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# Easy trig problem
• Jul 2nd 2010, 06:36 AM
dapore
Easy trig problem
• Jul 2nd 2010, 10:31 PM
eumyang
Maybe it's me, but this didn't seem easy!?!? I'm getting an answer of sin a = 1; is this correct?
Here's a summary of what I did:
You have the cosine of a difference identity:
$cos (a-b) = cos\, a\: cos\, b + sin\, a\: sin\, b \quad$ (Eq1)
Use the Law of sines to write sin b in terms of sin a:
$sin\, b = \frac{3}{4}sin\, a \quad$ (Eq2)
Use the pythagorean identity to write cosine in terms of sine:
$cos\, a = \sqrt{1-sin^2\, a}$ (Eq3a)
$cos\, b = \sqrt{1-sin^2\, b}$ (Eq3b)
Plug (2), (3a), and (3b) into (1), plus the fact that cos (a-b) = 3/4:
$\frac{3}{4} = \sqrt{1-sin^2\, a}\: \sqrt{1-\left(\frac{3}{4}sin\, a\right)^2} + sin\, a\: \left(\frac{3}{4}sin\, a\right)$ (Eq4)
Solved for sin a and I got sin a = 1.
I'm sure I did something wrong here.
• Jul 3rd 2010, 12:04 AM
simplependulum
In general , if $|ac| = B ~,~ |bc| = A ~,~ \cos(a-b) = X$
The method to find the value of $\sin(a)$ is as follows :
First determine which of the angles $a,b$ is larger by comparing their opposite sides , let's say $a > b$ .
Let $d$ be the other point on line $ab$ such that $|ac| = |cd| = B$
Then we have
$\angle bcd = a-b$ , by using cosine formula ,
$|bd| = \sqrt{A^2 + B^2 - 2ABX}$ ,
Therefore , $\sin(a) : A = \sin(a-b) : |bd|$
$\sin(a) =\frac{A \sin(a-b)}{ \sqrt{A^2 + B^2 - 2ABX} }$ | crawl-data/CC-MAIN-2018-09/segments/1518891816462.95/warc/CC-MAIN-20180225130337-20180225150337-00227.warc.gz | null |
Crude oil is the term for "unprocessed" oil, the stuff
that comes out of the ground. It is also known as petroleum.
Crude oil is a fossil fuel, meaning that it was made naturally
from decaying plants and animals living in ancient seas millions
of years ago -- anywhere you find crude oil was once a sea bed.
Crude oils vary in color, from clear to tar-black, and in viscosity,
from water to almost solid.
Crude oils are such a useful starting point for so many different
substances because they contain hydrocarbons. Hydrocarbons are
molecules that contain hydrogen and carbon and come in various
lengths and structures, from straight chains to branching chains
There are two things that make hydrocarbons exciting to chemists:
- Hydrocarbons contain a lot of energy. Many of the things
derived from crude oil like gasoline, diesel fuel, paraffin
wax and so on take advantage of this energy.
- Hydrocarbons can take on many different forms. The smallest
hydrocarbon is methane (CH4), which is a gas that is a lighter
than air. Longer chains with 5 or more carbons are liquids.
Very long chains are solids like wax or tar. By chemically
cross-linking hydrocarbon chains you can get everything from
synthetic rubber to nylon to the plastic in tupperware. Hydrocarbon
chains are very versatile!
The major classes of hydrocarbons in
crude oils include:
- general formula: CnH2n+2 (n is a whole number, usually
from 1 to 20)
- straight- or branched-chain molecules
- can be gasses or liquids at room temperature depending upon
- examples: methane, ethane, propane, butane, isobutane, pentane,
- general formula: C6H5 - Y (Y is a longer, straight molecule
that connects to the benzene ring)
- ringed structures with one or more rings
- rings contain six carbon atoms, with alternating double
and single bonds between the carbons
- typically liquids
- examples: benzene, napthalene
Napthenes or Cycloalkanes
- general formula: CnH2n (n is a whole number usually from
1 to 20)
- ringed structures with one or more rings
- rings contain only single bonds between the carbon atoms
- typically liquids at room temperature
- examples: cyclohexane, methyl cyclopentane
- general formula: CnH2n (n is a whole number, usually from
1 to 20)
- linear or branched chain molecules containing one carbon-carbon
- can be liquid or gas
- examples: ethylene, butene, isobutene
Dienes and Alkynes
- general formula: CnH2n-2 (n is a whole number, usually
from 1 to 20)
- linear or branched chain molecules containing two carbon-carbon
- can be liquid or gas
- examples: acetylene, butadienes
From Crude Oil
The problem with crude oil is that it contains
hundreds of different types of hydrocarbons all mixed together.
You have to separate the different types of hydrocarbons to
have anything useful. Fortunately there is an easy way to separate
things, and this is what oil refining is all about.
Different hydrocarbon chain lengths all have progressively higher
boiling points, so they can all be separated by distillation.
This is what happens in an oil refinery - in one part of the
process, crude oil is heated and the different chains are pulled
out by their vaporization temperatures. Each different chain
length has a different property that makes it useful in a different
To understand the diversity contained in crude
oil, and to understand why refining crude oil is so important
in our society, look through the following list of products
that come from crude oil:
- Petroleum gas - used for heating,
cooking, making plastics
- small alkanes (1 to 4 carbon atoms)
- commonly known by the names methane, ethane, propane,
- boiling range = less than 104 degrees Fahrenheit / 40
- often liquified under pressure to create LPG (liquified
- Naphtha or Ligroin - intermediate
that will be further processed to make gasoline
- mix of 5 to 9 carbon atom alkanes
- boiling range = 140 to 212 degrees Fahrenheit / 60 to
100 degrees Celsius
- Gasoline - motor fuel
- mix of alkanes and cycloalkanes (5 to 12 carbon atoms)
- boiling range = 104 to 401 degrees Fahrenheit / 40 to
205 degrees Celsius
- Kerosene - fuel for jet engines
and tractors; starting material for making other products
- mix of alkanes (10 to 18 carbons) and aromatics
- boiling range = 350 to 617 degrees Fahrenheit / 175
to 325 degrees Celsius
- Gas oil or Diesel distillate
- used for diesel fuel and heating oil; starting material
for making other products
- alkanes containing 12 or more carbon atoms
- boiling range = 482 to 662 degrees Fahrenheit / 250
to 350 degrees Celsius
- Lubricating oil - used for
motor oil, grease, other lubricants
- long chain (20 to 50 carbon atoms) alkanes, cycloalkanes,
- boiling range = 572 to 700 degrees Fahrenheit / 300 to
370 degrees Celsius
- Heavy gas or Fuel oil - used
for industrial fuel; starting material for making other products
- long chain (20 to 70 carbon atoms) alkanes, cycloalkanes,
- boiling range = 700 to 1112 degrees Fahrenheit / 370
to 600 degrees Celsius
- Residuals - coke, asphalt,
tar, waxes; starting material for making other products
- multiple-ringed compounds with 70 or more carbon atoms
- boiling range = greater than 1112 degrees Fahrenheit
/ 600 degrees Celsius
As mentioned previously, a barrel of crude oil has a mixture
of all sorts of hydrocarbons in it. Oil refining separates everything
into useful substances. Chemists use the following steps:
- The oldest and most common way to separate things into
various components (called fractions), is to do it using the
differences in boiling temperature. This process is called
fractional distillation. You basically heat crude oil up,
let it vaporize and then condense the vapor.
- Newer techniques use Chemical processing on some of the
fractions to make others, in a process called conversion.
Chemical processing, for example, can break longer chains
into shorter ones. This allows a refinery to turn diesel fuel
into gasoline depending on the demand for gasoline.
- Refineries must treat the fractions to remove impurities.
- Refineries combine the various fractions (processed, unprocessed)
into mixtures to make desired products. For example, different
mixtures of chains can create gasolines with different octane
The products are stored on-site until they
can be delivered to various markets such as gas stations, airports
and chemical plants. In addition to making the oil-based products,
refineries must also treat the wastes involved in the processes
to minimize air and water pollution.
- The various components of crude oil have different sizes,
weights and boiling temperatures; so, the first step is to
separate these components. Because they have different boiling
temperatures, they can be separated easily by a process called
fractional distillation. The steps of fractional distillation
are as follows:
You heat the mixture of two or more substances (liquids) with
different boiling points to a high temperature. Heating is
usually done with high pressure steam to temperatures of about
1112 degrees Fahrenheit / 600 degrees Celsius.
- The mixture boils, forming vapor (gases); most substances
go into the vapor phase.
- The vapor enters the bottom of a long column (fractional
distillation column) that is filled with trays or plates.
- The trays have many holes or bubble caps (like a loosened
cap on a soda bottle) in them to allow the vapor to pass
- The trays increase the contact time between the vapor
and the liquids in the column.
- The trays help to collect liquids that form at various
heights in the column.
- There is a temperature difference across the column
(hot at the bottom, cool at the top).
The vapor rises in the column.
- As the vapor rises through the trays in the column, it cools.
- When a substance in the vapor reaches a height where the
temperature of the column is equal to that substance's boiling
point, it will condense to form a liquid. (The substance with
the lowest boiling point will condense at the highest point
in the column; substances with higher boiling points will
condense lower in the column.).
- The trays collect the various liquid fractions.
- The collected liquid fractions may:
pass to condensers, which cool them further, and then go to
go to other areas for further chemical processing
Fractional distillation is useful for separating
a mixture of substances with narrow differences in boiling points,
and is the most important step in the refining process.
Very few of the components come out of the
fractional distillation column ready for market. Many of them
must be chemically processed to make other fractions. For example,
only 40% of distilled crude oil is gasoline; however, gasoline
is one of the major products made by oil companies. Rather than
continually distilling large quantities of crude oil, oil companies
chemically process some other fractions from the distillation
column to make gasoline; this processing increases the yield
of gasoline from each barrel of crude oil.
You can change one fraction into another by one of three methods:
- breaking large hydrocarbons into smaller pieces
- combining smaller pieces to make larger ones (unification)
- rearranging various pieces to make desired hydrocarbons
Cracking takes large hydrocarbons and breaks them into smaller
There are several types of cracking:
- Thermal - you heat large hydrocarbons at high temperatures
(sometimes high pressures as well) until they break apart.
- steam - high temperature steam (1500 degrees Fahrenheit
/ 816 degrees Celsius) is used to break ethane, butane
and naptha into ethylene and benzene, which are used to
- visbreaking - residual from the distillation tower is
heated (900 degrees Fahrenheit / 482 degrees Celsius),
cooled with gas oil and rapidly burned (flashed) in a
distillation tower. This process reduces the viscosity
of heavy weight oils and produces tar.
- coking - residual from the distillation tower is heated
to temperatures above 900 degrees Fahrenheit / 482 degrees
Celsius until it cracks into heavy oil, gasoline and naphtha.
When the process is done, a heavy, almost pure carbon
residue is left (coke); the coke is cleaned from the cokers
- Catalytic - uses a catalyst to speed up the cracking reaction.
Catalysts include zeolite, aluminum hydrosilicate, bauxite
- fluid catalytic cracking - a hot, fluid catalyst (1000
degrees Fahrenheit / 538 degrees Celsius) cracks heavy
gas oil into diesel oils and gasoline.
- hydrocracking - similar to fluid catalytic cracking,
but uses a different catalyst, lower temperatures, higher
pressure, and hydrogen gas. It takes heavy oil and cracks
it into gasoline and kerosene (jet fuel).
After various hydrocarbons are cracked into smaller hydrocarbons,
the products go through another fractional distillation column
to separate them.
Sometimes, you need to combine smaller hydrocarbons
to make larger ones -- this process is called unification. The
major unification process is called catalytic reforming and
uses a catalyst (platinum, platinum-rhenium mix) to combine
low weight naphtha into aromatics, which are used in making
chemicals and in blending gasoline. A significant by-product
of this reaction is hydrogen gas, which is then either used
for hydrocracking or sold.
Sometimes, the structures of molecules in one
fraction are rearranged to produce another. Commonly, this is
done using a process called alkylation. In alkylation, low molecular
weight compounds, such as propylene and butylene, are mixed
in the presence of a catalyst such as hydrofluoric acid or sulfuric
acid (a by-product from removing impurities from many oil products).
The products of alkylation are high octane hydrocarbons, which
are used in gasoline blends to reduce knocking.
Blending the Fractions
Distillated and chemically processed fractions are treated to
remove impurities, such as organic compounds containing sulfur,
nitrogen, oxygen, water, dissolved metals and inorganic salts.
Treating is usually done by passing the fractions through the
- a column of sulfuric acid - removes unsaturated hydrocarbons
(those with carbon-carbon double-bonds), nitrogen compounds,
oxygen compounds and residual solids (tars, asphalt)
- an absorption column filled with drying agents to remove
- sulfur treatment and hydrogen-sulfide scrubbers to remove
sulfur and sulfur compounds
After the fractions have been treated, they
are cooled and then blended together to make various products,
- gasoline of various grades, with or without additives
- lubricating oils of various weights and grades (e.g. 10W-40,
- kerosene of various various grades
- jet fuel
- diesel fuel
- heating oil
- chemicals of various grades for making plastics and other | <urn:uuid:9f5e316e-719d-434e-a294-d9bcba6eafc1> | {
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Embryo freezing is the process of taking embryos at any different stage of creation and freezing them. Depending upon how many embryos are to be used for uterine transfer in the future, one or more embryos may be frozen together in a batch. After extraction from the uterus, the embryos are then mixed with a cryoprotectant to prevent damage to the embryo during the process. At that point, the embryos are stored in liquid nitrogen to keep them frozen and stored.
The process of freezing embryos has become wildly popular for patients that have made unsuccessful attempts at alternative fertility treatments. While most experts agree that the procedure is safe, there are some potential risks and complications that a patient should be aware of before electing embryo freezing.
There are several processes that embryos have to go through in order to be kept frozen for future use. In order to do so, they are exposed to a variety of different toxins needed for freezing. While these toxins and cryoprotectants are essential for the freezing process to occur, there is the chance that some embryos make not be able to survive the process because of the drastic, unnatural changes that occur.
Every clinic is different in the survival rates that it boasts, but the average of intact embryos seems to be around 60%, with roughly 20% to 40% either not surviving or being damaged to the extent that they are no longer viable. It is important to keep in mind that the damage or lack thereof cannot be assessed until the embryos have gone through both the freezing and thawing stages.
Although studies regarding birth defects of frozen embryo transfers are limited, some of them have suggested an increase in the occurrence of birth defects. The problem with these studies is that the process of freezing embryos is realistically only 26 years old. There is limited information on the followup of children born out of embryo freezing and implantation. As the years continue to pass and the children born from embryo freezing can be evaluated, there should be more structured, scientific information to prove or disprove this theory. In the meantime, it is simply important for patients be aware that there is a minute risk of birth defects with this process.
Disease and Infection
The embryo freezing process always takes place in a sterile laboratory environment; however, because these embryos are being transferred through the air into a contained environment, there is the very small potential of them coming into contact with pathogens in the air. Studies regarding this are also fresh and point toward this being an extremely rare occurrence. However, it is still a potential risk and should be explained to patients accordingly. Currently experts do not believe that this type of cross-contamination would affect a fetus brought to term, but rather that it might hamper the ability of the embryo to survive the freezing and thawing process. | <urn:uuid:8d94bf92-3714-43ee-81c6-a010ac77bd4a> | {
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# Bar diagram for division
Use the bar diagram to solve each division equation. 2. Write your answer. Check your answer with multiplication. You will need: bar diagrams sheet, pencil, Do you know we can use bar models for multiplication and division problems? In this blog post, we illustrate some of the common types of word problems. A Plethora of Math Anchor Charts – Math Coach’s Corner. Bar models are an excellent way to help students choose an appropriate operation when tackling word. This worksheet is designed to give step by step practice using the bar model. Bar modeling multiplication and division Multiplication Anchor Charts, Big Idea: Bar models can be used to solve different kinds of multiplication and division word problems. Use bar models to solve one-step multiplication word.
View this answer now! It’s completely free.
## long division bar
Calculate the quotient showing long division math work. quotient (answer) space, exactly above the decimal point in the number under the division bar.The long divisions have dividends, divisors, quotients, and remainders. In a long division problem, the dividend is the large number that is divided by another. Long division with remainders showing the work step-by-step. Put the 1 on top of the division bar, to the right of the 0. Next, multiply 1 by 32 and. To get the long division symbol (not ÷) on Microsoft Word document – Type 27cc then press Alt+X. (If you’re not familiar, that meant to hold down the Alt key, bar should be blank because we have not started yet. Now, we can start our long division. There are four steps of long division they are: divide, multiply,
## division bar model worksheets
(For Distance Learning)The word problems in this worksheets pack are based on. Multiplication Division Worksheets 3rd – 4th Grade (Bar Models/Tape. In this worksheet, we will practice drawing bar models and writing equations to represent one-step division problems with numbers up to 100.Big Idea: Bar models can be used to solve different kinds of multiplication and division word problems. Use bar models to solve one-step multiplication word. Apr 30, 2017 – This worksheet is designed to give step by step practice using the bar model strategy of division.Learn how to create and use bar models with Easy Teacher Worksheets help. Bar models are fundamental for introducing students to division.
## bar model division 4th grade
Apr 30, 2017 – This worksheet is designed to give step by step practice using the bar model strategy of division.Bar Model- Division by Erica Goldstick – December 9, 2014.Results 1 – 24 of 1116 Browse division bar models resources on Teachers Pay Teachers, Multiplication Division Worksheets 3rd – 4th Grade (Bar Models/Tape. Nov 24, 2017 – Topics: Solve Multiplication and Division 2 Steps Word Problems for Whole Numbers using Bar Models/Tape Diagrams. (For Distance Learning)The. Do you know we can use bar models for multiplication and division problems? In this blog post, we illustrate. Peggy has 4 times as many stickers as Jill. | crawl-data/CC-MAIN-2023-14/segments/1679296950363.89/warc/CC-MAIN-20230401221921-20230402011921-00631.warc.gz | null |
# Use Taylor's theorem to evaluate the following limits. lim_{xrightarrow0}frac{xsin(x)-x^2}{cos(x)-1+frac{x^2}{2}}
Question
Limits and continuity
Use Taylor's theorem to evaluate the following limits. $$\lim_{x\rightarrow0}\frac{x\sin(x)-x^2}{\cos(x)-1+\frac{x^2}{2}}$$
2020-10-27
Evaluate limit using Taylor’s theorem.
Given:
$$\lim_{x\rightarrow0}\frac{x\sin(x)-x^2}{\cos(x)-1+\frac{x^2}{2}}$$
Taylor series expansion of trigonometric functions,
$$\sin x=\frac{x-x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...$$, $$-\infty Substitute the series, \(\lim_{x\rightarrow0}\frac{x\frac{x-x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...}{1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+...}-1+\frac{x^2}{2}$$
$$\lim_{x\rightarrow0}\frac{(x^2-\frac{x^4}{3!}+\frac{x^6}{5!}-\frac{x^8}{7!}+...) -x^2}{\frac{1-x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+...)-1+\frac{x^2}{2})}$$
Cancelling the term,
$$\lim_{x\rightarrow0}\frac{\frac{-x^4}{3!}+\frac{x^6}{5!}-\frac{x^8}{7!}+...}{\frac{x^4}{4!}-\frac{x^6}{6!}+...}$$
Divide $$x^4$$ in both numerator and denominator,
$$\lim_{x\rightarrow0}\frac{\frac{-1}{3!}+\frac{x^2}{5!}-\frac{x^4}{7!}+...}{\frac{1}{4!}-\frac{x^2}{6!}+..}$$
Apply limit, x tends to 0.
$$\Rightarrow\frac{\frac{-1}{3!}}{\frac{1}{4!}}$$
$$\Rightarrow\frac{-4!}{3!}$$
$$\Rightarrow\frac{4\cdot3\cdot2\cdot1}{3\cdot2\cdot1}$$
$$\Rightarrow-4$$
### Relevant Questions
Use Taylor's theorem to evaluate the following limits. $$\lim_{x\rightarrow0}\frac{3\sin^2(x)+2\sin^4(x)}{3x\tan(x)}$$
Use Taylor series to evaluate the following limits.
$$\lim_{x\rightarrow0}\frac{\sec x-\cos x-x^2}{x^4} \ (Hint: \text{The Maclaurin series for sec x is }1+\frac{x^2}{2}+\frac{5x^4}{24}+\frac{61x^6}{720}+...)$$
Use Taylor series to evaluate the following limits.
$$\lim_{x\rightarrow0}\frac{\sqrt{1+2x}-1-x}{x^2}$$
Use L'Hospital Rule to evaluate the following limits.
$$\lim_{x\rightarrow0}\frac{\tanh^{-1}x}{\tan(\pi x/2)}$$
Use Taylor series to evaluate the following limits. Express the result in terms of the nonzero real parameter(s).
$$\lim_{x\rightarrow0}\frac{e^{ax}-1}{x}$$
Use the method of your choice to evaluate the following limits.
$$\lim_{(x,y)\rightarrow(2,0)}\frac{1-\cos y}{xy^2}$$
$$\lim_{(x,y)\rightarrow(0,\pi/2)}\frac{1-\cos xy}{4x^2y^3}$$
Suppose the functions f(x) and g(x) are defined for all x and that $$\lim_{x\rightarrow0}f(x)=\frac{1}{2}$$ and $$\lim_{x\rightarrow0}g(x)=\sqrt2$$. Find the limits as $$x\rightarrow0$$ of the following functions. $$f(x)\frac{\cos x}{x-1}$$
$$\lim_{(x,y)\rightarrow(1,1)}\frac{x^2+xy-2y^2}{2x^2-xy-y^2}$$
$$\lim_{x\rightarrow0}(\tanh x)^x$$ | crawl-data/CC-MAIN-2021-21/segments/1620243989749.3/warc/CC-MAIN-20210510204511-20210510234511-00084.warc.gz | null |
Homework 3 Solutions
# Homework 3 Solutions - homework 03 – ALIBHAI ZAHID –...
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Unformatted text preview: homework 03 – ALIBHAI, ZAHID – Due: Feb 7 2007, 4:00 am 1 Question 1 part 1 of 1 10 points A ball rolling up a hill has vector velocities vectorv 1 and vectorv 2 at times t 1 and t 2 , respectively, as shown in the figure. v 1 initial v 2 final Which vector diagram below most accu- rately depicts the direction of the ball’s aver- age acceleration over the interval? 1. 2. 3. 4. 5. 6. correct 7. 8. 9. Zero vector. Explanation: In fact the two forces exerting on the ball, the gravitational force from the earth and the force from the incline remain unchanged dur- ing the interval, to total acceleration should be downward to the left and won’t change either. Question 2 part 1 of 2 10 points A truck driver attempting to deliver some furniture travels 6 km east, turns around and travels 2 km west, and then travels 11 km east to his destination. a) What distance has the driver traveled? Correct answer: 19 km (tolerance ± 1 %). Explanation: Basic Concept: d = | Δ x 1 | + | Δ x 2 | + | Δ x 3 | Let: Let North and East be positive Δ x 1 = 6 km , Δ x 2 = − 2 km , Δ x 3 = 11 km , and Δ y = 0 km . Solution: d = (6 km) + (2 km) + (11 km) = 19 km . Question 3 part 2 of 2 10 points homework 03 – ALIBHAI, ZAHID – Due: Feb 7 2007, 4:00 am 2 b) What is the magnitude of the driver’s total displacement? Correct answer: 15 km (tolerance ± 1 %). Explanation: Basic Concept: d 1 = Δ x 1 + Δ x 2 + Δ x 3 Solution: Displacement is a vector d 1 = (6 km) − (2 km) + (11 km) = 15 km . Question 4 part 1 of 2 10 points A commuter airplane starts from an airport and takes the route shown in the figure. It first flies to city A located at 191 km in a direction 28 ◦ north of east. Next, it flies 154 km 17 ◦ west of north to city B . Finally, it flies 155 km due west to city C . 1 9 1 k m 28 ◦ A 1 5 4 k m 17 ◦ B 155 km C R C x (km) y (km) 50 100 150 200 50 100 150 200 250 W E S N How far away from the starting point is city C ? Correct answer: 239 . 009 km (tolerance ± 1 %). Explanation: Given : a = 191 km , α = 28 ◦ , b = 154 km , β = 17 ◦ , and c = 155 km . a b α β The x-component of the resultant is r x = a x + b x + c x = a cos α − b sin β − c = (191 km) cos28 ◦ − (154 km) sin17 ◦ − 155 km = − 31 . 3823 km . The y-component of the resultant is r y = a y + b y + c y = a sin α + b cos β + 0 = (191 km) sin28 ◦ + (154 km) cos 17 ◦ = 236 . 94 km . and the resultant is R = radicalBig r x 2 + r y 2 = radicalBig ( − 31 . 3823 km) 2 + (236 . 94 km) 2 = 239 . 009 km . Question 5 part 2 of 2 10 points What is the direction of the final position vector r , measured from North? Use coun- terclockwise as the positive angular direction, between the limits of − 180 ◦ and +180 ◦ ....
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# How to express a 2nd order ODE as 1st order ODE's?
Express the 2nd order ODE
\begin{align}\mathrm d_t^2 u:=\frac{\mathrm d^2 u}{\mathrm dt^2}&=\sin(u)+\cos(\omega t)\qquad \omega \in \mathbb Z /\{0\} \\u(0)&=a\\\mathrm d_t u(0)&=b\end{align}
as a system of 1st order ODEs and verify there exists a global solution by invoking the global existence and uniqueness theorems.
I'm not sure how to express second order ODEs as first order ODEs, any tips?
Thanks.
-
Make a new variable, $v=\dfrac{\mathrm du}{\mathrm dt}$... – J. M. Oct 9 '11 at 1:15
How do you show there exists a global solution byt invoking the theorem? Theorem states: An IVP has a unique solution if the function f is continuous with respect to the 1st variable and Lipshitz continuous with respect to the 2nd variable. – Euden Sep 27 '12 at 12:14
Here's an example to get you started:
$$u^{(3)}(t)+t^3u''(t)+5u'(t)+\sin(t)u=e^{6t}$$
with initial values $u''(0)=1$, $u'(0)=2$, and $u(0)=3$
First, give new names to $u$ and its derivatives (stopping one short of the order of the ODE): $u=x_1$, $u'=x_2$, $u''=x_3$.
Substituting back into the DE (keeping in mind that $u^{(3)}(t)=x'_3(t)$) we get: $$x'_3(t)+t^3x_3(t)+5x_2(t)+\sin(t)x_1(t)=e^{6t}$$
Thus we have the equivalent system:
$$\begin{array}{ccrrrr} x'_1 & = & & x_2 & & \\ x'_2 & = & & & x_3 & \\ x'_3 & = & -\sin(t)x_1 & -5x_2 & -t^3x_3 & +e^{6t} \end{array}$$
Also, $x_1(0)=3$, $x_2(0)=2$, and $x_3(0)=1$.
-
To convert second-order ODE to a first-order system you have to introduce new variables:
$u_1=u$
$u_2=u'_t$
Now we can write following:
$(u_1)'_t=u_2$
$(u_2)'_t=u''_t=\sin(u_1)+\cos(\omega t)$
with the initial condition $u_1(0)=a$ , $u_2(0)=b$
- | crawl-data/CC-MAIN-2016-30/segments/1469257824499.16/warc/CC-MAIN-20160723071024-00143-ip-10-185-27-174.ec2.internal.warc.gz | null |
Today, there over one hundred different types of crayons being made by Crayola including crayons that: sparkle with glitter, glow in the dark, smell like flowers, change colors, and wash off walls and other surfaces and materials.
According to Crayola's "History of Crayons"Europe was the birthplace of the “modern” crayon, a man-made cylinder that resembled contemporary sticks. The first such crayons are purported to have consisted of a mixture of charcoal and oil. Later, powdered pigments of various hues replaced the charcoal. It was subsequently discovered that substituting wax for the oil in the mixture made the resulting sticks sturdier and easier to handle.
The Birth of Crayola CrayonsIn 1864, Joseph W. Binney founded the Peekskill Chemical Company in Peekskill, N.Y. This company was responsible for products in the black and red color range, such as lampblack, charcoal and a paint containing red iron oxide which was often used to coat the barns dotting America's rural landscape.
Peekskill Chemical was also instrumental in creating an improved and black colored automobile tire by adding carbon black that was found to increase the tire tread life by four or five times.
Around 1885, Joseph's son, Edwin Binney, and nephew, C. Harold Smith, formed the partnership of Binney & Smith. The cousins expanded the company's product line to include shoe polish and printing ink. In 1900, the company purchased a stone mill in Easton, PA, and began producing slate pencils for schools. This started Binney's and Smith's research into nontoxic and colorful drawing mediums for kids. They had already invented a new wax crayon used to mark crates and barrels, however, it was loaded with carbon black and too toxic for children. They were confident that the pigment and wax mixing techniques they had developed could be adapted for a variety of safe colors.
In 1903, a new brand of crayons with superior working qualities was introduced - Crayola Crayons. | <urn:uuid:81ba5a46-65a7-481d-9483-9cc3e8e9dabb> | {
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Tutor profile: Karrie G.
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Karrie G.
Tutor of various math subjects for 2+ years
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Subject:Geometry
TutorMe
Question:
If <ABC and <DEF are supplementary angles and <ABC is 102, what is the measure of <DEF?
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Karrie G.
1. Supplementary angles are angles that must add up to 180 <ABC + <DEF = 180 2. We are given measure of ABC and we can substitute 102 + <DEF = 180 3. Solve for <DEF <DEF = 180 - 102 <DEF = 78 - Final Answer
Subject:Pre-Algebra
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Find the Greatest Common Factor (GCF) of 18 and 24
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1. Find the prime factors of each number using a factor tree 18: 2 x 9 9 -> 3 x 3 18: 2 x 3 x 3 24: 2 x 12 12 -> 2 x 6 6 -> 2 x 3 24: 2 x 2 x 2 x 3 2. Find the numbers that they have in common : 2 and 3 3. Multiply the numbers that they have in common : 2 x 3 = 6 , 6 is the GCF
Subject:Algebra
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Question:
Write an equation of the line with slope 5 and x-intercept (-4,2)
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Karrie G.
A line with slope m and passes through a point (a,b) has an equation in the form of y-b = m (x-a) Using the given slope and point, we can write the equation of the line y-2=5(x-(-4)) Expand the equation by distributing the 5: y-2=5x-(-20) --> y-2 = 5x +20 Simplify by combining like terms and make the equation in the form of "y=...": y=5x+22
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# Chapter 5: Interpreting Fractions In The Classroom
Decent Essays
Chapter 5 is yet again another huge step involving fractions. It seems that each grade gets more and more complicated. For 5th grade students will learn representation of decimals in the thousands and comparing decimals in the thousands. It also expands on adding and subtracting of fractions, interpreting them as implied division, multiplying and dividing fractions as well. In the fifth grade, students move on to greater decimal places such as the thousandths place. This can get confusing for some students because we are mainly only teaching them to use this place value when being very specific. To represent this in the classroom it is beneficial to use a thousandths grid. Each grid is made up 100 sets of 10 rectangles. Another way to teach thousandths place is by using base ten blocks. It is important though when using…show more content…
First teachers have to be sure students understand that a/b multiplied by c is the same as saying a/b groups of c. This is similar to interpreting fractions as implied concepts. Possible ways of teaching this is threw visual aids. One visual aid is using a number line. Have students explain how the fractions are located within numbers on the number line. Or you can have them do this by filling in squares to represent the fractions being multiplied. Multiplying fractions to describe area is another subject they cover in this grade. The students should already know how to calculate area so all they have to do is apply previous learned concepts about multiplying fractions to do this. Taking multiplication of fractions farther, students in the fifth grade learn how to interpret multiplication by scaling. This is done by saying, “one object is four times as much as another.” For example, if two rectangles are laid side by side it is easy to see how one could be split up in to four pieces while the other stays whole. The rectangle not split up is considered four times bigger than the one split | crawl-data/CC-MAIN-2023-23/segments/1685224656737.96/warc/CC-MAIN-20230609132648-20230609162648-00459.warc.gz | null |
Tuesday, March 1, 2016
Geometry Problem 1193: 3-4-5 Right Triangle, Congruent Circles, Tangent, Radius
Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.
Click the figure below to view more details of problem 1193.
1. Let the points of tangency on the hypotenuse be M and N. Let the parallel to BC thro O2 meet the parallel to AB thro O1 meet at L
O1M = O2M = r and they are parallel to each other hence O1O2NM is a rectangle
Let AM = p
Then MN = 2r, CN = 5-p-2r, O1L = 3-p-r and O2L = r+p-1
Tr. O1O2L is similar to Tr. ABC since corresponding sides are parallel.
So 2r/5 = (3-p-r)/3 = (r+p-1)/4
Solving the simultaneous equations for p and r
p = 10/7 and r = 5/7
Sumith Peiris
Moratuwa
Sri Lanka
2. http://s22.postimg.org/3t229d6xd/pro_1193.png
Let AO1 and CO2 meet at O
Let r’ and r1 are radii of incircles of triangles ABC and O1DO2
Observe that O is the incenter of both triangles
.r’= area of Tri. ABC/half of perimeter of ABC= 6/6=1
O1DO2 and ABC are similar triangles => r1/r’= O1O2/BC= 2.r/5 => r1=2.r/5
We have r’=r1+r= 7/5.r =1 => r=5/7
3. Name T1, T2 tg points of O1, O2 Draw from O1//to AB , from O2 // to BC
They meet at P Triangle PO1O2 similar to ABC => T2C=1,5 T1A From similarity
again => AT1=2r => r=5/7 | crawl-data/CC-MAIN-2018-30/segments/1531676595531.70/warc/CC-MAIN-20180723071245-20180723091245-00262.warc.gz | null |
# 8.3.1: Solution of Initial Value Problems (Exercises)
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## Q8.3.1
In Exercises 8.3.1-8.3.31 use the Laplace transform to solve the initial value problem.
1. $$y''+3y'+2y=e^t, \quad y(0)=1,\quad y'(0)=-6$$
2. $$y''-y'-6y=2, \quad y(0)=1,\quad y'(0)=0$$
3. $$y''+y'-2y=2e^{3t}, \quad y(0)=-1,\quad y'(0)=4$$
4. $$y''-4y=2 e^{3t}, \quad y(0)=1,\quad y'(0)=-1$$
5. $$y''+y'-2y=e^{3t}, \quad y(0)=1,\quad y'(0)=-1$$
6. $$y''+3y'+2y=6e^t, \quad y(0)=1,\quad y'(0)=-1$$
7. $$y''+y=\sin2t, \quad y(0)=0,\quad y'(0)=1$$
8. $$y''-3y'+2y=2e^{3t}, \quad y(0)=1,\quad y'(0)=-1$$
9. $$y''-3y'+2y=e^{4t}, \quad y(0)=1,\quad y'(0)=-2$$
10. $$y''-3y'+2y=e^{3t}, \quad y(0)=-1,\quad y'(0)=-4$$
11. $$y''+3y'+2y=2e^t, \quad y(0)=0,\quad y'(0)=-1$$
12. $$y''+y'-2y=-4, \quad y(0)=2,\quad y'(0)=3$$
13. $$y''+4y=4, \quad y(0)=0,\quad y'(0)=1$$
14. $$y''-y'-6y=2, \quad y(0)=1,\quad y'(0)=0$$
15. $$y''+3y'+2y=e^t, \quad y(0)=0,\quad y'(0)=1$$
16. $$y''-y=1, \quad y(0)=1,\quad y'(0)=0$$
17. $$y''+4y=3\sin t, \quad y(0)=1,\quad y'(0)=-1$$
18. $$y''+y'=2e^{3t}, \quad y(0)=-1,\quad y'(0)=4$$
19. $$y''+y=1, \quad y(0)=2,\quad y'(0)=0$$
20. $$y''+y=t, \quad y(0)=0,\quad y'(0)=2$$
21. $$y''+y=t-3\sin2t, \quad y(0)=1,\quad y'(0)=-3$$
22. $$y''+5y'+6y=2e^{-t}, \quad y(0)=1,\quad y'(0)=3$$
23. $$y''+2y'+y=6\sin t-4\cos t, \quad y(0)=-1,\; y'(0)=1$$
24. $$y''-2y'-3y=10\cos t, \quad y(0)=2,\quad y'(0)=7$$
25. $$y''+y=4\sin t+6\cos t, \quad y(0)=-6,\; y'(0)=2$$
26. $$y''+4y=8\sin2t+9\cos t, \quad y(0)=1,\quad y'(0)=0$$
27. $$y''-5y'+6y=10e^t\cos t, \quad y(0)=2,\quad y'(0)=1$$
28. $$y''+2y'+2y=2t, \quad y(0)=2,\quad y'(0)=-7$$
29. $$y''-2y'+2y=5\sin t+10\cos t, \quad y(0)=1,\; y'(0)=2$$
30. $$y''+4y'+13y=10e^{-t}-36e^t, \quad y(0)=0,\; y'(0)=-16$$
31. $$y''+4y'+5y=e^{-t}(\cos t+3\sin t), \quad y(0)=0,\quad y'(0)=4$$
## Q8.3.2
32. $$2y''-3y'-2y=4e^t, \quad y(0)=1,\; y'(0)=-2$$
33. $$6y''-y'-y=3e^{2t}, \quad y(0)=0,\; y'(0)=0$$
34. $$2y''+2y'+y=2t, \quad y(0)=1,\; y'(0)=-1$$
35. $$4y''-4y'+5y=4\sin t-4\cos t, \quad y(0)=0,\; y'(0)=11/17$$
36. $$4y''+4y'+y=3\sin t+\cos t, \quad y(0)=2,\; y'(0)=-1$$
37. $$9y''+6y'+y=3e^{3t}, \quad y(0)=0,\; y'(0)=-3$$
38. Suppose $$a,b$$, and $$c$$ are constants and $$a\ne0$$. Let $y_1={\cal L}^{-1}\left(as+b\over as^2+bs+c\right)\quad \text{and} \quad y_2={\cal L}^{-1}\left(a\over as^2+bs+c\right). \nonumber$
Show that $y_1(0)=1,\quad y_1'(0)=0\quad \text{and} \quad y_2(0)=0,\quad y_2'(0)=1.\nonumber$
HINT: Use the Laplace transform to solve the initial value problems
$\begin{array}{lll}{ay''+by'+cy=0,}&{y(0)=1,}&{y'(0)=0}\\[4pt]{ay''+by'+cy=0,}&{y(0)=0,}&{y'(0)=1} \end{array}\nonumber$
This page titled 8.3.1: Solution of Initial Value Problems (Exercises) is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench. | crawl-data/CC-MAIN-2024-38/segments/1725700651422.16/warc/CC-MAIN-20240912043139-20240912073139-00015.warc.gz | null |
# Unit Test Review - Linear Functions
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Quizzes Created: 1 | Total Attempts: 177
Questions: 12 | Attempts: 177
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• 1.
