ancestors had migrated from Africa and their further evolution took place in separate geographical regions. The remains of the mixed modern and archaic skull types found across the globe suggest that evolution of mankind took place simultaneously in different parts of the world; probably by the process of ‘genes flowing between populations.’
However, I do not believe that the evidence of the regional continuity model justifies the origin of humans. The replacement theory and its available evidences would be the best to justify it. According to this theory, Homo sapiens originated in Africa. Between 100,000–120,000 years ago, they migrated to Europe, Asia and Australia. This period was marked by the extinction of the earlier hominid species and the sustenance of Homo sapiens. Gradually and eventually, the Homo sapiens had spread across different parts of the world. This is regarded as the reason behind the degree of similarity among all modern humans (since they all have a common place of origin) by the replacement theorists. The fact that the oldest human fossil has also been excavated from Africa further reinforces my belief on the replacement theory.
Page No 28:
Which of the following do you think is best documented in the archaeological record: (a) gathering, (b) tool making, (c) the use of fire?
The technique of tool making is best documented in the archaeological records. The earliest evidence of making and using stone tools comes from the archaeological sites in Ethiopia and Kenya. The remains of various types of tools found after excavations prove that man had mastered the skill of tool making. Moreover, according to the need of the time, the shape and size of the tools were also changed.
Page No 28:
Discuss the extent to which (a) hunting and (b) constructing shelters would have been facilitated by the use of language. What other modes of communication could have been used for these activities?
With the passage of time, the capacity of human brain developed, which gradually led to the communication among early humans. Initially, the communication remained highly restricted to the non-verbal modes involving gestures. However, with the passage of time, the evolution of the voice box took place and the communication methods became more advanced. Simple gestures were now replaced by whistling, talking and singing (together they can be regarded as language used by the early man). This further simplified communication; the ideas and thoughts could be easily expressed. All this highly facilitated the early man in the efficient conduct of daily errands involving hunting and constructing shelters.
The extent to which hunting and constructing shelters have been facilitated by the use of language has been explained below.
ii. Planning and executing hunting strategies became easier
iii. Sharing of experiences led to easy diffusion of the tool-making technical know-how and successful hunting techniques. These shared stories of success, in turn, infused early man with the confidence to hunt more efficiently
iv. The use of language enabled early humans to caution their associates of any approaching danger. Thus, they acted as support for each other in times of any exigency.
b) Constructing shelters
Besides facilitating hunting, the evolution of language also enabled early man in constructing shelters. He could now discuss the choice of the site for building shelters along with his construction plans. Coordination in the process of construction of shelters was also possible by communication.
Other than the use of language, work of art such as paintings and engravings also served as means of communication. Paintings were made to share the news of successful hunting expeditions, techniques and tools so used. The presence of such paintings on the cave walls argues that the early humans used to gathered together to share their experiences and socialise.
Page No 28:
Choose any two developments each from Timelines 1 and 2 at the end of the chapter and indicate why you think these are significant.
According to me, the two most significant developments from timelines 1 and 2 are as follows:
1. Earliest stone tools: The making of the earliest stone tools is significant as it marked the initial phase of technological innovation. As the early man started making tools, executing daily tasks such as hunting and construction got easier. Simultaneously, he started crafting tools to suit farming needs. Farming provided a comparatively secure and stable source of food. This allowed early man to give up his nomadic life and settle down at one place. It can thus be rightly stated that the making of earliest tools marked the beginning of the initial phase of human civilisations.
2. Development of the voice box: The development of the voice box in early humans around 200000 years ago helped man to start speaking or communicating. Gestures, as mode of communication, were replaced by speech. Expression and communication of ideas and emotions became less cumbersome. The power to speak also helped the early man to conduct hunting and constructing shelters in the following manner:
ii. Planning and executing hunting strategies became easier.
iii. Sharing of experiences led to easy diffusing of the tool making technical know-how and successful hunting techniques. These shared stories of success, in turn, infused early man with confidence to hunt more efficiently.
iv. The use of language enabled early man to caution his associates of any approaching danger. Thus, they acted as support for each other in times of any exigency.