### Given: f(x) = 3x - 2 Find f(0)
• A.
-2
• B.
-1
• C.
0
• D.
2
A. -2
Explanation
substitute in zero for x and evaluate the right side of the equation
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• 2.
### Given: f(x) = 3x - 2 Find x if f(x) = 7
• A.
7
• B.
1
• C.
3
• D.
5
C. 3
Explanation
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• 3.
### Translate the following statement into a coordinate point: h(3) = -1
• A.
(-1, 3)
• B.
(3, -1)
• C.
(1, 3)
• D.
(3, 1)
B. (3, -1)
Explanation
the quantity inside the parentheses is always the x value
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• 4.
### True or False: The relation shown above is a function.
• A.
True
• B.
False
A. True
Explanation
It passes the vertical line test. There is really only one y value at x = 2 because of the "hole" in the graph.
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• 5.
• A.
1
• B.
2
• C.
3
• D.
4
C. 3
• 6.
### What is the value of x when f(x) = 3?
• A.
1
• B.
2
• C.
3
• D.
Both a and c are correct
D. Both a and c are correct
Explanation
The value of x when f(x) = 3 can be either 1 or 3. This is because "Both a and c are correct" implies that both options 1 and 3 are correct answers. Therefore, either 1 or 3 can be the value of x that satisfies the equation f(x) = 3.
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• 7.
### What is the domain of the relation shown above?
• A.
[1, 3]
• B.
(1, 3)
• C.
[1, 2) U (2, 3]
• D.
{1} U (2, 3]
A. [1, 3]
Explanation
The domain of a relation refers to the set of all possible input values or x-values. In this case, the relation is shown to have values ranging from 1 to 3, inclusive of both endpoints. Therefore, the correct answer is [1, 3].
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• 8.
### Find an equation of a linear function given g(0) = 5 and g(-2) = 4.
• A.
G(x) = -2x + 5
• B.
G(x) = 4x
• C.
• D.
D.
Explanation
Take the points (0, 5) and (-2, 4) and find the slope. Then you can substitute into the point-slope formula using one of the points OR the slope-intercept formula since you can see the first point is the y-intercept.
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• 9.
### Lia joins an art club that has an enrollment fee of \$100 and costs \$20 per month. Which equation correctly describes this situation with cost as a function of months?
• A.
C(m) = 100m + 20
• B.
C(m) = 20m + 100
• C.
M(c) = 100c + 20
• D.
M(c)= 20c + 100
B. C(m) = 20m + 100
Explanation
The equation C(m) = 20m + 100 correctly describes the situation with cost as a function of months. The variable m represents the number of months, and the equation shows that the total cost C is determined by multiplying the number of months by 20 (the monthly cost) and adding the enrollment fee of \$100.
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• 10.
### Which equation correctly represents the linear function shown?
• A.
Y = 2x
• B.
Y = 2x + 1
• C.
Y = x + 1
• D.
Y = x
A. Y = 2x
Explanation
Since the graph goes through the origin you know the y-intercept is zero. Then you can see it goes up 2, and right 1, to the point (1, 2) giving you a slope of 2/1 which is equal to 2.
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• 11.
### Maddie's theater company put on a show and sold 500 tickets to the show. Floor seats cost \$10 and balcony seats cost \$5. Total ticket sales were \$4500. Set up a system of equations and solve it to find the number of floor seats. Your answer should just be a number.
400
Explanation
Your system of equations should be f + b = 500 and 10f + 5b = 4500.
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• 12.
### Maddie's theater company put on a show and sold 500 tickets to the show. Floor seats cost \$10 and balcony seats cost \$5. Total ticket sales were \$4500. Set up a system of equations and solve it to find the number of balcony seats. Your answer should just be a number.
100
Explanation
Let's assume the number of floor seats sold is F and the number of balcony seats sold is B. The total number of tickets sold is 500, so we have the equation F + B = 500.
The price of each floor seat is \$10, so the total revenue from floor seats is 10F. Similarly, the price of each balcony seat is \$5, so the total revenue from balcony seats is 5B.
The total ticket sales were \$4500, so we have the equation 10F + 5B = 4500.
By solving the system of equations, we can find the number of balcony seats, which is 100.
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for National Geographic News
Developing ultrasound blasts to disrupt enemy sonar may sound more like a submarine arms race than animal evolution. But, believe it or not, some moths have done just that to evade hungry bats, a new study says.
Bats emit high-pitched cries, then listen as the sound waves bounce off nearby objects—allowing the bats to find and eat tiny insects in the dark, among other things.
Yet bats aren't the only ones making waves.
Some tiger moth species make ultrasonic clicks with their bodies.
"These clicks were puzzling to us, because we did not know if they were being used to startle attacking bats, warn the bats that the moths tasted bad, or somehow confuse the bats by jamming their sonar," said study co-author William Conner, a biologist at Wake Forest University.
To find out, Wake Forest research team had so-called big brown bats hunt tiger moths in a chamber fitted with ultrasonic recording equipment and high-speed infrared video.
If the moth sound is used to startle bats, then in the chamber the bats should be disrupted on first attack, then learn to ignore the ultrasonic click, the team figured.
That didn't happen.
If the moths' clicks are warnings that the insects taste bad, then the bats should hear the click, bite the moth—and never do so again whenever they hear the sound.
That didn't happen either.
Instead, the bats regularly missed the moths when the ultrasonic clicks were emitted—proof, the team says, that moths have evolved a way to jam bat sonar.
(See bat pictures from National Geographic magazine.)
Findings published in today's issue of the journal Science.
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So let me just start by defining color as the characteristics of human perception. Using the light spectrum our eyes interpret color. Some people may see color differently. There is certainly color blindness in the world as well. Color is usually identified in the design world one of two ways, RGB (Red, Green, and Blue) or CMYK (Cyan, Magenta, Yellow, Black). Before we get into the more film related color jargon, lets make sure you understand this concept.
Additive color is light created by mixing together light of two or more different colors. RGB are the primary colors normally used in additive color systems.
Subtractive color uses, dyes, inks, or filters to absorb some wavelengths of light and not others.
Additive and Subtractive color is the reason why adding all the colors in the spectrum of light creates white (additive), will combing all the colors in paint creates black (subtractive).
Color can be described in 3 ways:
- The Hue, which is the color itself.
- The Saturation, which is the intensity of the color.
- The Value, which is the lightness and darkness of a color.
Check out how color has been used in these films:
Color from a film theory perspective
Humans have been conditioned to perceive certain colors differently than others. We also assign emotions to colors whether we know it or not. If I say think of something red, you may think of a heart, you may start to feel love/passion, or you may think of a stop sign which causes you to pause. So just in that one color example, I am able to communicate so much just from one color.
Color can affect us emotionally, psychologically, without us being aware of it. Color in film can complete change the tone of a scene. Here are some of the ways you can use color:
- Elicit psychological reactions with the audience
- Draw focus to significant details
- Set the tone of the movie
- Represent character traits and more
- Show changes or arcs in the story
As a filmmaker, choose your film palette carefully to maximize emotional effect.
Associative Colors in film means that the writer, director, or artist associates a color with a character, emotion, or theme. You can also use color as a transition in the story line. Transitional colors can represent a change in a character or theme.
“The color scheme is the combination of multiple colors to communicate the thematic context.”
A great resource to see the different color schemes in film is www.moviesincolor.com.
The four most common types of balanced color schemes are Monochromatic, Analogous, Complementary, and Triadic.
Discordant Colors are any deviations from the film’s color scheme. This is often used to refocus viewer’s attention to an important person, place, or thing. It can also help a character, detail, or moment stand out from the rest of the film.
Understanding color is an important part of film-making. You must not only learn what color does, but also use and apply that knowledge.
Thank you for reading: If you want more content like this be sure to support the blog on Patreon. If you have any questions, ask me in the Capturing Light Community on Facebook. I would love to hear from you. https://www.facebook.com/groups/capturinglightcommunity | <urn:uuid:0e240d6d-ec40-4cfa-99bb-2298b7401e76> | {
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Before you can use the sundial properly, you need to do a few simple tasks. First, you need to find a flat surface on which to place the sundial. In order to maintain the accuracy, the surface should be as horizontal as possible. If you wish to be meticulous, you can accomplish this by aligning a level both North-South and East-West on the table and adjusting the legs until both levels are level. But this is not necessary. You can eyeball a level surface, and generally that is good enough. Note: the further the sundial is from the horizontal, the less accurate the sundial is. Secondly, you need to orient the sundial as indicated in the upper right corner of figure 3. One can use a compass to find north, but do note that a compass points to magnetic north, and not to true north. For Bloominton magnetic north is about degrees to the west of true north. For accurate alignment, one must correct for this discrepancy. However, for the sundial in this handout, magnetic north will do. Lastly, you need to acquire a gnomon. The enclosed sundial uses a vertical gnomon that is specifically 0.5 inches in height. Any thing will work. Some ideas are a tooth pick, a twig, or a triangluar sheet of paper. The later has the advantage that it can be taped to the paper and placed into the vertical position whenever you want to use the sundial.
Figure 1: This shows the construction of the triangular gnomon.
To set up the triangular gnomon, you need to obtain a sheet of paper with square corners, a protractor, a ruler, and a pair of scissors. Make sure the sheet of paper you obtain has square corners. If you use a piece of paper that does not have square corners, your sundial will not give the correct time. On your sundial, you will see two x's. If you look at figure 3, you will see that these x's are labeled the Vertical Gnomon Position, and the Polar Gnomon Position. With your protractor, you need to make a mark on one edge of the paper that is exactly one-half an inch from a corner. Then from this point you need to use the protractor to draw a line that makes an angle with the edge of the paper which is equal 90.0 degrees minus your latitude. For example, in Bloomington, Indiana the latitude is about 40 degrees. The angle between the line you draw on the page and the edge of the page with the 0.5 inch mark should be 90.0 - 40.0 = 50.0 degrees. You should have something that looks like figure 1. Now cut along the drawn line. You should be left with a small triangle with one edge that is 0.5 inches in length. This edge is your gnomon. Now all you need to do is attach the triangle to the sundial as shown in figure 2 in a vertical position.
Figure 2: Method used to attach the triangular gnomon to the sundial.
Once you have obtained a suitable gnomon, you need to place it on the sundial in the appropriate position. On the sundial you will see two x's. One is the polar gnomon position, and the other is the vertical gnomon position. The gnomon/stick should be place on the x labeled the vertical gnomon position. Please see attached sheet for a diagram. Once you have done the above, the sundial should be in working order. | <urn:uuid:eaa8c24f-c26c-454c-bc7d-f3366aa0206c> | {
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true false Addition / Subtraction - Combine like terms (i.e. If then becomes and is a real number. To factor out the imaginary unit, rewrite the square root of the product as the product of square roots. (Note: and both can be 0.) The record bi means the same as 0+ bi. Write the square root as a pure imaginary number. For example, $5+2i$ is a complex number. Imaginary Part (of a complex number) How many goats do you have? Let z be a complex number, i.e. If … Figure $$\PageIndex{1}$$ Imaginary numbers are distinguished from real numbers because a squared imaginary number produces a negative real number. That particular form is sometimes called the standard form of a complex number. 2 is the imaginary part. A number of the form bi, where b ≠ 0, is called a pure imaginary number. Numbers with real part of zero are sometimes called "pure imaginary", with the term "complex" reserved for numbers with both components nonzero. A complex number is any number that can be written in the form a + b i where a and b are real numbers. Combining pure oscillations of the same frequency. Can you take the square root of −1? Learn about the imaginary unit i, about the imaginary numbers, and about square roots of negative numbers. In order for a+bi to be a complex number, b must be nonzero. To add (or subtract) two complex numbers, you add (or subtract) the real and imaginary parts of the numbers separately. Imaginary numbers and real numbers together make up the set of complex numbers. ! If b≠ 0, the number a + bi is called an imaginary number. What is a complex number ? Simplifying the Square Root of a Negative Number. A complex number is written in a + bi form (standard form), where a is the 'real part' and bi is the 'imaginary part'. the imaginary number $$j$$ has the property that $$j^2=-1$$. A complex number is any number that can be written in the form a + b i where a and b are real numbers. Express your answer in the form a + bi. The value of bbb is zero. Pure Imaginary Numbers Numbers Directions: Evaluate. Which of the following statements is not true? (-5+61) (-5 - 61) Perform the indicated operation and simplify. An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2 = −1. This is true, using only the real numbers.But here you will learn about a new kind of number that lets you work with square roots of negative numbers! b (2 in the example) is called the imaginary component (or the imaginary part). B. The solution is given by an imaginary number − 1 \sqrt{-1} − 1 , denoted by i which is called the imaginary unit. It is mostly written in the form of real numbers multiplied by … Google Classroom Facebook Twitter. Complex numbers can be graphed in a coordinate plane with a real axis and an imaginary axis. If b = 0, the number a + bi is a real number. If then is an imaginary number. The real and imaginary components. The real axis is the horizontal axis in the complex plane and represents the set of real numbers. Today, we find the imaginary unit being used in mathematics and science. The form for a complex number is a + bi, where a & b can be any real numbers (so if a = 0, then the number is pure imaginary; and if b=0, then it is a real number). Also, as usual, if a term is 0, or a coefficient is 1, we often omit it; so $$0+1i$$ (correct standard form) is often written simply as $$i$$. A complex number is a number that can be written in the form a + b i a + bi a + b i, where a a a and b b b are real numbers and i i i is the imaginary unit defined by i 2 = − 1 i^2 = -1 i 2 = − 1. Step-by-step explanation: A complex number is written in the form a+bi. Complex numbers in the form a + bi can be graphed on a complex coordinate plane. The real axis is the line in the complex plane consisting of the numbers that have a zero imaginary part: a + 0i. If b = 0, the number a + bi = a is a real number. Let the components of the input and output planes be: z = x + i y and w = u + i v . Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. If a= 0 (0+ bi), the number is a pure imaginary number. If a = 0 and b ≠ 0, the complex number is a pure imaginary number. Addition and Subtraction: Combine like terms. Write the standard form of the complex number: Rewrite any square roots of negative numbers as pure imaginary numbers. The following diagram shows the relationship among these sets of numbers. Imaginary Number The square root of a negative number, written in the form bi, where b is a real number and i is the imaginary unit. All multiples of i, written in the form ni (where n is some nonzero real number), are called pure imaginary numbers. For 3+i2\sqrt{3}+i\sqrt{2}3+i2, the value of aaa is 3\sqrt{3}3. We usually use a single letter such as z to denote the complex number a+ bi. But in electronics they use j (because "i" already means current, and the next letter after i is j). A pure imaginary number can be written in bi form where b is a real number and i is √-1. A complex number is any number that can be written in the standard form a + bi, where a and b are real numbers and i is the imaginary unit. Imaginary Numbers are not "Imaginary". A complex number is the sum of a real number and an imaginary number. Complex Number – any number that can be written in the form + , where and are real numbers. any number that can be written in the form of a + bi where a and b are real numbers. It takes about six paragraphs. Write each number in the standard form of a complex number. 2. 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Note these examples of complex numbers written in standard a + bi form: 2 + 3i, -5 + bi . A. Kumar's Maths Revision Further Pure 1 Complex Numbers The EDEXCEL syllabus says that candidates should: a) understand the idea of a complex number, recall the meaning of the terms real part, imaginary part, modulus, argument, conjugate, and use the fact that two complex numbers are equal if and only if both real and imaginary parts are equal; For example, 3 + 2i. It is said that the term “imaginary” was coined by René Descartes in the seventeenth century and was meant to be a derogatory reference since, obviously, such numbers did not exist. A number of the form bi, where b ≠0, is called a pure imaginary number. A strictly real or imaginary number is also complex, with the imaginary or real part equal to zero, respectively. Equality of Complex Numbers – Two complex numbers a + biand c + di, written in standard form, are equal to each other a bi c di if and only if a = cand b = d. Week 3 Complex Numbers MTH255 21.1 Complex Numbers in Rectangular Form The imaginary unit is written as square root of … A complex number 0+ bi is called a pure imaginary number. ... and Vertex Form The union of the set of all imaginary numbers and the set of all real numbers is the set of complex numbers. In this case a is the real part of z,writtena =Rez, and b is the imaginary part of z,written b =Imz. 1 i iyx 10. Some examples are 1 2 i 12i 1 2 i and i 1 9 i\sqrt{19} i 1 9 . z = (x, y) x is the real part of z, and y is the imaginary part of z. Complex Numbers a + bi Real Numbers, a Imaginary Numbers, bi Example: p. 127 Write the number in standard form 1 + √-8 simplify √-8 = 1 + 2√2 i 18. The imaginary axis is the line in the complex plane consisting of the numbers that have a zero real part:0 + bi. Also called a pure imaginary number. 4 +2i. Complex numbers form what is called a field in mathematics, which (in a nutshell – this is not a text in pure mathematics) means that: products and sums of complex numbers are also complex numbers Each complex number corresponds to a point (a, b) in the complex plane. The square root of any negative number can be rewritten as a pure imaginary number. . For example, we can write, 2 = 2 + 0.i. We define. 18. (−9) 3 ⋅()2i 6 Complex Numbers Numbers • Complex numbers are written as a + bi, where a represents the real number and bi represents the pure imaginary number. The pure imaginary part of the complex number needs to be represented on a second number line. The complex plane is used to locate points that represent complex numbers in terms of distance from the real axis and the imaginary axis. Adding complex numbers. All complex numbers have a real part and an imaginary part, although one or both of these parts may be equal to zero. 1. If a = 0 and b uni2260.alt1 0, the number a + bi is a pure imaginary number. A complex number is the sum of a real number and a pure imaginary number. Remember that a complex number has the form a + bi. Imaginary Axis is the y-axis of a complex plane or Argand diagram. Here is a picture of the number $2+3i$, represented by a point. For example, $5+2i$ is a complex number. Learn more about besselj besseli. lets take the example of the square function w = … An imaginary number is defined where i is the result of an equation a^2=-1. There is a thin line difference between both, complex number and an imaginary number. Got It? 2. So, too, is $3+4i\sqrt{3}$. Pure real values always square to a positive value and pure imaginary values always square to a negative value. 3. If the real part of is zero, and the imaginary part non-zero, then is called an imaginary number. You have 3 goats and you lost 5. Real numbers written as complex are $(x, 0), \ \ x \in \mathbb{R}$ Each complex number (x, y) have a relevant point on the $\frac{1}{2}\log(-\exp(i2\pi q))$, //for a real "input" q. This imaginary number has no real parts, so the value of … The imaginary axis is the vertical axis in the complex plane and represents the set of pure imaginary numbers. All multiples of i, written in the form ni (where n is some nonzero real number), are called pure imaginary numbers. As I don't know much about maths, what I've tried untill now was to prove it by applying Euler's formula, but … In the history of mathematics we have been inventing different types of numbers as we needed. A complex number is an expression that can be written in the form where and are real numbers (and multiplies). What is complex number system? Graphing complex numbers. Also if a complex number is such that a = 0, we call it a purely imaginary number. Addition and Subtraction of Complex Numbers The value of bbb is 2. The square of an imaginary number bi is −b2. Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. Therefore, every real number can be written in the form of a + ib; where b = 0. Course Hero is not sponsored or endorsed by any college or university. Write −3i as a complex number. Intro to the imaginary numbers. So, too, is $3+4i\sqrt{3}$. A complex number is a number that can be written in the form a + b i a + bi a + b i, where a a a and b b b are real numbers and i i i is the imaginary unit defined by i 2 = − 1 i^2 = -1 i 2 = − 1. It is the square root of negative 1. A complex number is in standard form when written as where a and b are real numbers. T RUE OR FALSE i2 = square root of Example: 7 + 2i A complex number written in the form a + bi or a + ib is written in standard form. The real and imaginary components. More lessons about complex numbers. A complex number is a real number a, or a pure imaginary number bi, or the sum of both. (−i 2)5 ⋅(−3i10)3 12. Complex numbers are written in the form (a+bi), where i is the square root of -1.A real number does not have any reference to i in it.A non real complex number is going to be a complex number with a non-zero value for b, so any number that requires you to write the number i is going to be an answer to your question.2+2i for example. Powers of i. A pure imaginary number is any complex number whose real part is equal to 0. The reason for the name “imaginary” numbers is that when these numbers were first proposed several hundred years ago, people could not “imagine” such a number. Imaginary no.= iy. Division of complex numbers written in polar form is done by the rule (check it by crossmultiplying and using the multiplication rule): r ei = r e i ( − ); division rule r ei r to divide by a complex number, divide by its absolute value and subtract its angle. If bz 0, the number a + bi is called an imaginary number.A number of the form bi, where is called a pure imaginary number. For −3+0i-3+0i−3+0i, the value of aaa is −3-3−3. View Week 3 Complex Numbers.docx from MTH 255 at Seneca College. In this non-linear system, users are free to take whatever path through the material best serves their needs. Electrical engineers use the imaginary unit (which they represent as j ) in the study of electricity. TRUE OR FALSE The minimum value is the smallest y-value of a function. All real numbers can be written as complex numbers by setting b = 0. Video Examples: Developing the Imaginary Axis Example of Imaginary Axis.... imaginary axis noun (mathematics) The vertical line in the complex plane, every point on which corresponds to a complex number having zero real componentimaginary number.... imaginary axis The set of all points representing imaginary numbers, … The coordinates of the point are (−3,9)(-3,9)(−3,9). That is, all complex numbers other than real numbers (a) are imaginary--not just bi, which is called pure imaginary. TRUE OR FALSE The minimum value is the smallest y-value of a function. If then becomes and … The coordinates are (−3,0)(-3,0)(−3,0). At the beginning we only had the natural numbers and they didn't need anything else. The standard form of the complex number 19\sqrt{19}19 is 19+0i\sqrt{19}+0i19+0i, which shows that its imaginary part is zero. A complex number written in polar form may be converted to rectangular form by the relations a = Acos(θ) (1.16) b = Asin(θ) (1.17) These are immediately obtained by substituting the Euler relation into the polar form of a complex number. A. Any number in the form of a+-bi , where a and b are real numbers and b not equal 0 is considered a pure imaginary number. For example, 3 + 2i. A number of the form bi, where b≠ 0, is called a pure imaginary number. Multiplying complex numbers. Imaginary numbers are distinguished from real numbers because a squared imaginary number produces a negative real number. However real and imaginary parts together cover the whole plane. Here is what is now called the standard form of a complex number: a + bi. Some examples are 12i12i12i and i19i\sqrt{19}i19. By … b (2 in the example) is called the imaginary component (or the imaginary part). (Observe that i2 = -1). Any complex number c ∈ ℂ may be written in the form c = a + b i where i is the imaginary unit i = - 1 and a and b are real numbers ( a , b ∈ ℝ ). In general, a is known as the “real” part and b is known as the “imaginary” or the complex part of the imaginary number. is called the real part of, and is its imaginary part. a—that is, 3 in the example—is called the real component (or the real part). 6i13 ⋅18i3 10. Imaginary numbers are distinguished from real numbers because a squared imaginary number produces a negative real number. besselj besseli for pure imaginary argument. A pure imaginary number can be written in bi form where b is a real number and i is √-1. The value of bbb is –8. I’m going to give the real definition and motivation for complex numbers. In other words, we need a two-dimensional picture to represent complex numbers. (2 plus 2 times i) . The coordinates are (5,−8)(5,-8)(5,−8). A complex number is expressed in standard form when written a + bi where a is the real part and bi is the imaginary part. Square roots of negative numbers can be simplified using and All imaginary numbers are complex numbers but all complex numbers don't need to be imaginary numbers. For 0+2i0+2i0+2i, the value of aaa is zero. Complex numbers can be written in the form, Pure imaginary numbers can be combined with real numbers to form a different type of number. For example, the records 5 + 0 i and 5 – 0 i mean the same real number 5 . Complex numbers are denoted by $\mathbb{C}$ The set of real numbers is its subset. For example, the records 5 + 0 i and 5 – 0 i mean the same real number 5 . So, too, is $3+4\sqrt{3}i$. For example, 5i is an imaginary number, and its square is −25. Imaginary numbers occur when a quadratic equation has no roots in the set of real numbers. Every real number graphs to a unique point on the real axis. Real and imaginary numbers are both subsets of complex numbers: A coordinate plane is used to locate points in terms of distance from the xxx- and yyy-axes. Any number in the form of a ± bi , where a and b are real numbers and b 0 is considered a pure imaginary number. For −3+9i-3+9i−3+9i, the value of aaa is –3. (9.6.1) – Define imaginary and complex numbers. Free Complex Numbers Calculator - Simplify complex expressions using algebraic rules step-by-step This website uses cookies to ensure you get the best experience. All pairs of numbers, written in the form a + bi (for example: 3 + 5i, or 7 - 2i, etc. formed by adding a real number to an imaginary number. By definition, zero is … Imaginary numbers have the form bi and can also be written as complex numbers by setting a = 0. When you are accustomed to real numbers it is no wonder we call it an imaginary number: indeed a strange thing that the square of a ‘number’ is negative. a is called the real part, b is called the ... an imaginary number, and a pure imaginary number. If a = 0 (0+ bi), the number is a pure imaginary number. Overview of Pure Imaginary Numbers The imaginary unit i is the backbone of all imaginary numbers. Imaginary numbers are always written in terms of the imaginary number i, ... A pure imaginary number is any complex number whose real part is equal to 0. I sense some confusion in your question. Imaginary numbers are the numbers when squared it gives the negative result. In mathematics the symbol for √(−1) is i for imaginary. A complex number is a real number a, or a pure imaginary number … 4 is the real part . Unit Imaginary Number. V-1*V-8 Perform the indicated operation and simplify. Fortunately complex numbers are more neat than this. A pure imaginary number can be written in bi form where b is a real number and i is √-1 A complex number is any number that can be written in the standard form a + bi, where a and b are real numbers and i is the imaginary unit.. Well i can! The value of bbb is 9. A complex number is a number that can be written in the form a+bi where a and b are real numbers. An imaginary number, also known as a pure imaginary number, is a number of the form bibibi, where bbb is a real number and iii is the imaginary unit. A complex number is expressed in standard form when written a + bi where a is the real part and bi is the imaginary part. a is called the real part, b is called the imaginary part, and i is called the imaginary unit.. Where did the i come from in a complex number ? Every complex number can be written uniquely as a+bi,wherea and b are real numbers. This is also what Merriam Webster's Collegiate Dictionary, Eleventh Edition (published 2014!) Note that this really is a remarkable definition. The square of an imaginary number bi is −b 2.For example, 5i is an imaginary number, and its square is −25.By definition, zero is considered to be both real and imaginary. C. Imaginary Numbers were once thought to be impossible, and so they were called "Imaginary" (to make fun of them).. a – 3i. says--and this is a 1,600+-page dictionary with terms ranging … Imaginary number is expressed as any real number multiplied to a imaginary unit (generally 'i' i.e. Email. An imaginary number is the product of a nonzero real number multiplied by an imaginary unit (such as i) but having having real part 0. The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. The complex number z is real if z =Rez, or equivalently Imz = 0, Here is what is now called the standard form of a complex number: a + bi. Since −3i is an imaginary number, it is the imaginary part (bi) of the complex number a + bi. Though these numbers seem to be non-real and as the name suggests non-existent, they are used in many essential real world applications, in fields like aviation, electronics and engineering. These unique features make Virtual Nerd a viable alternative to private tutoring. A complex number is written in a+ biform (standard form), where ais the 'real part' and biis the 'imaginary part'. T RUE OR FALSE i2 = square root of The value of bbb is 2\sqrt22. Complex numbers have the form a + bi, where a and b are real numbers and i is the square root of −1. true false 19. i^2=√ -1 true false 20.Complex numbers can be graphed on the xy coordinate plane. It is the real number a plus the complex number . Complex Numbers are the combination of real numbers and imaginary numbers in the form of p+qi where p and q are the real numbers and i is the imaginary number. Intro to the imaginary numbers. An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i2 = −1. DEFINITION A complex number z is a number of the form where x is the real part and y the imaginary part, written as x = Re z, y = Im z. i is called the imaginary unit If x = 0, then z = iy is a pure imaginary number. where a is the real part and b is the imaginary part. a + bi . pure imaginary number an imaginary number of the form a+bi where a is 0; , A number of the form bi, where b ≠ 0. Any number in the form of a+-bi , where a and b are real numbers and b not equal 0 is considered a pure imaginary number. The coordinates are (3,2)(\sqrt3,\sqrt2)(3,2), or about (1.7,1.4)(1.7,1.4)(1.7,1.4). 3. For example, $5+2i$ is a complex number. All the imaginary numbers can be written in the form a i where i is the ‘imaginary unit’ √ (-1) and a is a non-zero real number. Conversely, these equations may be inverted, and a complex number written in rectangular form may be Up to now, you’ve known it was impossible to take a square root of a negative number. You need to figure out what a and b need to be. (2 i 9)5 11. CCSS.Math: HSN.CN.A.1. A complex number is expressed in standard form when written $a+bi$ where $a$ is the real part and $bi$ is the imaginary part. −3i21 9. A little bit of history! A complex number is any number that can be written in the standard form a + bi, where a and b are real numbers and i is the imaginary unit. Substitute the pure imaginary number into the original expression. a—that is, 3 in the example—is called the real component (or the real part). A complex number 0+ bi is called a pure imaginary number. I've met this formula and I need to demonstrate that it is purely imaginary (it has no real part). 2.4 Complex Numbers Definition of a Complex Number If a and b are real numbers, the number a + bi is a complex number, and it is said to be written in standard form.If b = 0, the number a + bi = a is a real number. The coordinates are (0,2)(0,2)(0,2). In order to find roots of complex numbers, which can be expressed as imaginary numbers, require the complex numbers to be written in exponential form. The imaginary unit i. We can use i or j to denote the imaginary units. Definition of a Complex Number – If a and b are real numbers, the number a + bi is a complex number, and it is said to be written in standard form. Key Concept Complex Numbers You can write a complex number in the form a + bi, where a and b are real numbers. Definition and examples. For example, the standard form of the complex number 12i12i12i is 0+12i0+12i0+12i, which shows that its real part is zero. Identify the coordinates of each point, and write them in the form (a,b)(a,b)(a,b). If b≠ 0, then a+biis called an imaginary number. A real number a can also be written in the shape of a complex number: a+ 0 i or a – 0 i. A. a complex number B. a real number C. an imaginary unit D. a pure imaginary number 2. Example: 3i If a ≠0 and b ≠ 0, the complex number is a nonreal complex number. An imaginary number, also known as a pure imaginary number, is a number of the form b i bi b i, where b b b is a real number and i i i is the imaginary unit. Intro to the imaginary numbers. 2 is the imaginary part Imaginary numbers occur when a quadratic equation has no roots in the set of real numbers. For 5−8i5-8i5−8i, the value of aaa is 5. 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a pure imaginary number is written in the form 2021 | crawl-data/CC-MAIN-2024-26/segments/1718198861806.64/warc/CC-MAIN-20240619060341-20240619090341-00781.warc.gz | null |
# Prism
Lateral edge: $$\ell$$
Altitude: $$h$$
Sides of the base: $${a_1},{a_2}, \ldots ,{a_n}$$
Perimeter of the cross section: $$p$$
Volume: $$V$$
Lateral surface area: $${S_L}$$
Area of the base: $${S_B}$$
Area of the perpendicular cross section: $${S_C}$$
Total surface area: $$S$$
1. A prism is a polyhedron whose bases are polygons and the lateral faces are parallelograms. The bases of a prism are equal polygons lying in parallel planes.
2. A prism is called a right prism if its lateral edges are perpendicular to the bases. Otherwise it is an oblique prism.
3. If the bases of a prism are parallelograms, then the prism is called a parallelepiped. In a particular case, when the bases are rectangles and the prism is a right prism, it is called a rectangular parallelepiped.
4. A right prism is called regular if its bases are regular polygons. In particular, if the bases and lateral faces of a prism are squares, the prism is called a cube.
5. Lateral surface area of a reqular prism
$${S_L} = {P_B}\ell =$$ $$\left( {{a_1} + {a_2} + \ldots + {a_n}} \right)\ell,$$
where $${P_B}$$ is the perimeter of the base of the prism, $${a_1},$$ $${a_2}, \ldots ,$$ $${a_n}$$ are the sides of the base, $$\ell$$ is the length of the lateral edge (in a right prism, the lateral edge coincides with the altitude $$h$$).
6. Lateral surface area of an oblique prism
$${S_L} = p\ell$$,
where $$p$$ is the semiperimeter of a cross section of the prism, $$\ell$$ is the lateral edge.
7. Volume of a prism
$$V = {S_B}h = {S_C}\ell$$,
where $${S_B}$$ is the base area, $$h$$ is the altitude of the prism, $${S_C}$$ is the area of a cross section, $$\ell$$ is the lateral edge.
8. Cavalieri’s principle
Given two solids included between parallel planes. If every plane cross section parallel to the given planes has the same area in both solids, then the volumes of the solids are equal. | crawl-data/CC-MAIN-2021-04/segments/1610703520883.15/warc/CC-MAIN-20210120120242-20210120150242-00157.warc.gz | null |
Our City-State Laws
If a person should lie to their parents he or she
shall get their tongue cut off.
If a person shall beat or steal from another, they will get their
hand cut off.
The laws applied to everyone including children. These were the
first recorded laws of government in history.
Cylinder seals were used for different
things like, showing ownership, name and record of agreement.
How it works is by taking the seal and rolling it in wet clay.
They were probably the first stamps. The result came out as a
raised nice picture. This was the beginning of cuneiform writing.
It was important for communication and signatures at the bottom
Bulla and Tokens
The bulla and tokens were used for keeping track
of business deals. This could have led to the first writing system.
In order to help keep track of the records, they used small stone
or clay tokens and each token was a different size or shape which
stood for different projects. They put them into a football shape
or round container called a bulla.
Mesopotamia means "land between two
rivers." The rivers are called the Tigris and Euphrates.
Mesopotamians built boats to use for trading in distant places
and to collect food from the rivers. Modern Iraqi boats still
are built very much like this Mesopotamian boat used 4,500 years
If you can view
QTVR, please examine our boat. | <urn:uuid:16642e32-c99e-4318-b41b-fea8c1a26ecf> | {
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This is a FREE Featured Video! Sign up here to get access to all Futures Channel Videos!
Subject: Mathematics Problem Solving
Grade Levels: 4th Grade, 5th Grade, 6th Grade,
Synopsis: Imagine 100 people coming to dinner. For Chef Dennis Burrage that means creating new and different recipes for a unique dining experience. How does he do it? He and his team use math to figure out the right amount of ingredients needed for their recipes.
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Hives (or urticaria) will affect 1 out of 5 people during their lifetime. They are itchy, red or skin colored bumps with redness around them that come and go. Histamine is the substance that actually causes the hives. This means that if you have hives, they are the result of histamine being released from your mast cells.
If we track down what caused the histamine release then we know the cause of the hives! Some examples are:
- An allergic reaction occurs when an allergy antibody (IgE) meets the foreign substance it recognizes (in essence, this is the substance you are allergic to). This is a very common cause of hives and it happens very soon after exposure. The reaction happens each time you have exposure and is often accompanied by other symptoms like runny nose, difficulty breathing, swelling of the throat, etc. An Allergist will review the history of the event with you because that gives the main clues to what you might be allergic to. Skin or blood allergy testing is often done to confirm the cause of the hives.
- Direct release of histamine from the mast cell can be caused by a number of things. Insects, like mosquitos, spit a blood thinner into your skin with their sting and this releases the histamine that causes hives. Medications such as morphine, codeine, or vancomycin directly release histamine and make certain people feel very itchy. Certain foods like strawberries can do this, too.
- Other parts of the immune system release histamine, too. Many infections and some reactions to medications can set off the Compliment or Kallikrein Systems. We see three to ten day hive outbreaks in children quite commonly because of this. It can be miserable! In this case, to stop the hives you must get over the infection or stop taking the drug causing the hives.
- Physical Urticarias are uncommon but no less itchy! For those who suffer from physical urticaria, getting too cold, too hot, the wrong frequency of vibration or light, or even getting wet will set off the itch.
- In many patients with chronic, spontaneous hives that have gone on well beyond six weeks, an autoimmune mechanism is responsible. Their immune system incorrectly recognizes part of the mast cell as being foreign. This reaction causes the mast cell to then release histamine and makes one itchy.
Whatever is causing your hives, we know that the itch is terrible! Getting relief quickly is important.
If you or a loved one suffer from hives, you need to start paying careful attention to the “Why” (why you are having the reaction, or more specifically, what is causing the reaction) and then “Avoid or Cure”. Your primary care provider can be very helpful in getting this done right way. Then, getting appropriate evaluation and treatment is very important. Not all hives need expensive labs and testing. The history and physical examination are the most important part of finding the “Why”.
Allergists and Dermatologists tend to see the more puzzling cases. An Allergist is most often involved with cases requiring allergy testing for confirmation of diagnosis. If you are needing additional help diagnosing your hives, Dakota Allergy & Asthma is here to help.Schedule your appointment HERE. | <urn:uuid:0e81dab2-ee99-427f-8191-5737758d6359> | {
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The disease that's threatening bats and our ecosystem
GATESVILLE, N.C. — In the last ten years, more than five million bats in the U.S. have died from a fungal disease. This disease, known as white-nose syndrome, has now spread from northeastern states to central and southern states, threatening even more bats.
"Bats are very important to our ecosystem and we really cannot take risks to lose them," says Han Li, a post-doctoral fellow at UNC-Greensboro who also studies bats and their sounds.
Li explains that bats play a critical role in keeping insect populations in check, saving the farming industry billions on pesticides or other insect prevention methods. They also pollinate some plants including the succulent agave—the source of tequila. Like Li said, they're important to our ecosystem, and at risk—so is there help for our nocturnal, winged friends?