View NCERT Solutions for all chapters of Class 14 | <urn:uuid:480bf257-393b-4359-8212-be3055bcbda7> | {
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## Access NCERT Solutions for Class 6 Chapter 8: Decimals
Exercise 8.1 page no: 167
1. Write the following numbers in the given table.
2. Write the following decimals in the place value table.
(a) 19.4
(b) 0.3
(c) 10.6
(d) 205.9
Solutions:
Hundreds Tens Ones Tenths 19.4 0 1 9 4 0.3 0 0 0 3 10.6 0 1 0 6 205.9 2 0 5 9
3. Write each of the following as decimals:
(a) Seven-tenths
(b) Two tens and nine-tenths
(c) Fourteen point six
(d) One hundred and two ones
(e) Six hundred point eight
Solutions:
(a) The decimal form of Seven-tenths is 7 / 10 = 0.7
(b) The decimal form of two tens and nine tenths is 20 + 9 / 10 = 20.9
(c) The decimal form of fourteen point six is 14.6
(d) The decimal form of one hundred and two ones is 100 + 2 = 102.0
(e) The decimal form of six hundred point eight is 600.8
4. Write each of the following as decimals:
(a) 5 / 10
(b) 3 + 7 / 10
(c) 200 + 60 + 5 + 1 / 10
(d) 70 + 8 / 10
(e) 88 / 10
5. Write the following decimals as fractions. Reduce the fraction to lowest form.
(a) 0.6
(b) 2.5
(c) 1.0
(d) 3.8
(e) 13.7
(f) 21.2
(g) 6.4
Solutions:
(a) 0.6 = 6 / 10
= 3 / 5
(b) 2.5 = 25 / 10
= 5 / 2
(c) 1.0 = 1
= 1
(d) 3.8 = 38 / 10
= 19 / 5
(e) 13. 7 = 137 / 10
(f) 21.2 = 212 / 10
= 106 / 5
(g) 6.4 = 64 / 10
= 32 / 5
6. Express the following as cm using decimals.
(a) 2 mm
(b) 30 mm
(c) 116 mm
(d) 4 cm 2 mm
(e) 162 mm
(f) 83 mm
Solutions:
We know that
1 cm = 10 mm
1 mm = 1 / 10 cm
(a) 2 mm = 2 / 10 cm
= 0.2 cm
(b) 30 mm = 30 / 10 cm
= 3.0 cm
(c) 116 mm = 116 / 10 cm
= 11.6 cm
(d) 4 cm 2 mm = [(4 + 2 / 10)] cm
= 4.2 cm
(e) 162 mm = 162 / 10 cm
= 16.2 cm
(f) 83 mm = 83 / 10 cm
= 8.3 cm
7. Between which two whole numbers on the number line are the given numbers lie?
Which of these whole numbers is nearer the number?
a) 0.8
(b) 5.1
(c) 2.6
(d) 6.4
(e) 9.1
(f) 4.9
Solutions:
(a) 0.8 lies between 0 and 1
0.8 is nearer to 1
(b) 5.1 lies between 5 and 6
5.1 is nearer to 5
(c) 2.6 lies between 2 and 3
2.6 is nearer to 3
(d) 6.4 lies between 6 and 7
6.4 is nearer to 6
(e) 9.1 lies between 9 and 10
9.1 is nearer to 9
(f) 4.9 lies between 4 and 5
4.9 is nearer to 5
8. Show the following numbers on the number line.
(a) 0.2
(b) 1.9
(c) 1.1
(d) 2.5
Solutions:
(a) 0.2 lies between the points 0 and 1 on the number line. The space between 0 and 1 is divided into 10 equal parts. Therefore each equal part will be equal to one-tenth. 0.2 is the second point between 0 and 1