A safe haven for bats in North Carolina
"I think the habitat is the key," says Li. "This kind of unique combination of water and trees, this kind of swampy bottom level… Put everything together, it’s a good habitat."
But first, wildlife biologists want to make sure the bats are not infected with white-nose syndrome. That's the mission of Brandon Sherrill, Ed Corey and their netting team. Together they investigate the bats of Merchants Millpond State Park in eastern N.C.
"Netting actually gives us a chance to see how the bats are doing physically. So, while we can detect bats acoustically, we’re not able to see how those individuals are faring," says Corey. "So, if an animal’s been exposed to white-nose syndrome, we should be able to see scarring on the wing membranes, on the exposed surfaces like the tail, the nose, things like that."
In order to do this, the team constructs 20-foot nets to capture and observe the flying animals.
"When we’re looking down for a placement for that net site, we’re looking for where vegetation is on both sides of the net, but also we have canopy cover above, so it’s basically funneling bats down that corridor, into our net,” says Sherrill. “We’ll wait to open those nets until closer to dark, when bats would start flying.”
Once they do this, they monitor the nets every eight to ten minutes to ensure any other captured bats are removed.
The challenge of the catch
"Last night we were able to do the three nets over at a site nearby and we didn’t have any success in the nets," says Corey. "But this time of year is very challenging, particularly the fact that we had a full moon last night, which can create a lot of problems with capture."
Li, who is working with the team of wildlife biologists, has more luck with his sound detectors.
"Right here we have a recording that is potentially from genus Myotis, which includes northern long-eared bats, little brown bats—a lot of species impacted by white-nose syndrome," he says.
Despite not catching a bat to check for white-nose syndrome, scientists have documented several species of bats that live in this swampy, forested habitat. A habitat that may provide refuge from the fungal threat to this vital species. | <urn:uuid:f3f7eb76-6bdc-47a3-9883-6ee1289d161c> | {
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One entry found for rehearse.
Main Entry: re·hearse
Inflected Form(s): re·hearsed; re·hears·ing
Etymology: Middle English rehersen "to say again, repeat," from early French rehercier "to go over again and again," literally, "to harrow again," from re- "again" and hercier "to harrow," from herce "a harrow" 1 a: to say again : REPEATb: to recount in order : ENUMERATE <they rehearsed their complaints in a letter> 2 a: to practice (a play or scene) for public performance b: to train or instruct (as actors) by rehearsal 3: to engage in a rehearsal - re·hears·ernoun Word History In the Middle Ages, French farmers used a tool they called a herce. This was a triangular wooden frame with sturdy pegs or teeth on one side. It was pulled over plowed farmland to break up the soil in order to make it smooth for planting. The early French verb used to describe this action was hercier, which meant "to harrow." In most cases the process had to be repeated over and over, so the word rehercier was formed, meaning "to harrow again" or "reharrow." In time, rehercier came to be used with more general meanings like "to go over something again (and again)," as in repeating a school lesson or a story. The word came into Middle English as rehersen, meaning "to say again, repeat." Through the years the English word, now spelled rehearse, has picked up new meanings. Perhaps the most familiar one now is "to go through (a scene or play) over and over for practice until it is ready for performance." | <urn:uuid:a70049ef-526b-44ae-aa77-f64b456f1b2d> | {
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Strasbourg, France, is a picturesque city on the Rhine river—with a dark stain on its history. On February 14, 1349, at the height of the Black Death that swept across Europe, residents rounded up and murdered several hundred of the city’s Jews.
Today there is little sign of that violent event, apart from a plaque on the wall of the city’s opera house, and yet the city may still be paying for its historical crimes.
Europe still struggles with anti-Semitism. According to Tel Aviv University’s annual report on anti-Semitism, there were 766 violent incidents targeting Jews across the continent in 2014, the year that Israel launched a military operation in the Gaza Strip. That was more than in any other year in the previous decade. “The overall feeling among vast parts of the Jewish population is one of living in an intensifying anti-Jewish environment that has become not only insulting and threatening, but outright dangerous,” the report states. In a sign of growing tensions, a gunman killed four people in a kosher supermarket in Paris in January 2015.
Of course, Jews are not the only victims of the most recent wave of populist bigotry, which has chiefly targeted Muslims and immigrants. Yet intolerance may be bad economics, and research focused on anti-Semitism illustrates why.
Anti-Semitism can pollute a culture for centuries, according to academic findings. Historical episodes of violence against Jews may affect the present size of an area’s middle class, prevailing wages, and investment habits. Taken together, the research findings indicate that prejudice can be costly—and painfully persistent.
The deep roots of Jew hating
After the Roman Empire officially adopted Christianity in the fourth century, it became more difficult for people to practice other faiths. As the centuries passed, Jews and other minorities were at times isolated in Western Europe, made to take out special permits to settle in an area—and sometimes forced to leave. By the Middle Ages, Jews were being persecuted in many Western European countries, at times massacred or expelled. Some were restricted to living in certain areas and engaging in certain occupations.
History does not always confine itself to the past. Researchers Nico Voigtländer of UCLA and Hans-Joachim Voth, of the University of Zurich, mapped the persistence of anti-Semitism from the Middle Ages into the 20th century. They find that the areas that experienced the most frequent violent attacks on Jews during the Black Death were the same regions where, six centuries later, Germans were most likely to vote for the Nazi Party and engage in anti-Semitic violence.
The researchers offer as an example two similarly sized German cities: Würzburg in Bavaria, which experienced a pogrom during the Black Death; and Aachen in North Rhine-Westphalia, which did not.
In Würzburg, where Jews had lived since the 11th century, some 900 Jews were murdered in 1298 after having been accused of desecrating the sacramental bread, according to Yad Vashem, the Holocaust research center in Jerusalem. Fifty years later, during the Black Death, residents accused Jews of poisoning the city’s wells.
By the 1920s, when the Nazis were growing in popularity, Würzburg saw intermittent violence against Jews. According to the researchers, its residents published ten times more anti-Semitic letters in Nazi newspaper Der Stürmer than any other area, and the Nazi Party scored 6 percent in local elections there in 1928, almost double the German district average. According to records from the German Federal Archive, 44 percent of Würzburg’s Jews were deported, many to concentration camps, during World War II.
In contrast, Aachen had no pogrom during the Black Death, and no anti-Semitic violence in the 1920s. Its residents wrote less than half the number of anti-Semitic letters to the editor that Würzburg did, say Voigtländer and Voth, and only 1 percent of the population voted for the Nazis in 1928. Jews suffered from federal anti-Semitic legislation put in place during the run-up to World War II, but the city ultimately deported a lower percentage—37 percent—of its Jews.
Voigtländer and Voth find a few locations where anti-Semitism weakened or even disappeared, as it did in towns that specialized in long-distance trade, where it was costly to discriminate against outsiders. Those exceptions aside, “the influence of medieval pogroms for 20th century anti-Semitism underlines the importance of deeper historical antecedents of post-WWI German anti-Semitism at the local level,” they write. Anti-Semitism may ebb and flow, as it did in the years between the Black Death and Nazi rule, but even in its dormancy it can be destructive.
Anti-Semitism leads to lower stock-market participation
Economists are quantifying the effects of such dormant hate, arguing, for example, that anti-Semitism is linked to people distrusting financial institutions, including the stock market, commercial banks, and local banks.
Jews have a reputation for being involved in finance and moneylending, although their role is a matter of debate among historians and other academics. While some argue that Jews excelled in moneylending due to factors such as high literacy levels, the University of Chicago’s David Nirenberg says that Jews in finance is an old, anti-Semitic, and unwarranted cliché. He says that after playing prominent roles in moneylending for short periods of time in some medieval Christian societies, Jews came to represent those roles in the Christian imagination and literature. “There were no Jews in Chaucer’s or in Shakespeare’s England, but both used Jews as representations of avarice and moneylending,” says Nirenberg, who adds that Jews only became significant in European banking starting in the late 18th century, and always remained a small minority in the financial sector, even as that sector came to be stereotyped as “Jewish.”
To examine more closely the lasting economic effects of anti-Semitism, the University of Maryland’s Francesco D’Acunto, Leibniz University Hanover’s Marcel Prokopczuk, and Chicago Booth’s Michael Weber used data on historical persecution of Jews, including Voigtländer and Voth’s data, election results, and a survey of a representative sample of contemporary Germans, collected between 1984 and 2010. The researchers find that in German counties with higher rates of historical persecution of Jews, contemporary residents trusted the stock market significantly less than other Germans. In some places, many people avoided investing their money in stocks—a decision generally regarded as bad for an economy. And irrespective of the present-day level of anti-Semitism, residents in counties with higher historical anti-Jewish sentiment still mistrusted the stock markets and were less likely to invest in stocks.
The researchers looked back to 1349, when not only were Jews massacred in Strasbourg, there were also pogroms in a string of other European cities, including Erfurt, Germany; Basel, Switzerland; Aragon, an autonomous region of Spain; and Flanders, Belgium.
Households in counties that experienced a pogrom in 1349 were, centuries later, significantly less likely to invest than households in counties that didn’t have a pogrom, the researchers find. Pogroms then correlated with a 2 percentage point lower participation rate in the financial markets. Moreover, households in counties that had high levels of persecution in 1349 were 10 percent less likely to have a mortgage, despite average levels of home ownership. And where persecution existed, people held fewer bank deposits and “appear more likely to keep their money in cash form,” the researchers write.
D’Acunto, Prokopczuk, and Weber see several possible explanations. Jewish persecution may correlate with what they describe as “backwardness,” which manifests itself as xenophobia and generalized distrust. Also, households that remain anti-Semitic even now may continue to associate stock markets with Jews, and therefore not put their money in stocks, the researchers hypothesize. Yet they doubt that these two possible explanations could completely explain the effects they observe, as those effects are consistent across households’ varying education levels.
They gravitate toward a third explanation: areas with a history of persecution may distrust financial institutions, and the deep-rooted distrust in finance may have been transmitted from one generation to the next. “This last reason is particularly interesting when we bring education into the mix,” Weber notes. Since World War II, the German government has provided education that has specifically addressed and decreased anti-Semitism, he says, but the government doesn’t put the same emphasis on financial literacy or economic education. Education appears to be chipping away at anti-Semitism but not at a prejudice that may be affiliated: the general mistrust of financial institutions.
Anti-Semitism hampers entrepreneurship
While anti-Semitism lowers investment rates, it may also produce a more general distrust of business. In areas with a long history of anti-Semitism, residents surveyed by researchers expressed less satisfaction with the economy and engaged less in entrepreneurship.
This finding comes from a study of the Pale of Settlement, the area to which Jews were confined in the Russian Empire for 123 years leading up to World War I. The region encompasses large portions of what is today Poland, Lithuania, Belarus, Ukraine, western Russia, and Moldova. Before World War II, Jews accounted for 37 percent of the urban population there, and 11 percent of the total. The majority of Jews in the Pale had fled by the end of 1942. But while Jews are gone, as is the official Pale itself, a mindset remains: another set of economists argues that ethnic hatred toward the Jews created a persistent antimarket culture.
Irena Grosfeld and Ekaterina Zhuravskaya, both of the Paris School of Economics, and Alexander Rodnyansky, a PhD candidate at Princeton University, looked at residents of what they describe as “transition countries” affected by the fall of the Soviet Union and its satellites. The researchers aligned this data with geographic information on the Pale, demographic data, and historical numbers on pogroms.
Over the centuries, Jews and non-Jews exhibited considerable hostility and rivalry in the Pale. While the groups had many market transactions, they had few social interactions, as documented by historians including Yuri Slezkine in his 2004 book The Jewish Century. Grosfeld, Rodnyansky, and Zhuravskaya argue that the presence of a group with an alien religion, language, and traditions gave non-Jews a feeling of solidarity. “Self-identification of one ethnic group and cohesion among its members may depend on the co-existence with another (rival) group,” they write.
The us-versus-them feeling manifested itself in business dealings. A number of previous studies, including Slezkine’s, suggest that the majority of Jews in the Pale had predominantly white-collar occupations. While most non-Jews farmed and did other less-skilled work, many Jews engaged in activities such as trading and finance—which many historians believe helped develop markets and capitalism in the region. The proportion of entrepreneurs and self-employed individuals was much higher among Jews than among their non-Jewish counterparts.
Jews came to represent a liberal, promarket force—one that triggered a conservative, antimarket, and anti-Jewish backlash. Analyzing pogroms in the area between 1821 and 1946, the researchers find that areas that experienced the most pogroms during that time also had the highest antimarket sentiments in the late 20th century.
They also find that recent residents of what had been the Pale, compared to their counterparts elsewhere in Russia, voted more often for antimarket parties with socialist or communist leanings and had less interest in markets, entrepreneurship, and democracy. Centuries of anti-Semitic practices and beliefs have left behind a distrust of markets and business. “The Pale of Settlement and the Holocaust have tangible consequences for political and social development of Eastern Europe today,” the researchers argue.
Anti-Semitism destroys the middle class
MIT’s Daron AcemoÄŸlu, Chicago Booth’s Tarek Alexander Hassan, and University of Chicago’s James A. Robinson didn’t study anti-Semitism per se, but a result of it—the mass murder of Jews that occurred during the Holocaust. What, they ask, is the enduring effect of the Holocaust on the societies left behind? The result, they find, is a devastated middle class and weakened economic prospects in the long run.
The researchers looked at 278 cities across the Soviet Union, 76 of which were occupied by the Germans during World War II. While a handful of those cities were located in the Pale of Settlement, the majority were in areas farther east where Jews migrated after the restrictions of the Pale were lifted in 1917. Using census data and German death-squad reports, the researchers looked at 48 oblasts, administrative units larger than US counties but smaller than US states.
Before Germany invaded the Soviet Union in June 1941, Jews were “heavily overrepresented in what we would typically consider to be ‘middle class’ occupations,” write Acemoğlu, Hassan, and Robinson. More than two-thirds of Jews in the 48 oblasts had white-collar jobs, while only 15 percent of non-Jews held such positions. In oblasts with the largest Jewish populations, 68 percent of physicians and 10 percent of all white-collar workers were Jewish, despite the fact that Jews represented only 1 percent of the population.
The researchers find that in oblasts in which Jews constituted 1 percent of the middle class in 1939, the middle class shrank 5 percent by 1989. The Holocaust thus appears to have set these areas on a divergent course from that followed by other places. Removing Jews from these oblasts created an enormous economic and social shock. The disappearance of middle-class Jews “may have changed the overall economic and social development of the areas and set them on a path that does not allow for the creation of middle-class jobs,” Hassan says. They may, he adds, not be places that attract aspiring professionals long term.
Oblasts where Jews were most persecuted and displaced had, later on, lower wages and per-capita income than the national average. These areas showed greater support for communist candidates in the 1990s, were less reform minded, and were more likely to cling to old loyalties—such as voting in support of the preservation of the Soviet Union in March 1991. The authors used support for noncommunist candidates in the 1999 Duma elections as a proxy for political development, and compared this with population and income growth in cities that were impacted most by the Holocaust. In these areas, the researchers find, the middle class has yet to recover.
Anti-Semitism damages education for all
The loss of teachers, in particular, has had significant, long-lasting effects. In 1933, soon after the Nazi Party took power, it passed a law that allowed the government to purge Jews from the civil service. More than 15 percent of university professors, schoolteachers, doctors, and other white-collar professionals were dismissed as a result.
The departure had a direct and quantifiable effect on students. Mevlude Akbulut-Yuksel and Mutlu Yuksel, both of Dalhousie University in Nova Scotia, find that adults who were school aged during Nazi rule wound up with six months less of schooling on average in adulthood than the national average. Those who lived in cities that had the highest fraction of Jews prior to the war had almost 10 months less formal education. Children in Frankfurt, where Jews had been a relatively large 3.25 percent of the population, had around one less year of schooling.
Germans affected by the teacher exodus were later less likely to have gone to college or to have obtained postgraduate degrees. They ended up earning less money. The experience of the war made them less likely to have an interest in politics and conditioned them to take fewer risks as adults—effects that continue to the present day, say the researchers. Residents of Frankfurt who were in school during the Nazi era remain 23 percent less likely to show an interest in politics than the same cohort in Bremen, where Jews comprised a smaller 0.4 percent of the population.
The dismissal of scientists all over Germany had a similarly significant effect. In 1933, more than 1,000 academics were dismissed from German universities, including 15 percent of physicists, 14 percent of chemists, and 19 percent of mathematicians. Fabian Waldinger of the University of Warwick points out that the majority dismissed were Jewish, and the rest were “politically unreliable” individuals.
In this period, Albert Einstein resigned from the Prussian Academy of Sciences, and 11 Nobel laureates lost their jobs. In the fall of 1933, only 590 Jewish students were left in German universities, compared with 3,950 the previous summer. Anti-Semitic faculty and Hitler Youth activists soon forced out the rest.
Waldinger observes that removing faculty in physics, chemistry, and math hurt the productivity of faculty who remained behind, if they lost a coauthor. He notes that in physics, the loss of a coauthor lowered productivity of the remaining scientist by 13–16 percent.
Before World War II, Germany was the world’s scientific superpower. Universities in Göttingen and Berlin had top German scholars on their faculties and attracted an array of international scientists at the pinnacle of their professions. Among those were Arthur Compton, who won the Nobel Prize in Physics in 1927; Julius Robert Oppenheimer, a theoretical physicist who helped develop the first atom bomb; and Enrico Fermi, an Italian physicist who helped develop the first nuclear reactor, and whose wife was Jewish. German scientists working in the universities at that time included James Franck, who won the Nobel Prize in Physics in 1925, and Werner Heisenberg, who won the award in 1932.
Using data from 105 science departments, Waldinger estimates that the dismissals reduced output by German and Austrian science departments by 34 percent. He argues that productivity declines persisted until 1980 and helped Germany lose its preeminence in science to the United States.
Losing academics proved more destructive than physical bombings of buildings and labs. Waldinger’s data indicate it took only 10–15 years to rebuild damaged and destroyed property, but German universities never recovered from the loss of human capital.
Protecting minorities, protecting society
Jews are far from the only minority group to have been scapegoated over the centuries. The Roma, homosexuals, and Muslims are just three examples of groups that have historically—and very recently—been victims of intolerance.
In the past year, rhetoric about Muslims and other perceived outsiders has grown as a political issue. US presidential hopeful Donald Trump built his campaign on demonizing Mexican and Muslim immigrants, echoing historical anti-immigrant sentiment. This has proven popular, even though—as the nonprofit, nonpartisan Economic Policy Institute points out—deporting unauthorized immigrants, “would actually hurt, not help, the economy and the jobs situation.” In Europe, concern over the influx of immigrants has solidified far-right parties such as France’s National Front, which dominated the first round of regional elections last year.
Strasbourg, whose residents once massacred Jews, is now the seat of the European Parliament, where lawmakers are grappling with how to handle a flood of more than 1 million refugees, a good portion of them fleeing the civil war in Syria. The response of some sovereign countries has been to shut their doors. Hungary built a razor-wire fence to keep migrants from entering the country. Even Sweden and Denmark, which have traditionally welcomed immigrants, closed their borders this year. Germany’s open-door policy is likely to come under increasing pressure.
Policy makers would do well to pause, and check the data. While the migrant crisis is complex, the research suggests that xenophobia can be costly. Openness, rather than intolerance, may be a better way to economic growth. | <urn:uuid:4a1f8c81-cde1-4a1d-9d9a-63e7f9a3247c> | {
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Your shin bone (tibia) is the bone at the front of your lower leg that runs from your knee to your ankle.
Shin splint’s is a general term used to describe any condition that causes pain down the middle, or on either side of your shin. Exercise-induced pain usually manifests itself in the front aspect of the lower legs. The medical name for this is medial tibial stress syndrome. The underlying problem is inflammation of the outer covering of the bone (periosteum).
Depending on the type of injury you have, the pain may come on gradually or you may have a sudden twinge of pain. Shin splints usually develop in people who do repetitive activities and sports – either during or after strenuous activity – that put a lot of stress on the lower legs, such as running, dancing, aerobics, gymnastics, football and hockey; i.e. sports with sudden stops and starts. Some soldiers also complain of shin splints during loaded marches.
- Tenderness along the front, or inside, of the lower leg;
- Aching or sharp pain along the front, or inside, of the lower leg;
- Pain at the start of exercise which often eases as the session continues;
- Pain often returns after activity and may be at its worse the next morning;
- Sometimes some swelling;
- Lumps and bumps may be felt when feeling the inside of the shin bone;
- Pain when the toes or foot are bent downwards; and/or
- Redness over the inside of the shin (not always present).
The pain is often worse when you do activities that involve supporting your body weight. You may feel pain along the whole length of your shin, or only along a small section.
The pain may build up during exercise and it will become more severe the longer you exercise, and if you ignore it and continue exercising it can become extremely painful and force you to stop sport altogether.
It is really important not to ‘run through the pain’, as the shin pain is a sign of injury to the bone and surrounding tissues in your leg. Continued force on the legs will make the injury and your pain worse.
Instead, you should rest and take a break from the sport for at least two weeks. You can still exercise during this time off, but choose activities that will not put too much force on your shins, such as cycling or swimming.
Causes & Risk Factors
Shin splints can be caused by a number of factors which are mainly biomechanical (abnormal movement patterns) and errors in training. Here are the most common causes:
- Overpronation of the feet (rolling feet inwards);
- Oversupination of the feet (rolling feet outwards);
- Inadequate footwear;
- Increasing training too quickly;
- Running on hard surfaces;
- Decreased flexibility at the ankle joint;
- Stress fractures: these are an overuse injury. They develop after repeated periods of stress on your bones; for example, running or dancing over a long period of time; and
- Compartment syndrome: this happens when your muscle swells. Your muscle is within a close compartment and so does not have much room to expand. When the pressure in your muscle increases it causes the symptoms of compartment syndrome.
All of these conditions can develop when you put too much stress and strain on your shin bone. This happens when there is repetitive impact on your shin bone during weight-bearing sports or activities. You are more at risk of developing shin splints if:
- You increase your running distance;
- You are an inexperienced runner;
- Your sport or activity involves running or jumping on a hard surface;
- You do a lot of hill running;
- You increase your frequency of running and do not allow a rest day between runs;
- Your shoes do not fit well or do not have enough cushioning and support;
- You are overweight, as this places extra weight on your legs;
- You have weak ankles or a tight Achilles tendon (band of tissue connecting the heel bone to the calf muscle);
- You have flat feet or your feet roll inwards (pronate), as this places more pressure on the lower leg;
- You change your running pattern and the surface that you run on; for example, going from running on a treadmill to running on the road; and/or
- You participate in loaded marches, especially when unconditioned.
Rest and Recovery
You should rest your injury and think about what may have caused your shin splints.
You should be able to recover fully from shin splints if you rest for at least two weeks. This means you should not do any running or ‘stop and start’ sports during this time, although walking, swimming and cycling are OK.
Pain and any swelling can be relieved by raising your leg and holding an ice pack to your shin (try a bag of frozen peas wrapped in a tea towel). Do this for 10 minutes every few hours for the first two days. However, you should also consider the treatment options outlined below.
Treatment for shin splints involves identifying training and biomechanical problems which may have caused the injury initially. Rest to allow muscles to return to their original condition and gradually return to training.
- Rest to allow the injury to heal;
- Apply ice or cold therapy in the early stages, particularly when it is very painful. Cold therapy reduces pain and inflammation;
- Over-the-counter painkillers, such as ibuprofen or paracetamol, may also help by reducing the pain and inflammation. Follow the instructions in the patient information leaflet that comes with the medicine and if you have any questions, ask your pharmacist or medical professional for advice.
- Shin splint stretches should be done to stretch the muscles of the lower leg. In particular the tibialis posterior which is associated with shin splints;
- Wear shock absorbing insoles in shoes as this helps reduce the shock on the lower leg. Check your trainers or sports shoes to see whether they give enough support and cushioning. Specialist running shops can give you advice and information about your trainers. An experienced adviser can watch you run and recommend suitable shoes for you.
- Maintain fitness with other non-weight bearing exercises such as swimming, cycling or running in water;
- Apply heat and use a heat retainer or shin and calf support after the initial acute stage and particularly before training. This can provide support and compression to the lower leg helping to reduce the strain on the muscles. It will also retain the natural heat which causes blood vessels to dilate and increases the flow of blood to the tissues to aid healing; and/or
- Shin splints strengthening exercises may help prevent the injury returning.
It is important that you think about how much exercise you are doing and if it is causing shin splints. You may need to reduce the amount of exercise you are doing or change your training routine.
A physiotherapist can help devise a graduated training programme to promote recovery and help you return to your usual sports activities. A physiotherapist can:
- Help to restore any loss of range to your lower limb joints and muscles that may be contributing to shin splints;
- Advise on a strengthening programme, especially to the calf muscle; and/or
- Use acupuncture, tape or soft tissue techniques that may help reduce pain.
A podiatrist (a health professional who specialises in conditions that affect the feet) can provide advice about foot care. S/he can also supply shoe inserts (orthotics) to control the inward roll of your feet if necessary.
If your shin splints are caused by compartment syndrome and the pain is severe, your medical professional may suggest an operation called a fasciotomy. This releases the pressure on the muscles in your lower leg. Talk to your medical professional or physiotherapist for more information.
Other Things Your Medical Professional, Physiotherapist or Podiatrist May Do
- Tape the shin for support: a taping worn all day will allow the shin to rest properly by taking the pressure off the muscle attachments;
- Perform gait analysis to determine if you overpronate or oversupinate; and/or
- Use sports massage techniques on the posterior deep muscle compartment but avoid the inflamed periostium close to the bone.
Getting Back To Your Usual Exercise Programme
You can return to your usual activity after at least two weeks of rest, and only when the pain has gone. Increase your activity level slowly by gradually building up the time you spend running or doing sports. It is also important that you warm up and stretch before you start exercising. If the pain returns, stop immediately.
A sports physiotherapist will be able to advise you on a suitable graded running programme. You can ask your medical professional for a referral on the NHS or arrange an appointment yourself privately with a physiotherapist or medical professional specialising in sport and exercise medicine.
The following steps can help reduce your risk of developing shin splints:
- Get fitted for supportive running shoes or wear supportive footwear that is appropriate for your sport or activity;
- Using shock-absorbing insoles or (if you have flat feet) insoles to support the foot better (your medical professional, podiatrist or physiotherapist can provide specialist advice on this);
- Avoid training on hard surfaces and exercise on a grass surface, if possible; and/or
- Build up your activity level gradually.
When to See Your Medical Professional
See your medical professional if the pain does not improve. They will investigate other possible causes, such as:
- Reduced blood supply to the lower leg;
- Tiny cracks in the shin bone (a stress fracture);
- A leg muscle bulging out of place (muscle hernia);
- Swelling of the leg muscle that compresses nearby nerves and blood vessels, known as compartment syndrome; and/or
- A nerve problem in your lower back, known as radiculopathy.
Further, see your medical professional immediately if the:
- Pain is severe and follows a fall or accident;
- Shin is hot and inflamed;
- Swelling getting worse; and/or
- Pain persists during rest.
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In 2004, a team of geologists discovered something extraordinary while exploring the Gulf of Mexico. They were searching for sites where oil and gas seep out of the ocean floor, but instead, two miles below the ocean’s surface, they found a field of dormant black volcanoes. And unlike typical volcanoes that spew out molten rock, these had once belched asphalt. They looked like they had been fashioned from the same stuff used to pave highways, because that’s exactly what they were. The team named one of them Chapopote after the Nahuatl word for “tar.”*
Even if the volcanoes aren’t erupting any longer, a world of asphalt seems like a particularly inhospitable environment. And yet, the team found that life flourished on the volcanoes. Tubeworms, sea lilies, and corals had embedded themselves among the asphalt. Clams and mussels were thriving among sediments that were slick with oil. Crabs scuttled over them, while fish swam past. Life, as they say, finds a way, even when that way involves growing on tar.
Many of these animals likely flourished by forming partnerships with microbes, which use chemicals like hydrogen sulfide and methane to make their own food. This way of life, known as chemosynthesis, is the oldest on the planet. It allows bacteria to thrive in deep-sea habitats that are untouched by sunlight and choked by toxic chemicals. And it allows animals to colonize those same worlds by relying on the bacteria for their nutrition.
Nicole Dubilier, from the Max-Planck Institute for Marine Microbiology, has spent much of her career studying chemosynthetic microbes and their animal hosts. She has now visited Chapopote and the asphalt volcanoes twice. “When the submersible comes up, it reeks of petroleum, and it’s filthy. We have to clean it with WD-40; it’s the only thing that works,” she says. “It’s shocking that animals can tolerate these conditions.”
In 2006, Dubilier collected two of the yellow mussels that grow on the vents. In their gills, she found not just the usual chemosynthetic microbes, but also a group of bacteria called Cycloclasticus. These are oil-eaters. When the Deepwater Horizon rig exploded in 2010, releasing 750 million liters of crude oil into the Gulf, Cycloclasticus were among the microbes that showed up to digest the slick. Their presence suggested that the mussels could indirectly be digesting the oil and gas that regularly seep out of the volcano fields.
To confirm this idea, Dubilier returned to the site in 2015 and collected more mussels. Her colleague Maxim Rubin-Blum exposed them to naphthalene—a petroleum-derived chemical. And the mussels, to his surprise, did nothing. They were not digesting the naphthalene at all. “Max nearly knocked himself out trying to get the experiments to work,” Dubilier says.
Rubin-Blum worked out what was going on by sequencing the genomes of the mussels’ microbes. When Cycloclasticus grows on oil, independent of the asphalt-volcano mussels, it attacks a group of chemicals called polycyclic aromatic hydrocarbons (PAHs), of which naphthalene is a member. These are usually very hard to break down because they contain tough ring-shaped chemical bonds, but Cycloclasticus has a large toolbox of genes that can tear these bonds apart. (Their name comes from the Greek for “ring” and the Latin for “breaker”.)
But Rubin-Blum found that the Cycloclasticus strains in the mussels have lost these PAH-breaking genes. Instead, they dine on chemicals in oil like ethane, propane, and other alkanes, which are simpler in structure, and take less energy to digest.
“It’s a jaw-dropping finding,” says Mandy Joye from the University of Georgia, who studies the microbes that bloom at oil spills. Those strains were thought to focus on PAHs. But Dubilier found that several of the genes that the mussel-bound microbes use to digest alkanes were also present in the Cycloclasticus strains that showed up at Deepwater Horizon. This suggests that free-living microbes have much broader range of oil-digesting strategies than previously assumed.
In open water, Dubilier thinks that microbes break down alkanes very quickly, forcing Cycloclasticus to focus on the tougher PAHs. But the mussels provide the microbes with a constant supply of alkanes, by continuously pumping oil-contaminated water over their gills. In this cossetted world, with a conveyor belt of snacks and no competitors, Cycloclasticus has effectively become domesticated. It lost the ability to digest PAHs and adapted to a more abundant and considerably easier source of food. “It’s like they’ve evolved to live off cake,” says Dubilier.
“It’s all about food,” says Colleen Cavanaugh from Harvard University, who first discovered chemosynthetic microbes in the 1980s. The microbes get a regular delivery of fast food from their hosts, and the mussels live off the byproducts of their partners’ digestive work. “This allows the partners to colonize and thrive in the deep-sea—an otherwise inhospitable environment due to the lack of food.”
Dubilier notes that the mussels she studied on volcanoes evolved from shallow-water relatives around 50 million years ago. And there are more than 50 related species that have all colonized inhospitable environments like hydrothermal vents and asphalt volcanoes by teaming up with microbes. “They’re like Darwin’s finches,” she says.
* The story originally referred to Chapopote as the Aztec word for tar; “Aztec” refers to a group of people, and the language they used was Nahuatl. We regret the error.
We want to hear what you think about this article. Submit a letter to the editor or write to [email protected]. | <urn:uuid:92f7076e-77da-4811-8c44-ae0db061037c> | {
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The record suggests that birds would be the last living dinosaurs, called bird dinosaurs, having developed from forefathers that are feathered within the group of dinosaurs. Birds in South America endured this occasion and after that moved to the rest of the globe via several property connections while diversifying throughout periods of worldwide cooling. Archaic birdlike dinosaurs that lay outside course Aves appropriate, in the more comprehensive team Avialae, have already been discovered dating back to the mid-Jurassic period. Several of the early "stalk-fowl", including Archaeopteryx, are not yet capable of completely powered flight, and several maintained archaic features like toothy teeth rather than beaks, and long bony tails.
Birds have wings that tend to be less or more grown according to the types; the only recognized groups without wings are hippo birds and the vanished moas. Wings, which developed from fore-limbs, provide most birds the skill to fly, even though additional speciation h-AS light emitting diode to some parrots, including varied endemic island varieties of fowl and ratites. The breathing and intestinal techniques of fowl will also be uniquely adapted for trip. Associates of the goose family, especially these flightless penguins some bird types of water surroundings, also have developed for swim. Fowl, particularly the finches of Darwin, performed with a significant component in the origin of Darwin's principle of development by organic selection.
Birds imagesSome birds, chickens and notably corvids, are on the list of most educated creatures; a lot of social types give information across decades, which will be regarded a kind of tradition, and several bird types use and make resources. Several types per annum progress fantastic distances. Fowl are interpersonal, mobbing of predators, and taking part in such societal behaviors as hunt and cooperative-breeding, clumping, and conveying with visible calls, and bird songs. The great majority of bird types are monogamous for one mating period at a period, sometimes for years, but seldom for-life. Additional varieties have polygynous ("several ladies") or, seldom, polyandrous ("several men") reproduction techniques. Offspring is produced by fowl by lounging ova which are fertilized through sexual imitation. They incubated from the parents and are typically set in a home. Many birds have a protracted period of parent care. Although unfertilized ova tend not to produce offspring some birds, for example chickens, lay ova also when maybe not fertilized.
Several varieties of birds are not cheaply unimportant. Trained and wild birds (chicken and game) are significant sources of eggs, beef, and feathers. Additional species, birds, and song birds are well-liked as animals. Guano (fowl waste) is picked to be used as a plant food. Individual tradition is conspicuously figured for the duration of by fowl. About 120 130 varieties are becoming vanished thanks to individual exercise since the 17th millennium, and 100s mo Re before then. Are under way to protect them. attempts about 1,200 bird varieties with annihilation, although is threatened by Act Birding that is amateur is a vital component of the eco-tourism sector. | <urn:uuid:80af24df-fab3-4297-a2b4-e66c7aa01646> | {
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For the past 40 years, evolutionary biologists have been investigating
the possibility that some evolutionary changes occur in a clock-like
fashion. Over the course of millions of years, mutations may build up in any given stretch of DNA at a reliable rate.
For example,the gene that codes for the protein alpha-globin (a component of hemoglobin)
experiences base changes at a rate of .56 changes per base pair per
billion years*. If this rate is reliable, the gene could be used as a molecular clock.
When a stretch of DNA does indeed behave like a molecular clock, it becomes
a powerful tool for estimating the dates of lineage-splitting events.
For example, imagine that a length of DNA found in two species differs
by four bases (as shown below) and we know that this entire length
of DNA changes at a rate of approximately one base per 25 million years.
That means that the two DNA versions differ by 100 million years of
evolution and that their common ancestor lived 50 million years ago. Since each lineage
experienced its own evolution, the two species must have descended
from a common ancestor that lived at least 50 million years ago.
This general technique has been used to investigate several important issues, including the origin of modern humans, the date of the human/chimpanzee divergence, and the date of the Cambrian "explosion."
Using molecular clocks to estimate divergence dates depends on other methods of dating. In order to calculate the rate at which a stretch of DNA changes, biologists must use dates estimated from other relative and absolute dating techniques.
*This number is for changes that affect the structure of the protein | <urn:uuid:94f7355d-831c-4914-8c2d-3311618f89f8> | {
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Generating Function via Recurrence Relation
I am trying to find the solution to the following recurrence for polynomials: \begin{align*} h^{[0]}(z) &= z \\ h^{[n+1]}(z) &= z h^{[n]}(z) (z+z^2+...+z^{n+1}) +z \end{align*} I calculated the first polynomials, yet couldn't find any obvious pattern (neither could I find it with the help of OEIS). Also my limited Maple-knowledge wasn't enough to find a solution (I tried rsolve, but I guess I don't understand the syntax for polynomials completely).
Is there a closed-form expression for these polynomials? And how can I solve such recurrences with Maple or Mathematica?
Fortunately that summation term z+z^2+...+z^(n+1) can be put into a closed form. Otherwise you might have to combine what can be thought of as a mixed pair of recurrences.
That summation term can be dealt with by either rsolve or, more simply, the sum command.
palt:=rsolve({b(n)=b(n-1)+z^(n),b(1)=z},b(n));
2 n
z z z
palt := z - ------ + ------
-1 + z -1 + z
p:=sum(z^i,i=1..n);
(n + 1)
z z
p := -------- - ------
-1 + z -1 + z
simplify( p - palt );
0
Now we can solve the problem. Below, I'll focus on finding h(n).
sol:=rsolve({h(n)=h(n-1)*z*p+z,h(0)=z},h(n)):
where sol has products and summations (with n in the index bounds) but is no longer a recurrence relation.
lprint(sol);
(z^2/(-1+z))^n*(-1+z)*(product(z^(n0+1)-1, n0 = 0 .. n))*(sum((z^2/(-1+z))^
(-n1)/(product(z^(n0+1)-1, n0 = 0 .. n1)), n1 = 0 .. n-1))/((z^(n+1)-1)*z)
+(product(z^(n0+1)-1, n0 = 0 .. n))*(z^2/(-1+z))^n*z/(z^(n+1)-1)
We may test that result for a few cases of n, by comparing with a recursive procedure set up to compute similar to the original recurrence.
It's your choice whether to put the results into expanded, factored, or otherwise simplified form.
seq(factor(simplify(eval(sol,n=i))),i=0..3);
/ 2 \ / 5 4 3 2 \
z, z \z + 1/, z \z + z + z + z + 1/,
/ 9 8 7 6 5 4 3 2 \
\z + 2 z + 3 z + 3 z + 2 z + 2 z + z + z + 1/ z
makeh:=proc(n::nonnegint)
if n=0 then z;
end if;
end proc:
seq(factor(simplify(makeh(i))),i=0..3);
/ 2 \ / 5 4 3 2 \
z, z \z + 1/, z \z + z + z + z + 1/,
/ 9 8 7 6 5 4 3 2 \
\z + 2 z + 3 z + 3 z + 2 z + 2 z + z + z + 1/ z
seq( simplify( makeh(i) - eval(sol,n=i) ), i=0..10 );
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 | crawl-data/CC-MAIN-2019-39/segments/1568514574377.11/warc/CC-MAIN-20190921084226-20190921110226-00394.warc.gz | null |
Histogram
A histogram is a way to visually represent, quantitative data. It is useful in describing data that has considerable variability. The reason for this is that it takes the range of the dataset, dividing it into even groups, called bins, and then counting the number of numbers that fall in each one of those bins, and then displaying that amount with bars. To look at how to create a histogram, take the following dataset.
For this example, we are going to use a bin width of 5. With our minimum value being 1 our bins would be 1 – 6, 6.1 – 11, 11.1 – 16, 16.1 – 21, 21.1 – 26, 26.1 – 31, and 31.1 – 36.
Now that we have the width of all the bins, we can go through the dataset and count the number of values fall in each of those bins. The first term in the dataset is an 18, which falls in the 16.1 – 21 bin. The second number is 16 which falls in the 11.1 – 16 bin. The third number is 11, which falls in the 6.1 – 11 bin. Continuing on with this same process, until all the data has been counted, gives us the following table.
Bin Width Number of Values in each Bin
1 – 6 9
6.1 – 11 14
11.1 – 16 8
16.1 – 21 5
21.1 – 26 3
26.1 – 31 0
31.1 – 36 1
The above table creates the below histogram.
Determining the bin width is the most critical aspect of creating a histogram. If the bin width is too small, you get quite a bit of information about the data, but because of the inherent variability in quantitative data, the graph can display quite a bit of noise, which can obscure what the data is trying to say. For example, the next histogram is showing the same data, but it has a bin width of 1.
The above graph with a bin width of one shows how much variability there is with this dataset. There is so much variability in fact that there is little else we can tell about this data besides its high variability.
On the other hand, if the bin width is too large, such as in the next histogram which has a bin width of 10, then lose a lot of details, which also makes it difficult to draw conclusions from the graph. | crawl-data/CC-MAIN-2020-24/segments/1590347402885.41/warc/CC-MAIN-20200529085930-20200529115930-00456.warc.gz | null |
Africa and India have had a long history and relationship together in areas like trade, religion, music, arts, and architecture, dating far back as the 1st century, but their historical link is rarely discussed.
A notable place during the Common Era where modern Africans and Indians co-existed was in the princely state of Sachin, India. The Sachin state was an African ruled state in Gujarat in India, established in 1791. Sachin was a self-contained nation that had its own coat of arms, stamped paper, currency, Calvary and also a mixed Royal court of Africans and Indians. Princely states in India were autonomous feudatory kingdoms that operated as vassal or subsidiary allies to the regional hegemonies of India.
Sachin was merged into Independent India in 1948 along with other princely states in the region. At this point, they had a population of about 26,000 which comprised of mostly Hindu worshippers and a smaller population of Muslim followers.
Sachin state was established on 6 June 1791 with over 85% of its population being Hindus, while the other parts, mostly their rulers, being Sunni Muslims of the Sidi dynasty of Danfa-Rajpuri and Janjira State. The Sidi dynasty is of Habesha origin, people culturally and ancestrally related to the ethnic groups in the Ethiopian highlands in Africa.
Sachin state, before it came under the British protectorate, was under the protection of the Maratha Peshwa (likened to a modern-day prime minister). In 1829, the state became bankrupt; this brought the state under British civil administration between 1835 and 1864. It had its own currency, Calvary, and stamped paper, including a state band with Africans inclusive.
One of India’s cinemas earliest superstars, Fatima Begum (1892- 1983), who was also India’s first female film director, was said to have been allegedly married to Nawab Sidi Ibrahim Muhammad Yakut Khan III of Sachin state. But sources from the Sachin royal family throw a veil over this, and they claim no record of the marriage or contract between the Fatima Begum and the Nawab. They also claim no record of the Nawab recognizing her children, Sultana, Zubeida and Shehzadi as his own. Fatima Begnum’s daughter, Sultana, became a key figure in early Indian movies. Zubeida, Sultana’s younger sister, became a leading actress in Indian’s first talkie film Alam Ara in 1931.
Nawab Sidi Ibrahim Muhammad Yakut Khan III, the last ruler of Sachin state, signed the agreement to join the Indian union on 8 March 1948 and the state became part of Surat district in Bombay Province.
Zubaida stayed in India after the partition, while her sister moved to Pakistan where she got married and gave birth to a girl child, Jamila Razzaq, who eventually became a prominent actress in Pakistan between the mid-1950s and the mid-1960s.
A painting of Nawab Sidi Haidar Khan of Sachin
Location of Sachin
The Sachin State (Pink) within the Surat Agency
All rulers in Sachin were addressed by a title “Nawab,” and they were all granted a nine-gun salute by the British authorities.
- Abdul Karim Mohammad Yakut Khan I: ruled from 6th June 1791 to 9th July 1802 (birth was around the 1700s (uncertain) and died in 1802)
- Ibrahim Mohammad Yakut Khan I: ruled from 9th July 1802 to 25th March 1853 (birth date is uncertain while he died in 1853)
- Abdul Karim Mohammad Yakut Khan II: ruled from 25th March 1853 to 1st December 1868 (born 1802 and died 1868)
- Ibrahim Mohammad Yakut Khan II: ruled from 1st December 1868 to 4th March 1873 (born in 1833 and died in 1873)
- Abdul Kadir Khan: ruled from 4th March 1873 to 7th Jan 1887 (born 1865 and died 1896)
- Ibrahim Mohammad Yakut Khan III: ruled from 7th February 1887 to 19th November 1930 (born 1886 and died 1930)
- Haydar Mohammad Yakut Khan: ruled from 19th November 1930 to 15th August 1947 (born 1909 and died 1970)
There were also records of regents at certain times in the history of Sachin State, between 4th of March 1873 to July 1886, and 7th February 1887 to 4th May 1907.
HISTORY OF RULE
Sidi Abdu Karim, the heir, and son of Sidi Abdul Rahman, who was the Ruler of Rajapore and Janjira, fled to Poona around the year 1784. The reason for this event was not farfetched; he was on the run because his inheritance was seized by Sidi Johor. He signed an agreement with the Peishwa of Marathas in 1791, this led to him giving up all his right to Janjira, but he was given Sachin and all its dependencies instead.
He was forced to give up active administration of the state by the United Company of Merchants of England Trading to the East Indies, commonly called the Honourable East India Company (HEIC), in 1829, following a financial and administrative managerial breakdown. Nawab Sidi Ibrahim Muhammad Yakut Khan I, and his son, Nawab Sidi Abdul Karim Muhammad Yakut Khan II, ruled as nominal rulers until ruling power was fully restored in 1864. Thereafter, the history of the state was relatively free and peaceful under the benevolent and friendly rule of successive Nawabs.
The family entered various marriage alliances with the Muslim aristocracy of Haidarabad. The family also introduced early conversions to European education. Various members of the family attended different universities in England, some became lawyers and served as military officers and administrators. Notable was Nawab Sidi Ibrahim Muhammad Yakut Khan III who served with great distinction in the East African campaign during the Great War. He was honoured with a salute of 11-guns rendered in the style of Highness. Finally, in August 1947, Nawab Sidi Muhammad Haidar Muhammad Yakut Khan consented to the dominion of India over them, and the state was merged in 1948 with the presidency of Bombay.
The Sachin State has a coat of arm with a shield in three, Dexter, a ship at sea with flags and masthead; sinister, a castle with two towers above the walls, a reversed five-pointed star, and a crescent tilted. Also at the top a lion passant guardant turned sinister and holding a fish in its raised paw is seen. Supporters: Guards armed with swords and dressed in striped jackets, wearing hats and countercharged.
The Sachin state flag was a horizontal flag with five equal stripes of red, green, yellow, pink, and dark-blue (from top to bottom)
DECORATIONS AND ORDERS
During the time of some of the Nawabs, especially during the time of Nawab Sidi Ibrahim Muhammad Yakut Khan III, some certain orders were awarded, and some decorations were given to deserving persons. Some of the decorations are:
- Nishan-i-Sardari (the Decoration of the Nobility): founded in August 1918 by Nawab Sidi Ibrahim Muhammad Yakut Khan III, it was awarded in two classes, first class in Gold and second class in silver.
- Tamgha-i-Liaqat-i-Kidmat (Meritorious Service Medal): Founded in August 1918 and awarded in two classes, first class in Gold, second class in Gold, and Second Class in Silver.
- Nishan-i-Yakut Zaman (the Decoration of the Garnet of the Age): instituted in 1907 to commemorate Nawab Sidi Ibrahim Muhammad Yakut Khan III’s coming of age and coming into full ruling power. Awarded in a single class, a silver medal.
- Nishan-i-Sultan Manzoor (the decoration of the ruler’s Admiration): was instituted and awarded in a single class, a silver medal.
- Nishan-i-Hadani (the decoration of the hadani): awarded in a single class, a silver medal.
Special names were used to address a special class of persons in the Sachin state. Some include:
The Ruling Prince
The ruling prince was called by some of these names
- Nawab Sidi (his personal name) Khan Bahadur
- Mumbariz ud-Daula
- Muzaffar ul-Mulk
The consort of the ruling prince
Addressed by the following names
- Nawab Begum Sahiba (personal title)
The heir apparent
- Nawabzada Sidi Khan Bahadur (the general name for all the sons of the ruling prince)
- Wali Ahad Sahib
The daughters of the ruling prince were addressed as Nawabzadi Begum Sahiba.
The grandsons and other male descendants of the ruling prince were addressed as Sahibzada Sidi Khan while the females were addressed as Sahibzadi Begum Sahiba.
Some notable pictures from Sachin
Fatima Begum, whose marriage with Nawab of Sachin Ibrahim Muhammad Yakut Khan III was withheld from public recognition.
Nawab Ibrahim Muhammad Yakut Khan II of Sachin (1833 – 1873)
The Sachin state Merchant flag
A 1904 picture showing Africans guarding and escorting a royal procession.
The study of Sachin state has revealed a lot about the relationship built between Africans and Indians and how they came to be a strong force among the Indian community. Revisiting these histories between these people provides the opportunity to build a mutual understanding of how Africa and India have contributed to the global fabric of the world we live in today. Despite the fact that some of these historical relations between Africa and India may in time be down-played by modern India, orchestrated efforts have been made by people and factions to research into these areas.
Today, we can find Indians in Kenya, South Africa, Ethiopia and Tanzania who identify themselves as Africans. Also, there are descendants of African migrants who reside in India and call India their home. Unfortunately, when history is not presented objectively, ignorance perpetuates discrimination, prejudice, judgmental errors and even violence against dark-skinned Indians. | <urn:uuid:7eeaaba3-41fc-4d15-965a-019ed854ec59> | {
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This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.
In an ever changing world, there are more and more threats to wildlife and the need for conservation is at its greatest. Polar bears are one of the flagship species of conservation and there are many threats to their species that lead to a decline their in populations. The polar bear is the only land mammal species that uses the Arctic as its main habitat. Despite inhabiting one of least accessible areas on Earth to humans, the polar bear is been extremely vulnerable to anthropogenic impacts (Belikov et al. 2010) such as climate change, the drilling of the ice in search minerals or the effect of hunting. There are many conservation measures that are now taken by zoos to protect this species such as a Species Survival Plan (SSP), European Endangered Species Programme (EEP) as well as in-situ and ex-situ conservation which will later be discussed.
Polar bears are marine mammals due to their ice surfaced habitat belonging to the taxonomic family of Ursidae, which are dog-like carnivores or caniforms.
Polar bears are highly adapted for the harsh environment of the Arctic. The polar bears adaptations aid temperature regulation, hunting and movement. They posses a sensitive sense of smell, used to locate seals hiding under the ice and thick curled claws used to the rip flesh of their prey. Polar bears also posses excellent eye sight which helps them to see seals lying on the ice. Being bow-legged and pigeon-toed, polar bears are able to travel quickly and stop immediately when moving and with hair on the soles of their feet they have more traction when running preventing them from slipping on the ice (Bertalan, 2010). This allows the polar bear to initiate attacks on their prey well before the victim becomes aware of its presence.
Their diets contain a high fat content gained from the blubber seals posses which serves as insulation during the winter. As food is scarce without the fat they consume they would not survive long enough to find other prey due to a lack energy.
They posses webbed feet for ease of movement through water and a water repellent fur coat allowing for less exhaustive swimming (Stirling, 1988). The polar bears coat, used to regulate body temperature and camouflage the animal, changes colour annually appearing white in the winter months and yellow during the summer before moulting.
During the months of April and May courtship and mating occurs in the best hunting areas. Polar bears are polygynous and males often engage in fighting with other males, frequently resulting in injury, for the rights to mate with a female. Males and females stay together for up to a week mating. The female gains 200kg the summer months in preparation for the winter and starts to prepare a den for her cubs in snowdrifts or permafrost (Sterling, 1988). Males however, spend the winter wandering the ice. When the den is complete the female enters a non-continual dormant state. Between Novermber and February, two cubs are born on average, weighing less than a kilo each (Rosing, 1996), they are blind and helpless. The family emerges in mid-April making their way towards the ocean where seals are plentiful. At this time females must be weary of males as they easily prey upon young cubs. For up to the first two and a half years of their lives the cubs will remain with their mother before being weaned and abandoned by her.
Female polar bear usually begin to breed at around the age of four, whereas males reach sexual maturity at around six years old. A Hudson Bay study showed that the maturnal weight and the reproductive success of females were seen to peak when they reached their mid teens (Derocher, Stirling, 1994). It is apparent that instead of dying of old age, starve due to the weakness old age can cause.
Polar bears aren't usually territorial and tend to shy away from confrontations but attacks are often predatory and are usually fatal. Adults are solitary but from time to time they have been observed when playing with eachother and sleeping besides one another (Bruemmer, 1989).
Conservation status and distribution
Found only in the Northern Hemisphere the polar bear is currently classified as Vulnerable by the IUCN Red List of Threatened Species, with the population actively decreasing. There is thought to be a total of 20,000 to 25,000 individuals in the wild that make up nineteen theorised subpopulations (Schliebe et al. 2008). Their range is limited due to their reliance on the Arctic habitat however can be found in areas such as; Alaska, Canada, North Russia, Greenland and East Siberia (Amstrup, 2003), depending on availability of food.
Threats to its future survival in the wild.
One of the most obvious threats to polar bear survival is climate change, which indirectly causes starvation due to the loss of habitat incurred. As temperatures rise, the ice that polar bears use to hunt seals melts earlier in the year, causing greater difficulty in finding food or building up sufficient fat reserves for the coming winter months. Polar bears are then force to either swim long distances, using up their energy which occasionally causes them to drown or stay on the ice where it is difficult to gain access to seals below due to the deformed melting ice (Amstrupl et al. 1989). Polar bears deaths that are a result of drowning could rise in the future pack ice continues to melt (Monnett and Gleason, 2006).
Due to the lack of quality food, polar bears are less likely to reproduce, if they do it is probable that the cubs will not survive (Derocher et al, 2004). The melting ice can also force polar bears to migrate south in search of food, where an increase in human-polar bear conflict could be seen if bears come into close proximity to humans targeting rubbish dumps which can lead to fatalities for polar bears.
There are many direct threats to the polar bears future suvival in the wild. Polar bear hunting has existing for hundreds of years and provides trophies to recreational game hunters as well as meat and fur for commercial hunters to sell. Hunting brings about the potential risk of over-harvesting of polar bears and causes significant drops in populations, as many as 200 animals were be killed annually in the 1920-1930s (Belikov et al. 2010).
Humans seek to interfere with the Arctics natural habitat, when planning to exploit the area for mineral extraction. The Arctic is endowed with petroleum, minerals, fish and forests that increasingly attract the interest (Lindholt, 2006). Such interest could result in a loss of habitat for the polar bear altering feeding and mating patterns. Minerals such as; oil and gas are thought to lie beneath the surface of the ice and extracting any type of mineral could lead to contaminants being released and possibly affecting polar bears directly or affect their fragile habitat.
There are many different conservation measures taken by zoos to ensure the survival of the polar bear species. A Species Survival Plan could be one measure, which manages and conserves animals that are endangered managing ex-situ species, with the cooperation of the Accredited Zoos and Aquariums (AZA, 2010)
Housing, food, enrichment etc. (25%)
Consideration should be taken when designing enclosures for polar bears so they much meet all areas of social, psychological, behavioural and physical needs (AZA, 2009). Wherever possible their habitat must replicate that of their natural environment with groups of animals not exceeding number that would be present in the wild. It is possible to create dynamic, stimulating and comfortable environments for polar bears using innovative exhibit design, feeding and enrichment strategies to maximise their welfare reducing the possibility of stereotypic behaviour (AZA, 2009). Exhibits must contain platforms for resting, nesting sites and must comply with the Polar Bear Protection Act , they should also be given access to all areas of the exhibit at all times unless it is necessary otherwise (PBPA, 2002). The substrate of the floor is required to be made of a 'soft' material rather than hard (Ames, 2000). Using structures or large rock for climbing and other items for enrichment provides the polar bears with mental and physical stimulation as well as allowing them vantage points, which should be safely accessible to bears on any age.
Due to the vast expanse of the Arctic polar bears tend to benefit from adequately sized enclosures suitable to avoid other polar bears in the area due to their tendency to be solitary animals and important behaviours such as; swimming, foraging and running. Polar bears create nests in their natural habitat and the enclosure should occupy 1350ft� of floor space that is covered by soil, wood chips or another suitably soft substrate (PBPA, 2002) with areas so perform behaviours such as. The public should only be able to view up to 180� so that bears can avoid the public if they choose to.
Polar bears can be susceptible to most diseases that other carnivores contract. They can become infected with viruses, bacteria, parasites, protozoa and fungi (Dierauf & Gulland 2001), not only this but they can also develop nutritional disease and developmental problems among other illnesses. To keep Polar bears in zoos, an efficient veterinary service is critical to ensure an animals well-being. Visual exams are conducted on polar bears approximately every 6 months to inspect any changes in behaviour, feeding patterns, weight, overall physical appearance, respiration and stool quality.
Nutritional diseases can occur due to captive polar bears diet. Two hand-reared cubs were reported to have developed rickets, but were cured with a change in diet (Kenny et al. 1999). Dermatitis has occurred in polar bears due to a lack of vitamin A in their diets which would be readily available in the wild. But dermatitis is easily treated with a vitamin A supplement such as cod liver oil (Kock et al. 1985).
There are only two main Viral diseases the affect polar bears; rabies and morbillivirus. Although polar bear with rabies have been recorded, they are not a threat to to the overall wild populations nor in captivity (Taylor et al., 1991). Morbillivirus affects many wild polar bears but despite how common the virus is, it has been found to pose no serious threat to their health (Garner, 1996; Garner et al., 2000).
A bacterial disease that affects polar bears is leptospirosis which brings about symptoms of weakness, diarrhoea, jaundice and sometimes muscle spasms (Nall & Maetz, 1975). The disease is carried by rodents which makes it essential to keep them away from the enclosures. Vaccinations should be enforced to reduce the risk of contracting the disease.
Mycotic diseases such as blastomycosis is described in polar bears as a pulmonary disease (Dierauf & Gulland 2001) and symptoms include weight loss, increased lathargy and anorexia but with a treatment of 4.3mg/kg/day of itraconazole recovery can be made (Morris, 1989).
Regular worming treatments and regular faecal analysis can prevent parasites occurring in captive polar bears. Parasites can cause many problems to polar bears depending on their type. There are two types; internal and external. Internal parasites can be difficult to be rid of, symptoms include; diarrhoea and dramatic loss of weight which can lead to death. Polar bears are often susceptible to flea and tick infestations that causes irritation the skin. | <urn:uuid:38ed0c71-2f6d-4d9d-8cd8-cbfb349e2c1b> | {
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Writing KS2 Literacy. Improve your writing skills with these links to free to use English KS2 resources.
Non Fiction Writing Power Point
A set of powerpoint resources looking at the six types of non fiction writing: discussions, explanations, instructions, persuasion, recounts and reports.
Story Structure Video
Find out why most stories consist of a beginning, a middle and an end.
The Lantern Video
A love story created by Jason Dettner as a wedding present for his wife. Teaching Ideas. Write a diary entry for the boy just after he spots the angel. Do some thought mapping and inner dialogue work, can he believe his eyes? The children can work on writing dialogue what would the boy and angel say to each other? Write instructions for 'How to catch a star.'
Create an emotions timeline or graph for the boy.
Retell the story from each of the characters point of view.
Writing : Non Fiction Interactive
When you are writing non-fiction it's important to use a style of writing that fits the subject.Use your knowledge of non-fiction writing to group the correct titles, text and pictures together.
Writing Instructions Interactive
Choose from a list of different activities such as making a sandwich, putting up a tent and making a robot. Write step by step instructions in English for how it should be performed from the perspective of someone who has never done it before. It sounds easy but it’s not quite as simple as you might think.
Writing Worksheets Printable
A selection of writing worksheets covering a variety of subjects. American site. | <urn:uuid:23bbd15d-9f31-4656-a61e-222fbe3b1ddb> | {
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# Another Convergence Problem
• Nov 15th 2008, 02:06 PM
RedBarchetta
Another Convergence Problem
Let $\sum\limits_{n = 1}^\infty {a_n }$ be a convergent series of positive terms.
What can be said about the convergence of $\sum\limits_{n = 1}^\infty {\frac{{a_1 + a_2 + \cdots + a_n }}
{n}}$
?
My Attempt:
$
\because \sum\limits_{n = 1}^\infty {a_n } = s_n \therefore \sum\limits_{n = 1}^\infty {\frac{{a_1 + a_2 + \cdots + a_n }}
{n}} = \sum\limits_{n = 1}^\infty {\frac{{s_n }}
{n}} = s_n \sum\limits_{n = 1}^\infty {\frac{1}
{n}}
$
Therefore, $
\sum\limits_{n = 1}^\infty {\frac{{a_1 + a_2 + \cdots + a_n }}
{n}}
$
is a divergent harmonic series?
• Nov 15th 2008, 02:17 PM
flyingsquirrel
Hi,
Quote:
Originally Posted by RedBarchetta
$\sum\limits_{n = 1}^\infty {\frac{{s_n }}
{n}} = s_n \sum\limits_{n = 1}^\infty {\frac{1}
{n}}
$
(Surprised) You can't do this, $s_n$ depends on $n$ !
Hint : for all $n\geq 1$, $s_n\geq a_1>0$ because $a_k>0$ for all $k\geq 1$.
• Nov 15th 2008, 02:20 PM
Mathstud28
Quote:
Originally Posted by RedBarchetta
Let $\sum\limits_{n = 1}^\infty {a_n }$ be a convergent series of positive terms.
What can be said about the convergence of $\sum\limits_{n = 1}^\infty {\frac{{a_1 + a_2 + \cdots + a_n }}
{n}}$
?
My Attempt:
$
\because \sum\limits_{n = 1}^\infty {a_n } = s_n \therefore \sum\limits_{n = 1}^\infty {\frac{{a_1 + a_2 + \cdots + a_n }}
{n}} = \sum\limits_{n = 1}^\infty {\frac{{s_n }}
{n}} = s_n \sum\limits_{n = 1}^\infty {\frac{1}
{n}}
$
Therefore, $
\sum\limits_{n = 1}^\infty {\frac{{a_1 + a_2 + \cdots + a_n }}
{n}}
$
is a divergent harmonic series?
What about this $\sum_{n=1}^{\infty}\frac{a_1+a_2+\cdots+a_n}{n}\si m\sum_{n=1}^{\infty}\frac{a_n}{n}\leqslant\sum_{n= 1}^{\infty}a_n$
• Nov 15th 2008, 02:30 PM
flyingsquirrel
Quote:
Originally Posted by Mathstud28
$\sum_{n=1}^{\infty}\frac{a_1+a_2+\cdots+a_n}{n}\si m\sum_{n=1}^{\infty}\frac{a_n}{n}$
What do you mean by $\sim$ ?
• Nov 15th 2008, 06:34 PM
Mathstud28
Quote:
Originally Posted by flyingsquirrel
What do you mean by $\sim$ ?
Sorry, I misread the problem. But here is how I would present the solution
Since this is a decreasing sequence of positive numbers let us apply Cauchy 'sCondensation test.
$\sum_{n=1}^{\infty}\sum_{k=1}^{n}a_k\frac{1}{n}$ converges iff $\sum_{n=1}^{n}2^n\cdot\sum_{k=1}^{2n}a_k\frac{1}{2 ^n}=\sum_{n=1}^{\infty}\sum_{k=1}^{2^n}a_k$ converges. From there it should be pretty obvious what the answer is. | crawl-data/CC-MAIN-2018-05/segments/1516084886946.21/warc/CC-MAIN-20180117142113-20180117162113-00163.warc.gz | null |
# CAT Practice : Averages, Ratios, Mixtures
When we mix two mixtures in a particular ratio, we get a third mixture. Given the third mixture how does one find the ratio in which they were mixed.
## Alligation
Q.27: 40% of a club’s revenue comes from people of 25 years of age while 60% of its revenue comes from people of 35 years of age. If the club raises its fee by 20% for its 25 years old members and 30% for 35 years old members, what is the percentage increase in overall revenue of the club?
1. 26%
2. 25%
3. 24%
4. 23%
Choice A. 26%
## Detailed Solution
The ages 25 years and 35 years are just to confuse and do not have any role in the solution.
Here, 40% and 60% are n1 and n2 while increase in 20% and 30% are A1 and A2 so,
= ) $\frac{(30-x)}{(x-20)} = \frac{40}{60}$
= ) $\frac{(x-20)}{(x-20)} = \frac{2}{3}$
= ) 90 – 3x = 2x – 40
= ) 130 = 5x = ) x = 26%
## Our Online Course, Now on Google Playstore!
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## More questions from Averages, Ratios, Mixtures
Averaages, Ratios and Mixtures XXXXXXXXXXXXXXXXXXXXXXXXXe. | crawl-data/CC-MAIN-2018-17/segments/1524125949036.99/warc/CC-MAIN-20180427041028-20180427061028-00448.warc.gz | null |
## Intermediate Algebra (12th Edition)
We are given that $f(x)=x^{2}+4$, $g(x)=2x+3$, and $h(x)=x-5$. We are asked to find $(h∘g)(-2)$. We know that $(h∘g)(x)=h(g(x))$. Therefore, $(h∘g)(-2)=h(g(x))=h(2(-2)+3)=h(-4+3)=h(-1)=-1-5=-6$. | crawl-data/CC-MAIN-2018-51/segments/1544376827639.67/warc/CC-MAIN-20181216095437-20181216121437-00535.warc.gz | null |
In order to pump blood through your body effectively, a heart must beat with a strong and consistent rhythm. When the heart loses its consistent rhythm, this is known as an ‘arrhythmia’. Atrial fibrillation – also known as “AFib” or “AF”—is a type of arrhythmia, which happens when the heart’s electrical rhythm is disrupted in such a way that it beats very quickly and chaotically. This prevents blood from being pumped efficiently, which can lead to stroke, weakness, breathlessness, fainting, and a significant reduction in one’s quality of life.
Atrial fibrillation is a common and growing problem, affecting over 2.7 million people in the United States.1 Fortunately, many successful methods for treating AFib have been developed, and are commonly used to help patients.
There are various options doctors use to treat AFib, with the goal of restoring a normal heart rhythm, and/or controlling its rate. The approach taken depends on many factors, including the type and severity of arrhythmia, prior treatments, and other medical conditions. Treatments can include lifestyle changes, medications to slow the heart, control its rhythm, or reduce the risk of blood clots and stroke, as well as catheter-based ablation procedures and surgery.
When lifestyle changes and medication are not effective enough to address AFib, ablation is one common next step. During this minimally-invasive procedure, a catheter is inserted through a vein in the leg and advanced into the heart, where energy is used to block abnormal electrical pathways by creating lines of scar tissue. This “ablation” is often an effective and low-impact way to restore a normal heart rhythm. Recovery is usually rapid and the procedure may be done with either sedation or under anesthesia.
Atrial fibrillation usually begins in one or more of the pulmonary veins, the vessels that carry oxygenated blood from the lungs to the left atrium of the heart. In this case, physicians perform a pulmonary vein isolation (PVI) procedure to create areas of scar tissue around the pulmonary veins, where each connects to the left atrium. This scar tissue serves to block the electrical signals causing arrhythmia, thereby electrically isolating the pulmonary veins from the atrium, and allowing the heart to beat with a normal rhythm once again.
The HeartLight System has been designed for physicians to perform PVI procedures with accuracy, precision, and confidence. To provide physicians with an additional layer of insight about each procedure, our innovative HeartLight catheter is equipped with a miniature video camera and “headlight” to deliver a direct, live-action view of the ablation site.
The HeartLight System also enables physicians to customize the amount of energy used for their ablations, based upon patients’ specific needs. And HeartLight utilizes a unique balloon design to adapt to your heart’s specific anatomy.
Find a physician performing the HeartLight Procedure near you:
FIND A DOCTOR
This is a generalized description of atrial fibrillation and treatment options. Please be sure to consult your physician about your specific situation and needs.
1. Benjamin EJ, et al. Heart Disease and Stroke Statistics – 2018 Update. Circulation. 2018;137:e67-e492. | <urn:uuid:7b4b9e74-7390-4832-af68-2e13ff4c2ef0> | {
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Home Styles
## How to Solve a 2x2 Rubik's Cube (Ortega Method)
Lets look at solving the 2x2 Rubik's Cube using the popular Ortega method. The Ortega method is a very fast way of solving the 2x2 (but not the fastest). When completely confident with all of the algorithms shown below you should be at least sub 5 (maybe even quicker).
Please Note: All images used in this guide are generic pictures of 2x2 Speed Cubes and may not be genuine Rubik's brand cubes. All images are for illustrational and educational purposes only.
# WHAT IS ORTEGA?
#### Step1
Solve the white face on the BOTTOM layer
#### Step 2
Orientate the TOP layer
#### Step 3
Permute the TOP and BOTTOM layer at the same time
# STEP 1 - Building THE FIRST SIDE
If you are reading this tutorial on solving your 2x2 with the Ortega method I can only assume that you have (at least) basic knowledge of solving the 2x2 and are confident using the LBL (layer by layer) method. I will not be going through how to solve the first layer as this is something you should be used to if you are trying to learn a fairly advanced method.
Lets solve the white side first.
1. Build the white face on the bottom layer not worrying about putting the pieces in the correct place.
2. We will come back later in step 3 and permute these pieces.
# Step 2 - orientating the last layer
In step 2 of the 2x2 Ortega method we bring all of the yellows to the top layer (you may have started with a different side of the cube, in which case you might not be solving the yellow face here, but in our example we are solving the yellows). Once all of the yellows are on the top we can move on to step 3.
# sTEP 3 - pERMUTING THE two laYERs
In step 3 of the Ortega method we permute both of the layers at the same time thus solving the 2x2 cube. This may take a little bit of time to learn but rest assured, once you are confident in finding and performing the correct algorithm you will be well on your way to sub 5.
- Nov 17, 2018
In step 2 you have an algorithm: R U2 R2 U’ R U’ R2 U2 R
The 5th turn should be R2 not R so: R U2 R2 U’ R2 U’ R2 U2 R
Also, in step 3 the algorithm: (R U2 R’ U’) (R U2) (L’ U R’ U’ L’) the last turn should be L not L’
- Dec 19, 2018
Good tutorial. Maybe you can be more specific on step 3 because I had to go watch a video to know more. The algorithms are correct and I can already feel myself getting faster
- Jan 03, 2019
This helped me a lot! I looked at so many videos and I didn’t understand but as soon as I looked at this I can go way faster!
- Mar 03, 2019
I can solve it in 13 sec. Bet i have to look for a long time (step 3) to see wich algorithm i have to use. And that takes a long time. Can i see in the begin wich algorithm i have to use? Bcs now it takes too long.
- Apr 13, 2019
there are some cases that arent on there
- Apr 13, 2019
there are some cases that arent on there
- Apr 13, 2019
I’m a bit confused, am I supposed to have to use multiple algorithms in step 3?
- Apr 13, 2019
Hi, thanks for the great page of algorithms. I have a compatition soon and I am really bad at 2×2. This makes me faster all ready, just as soon as I learned all the algorithms.
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£9.99 £8.99
£27.99 £26.99
£31.99 £30.89
£27.99 £26.99 | crawl-data/CC-MAIN-2019-18/segments/1555578655155.88/warc/CC-MAIN-20190424174425-20190424200425-00461.warc.gz | null |
# Parametric Equations and Polar Coordinates
### Contents
#### Key Terms
Limacon - A polar equation of the form r = a + b sin(θ) or r = a + b cos(θ), where a, b≠ 0.
Logarithmic Spiral - A polar equation of the form r = abθ.
Orientation - The direction of a plane curve as the parameter increases.
Parameter - A third variable (often time) which determines the values of x and y in parametric equations.
Parametric Equations - Two equations of the form x = f (t) and y = g(t), which specify the location of a point according to the variable t.
Plane Curve - The set of all points (f (t), g(t)), where x = f (t) and y = g(t) are parametric equations.
Polar Axis - The ray whose endpoint is the pole and which is the initial side of any angle measure in the polar plane.
Polar Coordinate System - The system in which a point in the plane is specified according to an ordered pair (r, θ) in which r is a length and θ is an angle. The length r refers to the distance from the point to a fixed origin, called the pole. The angle θ is the angle whose initial side is a fixed ray (the polar axis) and whose terminal side contains the point. Under these circumstances, the point (r, θ) is expressed in polar coordinates.
Pole - The fixed point in the polar coordinate system from which every point is r units away.
Rectangular Coordinate System - The coordinate system in which every point is specified by exactly one ordered pair (x, y). Here x is the distance between the point and a fixed line (the y-axis) and y is the distance between the point and a line fixed perpendicular to the other line (this line is the x-axis). The perpendicular lines are the axes, and the point (x, y) is expressed in rectangular coordinates.
Rose Curve - A polar equation of the form r = a sin() or r = a cos(), where n is an integer.
Spiral of Archimedes - A polar equation of the form r = + b. | crawl-data/CC-MAIN-2018-13/segments/1521257645538.8/warc/CC-MAIN-20180318052202-20180318072202-00044.warc.gz | null |
Huntington’s disease is an inherited progressive disorder that affects movement, cognition, and behavior. The hallmark symptom of Huntington’s disease is chorea, uncontrollable and often painful involuntary movement.
The cognitive and behavioral symptoms of dementia due to Huntington’s include depression, memory problems, impaired judgment, problems with short-term memory, organizing, coping, and concentrating. Delusions and hallucinations may occur. Symptoms that may also occur are irritability, anxiety, aggressive outbursts and social withdrawal.
Huntington’s disease does not skip generations. Each child of a parent with Huntington’s has a 50% chance of inheriting the defective gene. If a child does not inherit the gene, he or she cannot pass it on. If the child does inherit the gene, he or she can pass it on and will develop the disease.
The average lifespan after onset is 10 to 25 years, and the younger the age of onset, the more rapid the progression of the disease. Symptoms generally appear between the ages of 30 and 50, but can strike children and young adults.
The discovery of the Huntingtin gene has made possible a predictive test for Huntington’s disease from a blood sample allowing those at risk to find out whether or not they will develop the disease. Pre-and post-test counseling is critical. This testing may also pave the way to clinical trials of preventative therapies.
For more information about Huntington’s disease, visit our affiliated support group organization, UCI HD-CARE. | <urn:uuid:7cefd549-ac0c-4202-a8d4-b9e7b705bb1d> | {
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Ratio and Proportion For SBI PO : Set – 02
1) The ratio of the present age of A to that of B is 5 : 3. After 16 years the total of their ages will be 96 years. What will be the ratio of their ages at that time?
a) 5:4
b) 6:5
c) 7:4
d) 7:5
e) 8:5
(d)
A = 5x
B = 3x
After 16 years = (5x + 16) + (3x + 16) = 96
8x + 32 = 96
8x = 64
X = 8
Present ages of A & B = 40 & 24
After 16 years = 56: 40
= 7: 5
2) 16 liters are drawn from a cask full of wine and is then filled with water. This operation is performed three times. The ratio of the quantity of wine now left in cask to that of the water is 343:386. Now much wine the cask hold?
a) 34
b) 55
c) 62
d) 72
e) None of these
d)
X = ?; y = 16;
x=72
3) Consider two alloys A and B 70 kg of alloy A is mixed with 140 kg of alloy b) A contains brass and copper in the ratio 3 : 2, and B contains them in the ratio 4 : 3 respectively. What is the ratio of copper to brass in the mixture?
a) 84 : 52
b) 70:50
c) 50:12
d) 48:94
e) 44:61
e)
4) The ratio of the present ages of a sankar and kumar is 1 : 5 and that of his friends maha and kumar is 4:5. After 2 years the ratio of the ages of the sankar to that of his friend maha becomes 3:10. What is the present age of the kumar?
a) 37 years
b) 35
c) 44
d) 39
e) None of these
b)
Let the present age of the sankar be x years
Present age of the kumar = 5x
Present age of the maha=4x
after 2 years,
age of the Sankar = x+2
age of the maha = 4x+2
10(x+2)=3(4x+2)
10x+20=12x+6
2x=14
5x=5 *7=35
2x=14
Present age of the Kumar = 35 years
5) There are 43800 students in 4 schools of a city. If half of the first , two-third of the second, three-fourth of the third and four-fifth of the fourth are the same number of students, then find the ratio of number of students of A and D if A, B, C and D be the first, second, third and fourth schools respectively.
a) 5:9
b) 7:6
c) 9: 7
d) 8: 5
e) 9: 5
Ans. D
A: B = 4 : 3
B: C = 9: 8
C: D = 16: 15
A: D = 576: 360
A: D = 8: 5
6) Rs 900 were divided among A,B and C in such a way that A had Rs.60 more than B and C had Rs. 30 more than A. How much was C’s Share?
a) Rs 270
b) Rs 340
c) Rs.135
d) Rs.235
e) None of the above
b)
Let B have x Rs with him
Then A has = (60+x)
Then C has = (30+A) = (30+60+x) = 90+x
Hence A+B+C=900
60+x+x+90+x=900
3x+150=900
3x=750
x=250
Then C gets 90+x=90+250=340 Rs
7) Three friends Alice, Bond and Charlie divide \$1105 amongst them in such a way that if \$10, \$20 and \$15 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they got will be in the ratio of 11 : 18 : 24. How much did Charlie receive?
a) \$495
b) \$510
c) \$480
d) \$375
e) \$360
(a)
Let the sums of money received by A, B and C be x, y and z respectively.