Exercise 8.2 page no: 173
1. Complete the table with the help of these boxes and use decimals to write the number.
Solutions:
Rows Ones Tenths Hundreds Number (a) 0 2 6 0.26 (b) 1 3 8 1.38 (c) 1 2 8 1.28
2. Write the numbers given in the following place value table in decimal form.
Rows Hundreds Tens Ones Tenths Hundredths Thousandths 100 10 1 1 / 10 1/ 100 1 / 1000 (a) 0 0 3 2 5 0 (b) 1 0 2 6 3 0 (c) 0 3 0 0 2 5 (d) 2 1 1 9 0 2 (e) 0 1 2 2 4 1
Solutions:
(a) 3 + 2 / 10 + 5 / 100
= 3 + 0.2 + 0.05
= 3.25
(b) 100 + 2 + 6 / 10 + 3 / 100
= 102 + 0.6 + 0.03
= 102.63
(c) 30 + 2 / 100 + 5 / 1000
= 30 + 0.02 + 0.005
= 30.025
(d) 200 + 10 + 1 + 9 / 10 + 2 / 1000
= 211 + 0.9 + 0.002
= 211.902
(e) 10 + 2 + 2 / 10 + 4 / 100 + 1 / 1000
= 12 + 0.2 + 0.04 + 0.001
= 12.241
3. Write the following decimals in the place value table.
(a) 0.29
(b) 2.08
(c) 19.60
(d) 148.32
(e) 200.812
Solutions:
(a) 0.29
= 0.2 + 0.09
= 2 / 10 + 9 / 100
(b) 2.08
= 2 + 0.08
= 2 + 8 / 100
(c) 19.60
= 19 + 0.60
= 10 + 9 + 6 / 10
(d) 148.32
= 148 + 0.3 + 0.02
= 100 + 40 + 8 + 3 / 10 + 2 / 100
(e) 200.812
= 200 + 0.8 + 0.01 + 0.002
=200 + 8 / 10 + 1 / 100 + 2 / 1000
Hundreds Tens Ones Tenths Hundredths Thousandths 0 0 0 2 9 0 0 0 2 0 8 0 0 1 9 6 0 0 1 4 8 3 2 0 2 0 0 8 1 2
4. Write each of the following as decimals.
(a) 20 + 9 + 4 / 10 + 1 / 100
(b) 137 + 5 / 100
(c) 7 / 10 + 6 / 100 + 4 / 1000
(d) 23 + 2 / 10 + 6 / 1000
(e) 700 + 20 + 5 + 9 / 100
Solutions:
(a) 20 + 9 + 4 / 10 + 1 / 100
= 29 + 0.4 + 0.01
= 29.41
(b) 137 + 5 / 100
= 137 + 0.05
= 137.05
(c) 7 / 10 + 6 / 100 + 4 / 1000
= 0.7 + 0.06 + 0.004
=0.764
(d) 23 + 2 / 10 + 6 / 1000
= 23 + 0.2 + 0.006
= 23.206
(e) 700 + 20 + 5 + 9 / 100
= 725 + 0.09
= 725.09
5. Write each of the following decimals in words.
(a) 0.03
(b) 1.20
(c) 108.56
(d) 10. 07
(e) 0.032
(f) 5.008
Solutions:
The following are the decimals in words
(a) 0.03 = zero point zero three
(b) 1.20 = one point two zero
(c) 108.56 = one hundred eight point five six
(d) 10.07 = ten point zero seven
(e) 0.032 = zero point zero three two
(f) 5.008 = five point zero zero eight
6. Between which two numbers in tenths place on the number line does each of the given number lie?
(a) 0.60
(b) 0.45
(c) 0.19
(d) 0.66
(e) 0.92
(f) 0.57
Solutions:
(a) 0.60 lies between 0 and 0.1 in tenths place
(b) 0.45 lies between 0.4 and 0.5 in tenths place
(c) 0.19 lies between 0.1 and 0.2 in tenths place
(d) 0.66 lies between 0.6 and 0.7 in tenths place
(e) 0.92 lies between 0.9 and 1.0 in tenths place
(f) 0.57 lies between 0.5 and 0.6 in tenths place
7. Write as fractions in lowest terms.
(a) 0.60
(b) 0.05
(c) 0.75
(d) 0.18
(e) 0.25
(f) 0.125
(g) 0.066
Solutions:
(a) 0.60 = 60 / 100
= 6 / 10
= 3 / 5
(b) 0.05 = 5 / 100
= 1 / 20
(c) 0.75 = 75 / 100
= 3 / 4
(d) 0.18 = 18 / 100
= 9 / 50
(e) 0.25 = 25 / 100
= 1 / 4
(f) 0.125 = 125 / 1000
= 1 / 8
(g) 0.066 = 66 / 1000
= 33 / 500
Exercise 8.3 page no: 175
1. Which is greater?
(a) 0.3 or 0.4
(b) 0.07 or 0.02
(c) 3 or 0.8
(d) 0.5 or 0.05
(e) 1.23 or 1.2
(f) 0.099 or 0.19
(g) 1.5 or 1.50
(h) 1.431 or 1.490
(i) 3.3 or 3.300
(j) 5.64 or 5.603
Solutions:
(a) 0.3 or 0.4
Whole parts for both the numbers are same. We know that the tenth part of 0.4 is greater than that of 0.3
∴ 0.4 > 0.3
(b) 0.07 or 0.02
Both the numbers have same parts up to the tenth place but the hundredth part of 0.07 is greater than that of 0.02
∴ 0.07 > 0.02
(c) 3 or 0.8
The whole part of 3 is greater than that of 0.8
∴ 3 > 0.8
(d) 0.5 or 0.05
Whole parts for both the numbers are same. Here the tenth part of 0.5 is greater than that of 0.05
∴ 0.5 > 0.05
(e) 1.23 or 1.20
Here both the numbers have same parts up to the tenth place. The hundredth part of 1.23 is greater than that of 1.20
∴ 1.23 > 1.20
(f) 0.099 or 0.19
Whole parts for both the numbers are same. Here the tenth part of 0.19 is greater than that of 0.099
∴ 0.099 < 0.19
(g) 1.5 or 1.50
We may find that both numbers have same parts up to the tenth place. Here 1.5 have no digit at hundredth place. It represents that this digit is 0, which is equal to the digit at hundredth place of 1.50.
∴ Both these numbers are equal
(h) 1.431 or 1.490
Here, both the numbers have same parts up to the tenth place but the hundredth part of 1.490 is greater than that of 1.431
∴ 1.431 < 1.490
(i) 3.3 or 3.300
Here, both numbers have same parts up to the tenth place. There are no digits at hundredth and thousandth place of 3.3. It represents that these numbers are 0, which is equal to the digits at hundredth and thousandth place of 3.300.
∴ Both these numbers are equal
(j) 5.64 or 5.603
Here both numbers have same parts up to the tenth place but the hundredth part of 5.64 is greater than that of 5.603
∴ 5.64 > 5.603
2. Make five more examples and find the greater number from them.
Solutions:
Five more examples are
(a) 32.55 or 32.5
Whole parts for both the numbers are same. The tenth part are also equal, but the hundredth part of 32.55 is greater than that of 32.5
Hence, 32.55 > 32.5
(b) 1 or 0.99
The whole part of 1 is greater than that of 0.99
∴ 1 > 0.99
(c) 1.09 or 1.093
Here both the numbers have same parts up to the hundredth. But the thousandth part of 1.093 is greater than that of 1.09
∴ 1.093 > 1.09
(d) 2 or 1.99
The whole part of 2 is greater than that of 1.99
∴ 2 > 1.99
(e) 2.08 or 2.085
Here both the numbers have same parts up to the hundredth. But the thousandth part of 2.085 is greater than that of 2.08