Then x – 10 : y – 20 : z -15 is 11a : 18a : 24a
When \$10, \$20 and \$15 are removed, we are removing a total of \$45 from \$1105.
Therefore,
11a+18a+24a=1105-45=1060
53a=1060
or a= 20
We know that z – 15 = 24a = (24 * 20) = 480
Therefore, z = 480 + 15 = \$495
8) P, Q and R invest in a business. If the ratio of their time period are 3 : 4 : 5 and their profits are in the ratio 5 : 6 : 8. Find the ratio in which the investment are made by P, Q and R.
a) 50:45:48
b) 51:45:47
c) 51:46:48
d) 50 : 45 : 47
e) 50:47:48
a)
Ratio of their investment
50:45:48
9) A shopkeeper mixes two types of wheat, each costing Rs. 45/kg and Rs. 58/kg, so that by selling the resultant mixture at Rs. 55/kg, he makes a profit of 10%. In which ratio did he mix them?
a) 3:10
b) 1:1
c) 8:5
d) 2:7
e) None of these
c)
Using rule of allegation
Selling price = 55
Profit%=10
Therefore the mixed ratio is 8:5
10) There are three persons Abi, Bala and Chan, not on the same straight road. Two buses P and Q start simultaneously from Abi and Bala respectively towards Chan. By the time Q reaches Chan, P is exactly halfway to Chan. Immediately after Q reaches Chan, it starts travelling towards Abi and it crosses P at a point 165 km from Abi. The ratio of the speeds of P and Q is 3 : 5. Assume that the roads joining Abi to Chan, Bala to Chan and Bala to Abi all are in straight roads. If Bala is twice as far as from Abi as it is from Chan and P would take to cover the distance from Abi to Bala, how much time would Q take to cover the distance from Chan to Abi?
a) 2.4hr
b) 3hr
c) 2.5hr
d) 5hr
e) None of these
a)
Let Abi = A
bala=B
chan= C
BC= 5k
given by the time Q reaches C, P was half way to C
and
AC=6k
as Q met P ,165 km away from A ,the distance to the meeting point from A is
k=40
AC=240km
BC=200km | crawl-data/CC-MAIN-2018-30/segments/1531676596463.91/warc/CC-MAIN-20180723125929-20180723145929-00618.warc.gz | null |
Verify if the equation has any solutions 2x/(x+5)-x/(x-5)=50/(25-x^2) .
We have to determine if 2x/(x+5) - x/(x-5) = 50/(25-x^2) has any solutions.
2x/(x+5) - x/(x-5) = 50/(25-x^2)
=> [2x(x - 5) - x(x + 5)] / (x^2 - 25) = 50 / (25-x^2)
=> 2x^2 - 10x - x^2 - 5x + 50 = 0
=> x^2 - 15x...
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We have to determine if 2x/(x+5) - x/(x-5) = 50/(25-x^2) has any solutions.
2x/(x+5) - x/(x-5) = 50/(25-x^2)
=> [2x(x - 5) - x(x + 5)] / (x^2 - 25) = 50 / (25-x^2)
=> 2x^2 - 10x - x^2 - 5x + 50 = 0
=> x^2 - 15x + 50 = 0
=> x^2 - 10x - 5x + 50 = 0
=> x(x - 10) - 5(x - 10) = 0
=> (x - 5)(x - 10) = 0
x = 5 and x = 10
But x = 5 makes x/(x-5) indeterminate
So the required solution of the equation is x = 10
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Calculate the Total Capacitance for Parallel and Series Capacitors
Capacitors store energy for later use. The capacitance is the ratio between the amount of charge stored in the capacitor and the applied voltage. Capacitance is measured in farads (F).
Find the equivalent capacitance of parallel capacitors
You can reduce capacitors connected in parallel or connected in series to one single capacitor.
Consider the first circuit shown here, which contains three parallel capacitors. Because the capacitors are connected in parallel, they have the same voltages:
v1(t) = v2(t) = v3(t) = v(t)
Adding the current from each parallel capacitor gives you the net current i(t):
For parallel capacitors, the equivalent capacitance is
CEQ = C1 + C2 + C3
Find the equivalent capacitance for capacitors in series
For a series connection of capacitors, apply Kirchhoff’s voltage law (KVL) around a loop in the bottom diagram of sample circuit. KVL says the sum of the voltage rises and drops around a loop is 0, giving you
A series current has the same current i(t) going through each of the series capacitors, so
The preceding equation shows how you can reduce the series capacitance to one single capacitance: | <urn:uuid:62ea6bb5-abee-4a23-aec1-60a2ab22dac6> | {
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by Robert J. Friedman | Feb 19, 2010
Are you looking for connections through Jewish genealogy? Exploring a Jewish past that was lost due to intermarriage or conversion? Searching for family lost in the Holocaust? Today there are more resources than ever to attain those goals.
From early beginnings in the Mideast almost 6000 years ago, Jews migrated to all corners of the globe. Jews have not had a home territory or common vernacular language for most of the last two millenia.
Those who remained in the Mideast or went to North Africa or Asia are known as Mizrahi, or Eastern Jews. Those who accompanied the Romans to Spain, and later flourished under Muslim rule, became Sephardic Jews who spoke Ladino, a hybrid of Spanish, Hebrew, and Arabic.
As they reconquered Iberia, Catholic monarchs forcibly converted the Jews. These "New Christians" became known as "conversos" (Spanish) or "anusim" (Hebrew). Those who secretly continued to practice Judaism in private were formerly called "Marranos," a derogatory term meaning pigs, and are now properly referred to as "crypto-Jews."
Expelled from Spain, Portugal and their colonies by 1500, Sephardic Jews took their language and culture with them to existing Jewish communities in North Africa, Italy, Greece, Turkey, and the Netherlands. The first Jews to permanently settle in North America were Sephardic--forced from Portuguese Brazil, they found refuge in Dutch New Amsterdam (now New York) in 1654. Increasingly, Hispanic residents in the American Southwest, Latin America, and Spain are today discovering family traditions that hint at a Jewish past.
Ashkenazi Jews are descendants of those who settled along the Rhine River and other Roman trade routes in France and Germany from the 5th Century onward. Economic restrictions, expulsion edicts, and periodic anti-Semitic massacres kept the Jewish population in these areas limited, and prompted migration eastward to Poland, Lithuania, and Ukraine. Ashkenazi Jews also developed their own distinct language, Yiddish, combining German, Hebrew, and Slavic elements.
In 1650, the largest number of Jews lived in the Polish-Lithuanian Commonwealth, a huge country that extended deep into what is now modern Russia and Ukraine. By 1800, however, Poland and Lithuania ceased their independent existence and were divided among Russia, Prussia, and Austria.
Russia restricted the movement of its newly acquired Jews, allowing them to live only within "Congress Poland" and the "Pale of Settlement," regions within the annexed territory that already had the highest concentration of Jews. But 19th and 20th Century wars and political changes altered these borders considerably, so that your ancestor born in "Russia" in 1885 may have actually been born within the modern boundaries of Poland, Lithuania, Latvia, Estonia, Belarus, Ukraine, Moldova, or Russia!
By 1800, the Austrian (Habsburg) Empire also included areas with significant Jewish populations, including Bohemia, Moravia, Slovakia, Hungary, Transylvania, and "Austrian Poland" (Galicia and Bukovina). The Austro-Hungarian "Dual Monarchy" gave Hungary autonomy in 1867 and jurisdiction over Slovakia, Transylvania, and other areas now part of Ukraine, Romania, Serbia, Croatia, and Austria.
Jewish genealogy begins with oral history and "family archives" containing photos and documents. Specifically Jewish items include bar/bat mitzvah invitations, yahrzeit calendars (showing when to light a memorial candle for a deceased relative), ketubot (marriage contracts), and wimpels (made from an infant's swaddling cloths).
Interviewing older relatives may be a challenge, because immigrants often rejected contact with the societies they left behind. Jewish family life was violently disrupted over the last 200 years and memories can be painful. Jewish genealogists can help repair that damage by forging new, forward-looking connections.
After exhausting family sources, the next step is to sign up at JewishGen, a free web site, and register yourself in the Family Finder, where genealogists look for other people researching the same ancestral names and places. Also search the Family Tree of the Jewish People, where researchers share their data, and join a Jewish Genealogical Society to network and learn from fellow enthusiasts.
At this point, most of your research may focus on standard U.S. resources, like the census, vital records, immigration and naturalization records, city directories and telephone books. As you search, here are some pointers to keep in mind:
Just as we may have many nicknames today (like Rick, Dick, Richie, Ricky, etc., for Richard), the names of our Jewish ancestors also varied, especially in multiple languages. Generally Jews had at least two given names: one in Hebrew, used for official religious purposes, and a vernacular name in Yiddish and/or the language of the surrounding country.
Thus the Hebrew name Tzvi, meaning "deer," could be translated into German (Hirsch), Yiddish (Hirsh) and/or French (Cerf). These could appear in records as double names (Tzvi Hirsh, Aryeh Leib [lion]) or as interchangeable single names. Additionally, certain Biblical names were associated with specific symbols, leading to the possibility of three interchangeable names. For example, Benjamin is associated with a wolf (Zev in Hebrew, Volf in Yiddish).
For thousands of years, Jews used a patronymic system, in which the child's given name was followed by the father's given name (e.g., Moshe ben Yitzhak, or Moses son of Isaac). Many male given names eventually evolved into permanent surnames. Avraham became Abrahamsohn (German), Abramowicz (Polish), Abramovici (Romanian), etc. Among the most widespread Sephardic surnames are Rodriguez (child of Rodrigo), Henriquez (child of Henrique) , and Nunes (child of Nun). Less commonly, surnames were also derived from female given names, and called metronymics (Rachelson, Perlman).
Jews began using family names in Italy, Spain and Portugal as early as the 12th century, and in Prague and Frankfurt well before 1800. In medieval times, many names were based on the family's ornamental house sign. For example, a house with the sign of a red shield literally became the House of Rothschild. Others included Adler (eagle), Schiff (ship), and Stern (star). In the 1300s, prominent rabbinical families began maintaining hereditary surnames (Luria, Horowitz, Rapoport, and others).
However, most Jews in Europe did not use hereditary surnames until Christian authorities required them. Between 1780 and 1835, the Austrian and Russian Empires, France, and the German states issued decrees ordering Jews to adopt permanent surnames. Some took the name of their birthplace or former residence (Warshawsky, Frankfurter, Toledano). Occupational names were widespread, like Schneider (tailor), Molina (miller), and Gabay (sexton). Often personal characteristics became the basis for surnames: Crespi (curly hair), Slepak (blind), Lang (tall). Many artificial surnames just sounded appealing: Goldblum (gold flower), Silberfeld (silver field), Gr�nbaum (green tree).
To better cope with Eastern European alphabets and phonics, Jewish genealogists prefer to use the Daitch-Mokotoff Soundex system rather than those used for the Census and other U.S. records. See, for example, the Avotaynu Consolidated Jewish Surname Index. Before you search the index, be sure to read the section, What is a "Jewish Name"?
Sooner or later, you will find your ancestral town. Armed with that information, you can look for relevant genealogical records on line, on microfilm, in books, and in original documents stored in various archives. See below for web sites that can help you track down those records.
Many Jews are trying to document the fate of Holocaust victims to commemorate their names and lives. This genealogical research has often led to the discovery of family members who actually survived the Holocaust, unbeknownst to their American kin. Family reunions born of such discoveries are simultaneously joyous, poignant, and bittersweet. An essential role for the Jewish genealogist is to help repair the torn fabric of Jewish family life by addressing and healing these deep emotional scars.
Millions of pages of Holocaust documents have been preserved, and increasing numbers of them have been microfilmed, scanned, and made available to the public, including the largest collection of all, held by the International Tracing Service in Bad Arolsen, Germany. In addition to huge quantities of records created by the Nazis, extensive records have also recently become available from formerly Communist countries like Hungary, Romania, and Ukraine, to name a few. For more information, see the web sites listed below.
Start your free trial today to learn more about your ancestors using our powerful and intuitive search. Cancel any time, no strings attached. | <urn:uuid:98b891d4-e139-40a1-bc3d-b3ac45df6290> | {
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The Bill of Rights at 225
Winter 2016, Vol. 48, No. 4 | Historian's Notebook
By Jessie Kratz
The travels of the Declaration of Independence and the Constitution have been chronicled frequently over the years—in fact, they are fascinating stories. However, the third “Charter of Freedom”—the Bill of Rights—has been largely overlooked.
As we celebrate the 225th anniversary of the document’s ratification, let’s explore its history. A parchment document with 12 proposed constitutional amendments was created in September 1789, and copies were sent to the states for ratification.
By December 15, 1791, enough states had ratified amendments 3 through 12 to make them law. These became what we now call the Bill of Rights. By 1992, the original second amendment, limiting congressional pay, garnered enough state ratifications to become the 27th Amendment.
Before the National Archives was established, the Department of State safeguarded the federal government’s official records. Unlike the Declaration, which had been on display, the Bill of Rights remained in storage.
When the State Department moved with the rest of the government from New York to Philadelphia, the Bill of Rights went too. In 1800 it came to the new capital, Washington, D.C., and was removed to Leesburg, Virginia, only briefly in 1814 when the British burned the city.
Throughout the 19th century, the document was stored in various State Department offices and eventually made its way to the Old Executive Office Building. There, it was sewn into a large binder with other ratified amendments.
After the National Archives was established in 1934, it worked with the State Department to acquire the historical federal documents, and on March 16, 1938, the Bill of Rights was transferred to the National Archives.
Conservators removed the document from its binder and put it on display in the Rotunda—you can still see the holes from the sewing.
In 1947—the first time in 133 years—the Bill of Rights left Washington as part of the Freedom Train exhibit that traveled across the country.
On November 22, 1952, the document was sealed in a helium-filled glass case and, on December 15 (Bill of Rights Day), put on permanent display with the Declaration and the Constitution, which had been transferred to the National Archives from the Library of Congress just two days before.
Except for the 2001–2003 renovation of the National Archives Building, the Bill of Rights has been on exhibit in the Rotunda ever since. Now on display in its state-of-the-art case, the Bill of Rights has finally found its home.
Jessie Kratz is Historian of the National Archives. | <urn:uuid:035a63cc-fc34-4073-9281-908bf2dcacf2> | {
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This is an exciting project for the students. Trace a circle shape on a piece of paper. The template included here will make a completed circle about eighteen inches in diameter. To make a smaller circle, trace a circle on a sheet of paper and cut it out. Then fold it in half, in fourths and then in eighths. To give the finished circle a scalloped edge, make a deeper cut on the corners of the pie shape. One eighth (pie shape) will be the pattern for this project. Begin by giving each student one eighth of a circle for them to design.
Suggest that they make a small mark at equal distances from the top of the arc down a distance, and from the tip of the shape up, drawing a straight, curved or wavy line between the two opposite marks. In the example you’ll notice that the top section is filled with flowers, the middle section is an outdoor scene, and the bottom to the tip is mountainous. Give the students some ideas of what should be in each section, or let them improvise.
When one pie shape has been completed, print off seven copies, cut and tape them together, to complete the circle.
Options: After the design has been drawn with a pencil, copy off seven additional copies, before coloring them. Remind the kids to use the same colors on each of the copies.
Or: After the design has been drawn with a pencil, have the student trace the design seven additional times. This works well, if using typing paper for the circle.
• 9” Pie shape (Template)
• Colored marker, colored pencils or crayons
• Black Sharpie
1. On your pie shape, make a small mark at equal distances from the top of the arc down a distance, and from the tip of the shape up, drawing a straight, curved or wavy line between the two opposite marks.
2. With a pencil, draw designs on the pie shape.
3. Using colored markers, colored pencils or crayons, color your design. Use the black Sharpie to trace over all your pencil lines.
4. Print seven copies of your completed colored pie shape.
5. Carefully cut the pie shapes, lay them face down on a flat surface, match two pie shapes side to side, with the tips even and the sides overlapping slightly, and tape. Repeat with all the pie shapes to form a circle.
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Sometimes modern problems require ancient solutions.
A 1,400-year-old Peruvian method of diverting water could supply up to 40,000 Olympic-size swimming pools' worth of water to Lima each year. That information comes from a new study published in Nature Sustainability.
It's one example of how ancient methods could support existing modern ones in countries without enough water.
More than a billion people across the world face water shortages. Man-made reservoirs store rainwater and water overflow for use during drier times. But reservoirs are costly, require years to plan and can still fail to meet water needs. Recently, for example, the reservoirs in Chennai, India, went almost dry. The city’s four million people had to then depend on water transports from the government.
Peru's capital, Lima, depends on water from rivers high in the Andes Mountains. It takes only a few days for water to flow down to the city. So when the dry season begins in the mountains, the water supply quickly disappears. The city suffers shortages of 43 million cubic meters during the dry season. It resolves this with modern structures such as man-made reservoirs.
These reservoirs are not the only solution, however. Over a thousand years ago, indigenous people developed another way to solve water problems.
Boris Ochoa-Tocachi is a researcher at Imperial College London and lead writer of the study. He explored one of the last remaining water-harvesting systems in the small mountain community of Huamantanga, Peru. The system was developed even before the ancient Inca civilization.
Water diverted, delayed
The 1,400-year-old system is designed to increase the water supply during the dry season by diverting and slowing water as it travels down the mountains.
This nature-based method is made of special canals that guide water from its source to a series of water bodies and hillsides. The water goes slowly into the ground, then flows downhill through the soil and reappears in water bodies near the community.
Its aim was to increase the water's travel time from days to months in order to provide water throughout the dry season.
But Ochoa-Tocachi said the amount of water that could be harvested was an unknown before the study.
The researchers measured how much the system slowed the flow of water by injecting special dye in the highlands and noting when it reappeared in water bodies. The dyed water started to surface two weeks later and continued flowing for eight months — a huge improvement over the hours or days it would normally take.
"I think probably the most exciting result is that we actually confirmed that this system works," Ochoa-Tocachi said. "It's not only trusting that, yeah, we know there are traditional practices, we know that indigenous knowledge is very useful.” He said there is now proof the systems are valuable today and can be a tool to help solve modern problems.
Sizable increase in supply
The researchers next considered how using a larger version of the system could help Lima. They combined what they learned in Huamantanga with the knowledge of physical qualities of Lima's surroundings. The resulting estimates say the system could increase Lima's dry-season water supply by 7.5 percent overall and up to 33 percent at the start of the dry season. This amounts to nearly 100 million cubic meters of water each year — equal to 40,000 Olympic-size swimming pools.
Todd Gartner is director of the Natural Infrastructure Initiative at the World Resources Institute. He noted that this study "takes what we often just talk about…and it puts this into practice.” He said it does a lot of evaluation and observation and “puts real numbers behind it.”
The system is also economically sound. Ochoa-Tocachi estimated that building canals similar to those in Huamantanga would cost 10 times less than building a reservoir of the same size. He also said former highland societies in other parts of the world had methods for diverting and slowing water flow. And, they could use these methods today to support their costlier modern methods.
"I think there is a lot of potential in revaluing these water-harvesting practices that have a very long history," Ochoa-Tocachi said. He added that the idea of “using indigenous knowledge for solving modern engineering problems…is probably very valuable today."
I’m Alice Bryant. And I'm Caty Weaver.
Kerry Hensley wrote this story for VOA News. Alice Bryant adapted it for Learning English.
Words in This Story
divert – v. to change the direction or use of something
reservoir – n. a usually man-made lake used to store water for use in people's homes, businesses and other places
indigenous – adj. describing ethnic groups who are the original settlers to a specific region
canal – n. a long narrow place that is filled with water and was created by people
dye – n. a substance used for changing the color of something
actually – adv. used to refer to something that is true or real
evaluation – n. o judge the value or condition of (someone or something) in a careful and thoughtful way
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Smartick is an online platform for children to master math in only 15 minutes a day
Feb13
# Multiplication with Decimals and Some Examples
Have you learned how to multiply with decimals yet? Today we are going to review three different cases of multiplication with decimals.
### Multiplication with decimals and whole numbers
In this case, we are multiplying a decimal by another number without decimals, as in the example:
• Step 1: We place both numbers so that the longer factor is on the top and the shorter factor is on the bottom.
• Step 2: We solve the multiplication problem as we normally would with whole numbers. Afterward, we count the digits that come after the decimal point in the decimal and we place the decimal point in the answer so that it has the same number of decimal places after it as in the decimal in the factor position.
### Multiplication when both factors are decimals
In this case, both factors are decimals:
• Step 1: As in the previous case, the first thing we have to do is to place the numbers so that the longer factor is on the top and the shorter factor is on the bottom.
• Step 2: We solve the multiplication problem as we normally would with whole numbers. Afterward, we count the digits that come after the decimal points in both factors. The answer should have as many decimal places as can be found in both factors combined.
### Multiplication with decimals and a whole number ending in zero
In this case, the whole number factor ends in zero.
• Step 1: We break down the number into another number multiplied by 10:
• Step 2: We multiply the decimal by 10 (thereby getting rid of a decimal place).
• Step 3: We place the numbers and now we can multiply a decimal number by a whole number.
Multiplication with decimals is easy, isn’t it?
If you want to continue learning math with Smartick while having fun, click on this link to sign up for a free trial. | crawl-data/CC-MAIN-2020-45/segments/1603107891428.74/warc/CC-MAIN-20201026145305-20201026175305-00029.warc.gz | null |
By Heather Ye
Note: Click on the pictures to enlarge them
Missions were an important part of America’s history. They had a huge impact on America today.
Missions were formed by the Spanish in 1769 to colonize the territory of Alta California, and to convert Native Americans to the Catholic religion. At that time, they didn't know what to do with the missions though. There were a few suggestions for the purpose of the missions, but it was hard sailing from Spain to Alta California with the rough waves and the powerful waves to sail against. Spain also had other priorities. What caught Spain's attention was that the Russians started going farther down the west coast of North America from Alaska. The Russians were spotted near present day San Francisco in the 1760s.
Spain sent some settlers to the missions, but not very many wanted to go into the wilderness. The Spanish had good results in using the missions to claim other parts of North America.
The Franciscan padres saw this as an opportunity to convert the Native Americans to Catholic Faith. Most of the Native Americans were forced to go to the missions to be baptized, and others either came by choice or curiosity. Once they were baptized, they followed their traditions and lived in the missions. They thought that they could transform the Native Americans into “good people” before they died.
Father Junipero Serra formed the missions. Father Serra was a Spanish Franciscan friar and a Catholic priest. Father Serra’s goal was to Christianize the Native Americans. He was born on November 24, 1713, on a Spanish island of Mallorca, which is in the Mediterranean Ocean. His parents, Margarita Ferrer, Antonio Serra, sent him to a Franciscan school. In 1749, he traveled with his fellow Franciscans, who intended to work at a mission near Mexico City. Father Serra took went to Vera Cruz by ship. Despite his ill condition from the voyage, he insisted on walking all the way to Mexico City, which was over two hundred miles away.
|Photo from Google Images|
For about fifteen years, Father Serra worked in Mexico with the same tasks as he had in Spain, but he also took in the missionary work. In 1767, the Spanish emperor had missions built in both Baja California and Alta California.
Father Serra spent the rest of his life as the leader of the Franciscans and working at the missions in Alta California, but he was in a bad condition. He was over fifty years old, and he was alarmingly thin, suffering from asthma, and badly injured in one of his legs, determined Father Serra continued to found missions. He also is famous for his punishment caused by shame: wearing shirts with pointed wires jabbing in at his body, whipping himself until he was bleeding, and holding a lit candle to his chest, scarring his body.
Father Junipero Serra died on August 28, 1784, at the age of seventy, and is buried at Mission San Carlos Borroméo in the church. Near the end of his life, he told his friend and confessor, Father Francisco Palou: “I desire you to bury me in the church, quite close to Father Juan Crespi for the present; and when the stone church is built, they may put me where they want.”
There were twenty-one missions built in all from 1769 to 1823 in Alta California, mostly near the coast from San Diego to north of San Francisco. The chain of missions stretched for over five hundred miles. The first mission was Mission San Diego de Alcalá, founded on July 16, 1769, by Father Serra. The last mission to be was Mission San Francisco Solano, founded on July 4, 1823. There was also an extra nine missions in Baja California.
In order, the missions go from: Mission San Diego, Mission San Carlos Borroméo, Mission San Antonio, Mission San Gabriel Arcángel, Mission San Luis Obispo, Mission San Francisco, Mission San Juan Capistrano, Mission Santa Clara, Mission San Buenaventura, Mission Santa Barbara, Mission La Purisima Concepcion, Mission Santa Cruz, Mission Nuestra Senora, Mission San Jose, Mission Juan Bautista, Mission San Miguel Arcángel, Mission San Fernando Rey, Mission San Luis Rey, Mission Santa Ines, Mission San Rafael Arcángel, and Mission San Francisco Solano. The missions go from southern Alta California to northern Alta California.
|Photo from Google Images|
The missions had to have fresh water, good soil for growing crops, land for livestock, and Native California villages.
All of the missions had bells. The bells were usually hung in a bell tower or a companario. In some missions, they kept their bells in a bell wall.
Bells were used to call people to church at dawn. They were also used to notify people of the time and day, and to control daily life at the missions. In the mission period, nobody had watches. These mission bells started the day. Bells were also rung at midday to indicate a meal, and also at dusk to show that work was over.
In the early missions, the bells were sent by ship with other supplies from New Spain, also known as Mexico. They were seen as necessary. Even when the mission wasn’t built yet, they would hang a bell at the top of a pole.
The missions had a big effect on America. It changed the lives of most of the Native Americans. Once they were in the missions, most weren’t allowed to practice their own religions and had to follow the Catholic religion. Some of the Native Americans tried to run away, but they were caught. They adjusted to the mission life. Everyday at the mission was very uniform, the people ate meals at scheduled times, the Native Americans learned a new language (Spanish), and they would work for the rest of the day until the bell rings to call them back to their homes.
After the Mexican War of Independence, in 1833, the missions were secularized and sold by the Mexican Government. The mission land was either sold or given away. The Mexico’s leaders wanted to make Alta California’s economy stronger. Half of the mission land went to people who would start farms and ranches. That would bring trades to California. The other half was supposed to go to California Indians, but as usual, they were treated unfairly and very little California Indians got land. Most of the land grants went to Californios and new settlers. Even if the California Indians got land, they couldn’t understand Spanish and didn’t know what the people were saying.
When the mission land had been sold or given away, the buildings crumbled. It wasn’t until the 1900s when the missions were repaired. Even so, Alta California had changed. Father Serra had converted thousands of Native Americans and introduced agriculture to California. Unfortunately, the Native Americans were not able to continue their own religion.
Missions changed many lives of people and brought new ways of life to California. It would not be the same if missions had not been formed.
Mission San Juan Capistrano
|Photo from Google Images|
Mission San Juan Capistrano, “Jewel of the Missions”, was the seventh mission. It was first planned on October 30th, 1775, by Father Fermín Lasuén. It was quickly abandoned because there was news that there was a revolt on San Diego. The padres and soldiers decided to leave San Juan Capistrano and to go to San Diego to help them. The mission building crumpled during an earthquake. It was finally re-founded on November 1, 1776, when Father Serra led a party of people to San Juan Capistrano.
The Great Stone Church only stood six years until on December 8, 1812, when the earthquake shook most of Southern California. The church bell tower fell into the church, killing a few people. When the shaking finally stopped, about forty people had died and the church was in ruins. It was never rebuilt.
It took a long time to build Mission San Juan Capistrano. For the first two years, there was not enough water in the area to drink or water the growing crops. They decided to move near the an Acagchemem tribe where the water supply was large. But the friars and soldiers still needed help building the mission. They decided to be cunning and led the Indians by attracting them with food and jewels. The Indians were also curious at the tools that the Spanish were using. Eventually, some of the Acagchemem joined the missions and helped build it.
Some of the Acagchemem and the Spanish people gathered the materials in the area. They chopped down trees and cut the trees into planks.
Like the six missions before Mission San Juan Capistrano, it was to expand the boundaries for Spain, and to spread Christianity among the Native Americans here, to “save their souls”.
The tribe that was near Mission San Juan Capistrano was mainly Acagchemem tribe. When the Spanish arrived, they called the Native Americans the Juaneño. This tribe did not have a written history, but historians have been able to learn their way of life through artifacts and stories that have been passed down from generation to generation.
Like many other Native American tribes in Alta California, the Acagchemem lived in a small village, most of them near a source of water. They made their homes in a cone shape using a wooden build with reeds and brush on top of it. The outer parts were put on by layers, like a roof on a house, to keep the inside dry. These huts were called kiitcas.
The Acagchemem tribe’s life had a lot to do with nature. Their religion, clothing, food, homes, and weapons were all made or had nature to do with it. This was a good thing; when they needed to survive by on their own, they know what they need to get from their environment.
Though the Acagchemem were very attached to their way of life, the Spanish wanted them to follow Spain’s ways. The tribe’s lifestyle was changed forever when Mission San Juan Capistrano was founded. The missions baptized the Native Americans and taught them how to make adobe bricks for the walls.
Mission San Juan Capistrano was named after a 14th century theologian, Saint John of Capistrano. He was a Franciscan friar as well as a Catholic priest.
This mission is famous for the return of the swallows. The miracle of the swallows happens on March 19th, St. Joseph's Day, at Mission San Juan Capistrano. As these little birds fly all the way to Mission San Juan Capistrano every year, the village of San Juan Capistrano is alive with people that have come from around the world to witness the migration. When they arrive at Mission San Juan Capistrano at early dawn, they start rebuilding the mud nests that hang on to the remains of the Great Stone Church.
After spending a summer in the sheltered walls of the old mission, the swallows leave to South America, about 6,000 miles, returning next spring. On the Day of San Juan, October 3rd, they leave after circling the mission as if they were saying goodbye.
Mission San Juan Capistrano is built along the coast of California, on the coast, in present-day San Juan Capistrano, Orange County, Southern California. The founders noted that it was important to build it here because of the water source, three streams and the Trabuco Creek. The sea routes were very important, and that is why Mission San Juan Capistrano is built near the ocean. Some people come to the missions by ship.
The population in Mission San Juan Capistrano grew steadily. In 1797, there were 1,000 neophytes. The highest the population ever went was in 1812, where there were 1,361 people. When Mission San Juan Capistrano was secularized in 1833, there was still 861 neophytes.
If you walk in through the courtyard you would see a fountain in the courtyard. In front of you, there are the storerooms. To the left are the the workshops and to the right is the Serra Church. If you turn around, you would be facing the kitchens. When you go in the Serra Church from the courtyard, in front of you would be the cemetery. If you go all the way back to the entrance of the mission, on one side of the kitchen, is the soldiers’ quarters, and on the other side of the kitchen is the friars’ quarters. The bell wall is on the right of the friars’ quarters, and the Great Stone Church is on the right of the bell wall.
|Photo from Google Images|
Mission San Juan Capistrano, with its beautiful architecture with the Great Stone Church in a heap on the ground, is probably one of the most scenic missions.
A Day in the Missions
October 12, 1793
I woke up with a start, the bells ringing loudly. Another day at the mission. The routine for the missions was always the same for me: wake up, eat breakfast, work, eat lunch, work some more, eat dinner, and sleep, all at certain times and places. I wasn’t used to this schedule when I first joined the missions. Life for California Indians was very free, and that was what I wanted and enjoyed.
As I slipped out of bed, I thought about how I once tried to escape the missions. How clever the missionaries were to lure me into the missions with beads, and how foolish I was to fall into the trap! I live in a dormitory-like building called a monjerío. Unmarried women and girls over the age of eight lived here. Outside of the building was the only exit and entrance of the monjerío, the courtyard. An older woman, a matron, would guard the monjerío, either from harm or to prevent them from escaping. A couple of other girls tried to escape with me. We somehow all got past the matron, but some other guards caught us and we were led back to the mission and given a punishment.
I walked out of the building and into the kitchen where I took a bowl for a serving of food. I was still not used to eating this kind of food. It was very different from what I used to eat with my tribe. I looked longingly at the potatoes, beans, onions, peppers, squash, and some fruit on the counter, and wished I was eating freshly hunted and cooked venison, along with some blackberries and acorn meal. Even though I did eat beans and squash before, I didn’t like the rest of the food. But when the lady piled some food in my bowl, I ate it all anyway. There’s no point starving yourself when you have a full day of work ahead of you.
I finished my food quickly and waited until the bell rung again. It was time for work. I returned my bowl and headed outside. I walked into a room where the weaving loom was, and saw a pile of wool and some fresh string in a pile on the table. I was a weaver. It was very important work - we made our clothing, rugs, and blankets from weaving. We usually used wool from sheep. The men sheared the sheep every spring. I work at the loom, but some other people use hand carders to clean out the wool and make them into string. If I finished my work early, I usually help them or make some grass baskets. When we joined the missions, we continued making these baskets. Even the missionaries agreed that they were useful.
|Photo from Google Images|
There was no one there yet. Most people are a few minutes late. I took the wool, placed them into a grass basket, and set up the string onto the loom. Because all of the stuff is where it’s supposed to be, I began weaving. A few other people come in to help me. Smiling as my friend sat next to me to weave with me, we exchanged a few little quiet conversations. We aren’t supposed to talk while doing work, but since no one really comes in to check what we’re doing, I guess it’s alright to talk a little, as long as we’re still doing our work just as fast and good. Some other people positioned themselves at a loom, while others sit at the table and start combing the wool.
I worked at my loom until the bell rung again, summoning us to the kitchen for lunch. I walked back into the kitchen, grabbed my bowl, and scooped a serving of lunch. I eat all of my bread, apples, and potatoes. My fingers were a little sore from working at the loom for hours. I flexed my fingers before returning the bowl back on the counter with a loud clang. I watched people hurrying to places through the empty doorway before stalking back to my room where my loom was. After a while, the bell rang, and people poured out of the kitchen and separating into different rooms to continue their work.
I found that some people are already working. I quickly sat down and arranged the string on the loom. Threading the yarn in and out of the holes in the loom, I started wondering what my brother might be doing. I rarely get to see him once I joined the missions, since he’s not a weaver. What might he be doing right now? Feeding the animals? Shearing the sheep? Making soap and candles? Building houses out of adobe? I had no idea.
Interrupting my thoughts, my neighbor tapped on my shoulder. “Need more string?” she asked. It was one of the people who clean the wool. In her hand was a large bundle of yarn. I shook my head. Nodding to indicate she understood, she moved on, asking everyone if they needed more string. I looked down at my loom and concentrated on weaving.
When the bells rung again, my hands were aching. All of the people that I worked with slowly turned their heads away from the loom and stood up. I wandered outside and into the kitchen. I got my bowl and sat down. Without bothering to look what was in my bowl, I started eating it with my fingers. Finishing it quickly, I hurry back to my room, the sky darkening, but still continuing my work. My thoughts made me behind schedule.
I finish working on the loom and sat on the floor to weave some baskets. My fingers fly across the dry grass, pulling and stringing. The bell rung for us to go to sleep, but I kept on working on the basket.
When I was finally done, I sneaked out of the empty room and silently tiptoed back to my room. The guard was not there yet, so I crawl inside my room and drop into bed. The world faded away as I wearily fell asleep….
Startled, I woke up, the sounds of bells ringing in my head. Outside of my room, people were already hustling to places. The sounds of shouts, voices, and bells all woke me up. At first, I thought this was strange. Why would these people wake up so early? But then I reminded myself that this was nothing strange. Just another day at the mission.
The Importance of the Missions
The missions bought many things to California and had a certain importance in its history. First, they bought Catholicism to America. By converting the Native Americans, they were spreading their religion to California. Although many Native Americans wished to be left alone and to continue their own religion, it was a new lifestyle for all of them.
Secondly, the missions bought many trades such as hides and tallow. When the missions were secularized, the land was given to many people who have cattle, and they became ranchos. The land given away were called land grants. This trade, the hides and tallow from the cows, lured many ships, which brought money to the missions, another two reason why the missions were important. There were also many other trades that the missions brought by being secularized and turning it into something else. All someone had to do to claim the land was to draw a picture of it.
Twice a year at the ranchos, they held rodeos to round up the cows and brand the calves. When the rodeo was over, the fiestas started, which was another thing the missions started. These were often celebrated after people came to California. After the ships came, or people came by land, it also meant people were settling in California. This raised the population of California greatly.
Also, when the missions were founded, the presidios and pueblos were built. The pueblos were small towns near the missions, which became larger towns today. The missions were often a large part of a city. The pueblos and missions also required presidios, which protected both of them.
There were some hardships that formed because of the missions though. For example, they completely changed some Native Americans lives. When they were baptized, they were no longer allowed to go back to their tribe, forced to go by their tradition.
The Spanish also brought along diseases that killed many of the natives, nearly wiping out numerous tribes. They killed about ninety percent of the native’s population. Although they didn’t intentionally bring the diseases to use as a weapon, it greatly affected their people.
The journey to Alta California was hard and tiring for the explorers. Even if they did survive the brutal trip, they were taking over the Native Americans land. By building the missions, they were stealing their land without permission.
If they succeeded in getting the land (which they almost always did), there was the building of the missions to think of. Because they had to toss so many goods and supplies out in the tiresome expedition, they had to find new building materials in their surroundings. Since they weren’t really familiar to the plants and elements around them, who would they ask? The Native Americans. The buildings were hard to build because they first had to make a sturdy brick made of earth, straw, and manure. Then they had to be dried before it could be solid.
The Native Americans were not pleased by this arrangement. They often planned revolts, which included setting fire to buildings, killing the missionary people, and other attacks of this sort.
|Photo from Google Images|
As the missions had to be protected by presidios, the soldiers at the presidios had a hard time. They had a big job - protecting the missions and pueblos. It was the soldiers’ job to defend the other people from the revolts and predators.
Apart from the Native Americans not being happy about the missions, they were also sad that they had to be separated from their families. Some people had to be separated from their family because they were forced into the missions, but if they were lucky enough to be with their family, they were separated in the missions.
It was hard work, working at the missions all day. People’s fingers grew sore, they were exhausted from harvesting the plants, they walked all day trying to find a dim-witted and curious tribe to lure back to the missions, they were stiff and tired from hauling bricks to the builders, and other jobs.
For instance, Mission San Juan Capistrano, the seventh mission, is still being used today. The people who work there use great effort trying to preserve the mission itself. Some people go to the church regularly. Others may go there to visit the museum. Mission San Juan Capistrano is open to all people. It is both a historic landmark and a museum.
One place worth visiting is the Great Stone Church. Although it has never been rebuilt after the earthquake, it’s interesting to see the wreckage. Many people gather at Mission San Juan Capistrano every spring to see the swallows that make a temporary home at the Great Stone Church. Mission San Juan Capistrano is known for many things today and the swallows that wing their way back here with the crowds cheering them on will never be forgotten.
All in all, the missions brought many traditions and although it didn’t work out for the Native Americans who were here long before the Spanish, California might have been completely different if the missions weren’t here.
- Houghton Mifflin, History Social Science, California Edition, Grade 4, Boston, 2007
- “California Missions Resource Center”, www.missionscalifornia.com, 13th of March 2015
- “The Spanish Missions of California”, www.californias-missions.org, 13th of March 2015
- “Mission Life and Style”, www.studiesweekly.com, 13th of March 2015
- “The California Missions Trail”, http://www.parks.ca.gov, 24th of March 2015
- “Junipero Serra”, www.pbs.org, 24th of March 2015
- “Te Missions”, www.californiamissionsfoundation.org, 31st of March 2015
- “The California Missions Trail”, www.parks.ca.gov, 1st of April 2015 | <urn:uuid:3223c228-a5a3-4372-9ba1-af443491e6e0> | {
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# About 0.1 ev is required to break a “hydrogen bond” in a protein molecule.
1. Calculate the minimum frequency of photon that can break a Hydrogen bond.
2. Calculate the maximum wavelength of a photon that can break a Hydrogen bond.
The question aims to find the minimum frequency of a photon and its maximum wavelength that can break a Hydrogen Bond of a protein molecule.
The concepts needed to solve this problem include Planck’s Equation and photon’s (the smallest particle or packet of light) frequency using Planck’s equation. The equation is given as:
$E = h v$
It can also be written as:
$E = h \dfrac{ c } { \lambda }$
a) The energy of the photon is given as:
$E = 0.1 eV$
To calculate the correct value, we need to convert the unit of energy from $eV$ to $J (Joules)$. It is given as:
$1 eV = 1.6 \times 10^ {-19} J$
$0.1 eV \times 1 eV = 0.1 \times 1.6 \times 10^ {-19} J$
$0.1 eV = 1.6 \times 10^ { -20 } J$
We can use Planck’s Equation to calculate the frequency of the photon, which is given as:
$E = h v$
Here, $v$ is frequency of the photon, $E$ is the energy of the photon, and $h$ is Planck’s constant. The value of the Planck’ constant is given as:
$h = 6.626 \times 10^ { -34 } Js$
Rearranging the formula to calculate the frequency of the photon is given as:
$v = \dfrac{ E }{ h }$
Substituting the values in the given formula, we get:
$v = \dfrac{ 1.6 \times 10^ { -20 } J }{ 6.626 \times 10^ { -34 } Js }$
Solving the equation, we get:
$v = 2.4 \times 10^ {13} Hz$
b) To calculate the wavelength of the photon, we use the other form of the equation where the frequency is replaced by the speed of light and wavelength of the light. The equation is given as:
$E = h (\dfrac{ c }{ \lambda })$
The speed of light is given as:
$c = 3 \times 10^ { 8 } m/s$
Rearranging the formula to calculate the wavelength of the photon as:
$\lambda = \dfrac{ hc }{ E }$
Substituting the values, we get:
$\lambda = \dfrac{ (6.626 \times 10^ { -34 } Js) . (3 \times 10^ { 8 } m/s) }{ 1.6 \times 10^ { -20} J } Solving the equation, we get: \[ \lambda = 1.24 \times 10^ { -5 } m$
## Numerical Result
a) The minimum frequency of the photon required to break a hydrogen bond in a protein molecule while the energy of the photon is $0.1 eV$ is calculated to be:
$v = 2.4 \times 10^ { 13 } Hz$
b) The maximum wavelength of the photon to break a hydrogen bond in a protein molecule while the energy of the photon is $0.1 eV$ is calculated to be:
$\lambda = 1.24 \times 10^ { -5 } m$
## Example
Find the frequency of the photon with an energy of $5.13 eV$, which is required to break an oxygen bond in $O_2$.
The formula is given as:
$v = \dfrac{E}{h}$
$v = \dfrac{5.13 \times 1.6 \times 10^{-19} J}{6.626 \times 10^{-34} Js}$
$v = 1.24 \times 10^{15} Hz$ | crawl-data/CC-MAIN-2024-38/segments/1725700651722.42/warc/CC-MAIN-20240917004428-20240917034428-00029.warc.gz | null |
# Calculating partial pressure equilibrium constant Kₚ given initial pressure and equilibrium pressure
A reaction
$$\ce{A(g) <=> B(g) + C(g)}$$
happens in constant volume and constant temperature. The reaction starts only with gas $$\ce{A}$$ (no $$\ce{B}$$ or $$\ce{C}$$) with given pressure $$P_1 = \pu{6 atm}$$, in equilibrium the pressure of all three gases is $$P_2 = \pu{10 atm}$$. Calculate $$K_p.$$
It seems to me like a very simple question, however it seems that I don't understand a basic concept regarding gas equilibrium. As for my understanding it is suppose to be
$$K_p = \frac{P_2 \cdot P_2}{P_2} = P_2 = \pu{10 atm}$$
But the given solution is $$\pu{8 atm}$$ and I really don't get what miss.
• Make an I.C.E, table first. Jul 5, 2019 at 17:00
• I don't see how it make sense, since the initial amount of $A$ is $6\cdot \frac{V}{RT}$ and the final amount is $10\cdot \frac{V}{RT}$ (V,T are constants), but the amount of material can't grow. Jul 5, 2019 at 17:35
The problem is that you are using wrong pressures. By definition for the reaction at equilibrium partial pressures can be expressed via initial partial pressure $$P_1$$ and conversion factor $$α$$
$$\begin{array}{ccc} \ce{&A(g) &<=> &B(g) &+ &C(g)}\\ &(1 - α)P_1& & αP_1& & αP_1 \end{array}$$
equilibrium constant $$K_p$$ is to be found as
$$K_p = \frac{P(\ce{B})\cdot P(\ce{C})}{P(\ce{A})} = \frac{α^2P_1^2}{(1 - α)P_1} = \frac{α^2P_1}{1 - α}$$
Unknown $$α$$ can be found by equating total pressure at equilibrium $$P_2$$ to the sum of partial pressures of all gaseous components at equilibrium:
\begin{align} P_2 &= P(A) + P(B) + P(C) \\ &= (1 - α)P_1 + αP_1 + αP_1 \\ &= (1 + α)P_1 \end{align} \quad\implies\quad α = \frac{P_2}{P_1} - 1 = \frac{\pu{10 atm}}{\pu{6 atm}} - 1 = \frac{2}{3}
Finally, all the values can be plugged into the expression for $$K_p$$:
$$K_p = \frac{\left(\frac{2}{3}\right)^2\cdot\pu{6 atm}}{\left(1 - \frac{2}{3}\right)} = \pu{8 atm}$$
• Thanks, may you please explain why the statement in the question that $P_2(A)=P_2(B)=P_2(C)=10atm$ in equilibrium it translated to $P_2 = P(A)+P(B)+P(C)?$ I mean, how could I deduce it from the question ? Jul 6, 2019 at 2:30
• @user5721565 I added corresponding passage to the answer. Jul 6, 2019 at 8:10 | crawl-data/CC-MAIN-2024-18/segments/1712296818105.48/warc/CC-MAIN-20240422082202-20240422112202-00215.warc.gz | null |
Adolph Ochs, the son of a Knoxville Rabbi, started his newspaper
career at the "Knoxville Journal." He went on to found the "Chattanooga
Times." In 1896, he borrowed $75,000 and gained control of "The
New York Times." When he purchased the failing newspaper, its circulation
had fallen to 9,000 daily. When he died in 1935, circulation was
The Will Thomas Legion, a Confederate unit made up of Cherokee
and Mountaineers, were a terror in the War Between the States.
In 1865, they captured the city of Waynesville, North Carolina
in order to negotiate a fair surrender. One of the Legion's terms
was to be able to carry away their firearms.
On August 18, 1920, Tennessee Representative Harry Burns passed
a deciding vote in the Legislature. It made Tennessee the ratifying
state of the 19th Amendment to the Constitution. 6 days later,
a woman's right to vote became the law of the land.
The worst maritime disaster in U.S. history occured on the Mississippi
River eight miles north of Memphis. On April 27, 1865 the steamboat
Sultana's boiler exploded. Of 2,000 or more passengers on board,
over 1,500 were killed. The majority were Union soldiers recently
released from Southern P.O.W. camps.
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Facts on Recycling Symbols
The universal recycling symbols for recycling are actually Mobius loops comprising three changing arrows used to form a triangle, such as the one seen below.
History of the symbol
This Mobius loop was designed by Gary Anderson, a 23-year-old-college student in the late 1960s to 1970.
The design was the winning entry for an art contest sponsored by a Chicago-based recycled paperboard company to raise environmental awareness amongst high schools and colleges across the country.
Read more on the history of recycling.
What the symbol means
The triangle in the recycling sign represents the "Reduce Reuse Recycle" Waste Hierarchy.
This hierarchy in turn illustrates the most effective plan of action to reduce waste and conserve natural resources, through “reducing” first, then “reusing” and finally, “recycling”.
The three arrows in the symbol represent the three main stages in recycling.
The first arrow represents the first stage of recycling – collection and sorting the various recyclable materials, to prepare them for processing.
The second arrow represents the second stage of recycling – processing the recyclable materials into raw materials and using these raw materials for manufacturing new products.
The third arrow in the symbol represents the third and final stage of the recycling process – the sale and purchase of products created using recycled materials.
The three arrows form a closed loop, illustrating how the three main stages contribute and reinforce one another in the recycling process. The closed loop also means that should any of the stages in the recycling process be ineffective, the sustainability of the entire recycling effort would be affected.
Types of recycling symbols on products
The universal recycling symbol is not a trademark, and its use is not regulated. In other words, anyone is free to use the recycling symbol, although local laws may restrict its use in product labeling.
There are many variations to the universal recycling symbol. However, there are however, two main categories of recycling symbols.
One category is reserved for products which can be recycled after consumption.
This category of recycling symbols usually comprises the Mobius loop, either white with black outline or solid black, such as the two symbols below. In fact, these two symbols are often used interchangeably.
The second category is reserved for products that contain recycled materials, or make use of recycled materials in the manufacturing process.
This category of symbols usually comprises the Mobius loop inside a circle, either black on white or white on black, such as the two symbols below.
The white-on-black version is often used for 100% recycled materials, while the black-on-white version is often for products containing both recycled and non-recycled materials.
For convenience, some manufacturers may also include a label, such as “This product can be recycled” or “This product is made of recycled materials”, along with the symbol for recycling.
When a percentage is indicated within the symbol, such as the symbols below, it means that the particular percentage of the product has been made from recycled materials.
Thus, when making purchases, do look out for these symbols for recycling as well as the manufacturer’s claims.
Symbols for specific materials
Today, there are many different types of materials that can be recycled, as well as be processed and made into new products.
To help consumers identify these recycle products, symbols specific to certain materials were also created.
One example is paper.
Since the paper industry has one of the highest demand and supply of recycled products, it was quick to introduce some basic and easy-to-understand recycled symbols for consumers.
For example, the recycling sign below has been patented as a registered trademark by the Recycled Paperboard Alliance. It means that the paper product is made of 100% recycled paperboard.
Another example of a symbol for paper recycling can be seen below. It is a corrugated recyclables symbol. This symbol means that the corrugated material can (and should) be recycled after use.
Glass is another material that can be recycled and made into new glass products.
Most glass containers are recyclable. Hence, this symbol below merely reminds consumers to recycle their glass products.
Besides paper and glass, some types of plastic can also be recycled.
The various categories of plastics can be identified by the numbering in the centre of the recycling symbol triangle.
Read more about the different types of plastic recycling codes and what they mean.
Why bother about symbols for recycling?
These symbols for recycling matter because they help you and I identify the products that can be recycled, so that we will send them for recycling rather than throwing them out in the garbage.
The recycling codes also help us identify the products that contain recycled materials, such that we can make it a point to purchase these eco-friendly products to complete the recycling loop.
Once you become familiar with these symbols and codes, identifying these green products will become a breeze. It will become your second nature.
In turn, as more and more of us purchase eco-friendly products, more manufacturers will be more driven to participate equally in recycling and green efforts. All these will ultimately contribute in a big way to the health and wealth of our earth and human race.
Return from this page on Facts on Recycling Symbols to page on Interesting Recycling Facts
Return from this page on Facts on Recycling Symbols to All Recycling Facts Homepage | <urn:uuid:f55f022e-2cf1-4592-b063-e0995769f46b> | {
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1. ## polynomial factoring
2. Originally Posted by algebra2
The leading coefficient of the result of multiplying out your factorisation is 9, so it can't be right.
RonL
3. Hello, algebra2!
Your final factor is correct, but . . .
Your factoring is: .$\displaystyle 3x^4 - 4x^3 + 4x^2 - 4x + 1 \;=\;(x-1)\left(x-\frac{1}{3}\right)3(x^2+1)$
The preferred form is: .$\displaystyle (x-1)(3x-1)(x^2+1)$
If complex numbers are allowed,
. . . that quadratic also factors: .$\displaystyle (x-1)(3x-1)(x-i)(x+i)$
4. i thought that for (x - 1/3) you put the denominator in front of the X and leave the numerator the way it is, so it becomes (3x - 1).
step 1 . $\displaystyle (x-1)\left(x-\frac{1}{3}\right)3(x^2+1)$
so when you got:
step 2. $\displaystyle (x-1)(3x-1)(x^2+1)$
what happened to the "3" in front of (x^2+1) in step 1?
5. Originally Posted by algebra2
what happened to the "3" in front of (x^2+1) in step 1?
It was multiplied into this term: $\displaystyle (x-\frac{1}{3})$
6. what i'm trying to say is that isn't there a rule where:
(x - numerator/denominator)
can be rewritten as: (denominator times x - numerator)
for example:
(x - 1/4) ; (4x - 1)
(x - 2/5) ; (5x - 2)
(x - 1/3) ; (3x - 1)
and why was it multiplied to (x - 1/3) and not (x - 1)?
7. Originally Posted by algebra2
what i'm trying to say is that isn't there a rule where:
(x - numerator/denominator)
can be rewritten as: (denominator times x - numerator)
for example:
(x - 1/4) ; (4x - 1)
(x - 2/5) ; (5x - 2)
(x - 1/3) ; (3x - 1)
and why was it multiplied to (x - 1/3) and not (x - 1)?
There is no such rule. $\displaystyle x+\frac{a}{b} \ne bx+a$
This is what Soroban wrote for you: $\displaystyle 3(x-\frac{1}{3}) = 3x - \frac{3}{3} \Rightarrow 3x - 1$
8. ok thanks. | crawl-data/CC-MAIN-2018-22/segments/1526794867309.73/warc/CC-MAIN-20180526033945-20180526053945-00637.warc.gz | null |
I just want to say my name is Emmanuel Jal. And I come from a long way. I've been telling a story that has been so painful for me. It's been a tough journey for me, traveling the world, telling my story in form of a book. And also telling it like now. And also, the easiest one was when I was doing it in form of a music. So I have branded myself as a war child. I'm doing this because of an old lady in my village now, who have lost her children. There is no newspaper to cover her pain, and what she wants to change in this society. And I'm doing it for a young man who want to create a change and has no way to project his voice because he can't write. Or there is no Internet, like Facebook, MySpace, YouTube, for them to talk. Also one thing that kept me pushing this story, this painful stories out, the dreams I have, sometimes, is like the voices of the dead, that I have seen would tell me, "Don't give up. Keep on going." Because sometime I feel like stopping and not doing it, because I didn't know what I was putting myself into. Well I was born in the most difficult time, when my country was at war. I saw my village burned down. The world that meant a lot to me, I saw it vanish in my face. I saw my aunt in rape when I was only five. My mother was claimed by the war. My brothers and sisters were scattered. And up to now, me and my father were detached and I still have issues with him. Seeing people die every day, my mother crying, it's like I was raised in a violence. And that made me call myself a war child. And not only that, when I was eight I became a child soldier. I didn't know what was the war for. But one thing I knew was an image that I saw that stuck in my head. When I went to the training camp I say, "I want to kill as many Muslims, and as many Arabs, as possible." The training wasn't easy, but that was the driving force, because I wanted to revenge for my family. I wanted to revenge for my village. Luckily now things have changed because I came to discover the truth. What was actually killing us wasn't the Muslims, wasn't the Arabs. It was somebody sitting somewhere manipulating the system, and using religion to get what they want to get out of us, which is the oil, the diamond, the gold and the land. So realizing the truth gave me a position to choose: should I continue to hate, or let it go? So I happened to forgive. Now I sing music with the Muslims. I dance with them. I even had a movie out called "War Child," funded by Muslim people. So that pain has gone out. But my story is huge. So I'm just going to go into a different step now, which is easier for me. I'm going to give you poem called "Forced to Sin," which is from my album "War Child." I talk about my story. One of the journey that I tread when I was tempted to eat my friend because we had no food and we were like around 400. And only 16 people survived that journey. So I hope you're going to hear this. My dreams are like torment. My every moment. Voices in my brain, of friends that was slain. Friends like Lual who died by my side, of starvation. In the burning jungle, and the desert plain. Next was I, but Jesus heard my cry. As I was tempted to eat the rotten flesh of my comrade, he gave me comfort. We used to raid villages, stealing chickens, goats and sheeps, anything we could eat. I knew it was rude, but we needed food. And therefore I was forced to sin, forced to sin to make a living, forced to sin to make a living. Sometimes you gotta lose to win. Never give up. Never give in. Left home at the age of seven. One year later, live with an AK-47 by my side. Slept with one eye open wide. Run, duck, play dead and hide. I've seen my people die like flies. But I've never seen a dead body, at least one that I've killed. But still as I wonder, I won't go under. Guns barking like lightning and thunder. As a child so young and tender, Words I can't forget I still remember. I saw sergeant command raising his hand, no retreat, no surrender. I carry the banner of the trauma. War child, child without a mama, still fighting in the saga. Yet as I wage this new war I'm not alone in this drama. No sit or stop, as I reach for the top I'm fully dedicated like a patriotic cop. I'm on a fight, day and night. Sometime I do wrong in order to make things right. It's like I'm living a dream. First time I'm feeling like a human being. Ah! The children of Darfur. Your empty bellies on the telly and now it's you that I'm fighting for. Left home. Don't even know the day I'll ever return. My country is war-torn. Music I used to hear was bombs and fire of guns. So many people die that I don't even cry no more. Ask God question, what am I here for. And why are my people poor. And why, why when the rest of the children were learning how to read and write, I was learning how to fight. I ate snails, vultures, rabbits, snakes, and anything that had life. I was ready to eat. I know it's a shame. But who is to be blamed? That's my story shared in the form of a lesson. (Applause) Thank you. (Applause) What energized me and kept me going is the music I do. I never saw anybody to tell my story to them so they could advise me or do therapy. So the music had been my therapy for me. It's been where I actually see heaven, where I can be happy, where I can be a child again, in dances, through music. So one thing I know about music: music is the only thing that has power to enter your cell system, your mind, your heart, influence your soul and your spirit, and can even influence the way you live without even you knowing. Music is the only thing that can make you want to wake up your bed and shake your leg, without even wanting to do it. And so the power music has I normally compare to the power love when love doesn't see a color. You know, if you fall in love with a frog, that's it. One testimony about how I find music is powerful is when I was still a soldier back then. I hated the people in the north. But I don't know why I don't hate their music. So we party and dance to their music. And one thing that shocked me is one day they brought an Arab musician to come and entertain the soldiers. And I almost broke my leg dancing to his music. But I had this question. So now I'm doing music so I know what the power of music is. So what's happening here? I've been in a painful journey. Today is day number 233 in which I only eat dinner. I don't eat breakfast. No lunch. And I've done a campaign called Lose to Win. Where I'm losing so that I could win the battle that I'm fighting now. So my breakfast, my lunch, I donate it to a charity that I founded because we want to build a school in Sudan. And I'm doing this because also it's a normal thing in my home, people eat one meal a day. Here I am in the West. I choose not to. So in my village now, kids there, they normally listen to BBC, or any radio, and they are waiting to know, the day Emmanuel will eat his breakfast it means he got the money to build our school. And so I made a commitment. I say, "I'm gonna not eat my breakfast." I thought I was famous enough that I would raise the money within one month, but I've been humbled. (Laughter) So it's taken me 232 days. And I said, "No stop until we get it." And like it's been done on Facebook, MySpace. The people are giving three dollars. The lowest amount we ever got was 20 cents. Somebody donated 20 cents online. I don't know how they did it. (Laughter) But that moved me. And so, the importance of education to me is what I'm willing to die for. I'm willing to die for this, because I know what it can do to my people. Education enlighten your brain, give you so many chances, and you're able to survive. As a nation we have been crippled. For so many years we have fed on aid. You see a 20-years-old, 30-years-old families in a refugee camps. They only get the food that drops from the sky, from the U.N. So these people, you're killing a whole generation if you just give them aid. If anybody want to help us this is what we need. Give us tools. Give the farmers tools. It's rain. Africa is fertile. They can grow the crops. (Applause) Invest in education. Education so that we have strong institution that can create a revolution to change everything. Because we have all those old men that are creating wars in Africa. They will die soon. But if you invest in education then we'll be able to change Africa. That's what I'm asking. (Applause) So in order to do that, I founded a charter called Gua Africa, where we put kids in school. And now we have a couple in university. We have like 40 kids, ex-child soldiers mixed with anybody that we feel like we want to support. And I said "I'm going to put it in practice." And with the people that are going to follow me and help me do things. That's what I want to do to change, to make a difference in the world. Well now, my time is going, so I want to sing a song. But I'll ask you guys to stand up so we celebrate the life of a British aid worker called Emma McCune that made it possible for me to be here. I'm gonna sing this song, just to inspire you how this woman has made a difference. She came to my country and saw the importance of education. She said the only way to help Sudan is to invest in the women, educating them, educating the children, so that they could come and create a revolution in this complex society. So she even ended up marrying a commander from the SPLA. And she rescued over 150 child soldiers. One of them happened to be me now. And so at this moment I want to ask to celebrate Emma with me. Are you guys ready to celebrate Emma? Audience: Yes! Emmanuel Jal: All right. ♫ This one goes to Emma McCune ♫ ♫ Angel to rescue came one afternoon ♫ ♫ I'm here because you rescued me ♫ ♫ I'm proud to carry your legacy ♫ ♫ Thank you. Bless you. R.I.P. ♫ ♫ What would I be? Me! ♫ ♫ If Emma never rescued me? What would I be? ♫ ♫ What would I be? Me! ♫ ♫ Another starving refugee ♫ ♫ What would I be? ♫ ♫ What would I be? Me! ♫ ♫ If Emma never rescued me? Yeah! ♫ ♫ Yeah! Yeah! ♫ ♫ You would have seen my face on the telly ♫ ♫ Fat hungry belly ♫ ♫ Flies in my eyes, head too big for my size ♫ ♫ Just another little starving child ♫ ♫ Running around in Africa, born to be wild ♫ ♫ Praise God, praise the Almighty ♫ ♫ for sending an angel to rescue me ♫ ♫ I got a reason for being on this Earth ♫ ♫ 'Cause I know more than many what a life is worth ♫ ♫ Now that I got a chance to stand my ground ♫ ♫ I'm gonna run over mountains, leaps and bounds ♫ ♫ I ain't an angel, hope I'll be one soon ♫ ♫ And if I am, I wanna be like Emma McCune ♫ ♫ Me! What would I be? Me! ♫ ♫ If Emma never rescued me? ♫ ♫ What would I be? ♫ ♫ What would I be? Me! ♫ ♫ Another starving refugee ♫ ♫ What would I be? ♫ ♫ What would I be? Me! ♫ ♫ If Emma never rescued me? Yeah! Yeah!♫ ♫ Yeah, Yeah! ♫ ♫ I would have probably died from starvation ♫ ♫ Or some other wretched disease ♫ ♫ I would have grown up with no education ♫ ♫ Just another refugee ♫ ♫ I stand here because somebody cared ♫ ♫ I stand here because somebody dared ♫ ♫ I know there is a lot of Emmas out there ♫ ♫ Who is willing and trying to save a life of a child ♫ ♫ What would I be? Me! ♫ ♫ If Emma never rescued me? ♫ ♫ What would I be? ♫ ♫ What would I be? ♫ ♫ Another starving refugee ♫ ♫ I remember the time when I was small ♫ ♫ When I couldn't read or write at all ♫ ♫ Now I'm all grown up, I got my education ♫ ♫ The sky is the limit and I can't be stopped by no one ♫ ♫ How I prayed for this day to come ♫ ♫ And I pray that the world find wisdom ♫ ♫ To give the poor in need some assistance ♫ ♫ Instead of putting up resistance, yeah ♫ ♫ Sitting and waiting for the politics to fix this ♫ ♫ It ain't gonna happen ♫ ♫ They're all sitting on they asses ♫ ♫ Popping champagne and sponging off the masses ♫ ♫ Coming from a refugee boy-soldier ♫ ♫ But I still got my dignity ♫ ♫ I gotta say it again ♫ ♫ If Emma never rescued me ♫ ♫ I'd be a corpse on the African plain ♫ Is there anybody who's here in the back, some love. Big scream for Emma everybody. Yeah! I'm gonna get crazy now. ♫ What would I be? ♫ ♫ If Emma never rescued me? ♫ ♫ What would I be? ♫ ♫ Another starving refugee ♫ ♫ What would I be? ♫ ♫ If Emma never rescued me? ♫ ♫ Yeah, Yeah ♫ ♫ Yeah, I would have probably died from starvation ♫ ♫ Or some other wretched disease ♫ ♫ I would have grown up with no education ♫ ♫ Just another refugee ♫ (Applause) Thank you. (Applause) Go save a life of a child. (Applause) | The music of a war child | null |
And constructed-response items using pages 33 and 34 of session 3 the answer keys and scoring rubrics, used to score student responses, are located on pages 38 to 42 ileap practice test—grade 7 math http://www louisianabelievescom/ resources/ library/ assessment-guidance-2013-2014 math grade 7 page 1. Printable worksheets and online practice tests on fractions for grade 7 questions on fractions and operations on fractions for grade 7. Informational guide to grade 7 math summative assessment 2 overview this guide has been prepared to provide specific information about the parcc summative assessments the parcc assessments are based upon evidence- centered design (ecd) evidence-centered design is a systematic approach to test. This fractions test has 10 problems to test adding, subtracting, multiplying, and dividing fractions. Fractions and mixed numbers- grade 7 math questions and problems with answers grade 7 math multiple choice questions on fractions and mixed numbers with answers are presented the questions tests both the skills and concepts related to fractions and mixed numbers with some challenging. Grade 7 (pre-algebra) end-of-the-year test this test is quite long, because it contains lots of questions on all of the major topics covered in the math mammoth grade 7 complete curriculum its main purpose is to be a diagnostic test—to find out what the student knows and does not know about these topics you can use. Start test, unit 5: operations with fractions, 10 questions, randomized, from 42 questions overall, top scores start test, unit 6: equations, 10 questions, randomized, from 50 questions overall, top scores start test, unit 7: data analysis, 10 questions, randomized, from 72 questions overall.
10 andy gets {7} out of {25} questions wrong in his maths test what fraction of the questions does andy answer correctly \frac{7}{25} \frac{18}{25} \frac{7}{18} check score. 44% question 6: the two circles in the figure below intersect each other in m and n both circles have radii of 4 inches ab = 3 inches where a and b are the points of intersection of segment o1 and o2 with the two circles gre, circles, geometry what is the length o1o2 2 inches 3 inches 4 inches 5 inches question 7: mike. Send email invitation via edcite your message please modify your message as desired cc me add more send invite welcome you are about to start an assignment sbac practice test grade 7 math june 2014 29 questions start assignment there are 29 questions answer all questions before you submit. In these tutorials, we'll explore the number system we'll convert fractions to decimals, operate on numbers in different forms, meet complex fractions, and identify types of numbers we'll also solve interesting word problems involving percentages (discounts, taxes, and tip calculations.
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Directions: on the following pages are multiple-choice questions for the grade 7 practice test, a practice opportunity for the nebraska state accountability– mathematics (nesa–m) each question will ask you to select an answer from among four choices for all questions: • read each question carefully and choose the. Grade 7 fcat 20 mathematics sample questions the intent of these sample test materials is to orient teachers and students to the types of questions on fcat 20 tests by using these materials, students will box in the middle of an answer • be sure to write a decimal point or fraction bar in the answer box if it is a part of. Assessment checklists for kindergarten - new canadian edition assessment checklists and tests for grade 1 - new canadian edition assessment checklists, quizzes, and tests for grade 2 - new canadian edition quizzes and tests for grade 3 - new canadian edition. Mathematics test book 1 grade 7 21654 may 5–7, 2010 be sure to read carefully all the directions in the test book • read each question carefully and think about do not reproduce do not discuss contents until end of designated makeup schedule what is the value of the expression 2 + 32 + | –4 | 7 12 15 29 8.
D 14,200,000,000 3 the school cafeteria bought 15 tables after receiving a discount of $250, the total price was$5,000 which equation could be used to find the cost, t, of each table a 15t + 250 = 5,000 b 15t – 250 = 5,000 c 15t + 250t = 5,000 d 15t – 250t = 5,000 mathematics—grade 7 practice test ne g7 math. Use the resources in our test prep course to help your students get ready for the smarter balanced assessments - math grade 7 exam this course. | crawl-data/CC-MAIN-2018-43/segments/1539583513686.3/warc/CC-MAIN-20181021031444-20181021052944-00515.warc.gz | null |
delta T = i*Kf*m
You want the largest delta T (which will give the lowest freezing point).
Kf is constant so we can forget that. The two that matter are i and m
So multily i*m for the 5 and the largest number wins. Remember i is the van't Hoff factor which is the number of particles produced when the materials are placed in solution. sucrose is l. KCl is 2, etc.
I understand everything except the van't Hoff factor part. I do not understand how you figure that out.
That how the material ionizes.
KCl ==> K^+ + Cl^- and i = 2
MgCl2 ==> Mg&2+ + 2Cl^- and i = 3
Na2SO4 == 2Na^+ + SO4^2- and i = 3
Cr(SO4)3 ==> Cr^3+ + 3SO4^2- and i = 4
Sugar doesn't ionize so it is just 1 particle
Sugar ==> sugar(aq) and i = 1
Ok so then I just have to find the mass of each solution
so KCl = 74.55 X 2
MgBr2 = 184.11 X 3
Na2SO4 = 94.05 X 3
Cr(SO4)3 = 340.21 X 4
So Cr(SO4)3 would have the largest delta T, so the lowest freezing point.
Is this correct?
Why do you need the molar mass?
delta T = i*Kf*m
You know i from my previous response and you know m from the problem. i*m that gives the largest number will be the one that gives the largest delta T.
Ok so do you mean 0.25MgBr2 X 3 = 0.75 ?
i equals 3 for MgBr2 correct?
So I think that 0.40m Cr(NO3)3 has the largest delta T. Would you agree?
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chemistry - write a balanced equation for the reaction that occurs when an ... | <urn:uuid:32738dac-9567-4e72-be1f-a8243990ffac> | {
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## 2011-2012
The position of a particle (in inches) moving along the x-axis after t seconds have elapsed is given by the following equation:
s = f(t) = t4 – 2t3 – 6t2 + 9t
(a) Calculate the velocity of the particle at time t.
(b) Compute the particle’s velocity at t = 1, 2, and 4 seconds.
(c) When is the particle at rest?
(d) When is the particle moving in the forward (positive) direction?
(e) Calculate total distance traveled by the particle (i.e., forwards and backwards) after t = 5 seconds.
(f) Calculate the acceleration of the particle after 4 seconds.
(g) When is the speed of the particle constant?
### Solution:
(a) The velocity is the derivative of position, so the velocity is v(t) = 4t3 – 6t2 – 12t + 9.
(b) Simply plug into the velocity equation to get: v(1) = –5 in/sec, v(2) = –7 in/sec, v(4) = 121 in/sec.
(c) If you graph the velocity function on your calculator, you see that it appears to pass through x = –1.5. Use synthetic division to ensure that this is true and to factor the equation. You will get the following:
(t – 1/2)(4t2 – 12t + 6)
Now, use the quadratic formula to solve the quadratic part, and you’ll see that the velocity equals zero (in other words, is stopped) when t = –1.5, 0.6339745962, 2.366025404. Even though you can round to the third decimal place, you need to use these values for the remainder of the problem.
(d) If you plug in values into the velocity equation between the x-intercepts above, you will get positive values on the intervals (–1.5, 0.6339) and (2.366, ∞). Note that it doesn’t quite make sense to have negative time, so (0, 0.6339) is just as acceptable, and perhaps more so, for the first interval. We do this because positive velocity implies forward movement.
(e) First, substitute the “turn points” you found in part (c) into the position equation. When the velocity equals zero in this problem, the particle is stopping because it is turning to go the other way. You find thats(0.6339) = 2.946152423, s(2.366) = –7.446152423, and s(5) = 270. Note that the negative x-intercept is ignored because you cannot move back in time.
These numbers represent how far the particle is from the origin at specific times. So, the particle moves 2.9 inches to the right of the origin, then moves 7.44 inches left of it, and finally ends up 270 inches to the right of it. By the time t = 2.366 seconds, the particle has traveled to the right 2.9 inches, back 2.9 inches to the origin, then left 7.4 more inches. It then moves 7.4 inches back to the origin and ends up 270 more inches to the right of it. The final answer is 290.785 inches.
(f) The acceleration is the derivative of velocity, so a(t) = v’(t) = 12t2 – 12t – 12. The acceleration at t = 4 seconds is a(4) = 132 in/sec2.
(g) Set the acceleration equal to zero and solve using the quadratic equation: t = –0.618 sec or 1.618 sec.
## 2011-2012
During a taping for Circus of the Stars, beloved actress Betty White is shot out of a cannon. The firing goes completely awry and sends her on a collision course with a jet. As they converge, Betty and the jet plane at right angles to each other (see diagram below). Betty is 200 miles away from the point of impact and traveling at a constant rate of 600 mph. (Not even the laws of physics can slow Betty White!) The plane is 150 miles from impact and traveling at a constant rate of 450 mph.
At what rate is the distance d between Betty and the jet decreasing?
### Solution:
Consider the following diagram, which labels the legs of the right triangle as follows: b is the distance between Betty White and the point of impact and p is the distance between the plane and the point of impact.
The Pythagorean Theorem describes the relationship between the lengths of the sides of the triangle.
b2 + p2 = d2
Substitute b = 200 and p = 150 into the formula to solve for d, the distance between the two airborn objects at this moment.
You are asked to find the rate at which d decreases. In other words, you are calculating dd/dt. Apply implicit differentiation, with resepct to t.
Divide each of the terms by 2 and solve for dd/dt.
To calculate dd/dt, substitute all of the known information into the equation: b = 200, db/dt = –600, p = 150, dp/dt = –450, and d = 250. Note that db/dt and dp/dt are negative because the lengths of the legs of the right triangle are decreasing—the objects are on a collision course, so the distances between the objects and the point of impact are getting smaller.
The distance between Betty and the jet is decreasing at a rate of 750 mph.
## 2011-2012
An object is dropped from the second-highest floor of the Sears Tower, 1542 feet off of the ground. (The top floor was unavailable, occupied by crews taping for the new ABC special “Behind the Final Behind the Rose Final Special, the Most Dramatic Behind the Special Behind the Rose Ever.”)
(a) Construct the position and velocity equations for the object in terms of t, where t represents the number of seconds that have elapsed since the object was released.
(b) Calculate the average velocity of the object over the interval t = 2 and t = 3 seconds.
(c) Compute the velocity of the object 1, 2, and 3 seconds after it is released.
(d) How many seconds does it take the object to hit the ground? Report your answer accurate to the thousandths place.
(e) If the object were to hit a six-foot-tall man squarely on the top of the head as he (unluckily) passed beneath, how fast would the object be moving at the moment of impact? Report your answer accurate to the thousandths place.
Extra Credit: If the falling object killed the six-foot-tall man, is he actually luckier for not having to endure the Bachelor special taping on the top floor? (Spoiler alert: Yes.)
### Solution:
(a) The position function for a projectile is s(t) = –16t2 + v0t + h0, where v0 represents the initial velocity of the object (in this case 0) and h0 represents the initial height of the object (in this case 1,542 feet). Note that this position equation represents the height in feet of the object t seconds after it is released. Thus, the position equation is s(t) = –16t2 + 1,542. The vecocity equation v(t) is the derivative of the position equation: v(t) = –32t.
(b) Average velocity is the slope of the secant line, rather than the slope of the tangent line. Plug t = 2 and t = 3 into the position equation to calculate the height of the object at the boundaries of the indicated interval to generate two ordered pair: (2, 1478) and (3, 1398). Apply the slope formula from basic algebra to calculate the slope of the line passing through those points.
(c) Substitute t = 1, 2, and 3 into v(t).
(d) The object hits the ground when its position is s(t) = 0. Set the position equation equal to zero and solve for t.
(e) The problem asks you to calculate the velocity of the object when it is exactly six feet off of the ground, when s(t) = 6. Apply the same technique you completed in part (d), but instead of calculating the time t when the object’s position is 0, calculate the time t when its position is 6.
Now calculate the velocity of the object at that time: v(9.79795897113) = –32(9.79795897113) = –313.535 ft/sec.
## 2011-2012
Let f(x) be the function defined below:
Determine whether f(x) is continuous at x = 0 and explain your answer.
Note: You may use a graphing calculator to examine the graph of f(x).
### Solution:
If f(x) if continuous at x = 0, its left- and right-hand limits exist at x = 0, and they are both equal to f(0). Consider the graph of the function below.
This sine curve is a “damped” function; it is already zoomed in quite far, but feel free to zoom in to your heart’s content. The function will wriggle its way to a height of 0 as you approach the y-axis from the right and from the left. Therefore, the general limit exists, and it is equal to 0.