∴ 2.085 > 2.08
Exercise 8.4 page no: 177
1. Express as rupees using decimals.
(a) 5 paise
(b) 75 paise
(c) 20 paise
(d) 50 rupees 90 paise
(e) 725 paise
Solutions:
We know that there are 100 paise in 1 rupees
(a) 5 paise = 5 / 100 rupees
= Rupess 0.05
(b) 75 paise = 75 / 100 rupees
= Rupees 0.75
(c) 20 paise = 20 / 100 rupees
= Rupees 0.20
(d) 50 rupees 90 paise = [(50 + 90 / 100)] rupees
= Rupees 50.90
(e) 725 paise = 725 / 100 rupees
= Rupees 7.25
2. Express as metres using decimals.
(a) 15 cm
(b) 6 cm
(c) 2 m 45 cm
(d) 9 m 7 cm
(e) 419 cm
Solutions:
We know that there are 100 cm in 1 metre
(a) 15 cm = 15 / 100 m
= 0.15 m
(b) 6 cm = 6 / 100 m
= 0.06 m
(c) 2 m 45 cm = [(2 + 45 / 100)] m
= 2.45 m
(d) 9 m 7 cm = [(9 + 7 / 100)] m
= 9.07 m
(e) 419 cm = 419 / 100 m
= 4.19 m
3. Express as cm using decimals
(a) 5 mm
(b) 60 mm
(c) 164 mm
(d) 9 cm 8 mm
(e) 93 mm
Solutions:
We know that there are 10 mm in 1 cm
(a) 5 mm = 5 / 10 cm
= 0.5 cm
(b) 60 mm = 60 / 10 cm
= 6.0 cm
(c) 164 mm = 164 / 10 cm
= 16.4 cm
(d) 9 cm 8 mm = [(9 + 8 / 10)] cm
= 9.8 cm
(e) 93 mm = 93 / 10 cm
= 9.3 cm
4. Express as km using decimals.
(a) 8 m
(b) 88 m
(c) 8888 m
(d) 70 km 5 m
Solutions:
We know that there are 1000 metres in 1 km
(a) 8 m = 8 / 1000 km
= 0.008 km
(b) 88 m = 88 / 1000 km
= 0.088 km
(c) 8888 m = 8888 / 1000 km
= 8.888 km
(d) 70 km 5 m = [(70 + 5 / 1000)] km
= 70.005 km
5. Express as kg using decimals.
(a) 2 g
(b) 100 g
(c) 3750 g
(d) 5 kg 8 g
(e) 26 kg 50 g
Solutions:
We know that there are 1000 grams in 1 kg
(a) 2 g = 2 / 1000 kg
= 0.002 kg
(b) 100 g = 100 / 1000 kg
= 0.1 kg
(c) 3750 g = 3750 / 1000 kg
= 3.750 kg
(d) 5 kg 8 g = [(5 + 8 / 1000)] kg
= 5.008 kg
(e) 26 kg 50 g = [(26 + 50 / 1000)] kg
= 26.050 kg
Exercise 8.5 page no: 179
1. Find the sum in each of the following:
(a) 0.007 + 8.5 + 30.08
(b) 15 + 0.632 + 13.8
(c) 27.076 + 0.55 + 0.004
(d) 25.65 + 9.005 + 3.7
(e) 0.75 + 10.425 + 2
(f) 280.69 + 25.2 + 38
Solutions:
(a) Sum of 0.007 + 8.5 + 30.08
0.007
8.500
+ 30.080
__________
38.587
__________
(b) Sum of 15 + 0.632 + 13.8
15.000
0.632
+ 13.800
_________
29.432
__________
(c) Sum of 27.076 + 0.55 + 0.004
27.076
0.550
+ 0.004
_____________
27.630
______________
(d) Sum of 25.65 + 9.005 + 3.7
25.650
9.005
+ 3.700
__________
38.355
___________
(e) Sum of 0.75 + 10.425 + 2
0.750
10.425
+ 2.000
_________
13.175
__________
(f) Sum of 280.69 + 25.2 + 38
280.69
25.20
+ 38.00
__________
343.89
___________
2. Rashid spent Rs. 35.75 for Maths book and Rs. 32.60 for Science book. Find the total amount spent by Rashid.
Solutions:
Cost of Maths book = Rs 35.75
Cost of Science book = Rs 32.60
Total amount spent by Rashid is
35.75
+ 32.60
__________
68.35
___________
∴ Total amount of money spent by Rashid is Rs 68.35
3. Radhika’s mother gave her Rs 10.50 and her father gave her Rs 15.80, find the total amount given to Radhika by the parents.