According to the piecewise-defined function, f(0) = 0. (It’s a good thing, too, because substituting 0 intox2sin(1/x) would have been a deal-breaker. You’re not allowed to have a 0 in a denominator.)
Because the limit of f(x) exists as x approaches 0 and it equals f(0), you conclude that f(x) is continuous at 0.
## 2011-2012
Describe or draw a function, f(x), with the following characteristics:
• f(x) has domain (–∞,8)
• f(x) has range (–∞,9)
• f(4) = 0; f(5) = 0; f(7) = 0
• The limit, as x approaches –∞, of f(x) equals 9
• The limit, as x approaches 8 from the left, of f(x) equals –∞
• f(–1) = f(–3); f(–1) > f(–2)
• f(1) = 1
• The limit, as x approaches 1, of f(x) is 4 | crawl-data/CC-MAIN-2018-13/segments/1521257645824.5/warc/CC-MAIN-20180318145821-20180318165821-00602.warc.gz | null |
Evaluate: 6y^2 = 7y - 5
Question:
Evaluate: {eq}6y^2= 7y - 5 {/eq}
An equation which is of the form {eq}ax^2+bx+c=0 {/eq} where {eq}a, b \text{ and } c {/eq} are constants is called a quadratic equation in {eq}x {/eq}. It has two (either same or distinct) roots. The roots can be solved by using the quadratic formula which states:
$$x=\dfrac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$
The given equation is:
$$6y^2= 7y - 5 \\ \text{Subtract 7y and add 5 on both sides}, \\ 6y^2-7y+5=0$$
Comparing this with {eq}ay^2+by+c=0 {/eq}, we get:
$$a=6 \\ b=-7 \\ c=5$$
We substitute all these values in the quadratic formula:
\begin{align} \color{red}{ x} &\color{red}{ =} \color{red}{ \dfrac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}} \\[0.4cm] y&= \frac{-(-7) \pm \sqrt{(-7)^{2}-4 \cdot 6 \cdot 5}}{2 \cdot 6} \\[0.4cm] &=\frac{7 \pm \sqrt{49-120}}{12} \\[0.4cm] &=\frac{7\pm \sqrt{-71}}{12} \\[0.4cm] &=\frac{7\pm i\sqrt{71}}{12} & [ \because \sqrt{-1}=i ] \\[0.4cm] \color{blue}{ y} &\color{blue}{ =} \color{blue}{ \boxed{\mathbf{\frac{7}{12}+i \frac{\sqrt{71}}{12}; \,\,\,\, \frac{7}{12}-i \frac{\sqrt{71}}{12}}}} \end{align} | crawl-data/CC-MAIN-2020-10/segments/1581875146123.78/warc/CC-MAIN-20200225141345-20200225171345-00147.warc.gz | null |
The contraction of a moving body in the direction of its motion. It was proposed independently by H. A. Lorentz and G. F. Fitzgerald (1851–1901) in 1892 to account for the null result of the Michelson–Morley experiment. The contraction was given a theoretical background in Einstein's special theory of relativity. In this theory, an object of length l0 at rest in one frame of reference will appear, to an observer in another frame moving with relative velocity v with respect to the first, to have length l0√(l − v2/c2), where c is the speed of light. The original hypothesis regarded this contraction as a real one accompanying the absolute motion of the body. The contraction is in any case negligible unless v is of the same order as c. | <urn:uuid:3771df51-eafa-4af9-b1de-ecde87195179> | {
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Many medical conditions, such as chronic pain, cancer and diabetes, require medications that cannot be taken orally, but must be dosed intermittently, on an as-needed basis, over a long period of time. A few delivery techniques have been developed, using an implanted heat source, an implanted electronic chip or other stimuli as an "on-off" switch to release the drugs into the body. But thus far, none of these methods can reliably do all that's needed: repeatedly turn dosing on and off, deliver consistent doses and adjust doses according to the patient's need.
Researchers led by Daniel Kohane, MD, PhD of Children's Hospital Boston, funded by the National Institutes of Health, have devised a solution that combines magnetism with nanotechnology.
The team created a small implantable device, less than ½" in diameter, that encapsulates the drug in a specially engineered membrane, embedded with nanoparticles (approximately 1/100,000 the width of a human hair) composed of magnetite, a mineral with natural magnetic properties. When a magnetic field is switched on outside the body, near the device, the nanoparticles heat up, causing the gels in the membrane to warm and temporarily collapse. This opens up pores that allow the drug to pass through and into the body. When the magnetic force is turned off, the membranes cool and the gels re-expand, closing the pores back up and halting drug delivery. No implanted electronics are required.
The device, which Kohane's team is continuing to develop for clinical use, is described in the journal Nano Letters.
"A device of this kind would allow patients or their physicians to determine exactly when drugs are delivered, and in what quantities," says Kohane, who directs the Laboratory for Biomaterials and Drug Delivery in the Department of Anesthesiology at Children's.
In animal experiments, the membranes remained functional over multiple cycles. The size of the dose was controllable by the duration of the "on" pulse, and the rate of release remained steady, even 45 days after implantation.
Testing indicated that drug delivery could be turned on with only a 1 to 2 minute time lag before drug release, and turned off with a 5 to 10 minute time lag. The membranes remained mechanically stable under tensile and compression testing, indicating their durability, showed no toxicity to cells, and were not rejected by the animals' immune systems. They are activated by temperatures higher than normal body temperatures, so would not be affected by the heat of a patient's fever or inflammation.
"This novel approach to drug delivery using engineered 'smart' nanoparticles appears to overcome a number of limitations facing current methods of delivering medicines," says Alison Cole, Ph.D., who oversees anesthesia grants at the National Institutes of Health's National Institute of General Medical Sciences (NIGMS). "While some distance away from use in humans, this technology has the potential to provide precise, repeated, long-term, on-demand delivery of drugs for a number of medical applications, including the management of pain."
The study was funded by the NIGMS.
- Todd Hoare, Jesus Santamaria, Gerardo F. Goya, Silvia Irusta, Debora Lin, Samantha Lau, Robert Padera, Robert Langer, Daniel S. Kohane. A Magnetically Triggered Composite Membrane for On-Demand Drug Delivery. Nano Letters, 2009; DOI: 10.1021/nl9018935
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Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
Taxicab geometry is a special kind of geometry that works on city streets. With it you finally have a chance of finding treasure hidden in the city of Arborville.
Here's what you do: Pick an intersection and ask the computer how far it is to the treasure. The computer tells you the distance using taxicab geometry.
In taxicab geometry the shortest distance between two points is not a straight line, but rather the number of blocks a taxi has to travel along the streets. So, in the street plan of Arborville (shown below), the distance from the blue star to the red star is 4 blocks.
Now that you have looked at the map, it's time to have the computer hide the treasure! | <urn:uuid:2c96534a-14e6-400e-b618-567e789fbfce> | {
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In life and in math class we use the numerals 0 through 9 every day. They are the basis of our financial system and shape the way we understand value. We have a young Italian mathematician named Leonardo da Pisa, nicknamed Fibonacci, to thank for this. In 1202 he published a book called “Book of Calculation” that introduced these numerals to Europe, replacing Roman numerals and the abacus once and for all. Listen to learn more about the man and concept behind Fibonacci and his numbers.
Story Length: 4:44
Socrative users can import these questions using the following code: SOC-1234 | <urn:uuid:cb4f3223-9d2d-46c8-b2bb-c5d6c0251d7a> | {
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In a recent study, researchers reported that bumblebees were able to figure out the most efficient routes among several computer-controlled
"flowers," quickly solving a complex problem that even stumps supercomputers. We already know bees are pretty good at facial recognition, and
researchers have shown they can also be effective air-quality monitors.
Bumblebees can solve the classic "traveling salesman" problem, which keeps supercomputers busy for days. They learn to fly the shortest possible
route between flowers even if they find the flowers in a different order, according to a new British study.
Barbara Shipman, a mathematician at the University of Rochester, expands upon the research of physicist Karl Von Frisch, hypothesizing that bees have
an advanced understanding of quantum space and mathematics.
Karl Von Frisch has proven that honey bees communicate the location of food through specific dances, or “waggles,” that are geometrically
proportional to variables such as the distance between the hive and food.
Von Frisch concludes: “You have to wonder what makes the dance happen. Bees don’t have enough intelligence to know what they’re doing. How do
they know the dance in the first place? Calling it instinct or some other word just substitutes one mystery for another.”
While researching this mystery, Shipman discovered a direct correlation between the geometry of higher-dimension “manifolds” and the honey bees’
dance, suggesting a deeper, more quantum connection than previously observed.
She continues to suggest that the insect’s bodies have evolved to increase sensitivity between quantum fields, that they’re actually able to
physically communicate with the properties of quarks in a way that is beyond our current understanding of physics.
These cylinders were staggered into mazes with multiple levels of “Y” branch points that the bees encountered before reaching the desired feeder
station. In one set of experiments, the scientists trained bees to track a trail of colored marks, as in a scavenger hunt. The bees could then
follow—more or less—the same strategy in a completely unfamiliar maze. Amazingly enough, bees can use color in an abstract manner, turning right,
for instance, when the branch point is colored blue and left when it is colored green. Individual animals developed quite sophisticated strategies,
such as the right-turn rule, that always led to the goal, though not necessarily by the shortest route.
I've been careful to stress that any network possesses integrated information. The theory is very explicit on this point: Any system whose
functional connectivity and architecture yield a phi value greater than zero has at least a trifle of experience. This would certainly include the
brains of bees. Just because bees are small and fuzzy does not mean that they cannot have subjective states. So, the next time a bee hovers above your
breakfast, attracted by the golden nectar on your toast, gently shoo her away. She might be a fellow sentient being, experiencing her brief interlude
in the light.
Years ago there was an experiment preformed on bees related to a lake in a specific hives feeding grounds. Experimenters worked with the Bees that
acted a scouts. They were effective in creating a condition in which these bees, responded to a flowers placed in a small boat.
When these bees returned to the nest and transmitted the location of there find as being in a lake? In many cases they were killed by the other bees.
I mean granted animals do kill there own kind and especially in the case of the young when a problem is sensed. In this case there was actually
nothing wrong with what the bees were communicating, but an apparent response occurred as if there was something physically wrong with them.
However, bees are pretty good at remembering where things are and how to get to them. Not only can they tell other bees where something is, they can
return to it themselves, and the more times they do, the more efficiently they route their path.
If you've ever beelined, you will notice your first round marker bees making the trip faster and faster.
Again the bees respond to the messenger bee as if there is a genetic problem but there is not. Animals as well as insects do often respond to
medically determinable dysfunctions in relation to reproduction, where they either refuse to mate or kill the young. In this case we have a situation
where there is nothing wrong with the bee, with exception of the fact it identified a food source location that could be considered inappropriate,
without human intervention. The bees seem to think it is impossible for plants they can feed from to grow in lakes.
It is interesting as when you look at other animals that travel in groups? A disagreement as to where the food is, is something rather unknown with
exception of humans. Animals in general fight and kill each other over issues of territory, reproduction and food when it is scarce, but this is not
the same thing.
Interesting article. What makes it more interesting is what it says about us.
The emerging field of Quantum Biology is exciting to say the least. If migrating birds, DNA, Photosynthesis, sense of smell and now bees use quantum
properties like superposition, entanglement and non locality then it's just common sense that the brain could evolve to also access these
I'm already a proponent of Quantum Consciousness because it explains who we are perfectly instead of all of these convoluted and plainly lacking
explanations as to how consciousness emerged from the classical brain.
Quantum Conscious would also easily explain things like near death experiences, twin telepathy, psychic ability and more.
Tegmark's paper was aimed at refuting Hameroff's Orch OR theory, which required quantum coherence to be sustained for 25 ms. Thus Tegmark did not
show that coherence over shorter timescales could not support consciousness, because he was directing his argument at the longer timescales of
Hameroff's theory. Georgiev here queries whether there is any evidence that consciousness has to arise over a milliseconds timescale. If
consciousness could operate over a picosecond or shorter timescale then Tegmark's calculations do not present any problem for quantum consciousness.
It is pointed out that all neuroscience has been able to show to date is that consciousness does not operate on a scale slower than milliseconds.
Tests show that there is a minimum timescale of about 30 ms needed for a subject to distinguish two sensory inputs as being separate. This means that
consciousness cannot be slower than 30 ms. However, patients with time agnosia, who have subjective experience of the passage of time, confirm that it
is physically possible to have consecutive conscious steps that are experienced as simultaneous. From this it is argued that the real units of
consciousness could be at the picoseconds level, although such units cannot be discerned by the conscious subject.
I think there's a couple of things wrong with Tegmark's paper. First, he uses a different metric than Hameroff which of course will be at odds with
Hameroff. Hameroff was talking about sub units of microtubules which would provide a way to hold superposition longer. But, we might not find quantum
consciousness in microtubules. It might be somewhere else. This is why more research in these areas are needed.
Tegmark and others think the brain can be mimicked by a computer in a way where consciousness will be produced. What Penrose showed was that the brain
is non computable and therefore quantum mechanical. Consciousness doesn't work in a step by step fashion. Conscious experiences occur in ways that
aren't computable at least on a classical level.
Penrose basically says that coherent states are in superposition on a quantum level. They become entangled and when they reach a quantum/classical
threshold, a conscious experience occurs when these states decohere. This means the universe is conscious at the smallest scales of space-time
geometry. Fascinating stuff if you ask me.
Let's say you go into Rite Aid. Everything in the store would be coherent states of superposition on a quantum level. When you buy that Snapple and
bag of Baked Lays and walk out of the store, those coherent states of superposition decohere into one state and a conscious experience occurs. The
classical human brain is intelligent and it has evolved to the point where it can observe and is aware of these conscious experiences that occur.
This is why the article about the Bees is so great. It's because other animals may use the same quantum properties. It's just we have brains that are
advanced enough to be aware of these conscious experiences that occur on planck scales.
So when you walk into a store, quantum consciousness is putting things in a coherent state of superposition. The classical brain then makes the choice
and the coherent superposition decohere's into one state which is a conscious experience. I don't think the classical brain always makes the choice
though. I think these coherent states network and calculate the optimal choice. The brain is so advanced though, we can make choices that are less
I was just reading about how the universe is like a brain and it said this:
The physicists' simulation modeled the very early life of the universe, shortly after the Big Bang.
In the simulation, they looked at how quantum units of space-time smaller than subatomic particles "networked" with each other.
They learned the simulation mirrored that of other networks - some links between similar nodes had limited growth, but others acted as junctions for
many different connections.
Also, they found some connections are limited and similar, like a person who likes sports visiting many sports websites; while some connect to many
other parts of the network, like Google and Yahoo.
I think because of this, Physics is missing something. Like the guy said in the article:
“For a physicist it’s an immediate signal that there is some missing understanding of how nature works,” the Huffington Post quoted Krioukov
as tellinge Space.com.
What this means is that these coherent states network with each other on Planck scales in a way that's not random. They seem to favor these
connections that produce universes, human brains and internets.
The reason this will be met with HUGE resistance because it also means things like twin telepathy, near death experiences and more are easily
explained with these three words. Superposition, entanglement and non-locality.
Here's a great video:
edit on 9-3-2013 by neoholographic because: (no reason given)
The human body is a constant flux of thousands of inter-reactions and processes connecting molecules, cells, organs and fluids throughout the brain,
body and nervous system. Up until recently it was thought that all these countless interactions operated in a linear sequence, passing on information
much like a runner passing the baton to the next runner. However, the latest findings in quantum biology and biophysics have discovered that there is
in fact a tremendous degree of coherence within all living systems. It has been found through extensive scientific investigation that a form of
quantum coherence operates within living biological systems through what is known as biological excitations and biophoton emission. What this means is
that metabolic energy is stored as a form of electromechanical and electromagnetic excitations. It is these coherent excitations that are considered
responsible for generating and maintaining long-range order via the transformation of energy and very weak electromagnetic signals.
After nearly 20 years of experimental research, Fritz-Albert Popp put forward the hypothesis that biophotons are emitted from a coherent
electrodynamic field within the living system. What this effectively means is that each living cell is giving off, and resonating with, a biophoton
field of coherent energy. If each cell is emitting this field, then the whole living system is, in effect, a resonating field -- a ubiquitous
non-local field. And since it is by the means of biophotons that the living system communicates, then there is near instantaneous intercommunication
throughout. And this, claims Popp, is the basis for coherent biological organization -- referred to as quantum coherence.
The Above Top Secret Web site is a wholly owned social content community of The Above Network, LLC.
This content community relies on user-generated content from our member contributors. The opinions of our members are not those of site ownership who maintains strict editorial agnosticism and simply provides a collaborative venue for free expression.
All content copyright 2015, The Above Network, LLC. | <urn:uuid:eee11560-0931-47ff-b857-d2c817319d0f> | {
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This section is from the book "British Wild Flowers - In Their Natural Haunts Vol2-4", by A. R. Horwood. Also available from Amazon: A British Wild Flowers In Their Natural Haunts.
Zonal Character of the Coastal Vegetation. The vegetation of the sea-coast differs from every other type of vegetation in that it is entirely restricted to the junction of the sea with the land. This causes at once a more or less uniform altitude, the sole difference in this respect being defined by the rockiness or otherwise of the seaboard. Thus the maritime plants are at once confined to a fringe along the coast of little extent, rarely encroaching inland more than half a mile, or a little more where salt marshes, which are secondary products of the coastal vegetation, are concerned. It is, in fact, the marginal action of the sea, with its saline waters and peculiar deposits, that determines the formation of maritime vegetation.
There are two limits to the action of the sea, high-water mark and low-water mark, and as regards flowering plants these have little or no effect upon distribution. It is on the deposits thrown up and conserved above the high-water mark that the maritime plants are especially found, and these form the first zone, which may in the case of a low shore line be of sand or shingle. Where there are cliffs lashed at high tide by the sea there is a single zone, the rocks and cliffs. But on a low shore there are usually parallel with the first sandy shore or shingle beach dunes of aeolian origin, whilst a third zone is constituted by the salt marshes on the landward side of the dunes, though these may not everywhere be present, nor are dunes always developed on a low shore. To leeward of the salt marshes there may be a second line of dunes, and then inland vegetation. There are normally three or four zones of vegetation on the sea-coast.
One feature of most maritime tracts is the almost universal absence of trees. This is due to the regular occurrence of sea breezes and land breezes, which constantly subject the coast to unusual wind force, so that trees are unable to flourish except in a dwarfed state, and generally have their branches blown landwards. The exposed nature of the sea-coast also, apart from the wind, contributes to the absence of trees. Another reason is the character of the soil, which is saline, and usually of coarse texture unsuited to tree growth.
The fact that along most coasts there are relics of ancient submerged forests does not denote that the maritime border was formerly more suited to such conditions, but is an indication of the great amount of submergence or sagging that has occurred. Such forests were originally not only above the sea-level but a good distance inland. The maritime formations are thus without any native forests of their own. From this cause there is generally a relative absence of humus in the soil, except in the salt marshes where semi-marine peat is formed.
An exception must be made to the foregoing general rule in the case of sheltered coves and estuaries, as in Devonshire, Somerset, etc, where trees grow down to the sea margin, at any rate on rocky coasts. There are some shrubs that are characteristic of the sea-coast, such as Tamarisk, Sea Buckthorn, Coton-easter, and Elder is in many places common, as also the Tea Plant. | <urn:uuid:848c160b-7193-48ee-bfc3-d5b3d1f240c1> | {
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# 16.8: Stokes's Theorem
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Recall that one version of Green's Theorem (see equation 16.5.1) is
$$\int_{\partial D} {\bf F}\cdot d{\bf r} =\iint_\limits{D}(\nabla\times {\bf F})\cdot{\bf k}\,dA.\] Here $$D$$ is a region in the $$x$$-$$y$$ plane and $$\bf k$$ is a unit normal to $$D$$ at every point. If $$D$$ is instead an orientable surface in space, there is an obvious way to alter this equation, and it turns out still to be true: Stoke's Theorem Provided that the quantities involved are sufficiently nice, and in particular if $$D$$ is orientable,$$\int_{\partial D} {\bf F}\cdot d{\bf r}=\iint_\limits{D}(\nabla\times {\bf F})\cdot{\bf N}\,dS,\]
if $$\partial D$$ is oriented counter-clockwise relative to $$\bf N$$.
Note how little has changed: $$\bf k$$ becomes $$\bf N$$, a unit normal to the surface, and $$dA$$ becomes $$dS$$, since this is now a general surface integral. The phrase "counter-clockwise relative to $$\bf N$$" means roughly that if we take the direction of $$\bf N$$ to be "up", then we go around the boundary counter-clockwise when viewed from "above''. In many cases, this description is inadequate. A slightly more complicated but general description is this: imagine standing on the side of the surface considered positive; walk to the boundary and turn left. You are now following the boundary in the correct direction.
Example $$\PageIndex{2}$$:
Let $${\bf F}=\langle e^{xy}\cos z,x^2z,xy\rangle$$ and the surface $$D$$ be $$x=\sqrt{1-y^2-z^2}$$, oriented in the positive $$x$$ direction. It quickly becomes apparent that the surface integral in Stokes's Theorem is intractable, so we try the line integral. The boundary of $$D$$ is the unit circle in the $$y$$-$$z$$ plane, $${\bf r}=\langle 0,\cos u,\sin u\rangle$$, $$0\le u\le 2\pi$$. The integral is
$$\int_0^{2\pi} \langle e^{xy}\cos z,x^2z,xy\rangle\cdot\langle 0,-\sin u,\cos u\rangle\,du= \int_0^{2\pi} 0\,du = 0,\] because $$x=0$$. Example $$\PageIndex{3}$$: Consider the cylinder $${\bf r}=\langle \cos u,\sin u, v\rangle$$, $$0\le u\le 2\pi$$, $$0\le v\le 2$$, oriented outward, and $${\bf F}=\langle y,zx,xy\rangle$$. We compute$$\iint_\limits{D} \nabla\times{\bf F}\cdot {\bf N}\,dS= \int_{\partial D}{\bf F}\cdot d{\bf r}\]
in two ways.
First, the double integral is
$$\int_0^{2\pi}\int_0^2 \langle 0,-\sin u,v-1\rangle\cdot \langle \cos u, \sin u, 0\rangle\,dv\,du= \int_0^{2\pi}\int_0^2 -\sin^2 u\,dv\,du = -2\pi. \] The boundary consists of two parts, the bottom circle $$\langle \cos t,\sin t, 0\rangle$$, with $$t$$ ranging from $$0$$ to $$2\pi$$, and $$\langle \cos t,\sin t, 2\rangle$$, with $$t$$ ranging from $$2\pi$$ to $$0$$. We compute the corresponding integrals and add the results:$$
\int_0^{2\pi} -\sin^2 t\,dt+\int_{2\pi}^0 -\sin^2t +2\cos^2t =-\pi-\pi=-2\pi,
\]
as before.
An interesting consequence of Stokes's Theorem is that if $$D$$ and $$E$$ are two orientable surfaces with the same boundary, then
$$\iint_\limits{D}(\nabla\times {\bf F})\cdot{\bf N}\,dS =\int_{\partial D} {\bf F}\cdot d{\bf r} =\int_{\partial E} {\bf F}\cdot d{\bf r} =\iint_\limits{E}(\nabla\times {\bf F})\cdot{\bf N}\,dS. \] Sometimes both of the integrals$$\iint_\limits{D}(\nabla\times {\bf F})\cdot{\bf N}\,dS\qquad\hbox{and}\qquad\int_{\partial D} {\bf F}\cdot d{\bf r}\]
are difficult, but you may be able to find a second surface $$E$$ so that
$$\iint_\limits{E}(\nabla\times {\bf F})\cdot{\bf N}\,dS\] has the same value but is easier to compute. Example $$\PageIndex{4}$$: In example 16.8.2 the line integral was easy to compute. But we might also notice that another surface $$E$$ with the same boundary is the flat disk $$y^2+z^2\le 1$$. The unit normal $$\bf N$$ for this surface is simply $${\bf i}=\langle 1,0,0\rangle$$. We compute the curl:$$\nabla\times{\bf F}=\langle x-x^2,-e^{xy}\sin z-y,2xz-xe^{xy}\cos z\rangle.\]
Since $$x=0$$ everywhere on the surface,
$$(\nabla\times{\bf F})\cdot {\bf N}=\langle 0,-e^{xy}\sin z-y,2xz-xe^{xy}\cos z\rangle\cdot\langle 1,0,0\rangle=0,$$
so the surface integral is
$$\iint_\limits{E}0\,dS=0,\] as before. In this case, of course, it is still somewhat easier to compute the line integral, avoiding $$nabla\times{\bf F}$$ entirely. Example $$\PageIndex{5}$$: Let $${\bf F}=\langle -y^2,x,z^2\rangle$$, and let the curve $$C$$ be the intersection of the cylinder $$x^2+y^2=1$$ with the plane $$y+z=2$$, oriented counter-clockwise when viewed from above. We compute $$\int_C {\bf F}\cdot d{\bf r}$$ in two ways. First we do it directly: a vector function for $$C$$ is({\bf r}=\langle \cos u,\sin u, 2-\sin u\rangle\), so $${\bf r}'=\langle -\sin u,\cos u,-\cos u\rangle$$, and the integral is then$$\int_0^{2\pi} y^2\sin u+x\cos u-z^2\cos u\,du =\int_0^{2\pi} \sin^3 u+\cos^2 u-(2-\sin u)^2\cos u\,du =\pi.\]
To use Stokes's Theorem, we pick a surface with $$C$$ as the boundary; the simplest such surface is that portion of the plane $$y+z=2$$ inside the cylinder. This has vector equation $${\bf r}=\langle v\cos u,v\sin u,2-v\sin u\rangle$$. We compute $${\bf r}_u= \langle -v\sin u,v\cos u,-v\cos u\rangle$$, $${\bf r}_v= \langle \cos u,\sin u, -\sin u\rangle$$, and $${\bf r}_u\times{\bf r}_v=\langle 0,-v,-v\rangle$$. To match the orientation of $$C$$ we need to use the normal $$\langle 0,v,v\rangle$$. The curl of $$\bf F$$ is $$\langle 0,0,1+2y\rangle= \langle 0,0,1+2v\sin u\rangle$$, and the surface integral from Stokes's Theorem is
$$\int_0^{2\pi}\int_0^1 (1+2v\sin u)v\,dv\,du=\pi.\] In this case the surface integral was more work to set up, but the resulting integral is somewhat easier. Proof of Stokes's Theorem We can prove here a special case of Stokes's Theorem, which perhaps not too surprisingly uses Green's Theorem. Suppose the surface $$D$$ of interest can be expressed in the form $$z=g(x,y)$$, and let $${\bf F}=\langle P,Q,R\rangle$$. Using the vector function $${\bf r}=\langle x,y,g(x,y)\rangle$$ for the surface we get the surface integral$$\eqalign{\iint_\limits{D} \nabla\times{\bf F}\cdot d{\bf S}&= \iint_\limits{E} \langle R_y-Q_z,P_z-R_x,Q_x-P_y\rangle\cdot \langle -g_x,-g_y,1\rangle\,dA\cr &=\iint_\limits{E}-R_yg_x+Q_zg_x-P_zg_y+R_xg_y+Q_x-P_y\,dA.\cr}\]
Here $$E$$ is the region in the $$x$$-$$y$$ plane directly below the surface$$D$$.
For the line integral, we need a vector function for $$\partial D$$. If $$\langle x(t),y(t)\rangle$$ is a vector function for $$\partial E$$ then we may use $${\bf r}(t)=\langle x(t),y(t),g(x(t),y(t))\rangle$$ to represent $$\partial D$$. Then
$$\int_{\partial D}{\bf F}\cdot d{\bf r}=\int_a^b P{dx\over dt}+Q{dy\over dt}+R{dz\over dt}\,dt=\int_a^b P{dx\over dt}+Q{dy\over dt}+R\left({\partial z\over\partial x}{dx\over dt}+{\partial z\over\partial y}{dy\over dt}\right)\,dt.\] using the chain rule for $$dz/dt$$. Now we continue to manipulate this:$$\eqalign{\int_a^b P{dx\over dt}+Q{dy\over dt}+&R\left({\partial z\over\partial x}{dx\over dt}+{\partial z\over\partial y}{dy\over dt}\right)\,dt\cr
&=\int_a^b \left[\left(P+R{\partial z\over\partial x}\right){dx\over dt}+ \left(Q+R{\partial z\over\partial y}\right){dy\over dt}\right]\,dt\cr
&=\int_{\partial E} \left(P+R{\partial z\over\partial x}\right)\,dx+\left(Q+R{\partial z\over\partial y}\right)\,dy,\cr}\]
which now looks just like the line integral of Green's Theorem, except that the functions $$P$$ and $$Q$$ of Green's Theorem have been replaced by the more complicated $$P+R(\partial z/\partial x)$$ and $$Q+R(\partial z/\partial y)$$. We can apply Green's Theorem to get
$$\int_{\partial E} \left(P+R{\partial z\over\partial x}\right)\,dx+\left(Q+R{\partial z\over\partial y}\right)\,dy= \iint_\limits{E} {\partial\over \partial x}\left(Q+R{\partial z\over\partial y}\right)-{\partial\over \partial y}\left(P+R{\partial z\over\partial x}\right)\,dA.\] Now we can use the chain rule again to evaluate the derivatives inside this integral, and it becomes$$\eqalign{\iint_\limits{E} &Q_x+Q_zg_x+R_xg_y+R_zg_xg_y+Rg_{yx}-\left(P_y+P_zg_y+R_yg_x+R_zg_yg_x+Rg_{xy}\right)\,dA\cr&=\iint_\limits{E} Q_x+Q_zg_x+R_xg_y-P_y-P_zg_y-R_yg_x\,dA,\cr}\]
which is the same as the expression we obtained for the surface integral.
$$\square$$ | crawl-data/CC-MAIN-2021-49/segments/1637964363376.49/warc/CC-MAIN-20211207105847-20211207135847-00182.warc.gz | null |
Structurally, the Kharosthi and the Brahmi are nearly identical. The "letters" in both represent a constant followed by the short vowel /a/ (we'll denote this a "C-a" sign). Both denote change in vowel by adding marks to a sign. Consonant clusters are formed in both system by juxtaposing two signs closely together, sometimes forming a ligature. There are some difference, though. For one, while Brahmi had different signs for different initial vowels, Kharosthi used the same marks that change vowels in C-a signs on the sign for initial /a/ to denote other initial vowels. Another difference is that while Brahmi differentiated long and short version of the same vowel, Kharosthi used the same sign for both.
Eventually the Kharosthi Script fell out of use by the 3rd or 4th century CE, and the descendent of Brahmi eventually took hold in the northwestern South Asian.
This is the basic Kharosthi script.
And an example of strokes added to indicate different vowels following the consonant /k/. | <urn:uuid:4acdb19e-44a8-4d20-94aa-6a991785d8ed> | {
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Three years after the Supreme Court's Brown v. Board of Education decision, which officially ended public-school segregation, a federal court ordered Little Rock to comply. On September 4, 1957, Governor Orval Faubus defied the court, calling in the Arkansas National Guard to prevent nine African American students--"The Little Rock Nine"--from entering the building. Ten days later in a meeting with President Eisenhower, Faubus agreed to use the National Guard to protect the African American teenagers, but on returning to Little Rock, he dismissed the troops, leaving the African American students exposed to an angry white mob. Within hours, the jeering, brick-throwing mob had beaten several reporters and smashed many of the school's windows and doors. By noon, local police were forced to evacuate the nine students.
When Faubus did not restore order, President Eisenhower dispatched 101st Airborne Division paratroopers to Little Rock and put the Arkansas National Guard under federal command. By 3 a.m., soldiers surrounded the school, bayonets fixed.
Under federal protection, the "Little Rock Nine" finished out the school year. The following year, Faubus closed all the high schools, forcing the African American students to take correspondence courses or go to out-of-state schools. The school board reopened the schools in the fall of 1959, and despite more violence--for example, the bombing of one student's house--four of the nine students returned, this time protected by local police.
Little Rock Central High School National Historic Site was designated a unit of the National Park Service on November 6, 1998. It is located at the intersection of 14th and Park Streets in Little Rock, Arkansas.
Little Rock Central High School National Historic Site is the subject of an online-lesson plan produced by Teaching with Historic Places, a National Register program that offers classroom-ready lesson plans on properties listed in the National Register. To learn more, visit the Teaching with Historic Places home page. | <urn:uuid:8185e4de-1314-4322-8fa3-c89caea47185> | {
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# What is Gaussian quadrature: Definition and 17 Discussions
In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration. (See numerical integration for more on quadrature rules.) An n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree 2n − 1 or less by a suitable choice of the nodes xi and weights wi for i = 1, ..., n. The modern formulation using orthogonal polynomials was developed by Carl Gustav Jacobi 1826. The most common domain of integration for such a rule is taken as [−1, 1], so the rule is stated as
1
1
f
(
x
)
d
x
i
=
1
n
w
i
f
(
x
i
)
,
{\displaystyle \int _{-1}^{1}f(x)\,dx\approx \sum _{i=1}^{n}w_{i}f(x_{i}),}
which is exact for polynomials of degree 2n − 1 or less. This exact rule is known as the Gauss-Legendre quadrature rule. The quadrature rule will only be an accurate approximation to the integral above if f(x) is well-approximated by a polynomial of degree 2n − 1 or less on [−1, 1].
The Gauss-Legendre quadrature rule is not typically used for integrable functions with endpoint singularities. Instead, if the integrand can be written as
f
(
x
)
=
(
1
x
)
α
(
1
+
x
)
β
g
(
x
)
,
α
,
β
>
1
,
{\displaystyle f(x)=\left(1-x\right)^{\alpha }\left(1+x\right)^{\beta }g(x),\quad \alpha ,\beta >-1,}
where g(x) is well-approximated by a low-degree polynomial, then alternative nodes
x
i
{\displaystyle x_{i}'}
and weights
w
i
{\displaystyle w_{i}'}
will usually give more accurate quadrature rules. These are known as Gauss-Jacobi quadrature rules, i.e.,
1
1
f
(
x
)
d
x
=
1
1
(
1
x
)
α
(
1
+
x
)
β
g
(
x
)
d
x
i
=
1
n
w
i
g
(
x
i
)
.
{\displaystyle \int _{-1}^{1}f(x)\,dx=\int _{-1}^{1}\left(1-x\right)^{\alpha }\left(1+x\right)^{\beta }g(x)\,dx\approx \sum _{i=1}^{n}w_{i}'g\left(x_{i}'\right).}
Common weights include
1
1
x
2
{\textstyle {\frac {1}{\sqrt {1-x^{2}}}}}
(Chebyshev–Gauss) and
1
x
2
{\displaystyle {\sqrt {1-x^{2}}}}
. One may also want to integrate over semi-infinite (Gauss-Laguerre quadrature) and infinite intervals (Gauss–Hermite quadrature).
It can be shown (see Press, et al., or Stoer and Bulirsch) that the quadrature nodes xi are the roots of a polynomial belonging to a class of orthogonal polynomials (the class orthogonal with respect to a weighted inner-product). This is a key observation for computing Gauss quadrature nodes and weights.
View More On Wikipedia.org
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Homework Statement Evaluate the definite integral below numerically (between limits -1 and 1) using a couple of numerical methods, including Gauss-Legendre quadrature - and compare results. Homework Equations $$\int{(1-x^2)^\frac{1}{2}} dx$$ "Gauss quadrature yields the exact integral if φ...
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17. ### What is the Gaussian Quadrature?
I am not sure of the spelling, but I heard of the 'gaussian quadature' (or quadrature). It was spoken, and was in a mathematical equation. What the heck is it? | crawl-data/CC-MAIN-2024-22/segments/1715971059143.84/warc/CC-MAIN-20240528154421-20240528184421-00211.warc.gz | null |
The origin of Aboriginal peoples in Australia has been the subject of intense speculation since the nineteenth century. Until recently[when?], no theory of migration had gained wide acceptance. Genetic studies had shown the Aboriginal peoples to be related much more closely to each other than to any peoples outside Australia, but scholars had disagreed whether their closest kin outside Australia were certain South Asian groups or African groups. The latter would imply a migration pattern in which their ancestors passed through South Asia to Australia without intermingling genetically with other populations along the way. A 2009 genetic study in India found similarities among Indian archaic populations and Aboriginal people, indicating a Southern migration route, with expanding populations from Southeast Asia migrating to Indonesia and Australia.
In a genetic study in 2011, researchers found evidence, in DNA samples taken from strands of Aboriginal people's hair, that the ancestors of the Aboriginal population split off from the ancestors of the European and Asian populations between 62,000 and 75,000 years ago—roughly 24,000 years before the European and Asian populations split off from each other.
These Aboriginal ancestors migrated into South Asia and then into Australia, where they stayed, with the result that, outside of Africa, the Aboriginal peoples have occupied the same territory continuously longer than any other human populations. These findings suggest that modern Aboriginal peoples are the direct descendants of migrants to leave Africa up to 75,000 years ago. This finding is supported by earlier archaeological finds- of human remains near Lake Mungo that date to 45,000 years ago. The same genetic study of 2011 found evidence that Aboriginal peoples carry some of the genes associated with the Denisovan peoples of Asia; the study suggests that there is an increase in allele sharing between the Denisovans and the Aboriginal Australians genome compared to other Eurasians and Africans. Examining DNA from the finger, researchers from the Harvard Medical School in the US and the Max Planck Institute for Evolutionary Anthropology in Germany concluded that the Denisovans - a primitive group of humans descended from Neanderthals - migrated from Siberia to tropical parts of Asia. The researchers concluded that Denisovans interbred with modern humans in South-East Asia 44,000 years ago, before Australia separated from Papua New Guinea. They contributed DNA to Aborigines along with present-day New Guineans and an indigenous tribe in the Philippines known as Mamanwa. This study makes Aboriginal Australians one of the oldest living populations in the world and possibly the oldest outside of Africa, confirming they may also have the oldest continuous culture on the planet. The Papuans have more sharing alleles than Aboriginal peoples. The data suggest that modern and archaic humans interbred in Asia before the migration to Australia. | <urn:uuid:033568ff-3341-4e65-8f7e-35e7c253a085> | {
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# Use the remainder theorem to determine if the given number
Use the remainder theorem to determine if the given number c is a zero of the polynomial.