Solutions:
Amount given by Radhika’s mother = Rs 10.50
Amount given by Radhika’s father = Rs 15.80
Total amount given by her parents
10.50
+ 15.80
__________
26.30
___________
∴ Total amount of money given by Radhika’s parents is Rs 26.30
4. Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find the total length of cloth bought by her.
Solutions:
Cloth of shirt = 3 m 20 cm
Cloth of trouser = 2 m 5 cm
Total length of cloth is
3.20
+ 2.05
________
5.25
_________
∴ Total length of cloth bought by Nasreen is 5.25 m
5. Naresh walked 2 km 35 m in the morning and 1 km 7 m in the evening. How much distance did he walk in all?
Solutions:
Distance walked by Naresh in the morning = 2 km 35 m
= [(2 + 35 /1000)] km
= 2.035 km
Distance walked by him in the evening = 1 km 7 m
= [(1 + 7 / 1000)] km
= 1.007 km
Total distance walked by Naresh is
2.035
+ 1.007
_______
3.042
________
∴ Total distance walked by Naresh is 3.042 km
6. Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot in order to reach her school. How far is her school from her residence?
Solutions:
Distance travelled by bus = 15 km 268 m
= [(15 + 268 / 1000)] km
= 15.268 km
Distance travelled by car = 7 km 7 m
= [(7 + 7 / 1000)] km
= 7.007 km
Distance walked by Sunita = 500 m
= 500 / 1000
= 0.500 km
Total distance of school from her residence is
15.268
7.007
+ 0.500
________
22.775
________
∴ Total distance of the school from her residence is 22.775 km
7. Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850 g flour. Find the total weight of his purchases.
Solutions:
Weight of rice = 5 kg 400 g
= [(5 + 400 / 1000)] kg
= 5.400 kg
Weight of sugar = 2 kg 20 g
= [(2 + 20 / 1000)] kg
= 2.020 kg
Weight of flour = 10 kg 850 g
= [(10 + 850 / 1000)] kg
= 10.850 kg
Total weight of his purchases is
5.400
2.020
+ 10.850
___________
18.270
____________
∴ Total weight of his purchases is 18.270 kg
Exercise 8.6 page no: 181
1. Subtract:
(a) Rs 18.25 from Rs 20.75
(b) 202.54 m from 250 m
(c) Rs 5.36 from Rs 8.40
(d) 2.051 km from 5.206 km
(e) 0.314 kg from 2.107 kg
Solutions:
(a) Rs 20.75 – Rs 18.75
20.75
– 18.25
__________
2.50
___________
Rs 2.50
(b) 250 m – 202.54 m
250.00
– 202.54
___________
47.46
____________
47.46 m
(c) Rs 8.40 – Rs 5.36
8.40
– 5.36
_________
3.04
_________
Rs 3.04
(d) 5.206 km – 2.051 km
5.206
– 2.051
__________
3.155
__________
3.155 km
(e) 2.107 kg – 0.314 kg
2.107
– 0.314
_________
1.793
__________
1.793 kg
2. Find the value of:
(a) 9.756 – 6.28
(b) 21.05 – 15.27
(c) 18.5 – 6.79
(d) 11.6 – 9.847
Solutions:
(a) 9.756
– 6.280
_________
3.476
_________
(b) 21.05
– 15.27
___________
5.78
____________
(c) 18.50
– 6.79
___________
11.71
___________
(d) 11.600
– 9.847
____________
1.753
____________
3. Raju bought a book for Rs 35.65. He gave Rs 50 to the shopkeeper. How much money did he get back from the shopkeeper?
Solutions:
Money given to shopkeeper = Rs 50.00
Price of the book = Rs 35.65
Money that Raju will get back from the shopkeeper will be the difference of these two
∴ Money left with Raju is
50.00
– 35.65
___________
14.35
___________
Hence, money left with Raju is Rs 14.35
4. Rani had Rs 18.50. She bought one ice cream for Rs 11.75. How much money does she have now?
Solutions:
Money with Rani = Rs 18.50
Price of an ice cream = Rs 11.75
Now money left with Rani will be the difference of these two
Hence, money left with her is
18.50
– 11.75
__________
6.75
___________
∴ Money left with Rani is Rs 6.75
5. Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth from this for making a curtain. How much cloth is left with her?
Solutions:
Length of cloth = 20 m 5 cm
= 20.05 m
Length of cloth to make a curtain = 4 m 50 cm
= 4.50 m
Length of cloth left with Tina will be the difference of these two
Thus length of cloth left with her is
20.05
– 4.50
________
15.55
________
∴ The length of the remaining cloth left with Tina is 15.55 m
6. Namita travels 20 km 50 m every day. Out of this she travels 10 km 200 m by bus and the rest by auto. How much distance does she travel by auto?
Solutions:
Total distance travelled by Namita = 20 km 50 m
= 20.050 km
Distance travelled by bus = 10 km 200 m
= 10.200 km
Distance travelled by auto = Total distance travelled – Distance travelled by bus
∴ Distance to be travelled by auto is
20.050
– 10.200
________
9.850
________
∴ Namita travelled 9.850 km by auto
7. Aakash bought vegetables weighing 10 kg. Out of this, 3 kg 500 g is onions, 2 kg 75 g is tomatoes and the rest is potatoes. What is the weight of the potatoes?
Solutions:
Total weight of vegetables Aakash bought = 10.000 kg
Weight of onions = 3 kg 500 g
= 3.500 kg
Weight of tomatoes = 2 kg 75 g
= 2.075 kg
Weight of potatoes = Total weight of vegetables bought – (weight of onions + weight of tomatoes)
= 10.000 – (3.500 + 2.075)
3.500
+ 2.075
________
5.575
________
10.000
– 5.575
_________
4.425
_________
∴ 4.425 kg is the weight of the potatoes
Exercise Files
Chapter 8 Decimals.
Size: 0.00 B
Join the conversation | crawl-data/CC-MAIN-2024-38/segments/1725700651697.32/warc/CC-MAIN-20240916112213-20240916142213-00656.warc.gz | null |
by TeachThought Staff
The iPad is not magic, and as many educators have found integrating them meaningfully is by no means a just-add-water proposition.
The same applies to Project-Based Learning.
Project-Based Learning is a method of giving learners access to curriculum in authentic ways that promote collaboration, design, imagination, and innovation while also allowing for more natural integration of digital and social media. Below we’ve offered 23 ways that the iPad can be used in your classroom. While given strategies may or may not fit exactly into your curriculum or grade level, consider them instead as a kind of board of ideas to inspire your own thinking. If “Designing a tire” is beyond the ability of your 4th graders (and you’re certain of that), what else might they design instead? If analyzing narrative design sounds below your college freshman, what might them “consume and design” instead?
Note that the visual is also arranged in a kind of visual spectrum, as our past visuals have been. But this time, rather than being distributed by complexity, it is instead laid out in terms of the kind of workflow a learner might encounter in a 21st century, K-20, project-based learning environment.
Image attribution flickr user flickeringbrad | <urn:uuid:0a03f32c-5df8-4bee-9809-7184175a7165> | {
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"int_score": 4,
"language": "en",
"language_score": 0.9464403390884399,
"score": 3.609375,
"token_count": 268,
"url": "http://www.teachthought.com/technology/23-ways-to-use-the-ipad-in-the-21st-century-pbl-classroom/?_tmc=C05Mxs_7-1jkNWQuwwtGvqNH95h5aQI9R5XhLw73UZA"
} |
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