${x}^{4}+9{x}^{3}+22{x}^{2}+19x+45;c=-3$
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Step 1:Concept
According to remainder theorem, if we plug the given number -3 for x, and -f -3 is a zero, then the result should be 0.
Step 2:Solution
Plugging -3 for x
${\left(-3\right)}^{4}+9{\left(-3\right)}^{3}+22{\left(-3\right)}^{2}+19\left(-3\right)+45$
=81-243+198-57+45
$=24\ne 0$
So c=-3 is not a zero.
###### Did you like this example?
Annie Gonzalez
${x}^{4}+9{x}^{3}+22{x}^{2}+19x+45,c=-3$
By remainder theorem-
Replace x=-3,
So,
${\left(-3\right)}^{4}+9{\left(-3\right)}^{3}+22{\left(-3\right)}^{2}+19\left(-3\right)+45$
=81-243+198-57+45
=324-300
=24
By replace x=-3 in equation, we cannot get 0,
So, c=-3 is not a zero of the polynomial. | crawl-data/CC-MAIN-2022-49/segments/1669446711017.45/warc/CC-MAIN-20221205132617-20221205162617-00601.warc.gz | null |
Essays, articles and book excerpts on shakespeare's macbeth the metre of macbeth: blank verse and rhymed lines macbeth character introduction. Important questions about shakespeare's macbeth to use as essay ideas and topics for research papers. Macbeth study guide contains a biography of william shakespeare, literature essays, a complete e-text, quiz questions, major themes, characters, and a full summary. These essay topics will help students explore and understand the major themes and characters of macbeth these prompts will help students create.
The story of macbeth is about macbeth's ambitions for power, and how he will do anything to obtain that power. Nick miller period 3 macbeth exam essays due: 2-23-10 question #1 there are few literary works in today’s worldthat can truly be considered great. Get free homework help on william shakespeare's macbeth: play summary, scene summary and analysis and original text, quotes, essays, character analysis, and.
On this page you can learn about macbeth essay writing and download free macbeth essay example additionally find useful tips and structure suggestions. Macbeth - questions and answers 11 pages 2651 words january 2015 saved essays save your essays here so you can locate them quickly. Essays - largest database of quality sample essays and research papers on macbeth persuasive. Suggested essay topics and study questions for william shakespeare's macbeth perfect for students who have to write macbeth essays. Macbeth is a play full of dishonest deeds most of these deeds are brought up by power, hunger, and greed in the end these deeds led to mostly.
Macbeth and lady macbeth essay then, after murdering the king, macbeth comes to her with his hands all covered with blood and carrying the grooms' daggers. 301 moved permanently nginx/1103 (ubuntu. This free english literature essay on essay: macbeth is perfect for english literature students to use as an example. Read macbeth free essay and over 87,000 other research documents macbeth the witches of macbeth “if you had one shot, or one opportunity, to seize everything you.
Macbeth essay this essay macbeth essay and other 62,000+ term papers, college essay examples and free essays are available now on reviewessayscom. Macbeth essays are academic essays for citation these papers were written primarily by students and provide critical analysis of macbeth by william shakespeare. Improve your reasearch with over 3 pages of premium content about macbeth essay. Macbeth's character analysis essay essaysthroughout the play macbeth written by william shakespeare, macbeth shows himself to be a man of many sides macbeth displays. Read this english essay and over 87,000 other research documents macbeth “texts of integrity shift with time and place what was old can become new again.
Macbeth essay features samuel taylor colleridge's famous critique based on his influential shakespeare notes and lectures. Starting an essay on william shakespeare’s macbeth organize your thoughts and more at our handy-dandy shmoop writing lab. Macbeth - dozens of essays and reports on macbeth by william shakespeare. While the gravity of macbeth’s crimes cannot be overstated, he is a far more complex character than “this dead butcher”, as malcolm describes him in his closing. | <urn:uuid:db027881-59a3-4915-86ca-8ba988654a54> | {
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When mice that lack steroid receptor-2 (SRC-2) – a master regulator gene called a coactivator – fast for a day, their blood sugar levels plummet. If they go another day without food, they will die.
The severity of the hypoglycemia (low blood sugar) was unexpected, said Dr. Bert W. O'Malley, chair of molecular and cellular biology at Baylor College of Medicine and senior author of the report on the study that appears in the current issue of the journal Science. Normal mice live as long as seven days without food.
Further examination showed that the lack of SRC-2 prevents an important enzyme from converting sugar stored in the liver into a form that can go into the bloodstream. The finding has implications for a genetic disease called Von Gierke's disease and potentially adult-onset diabetes.
The symptoms suffered by mice resembled those of children born with Von Gierke's disease, said O'Malley. The disorder can create serious problems unless it is recognized early. Parents must wake the infants every few hours and feed them to keep their blood glucose levels up. As long as the glucose levels are high enough, the brain is nourished. If their blood glucose levels drop below a certain level, they suffer seizures, lose consciousness and can die.
Studies in O'Malley's laboratory in collaboration with researchers from Duke University Medical Center in Durham, N.C., revealed that SRC-2 works with an orphan nuclear receptor ROR alpha to affect the activity of the sugar-converting enzyme, glucose-6-phosphatase in the liver.
The liver produces 90 percent of the glucose circulating in the blood stream. Glucose stored in the liver has a phosphate molecular attached to it. This phosphorylated glucose cannot leave the liver until the enzyme removes the phosphate molecule. SRC-2 is critical to that removal process.
If the sugar cannot leave the liver, it remains there in the form of glycogen. Eventually, the buildup of this storage form of sugar can cause the liver to fail.
"It's one of the few examples of a metabolic genetic disease that can be created by a deficiency in a coactivator," O'Malley said.
He actually identified the first coactivator – SRC-1. His work with another called SRC-3 has led to better understanding of cancer and inflammation and led to the understanding of drugs such as tamoxifen in the treatment of breast cancer.
"This again shows that these coactivators are important master genes for physiology," said O'Malley. "In the case of SRC-3, if there is too much, you get cancer. Here, if you get too little SRC-2, you can't maintain your blood sugar levels."
He believes that potentially too much SRC-2 could raise the levels of glucose in the blood. That would call for increased production of insulin. Often, the pancreas fails after being forced to produce continuous, high levels of insulin. This can result in adult-onset diabetes.
O'Malley and his colleagues plan to start studying the activity in humans in the near future. Eventually, he hopes they can find ways to target the activity of SRC-2 with a drug.
Source: Baylor College of Medicine
Explore further: New guide to the genetic jungle of muscles can help health research | <urn:uuid:b89d8363-80b0-447d-be27-7938f177749f> | {
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# Equivalence Relations
## Definition of an Equivalence Relation
A binary relation on a non-empty set $$A$$ is said to be an equivalence relation if and only if the relation is
• reflexive
• symmetric, and
• transitive.
Two elements $$a$$ and $$b$$ related by an equivalent relation are called equivalent elements and generally denoted as $$a \sim b$$ or $$a\equiv b.$$ For an equivalence relation $$R$$, you can also see the following notations: $$a \sim_R b,$$ $$a \equiv_R b.$$
The equivalence relation is a key mathematical concept that generalizes the notion of equality. It provides a formal way for specifying whether or not two quantities are the same with respect to a given setting or an attribute.
## Examples of Equivalence Relations
### Equality Relation
The equality relation between real numbers or sets, denoted by $$=,$$ is the canonical example of an equivalence relation.
The equality relation $$R$$ on the set of real numbers is defined by
$R = \left\{ {\left( {a,b} \right) \mid a \in \mathbb{R}, b \in \mathbb{R}, a = b} \,\right\}.$
$$R$$ is reflexive since every real number equals itself: $$a = a.$$
$$R$$ is symmetric: if $$a = b$$ then $$b = a.$$
The relation $$R$$ is transitive: if $$a = b$$ and $$b = c,$$ then we get
$\left\{ \begin{array}{l} a = b\\ b = c \end{array} \right.,\;\; \Rightarrow a = b = c,\;\; \Rightarrow a = c.$
### Parity Relation
Two numbers are said to have the same parity if they are both even or both odd. Consider the set of integers and define a relation $$R:$$
$R = \left\{ {\left( {a,b} \right) \mid a \in \mathbb{Z}, b \in \mathbb{Z}, a \text{ and } b \text{ have the same parity}} \right\}.$
The parity relation $$R$$ is an equivalence relation.
$$R$$ is reflexive as, for any $$a \in \mathbb{Z},$$ the number $$a$$ has the same parity as itself: $$\left( {a,a} \right) \in R.$$
$$R$$ is symmetric. If $$\left( {a,b} \right) \in R,$$ and therefore both $$a$$ and $$b$$ have the same parity, then we can write $$\left( {b,a} \right) \in R.$$
The relation $$R$$ is transitive. If $$\left( {a,b} \right) \in R$$ and $$\left( {b,c} \right) \in R,$$ then all three numbers $$a, b,$$ and $$c$$ have the same parity, so $$\left( {a,c} \right) \in R.$$
### Congruence Modulo $$n$$
Let $$n$$ be a non-zero integer. The numbers $$a,b \in \mathbb{Z}$$ are said to be congruent modulo $$n$$ if $$n \mid \left( {a - b} \right),$$ that is $$n$$ divides $$\left( {a - b} \right).$$ This is written as
$a \equiv b \;\left( {\bmod n} \right).$
For example,
$7 \equiv 12 \;\left( {\bmod 5} \right).$
Congruence modulo $$n$$ is an equivalence relation. Let
$R = \left\{ {\left( {a,b} \right) \mid a \in \mathbb{Z}, b \in \mathbb{Z}, a \equiv b\;\left({\bmod n} \right)} \right\}.$
$$R$$ is reflexive since $$a - a = 0$$ is a multiple of any $$n.$$
$$R$$ is symmetric. If $$a \equiv b\;\left( {\bmod n}\right),$$ then $$a - b = n\cdot k,$$ where $$k$$ is an integer. Hence, $$b - a = n\cdot \left({-k}\right),$$ where $$-k$$ is also an integer. So we have $$b \equiv a\;\left( {\bmod n}\right).$$
The relation $$R$$ is transitive. Suppose that $$a \equiv b\;\left( \kern-2pt{\bmod n}\right)$$ and $$b \equiv c\;\left( \kern-2pt{\bmod n}\right).$$ We can write these equations as
$a - b = n \cdot k \;\text{ and }\;b - c = n \cdot \ell,$
where $$k, \ell$$ are some integers.
By adding these together, we have
$\left( {a - c} \right) = \left( {a - b} \right) + \left( {b - c} \right) = n \cdot k + n \cdot l = n\left( {k + l} \right).$
Since $$k$$ and $$\ell$$ are integers, then their sum $$k + \ell$$ is also an integer. It follows from here that $$a \equiv c\;\left({\bmod n}\right).$$ This proves the transitivity of $$R.$$
Note that congruence modulo $$n$$ for $$n = 2$$ is also called the parity relation considered above.
### Some Other Examples
The following relations are equivalence relations:
• "$$a$$ and $$b$$ live in the same city" on the set of all people;
• "$$a$$ and $$b$$ are the same age" on the set of all people;
• "$$a$$ and $$b$$ were born in the same month" on the set of all people;
• "$$a$$ and $$b$$ have the same remainder when divided by $$3$$" on the set of integers;
• "$$a$$ and $$b$$ have the same last digit" on the set of integers;
• Any relation that can be defined using expressions like “have the same” or “are the same” is an equivalence relation.
Any relation that can be defined using expressions like “have the same” or “are the same” is an equivalence relation.
• "$$a$$ and $$b$$ are parallel lines" on the set of all straight lines of a plane;
• "$$a$$ and $$b$$ are similar triangles" on the set of all triangles;
• Two functions $$f\left( x \right)$$ and $$g\left( x \right),$$ where $$x \in \mathbb{R},$$ are said to be equivalent as $$x \to {x_0},$$ if
$\lim\limits_{x \to {x_0}} \frac{{f\left( x \right)}}{{g\left( x \right)}} = 1,$
provided $${g\left( x \right)} \ne 0$$ at $$x = {x_0}.$$ For example, $$\sin x \sim x$$ as $$x \to 0.$$
## Equivalence Relation Closure
Let $$R$$ be an arbitrary binary relation on a non-empty set $$A.$$ To turn $$R$$ into an equivalence relation, we can take the reflexive, symmetric, and transitive closures of $$R.$$ This triple operation is denoted by $$tsr\left(R\right).$$
$$tsr\left(R\right)$$ is the the smallest equivalence relation that contains $$R.$$ The order of taking symmetric and transitive closures is essential. One can show, for example, that $$str\left(R\right)$$ need not be an equivalence relation.
The equivalence relation $$tsr\left(R\right)$$ can be calculated by the formula
$tsr\left( R \right) = t\left( {s\left( {r\left( R \right)} \right)} \right) = {\left( {R \cup I \cup {R^{ - 1}}} \right)^*},$
where the asterisk symbol denotes the connectivity relation. | crawl-data/CC-MAIN-2024-33/segments/1722640361431.2/warc/CC-MAIN-20240803060126-20240803090126-00705.warc.gz | null |
Deep-sea diving is primarily performed by professionals who are working underwater, such as welding oil rigging, or for scientific exploration. Recreational scuba diving is swimming to a depth up to 130 feet, and deep-sea diving is usually 130 feet down to 250 feet below the surface, when compressed air stops working effectively. Marine animals are a small but real threat to deep-sea divers, who typically have matters of bigger concern such as pressure, breathing and decompression issues.
Sharks don't feed on people typically, but as opportunistic feeders, they won't turn away an easy meal. They are often attracted to the scent of blood in the water or chemicals released by fish in distress, and they might sample a taste of a diver swimming near those scents. A deep-sea shark attack is rare, but because you must usually ascend slowly when diving deep, an attack can cause traumatic blood loss before you reach the safety of the surface.
Even thick wetsuits can't protect you from every stinging sea creature. You might happen upon some, such as jellyfish, and be unable to avoid their long tentacles. Others, like stonefish or venomous cone shells, you might brush against or pick up by accident. Most of these stings are painful but not deadly, especially when your suit or gloves take up part of the sting. However, some stings, such as a stingray or stonefish, can cause local paralysis and weakness that can affect your ascension to safety.
Sharks aren't the only sea creatures who bite. Fish nibbling at your toes are unlikely to cause any problems, but there are sea snakes and octopi that can. Sea snakes can be extremely poisonous, but they often can't inject poison into people because of the way their teeth are shaped. Even when no poison is injected, the bites can be deep and painful. Some octopus species, such as blue-ringed octopus, can also inject venom when they bite you with their center beak. The venom can paralyze you in minutes, but your wet suit might offer some protection.
Dangerous bites and stings from marine animals happen, but only rarely. A bigger danger for deep-sea divers is from equipment malfunction, since they rely completely on a breathing apparatus to provide air. General dangers from swimming under deep water pressure are also major concerns. Descending too rapidly can cause barotrauma, or damage to the inner ear, and ascending too quickly can lead to decompression sickness or a pulmonary embolism, both of which can be deadly. Divers who stay under the intense pressure of deep-sea water can suffer from nitrogen narcosis or oxygen toxicity. These conditions often lead to confusion and trouble seeing, but they can also be fatal.
- Photodisc/Photodisc/Getty Images | <urn:uuid:13cd9a1d-f059-4175-8132-76a720ab75bc> | {
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Today’s post comes from Meagan T. Frenzer, graduate research intern in the National Archives History Office in Washington, DC.
On June 20, 1782, the Confederation Congress approved and finalized the first Great Seal of the United States.
The First Continental Congress in 1776 originally commissioned Benjamin Franklin, Thomas Jefferson, and John Adams to create a national seal. As members of the First Great Seal Committee, these Founding Fathers intended to design a national emblem that reflected the independence and aspirations of the new nation.
This was no easy task. It took more than three committees and six years of congressional debate to complete the Great Seal.
It was Secretary of the Continental Congress, Charles Thomson, who submitted the final design for the Great Seal 233 years ago. Thomson’s design combined elements of submissions presented to the prior committees. His uncluttered, symbolic design fulfilled Congress’s expectations.
The face side of Thomson’s seal, also known as the “observe” side, displays a bald eagle with wings spread. The eagle clutches a bundle of 13 arrows (representing the 13 colonies) in its left talon and an olive branch in its right talon. Together, the items in the eagle’s talons stand for war and peace.
The eagle’s beak holds a banner that reads E pluribus unum. The Latin phrase roughly translates as “Out of many, one,” describing the formation of a single nation from 13 colonies.
On the eagle’s breast is a shield with 13 red and white stripes below a blue chief, or the upper region of the shield. The red and white chevrons stand for valor and purity, while the blue represents vigilance, perseverance, and justice.
A cloud floats above the eagle’s head and surrounds 13 stars forming a constellation. The formation of this constellation alludes again to the formation of the new nation.
The “reserve,” or back side, of the Great Seal contains a 13-step pyramid representing strength, while the Eye of Providence sits above the pyramid within a triangle. The year 1776 in Roman numerals rests at the base of the pyramid.
Inscribed above the Eye is the Latin motto, Annuit Coeptis, meaning “He [God] has favored our undertakings.” The inscription characterizes the favorable circumstances that bolstered the American cause for independence.
The scroll below the pyramid reads, Novus Ordo Seclorum, which is Latin for “A New Order of the Ages.” This phrase represents the beginnings of a new era for the United States.
The National Archives holds the first design of Thomson’s “observe” side, which features red and white chevrons as opposed to the vertical stripes used in the final design.
Additionally, the National Archives holds seal designs by Francis Hopkinson, signer of the Declaration of Independence and designer of the American flag.
As a participant of the Second Great Seal Committee, Hopkinson’s work inspired the addition of the 13 stripes on the shield, 13 stars, and an olive branch in Thomson’s final designs.
The first engraved metal die of the Great Seal, based on Thomson’s design, was used from September 1782 to 1841. The National Archives holds the first die, along with other seal dies used from 1841 to 1909. Thomson had designed the reverse in case Congress wanted to impress the back surfaces of wax pendant seals but a die for the reserve was never cut.
Two hundred and thirty-three years later, the Great Seal of the United States still reflects the traits and principles that the government aims to uphold. | <urn:uuid:0884fba3-18ad-4a41-95b6-c670787c57ba> | {
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Structurally, outcomes are obligations. You need outcomes for your course syllabus, and your program as whole has some form of outcomes. From a teaching and learning perspective, however, an outcome is much more than just a hoop. It’s at heart of why you’d bother to teach the course you do. Each outcome (and you don’t need that many), describes a skill, disposition, or set of complex knowledge that it is essential for your students to demonstrate to be successful in the course.
What does a good outcome look like?
You can read more about definitions of outcomes (what a student will do) and objectives (what an educator will teach) in another post from Gwenna Moss, but sometimes good examples can help clarify a definition. A good outcome satisfies key criteria, including:
- It starts with a specific, rigorous verb that reflects the type of thinking, attitude, or understanding you need students to demonstrate
- Each outcome is worthy enough that you’ll spend a good chunk of the course returning to it and building your students’ strength with it
- The outcome is written in language students understand and can explain in their own words
A bad outcome: Understand the definition of a just society
This outcomes is not good because there are too many ways the word “understand” could be interpreted. What would be good evidence of an outcome should be easy for students to understand the same way. Also, this outcome might be able to be satisfied with a definition from the professor’s PowerPoint, so it isn’t worthy and long lasting enough. It is easy to make the mistake of basically describing content in your outcome, rather than what your students will demonstrate.
A much better outcome: Justify arguments about social justice using precise, accurate examples.
This is better because it specifies the type of thinking and skills student will need to do (justify an argument) and at how (using precise, accurate examples). Social justice is a complex concept that the course will spend a long time on, deepening student conceptual knowledge overtime. Also, the skill of building an argument about social justice will built upon many multiple times in the course, sometimes in class discussions, sometime in an essay, and sometimes in an examination. A student reads the outcome and knows the course will help you refine your skills in building arguments, and that the content will relate to social justice.
How do I write good outcomes?
- List the key concepts, skills, and dispositions/attitudes you’ll want in the course. Check to ensure you aren’t just listing content.
- Group related things together until you have a smaller number of bigger things.
- Try writing statements describing things you’d accept as evidence that a student actually had the understanding, skill, or disposition you are trying to teach
- Look at the statements you’ve written, and ensure they each start with an active, specific verb. Try using this list to ensure you are asking for rigorous thinking, not something students can just memorize and forget.
- Get someone who is not an expert to read each outcome and tell you what it says, just to make sure it is clear enough
- Double check that each outcome represents something you’ll want to see from students multiple times in the class. If you wouldn’t want to grade things related to it more than once, it is not important enough to be an outcome. | <urn:uuid:fa7ec75b-9915-4136-a71c-b8cda444e113> | {
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# Find the smallest positive integer $\ell$ such that $3 \cdot \left(4^m + 1\right)$ divides $2^\ell-1$
Find the smallest positive integer $$\ell$$ such that $$3 \cdot \left(4^m + 1\right)$$ divides $$2^\ell-1$$
Hint: The sought $$\ell$$ is the multiplicative order of $$2$$ in the ring of integer residues modulo $$3\cdot(4^m+1)$$.
I am having trouble understanding the hint, are there any "special" characteristics of a ring of integer that might help me?
The answer is supposed to be $$4m$$ , and I have already managed to show that $$3 \cdot \left(4^m + 1\right)$$ divides $$2^{4m}-1$$ , but I do not know how to prove that this is the smallest positive solution.
• Thanks for the well-asked question! The divisibility you've already established shows that the order must at least divide $4m$. Is it possible for $3(4^m+1)$ to divide $2^\ell-1$ if $\ell\le 2m$? – Greg Martin Jan 15 at 20:15
• 3(4^m+1)>4^m=2^(2m) , so that mean that 3(4^m+1) can not divide 2^ℓ-1 if ℓ is smaller then 2m , but i still do know how to show that there is no other ℓ between 2m to 4m – user635073 Jan 15 at 21:09
• Do you know the following fact? If $a$ divides $2^\ell-1$, then the multiplicative order of $2$ in the ring of integer residues modulo $a$ divides $\ell$. (The point to emphasize here is that the order must not only be at most $\ell$ but must actually divide $\ell$.) – Greg Martin Jan 16 at 4:45
I may have done this a different way than from suggested in your hint OP.
Claim: $$2^{2m}+1 =4^m+1$$ does not divide $$2^{\ell}-1$$ for $$\ell < 4m$$.
Proof: $$(2^{\ell-2m}-1)(2^{2m}+1) = 2^{\ell}+2^{\ell-2m}-2^{2m}-1 < 2^{\ell}-1$$ if $$\ell$$ satisfies the inequality $$\ell -2m < 2m$$ or equivalently if $$\ell$$ satisfies the inequality $$\ell < 4m$$. On the other hand $$2^{\ell-2m} (2^{2m}+1) > 2^{\ell}-1$$. [Do you see how this implies that $$2^{2m}+1$$ indeed does not divide $$2^{\ell}-1$$? For some integer $$a$$, the integer $$a(2^{2m}+1)$$ is strictly less than $$2^{\ell}-1$$ yet the integer $$(a+1)(2^{2m}+1)$$ is strictly greater than $$2^{\ell}-1$$.]
So $$\ell$$ as in your problem must be at least $$4m$$.
However, $$\ell=4m$$ works; indeed
$$2^{4m}-1 = (2^{2m}-1)(2^{2m}+1) = (2^{2m}-1)(4^m+1).$$
So now it remains to show that $$3|(2^{4m}-1)$$. However, note that $$3|(2^{2m}-1)$$ for every integer $$m$$ [make sure you see why], so $$\ell=4m$$ indeed works; $$3\times(2^{2m}+1)$$ divides $$(2^{4m}-1)$$.
The ring of integers in the hint can be decomposed by the CRT into the product of $$A=\Bbb{Z}_3$$ by $$B=\Bbb{Z}_{4^m+1}$$. The order of 2 in each of these two rings is respectively 2 (because in $$A$$, $$2^2=1$$), and $$4m$$ (because in $$B$$, $$2^{2m}=-1$$) . Hence the order in the product is $$\operatorname{LCM}(2,4m)=4m$$.
• This answer does not prove the assertion that the order modulo $B$ equals $4m$. – Greg Martin Jan 16 at 4:46
• If we have in B, the equality x^s=-1that certainly shows the order of x divides 2s and cannot be s, nor a divisor of s. So it has to be 2s. – Patrick Sole Jan 16 at 13:38 | crawl-data/CC-MAIN-2019-30/segments/1563195525500.21/warc/CC-MAIN-20190718042531-20190718064531-00030.warc.gz | null |
# Best tricks to learn Table of 17 up to 20 times with pdf | 17 Ka Table
If you want to learn tables especially 17 ka table then you are reading the right article because we will teach you the tables in easy words step by step from the beginning in sha Allaah
Table of 17 should be learned by everyone because we use it in almost all types of calculations, whether it is to solve maths questions or daily calculations.
For example, suppose if a person buys 5 packets of household goods for Rs 17, then he can easily calculate that he has to give Rs 85 to the shopkeeper because (17 × 5 = 85) there are many other places like this. We can use the Table of 17 to make the calculation easier.
## Multiplication table of 17 | 17 Ka Table
Now we will try to learn the table of 17 by all those major methods which are as follows –
• 17 Ka Table in Math – Multiplication Method
• 17 Ka Table In Words – हिंदी में ( देवनागरी ) Method
• Hindi Numbers Multiplication method
• By English Method
### 17 Ka Table in Math – Multiplication Method
First of all we talk about Multiplication method that it is used in learning most of the tables, in this the tables are learned by multiplying the numbers respectively, so it is considered to be the most popular.
### 17 Ka Table In words – हिंदी में ( देवनागरी ) Method
अब हम इसे उन लोगो के लिए 17 का पहाड़ा सिखाने कि कोशिश करेंगे जिन्हे देवनागरी हिंदी अच्छे से आती हो अंग्रेजी उन्हें कम या बिलकुल नहीं आती हो वो भी इसे सीख सके।
### Hindi Numbers Multiplication method
Below we will learn 17’s table in Hindi numerals
### By English method
Below we learn the table of 17 in English
#### Tricks to Learn 17 Times Table
• If you know the table of 16, then you can easily learn the table of 17, just in the number you get from the table of 16, respectively 1,2,3,4,5…. or the number by which you want to multiply it. will add like-
• 16×1=16+1=17 ( 17×1=17 ), 16×2=32+2=34 ( 17×2=34 ), 16×3=48+3=51 ( 17×3=51 ) , 16×4=64+4=68 ( 17×4=68 )………
• The easiest way to learn and memorize it is to practice it by writing with speaking.
#### 17 Ka Table example
```There are 20 labours working in a factory , if 17 - 17 task are given to all of them, then how many task will be needed in total?
Answer- 340 because there are 17 × 20 = 340 which we learned above
Solve it and tell in the comment ️
40 people work in an office, if a person takes 17 rupees in the office, then tell how much money will be received by 5 people in total?```
#### What did we learn?
Table of 17 | Multiplication of 17 | 17 ka pahada | 17 का पहाड़ा | Multiplication of ten | 17 Times table | 17 table in Hindi | 17 table in English | 17 का पहाड़ा इंग्लिश में | 17 ka pahada photo | 17 Ka pahada 20 tak | 12 13 14 15 16 17 ka Pahada | 17 Ka Pahada English mein | 13 14 15 16 17 ka Pahada Hindi mein | 12 13 14 15 16 17 ka table | English mein 17 ka table | 17 ka Table 20 tak | 16 aur 17 ka table bataen
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##### FAQ – 17 ka Table
17 का पहाड़ा कैसे याद करें?
17 का पहाड़ा याद करने के लिए सबसे पहले तो आपको शुरुआत से स्टेप बाई स्टेप पहाड़े सीखने जिससे आपको 17 का पहाड़ा जल्दी याद हो जायेगा दूसरा यह कि आप इसका बोलते हुए लिखकर अभ्यास करे तब तक करे जब तक आपको यह याद न हो जाए
14 पंजे कितने होते हैं?
14 पंजे सत्तर ( 70 ) होते हैं- ( 14×5= 70 )
17 का पहाड़ा कैसे लिखें?
17 × 1 = 17
17 × 2 = 34
17 × 3 = 51
17 × 4 = 68
17 × 5 = 85
17 × 6 = 102
17 × 7 = 119
17 × 8 = 136
17 × 9 = 153
17 × 10 = 170
18 का पहाड़ा कैसे लिखें?
18 × 1 = 18
18 × 2 = 36
18 × 3 = 54
18 × 4 = 72
18 × 5 = 90
18 × 6 = 108
18 × 7 = 126
18 × 8 = 144
18 × 9 = 162
18 × 10 = 180
16 का पहाड़ा कैसे लिखें?
16 × 1 = 16
16 × 2 = 32
16 × 3 = 48
16 × 4 = 64
16 × 5 = 80
16 × 6 = 96
16 × 7 = 112
16 × 8 = 128
16 × 9 = 144
16 × 10 = 160
19 का पहाड़ा याद कैसे करें?
19 का पहाड़ा का याद करने के लिए सबसे पहले तो आपको शुरुआत से स्टेप बाई स्टेप पहाड़े सीखने जिससे आपको 19 का पहाड़ा जल्दी याद हो जायेगा दूसरा यह कि आप इसका बोलते हुए लिखकर अभ्यास करे तब तक करे जब तक आपको यह याद न हो जाए
#### Final words as Conclusion
Tables make calculations easy, whether addition, remainder, multiplication or division, you can easily do accurate and fast calculations with the help of tables, so today we learned 17 ka table and it is very easy.
In this series to teach tables, we have started with 2 ka tables, so you should try to learn the tables step by step from the beginning so that you can learn all the tables easily.
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Educational Articles | crawl-data/CC-MAIN-2024-18/segments/1712296817222.1/warc/CC-MAIN-20240418160034-20240418190034-00538.warc.gz | null |
WELLINGTON, Oct. 7 (Xinhua) -- New Zealand scientists are leading an international study to compare samples of volcanic sediment collected by NASA's Mars rover Curiosity with volcanic sites on Earth to help determine whether Mars was ever capable of supporting life.
The team led by scientists at the University of Auckland was using a new model to compare and detect whether volcanic eruptions on Earth and Mars interacted with water.
"This is the volcanic approach to searching for water on Mars and although the technique itself is not new, applying it to discovering volcanic eruption styles from other planets is entirely new," senior lecturer in geology and study leader Dr Michael Rowe said in a statement Tuesday.
Curiosity was the first in the rover series to carry a portable x-ray diffractometer, which analyses the structure of crystals, and early comparisons suggested Martian sediments were derived from relatively dry volcanic eruptions.
But Curiosity was currently climbing the red planet's Mount Sharp, which contained a detailed record of the surface of Mars and could yield interesting results.
Thirty different samples from volcanic fields on Earth at 10 different sites have been collected for the study by the team, which included scientists from the United States, Switzerland, Canada and New Zealand.
"The characteristics of eruptions that have occurred on Mars may have been quite different to those on Earth due to the difference in atmospheric pressure and gravity," Rowe said.
"But by understanding the relative timing of interaction between water and magma rising to the surface on Mars, we will better understand when water was present at or near the Martian surface and therefore when the environment may have been hospitable toward life." | <urn:uuid:e4c654ce-a69f-46a1-8904-a475f2f1f0a8> | {
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Mistaken identity is probably responsible for the myth that some snakes can magically break apart and reconnect the pieces like a puzzle. It's physically impossible for any snake to do so and live, but another type of reptile comes close. Lizards are able to cast off body parts when under attack then regrow them. This ability is called "regeneration." One species of lizard has a long, snakelike body and no legs. These lizards are commonly called "glass snakes" or "joint snakes," even though they are not snakes at all. Misidentification mixed with imagination is at the root of this story.
Snakes vs. Lizards
Nearly 3,000 species of snakes are known. All are carnivorous, but only 375 types kill their prey with venom. About 80 types of legless lizards have been identified. Snakes and legless lizards do have some things in common. Both reptiles have long, cylindrical bodies without legs. Their skins are completely covered with overlapping scales, they have forked tongues and they lay eggs. Sometimes they are found together in the same environment and might feed on similar prey. But they are also very different.
Snakes and lizards belong to the reptile class known as "squamata," which means "to have scales." Scales protect a reptile's skin from damage. Snakes have specialized belly scales and muscles that allow them to push their bodies along the ground in a fluid motion. Legless lizards don't have these scales or muscles and so can only use their side muscles to move in a jerky swinging motion. Snakes have developed clear scales that cover their eyes but have no eyelids or ears. Lizards have movable eyelids that let them blink, and they have ear holes.
A snake's skeleton is unique for its hinged jaw that allows it to eat prey much larger than its head. It doesn't have a breastbone, which allows the food to pass through its long digestive system more easily, and its ribs and spine are linked together like a chain. A break in this skeletal chain would severely disable the snake and probably kill it because its vital organs span nearly the full length of its body. And snakes can't regenerate body parts. Legless lizards don't have hinged jaws, so they prefer smaller prey. They have perforations along their spinal bones that allow them to cast off parts of their tail when they are attacked. All of their important organs are located in the front third of their body, so losing their tail doesn't disable them. They can regrow their tail only once in a lifetime, but the new one won't have a spine. Legless lizards have received the nicknames "glass snake" and "joint snake" because their tails often break into multiple sections.
A snake's nervous system is somewhat primitive and can continue to function for up to nine hours after death. This is the reason a snake's body may continue to twitch for a while even without a head and why the bodiless head of a venomous snake can bite. Lizards have a similar nervous system. The dropped tail of a legless lizard will wriggle wildly in order to distract a threat while the lizard escapes. The separated pieces of snakes and lizards may seem to be alive but they will eventually stop moving and die because their blood supply is cut. It's impossible for cut vessels and organs and nerves to reattach or realign on their own. | <urn:uuid:682724bc-71b0-4b28-8120-731e91519b74> | {
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Book by Michael Matthews explores the early history of railroads in Mexico
In “The Civilizing Machine: A Cultural History of Mexican Railroads, 1876-1910,” Elon University Assistant Professor Michael Matthews shows how railroads shaped the way citizens of the young republic viewed industrialization, technology & modernization as they struggled to form their national identity.
Mexico had a tough time finding its place in the modern world shortly after declaring its independence nearly two centuries ago. Social instability and political conflicts, the heavy influence of European superpowers, and the inability to stave off an American invasion in 1846 brought the republic to the brink of disintegration on multiple occasions.
That changed when Gen. Porfirio Díaz led army troops in a successful 1876 coup that would make him the president of Mexico for much of the next four decades. Díaz quelled the political infighting threatening his country’s stability and attracted investors to a nation that would soon build an economy largely on the development of its railroads.
The thousands of kilometers of track laid during Díaz’s reign opened the interior of his country to overseas markets that purchased agricultural goods and minerals mined from Mexico’s mountains. The railroads also permitted the movement of people. Migrant workers traveled by train across a terrain that until then limited mobility for citizens.
Railroads, however, weren’t without their critics. Most were foreign-owned and operated, and their reputation for poor safety soured their image among large numbers of the poor and working class. For Díaz’s opponents, and for those who bore the brunt of the railroads’ negative side effects, the locomotive came to symbolize something else entirely: death, destruction and disorder.
The tension between proponents and critics of railroads emerged in art, poetry, literature and music, but until now those cultural expressions have never been studied. Elon University Assistant Professor Michael Matthews explores such depictions in his first book, “The Civilizing Machine: A Cultural History of Mexican Railroads, 1876-1910,” published this fall by the University of Nebraska Press as part of its “The Mexican Experience” series.
“It’s a history of ideas, culture, how people interact, and what modernization and civilization meant to different social groups,” Matthews said of his book, based on his doctoral dissertation from the University of Arizona.
In addition to their economic benefits, railroads helped Mexico citizens develop a national identity in a place that was geographically diverse and where illiteracy was rampant. And, ironically, railroads came to represent the economic divide that led in part to another Mexican revolution in 1910 that swept Díaz from power.
“Matthews’s study is timely … with lively account and interesting analysis,” James Garza, an associate professor of history and ethnic studies at the University of Nebraska-Lincoln, said in his cover endorsement of the book.
Matthews’s interest in Mexican railroads developed as he studied for his master’s degree at Simon Fraser University. While researching his thesis, Matthews observed how the social history of railroads had been largely ignored, though trains took a prominent place in the music, poetry, artwork and news of the time.
“The Civilizing Machine” is the end result of that observation. Matthews said he is especially proud of the book’s inclusion in a series that sparked his interest in history as an undergraduate. “I hope I can affect a young 18- or 19-year-old at a university the same way,” he said.
Since joining the Elon faculty in 2008, Matthews - who grew up in Canada, Spain and Peru - has taught courses in colonial and modern Latin America, Mexican history, and the world in the 20th century. He is the recipient of two Elon Faculty Research and Development grants and one of the university’s 2009 Hultquist Awards, which assist new faculty in their research development.
He today serves as the coordinator of the Latin American Studies program.
Prior to entering academia, Matthews worked as an editorial assistant at the International History Review Journal. He is currently working on an edited volume that explores the role of poetry and music in modern Mexico as he explores how marginalized groups used song, verses, poetry, and more to challenge and subvert the ideological assumptions expressed by elite groups. | <urn:uuid:0fc39340-5560-4fe3-9f08-79d3c5f1edcb> | {
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# In a group of 120 people one-fifth are men one-fourth are…
Are you looking for correct answer of In a group of 120 people one-fifth are men one-fourth are…? Here we have shared detailed answer with explanations.
### In a group of 120 people, one-fifth are men, one-fourth are women and the rest children. The average age of women is five-sixth of the average age of men. Average age of children is one-fourth of the average age of men. If average age of men is 60 years, what is the average age of the group?
1. A. 32.75 yeras
2. B. 38.45 years
3. C. 45.25 years
4. D. 50.5 years
Here is complete explanation of In a group of 120 people one-fifth are men one-fourth are….
### Solution(By ExamCraze Team)
Number of men
= \$\$frac{1}{5}\$\$ × 120
= 24
Number of women
= \$\$frac{1}{4}\$\$ × 120
= 30
Number of children
= 120 - (24 + 30)
= 66
Average age of men = 60 years
Average age of children
= \$\$frac{1}{4}\$\$ × 60
= 15 years
Average age of women
= \$\$frac{5}{6}\$\$ × 60
= 50 years
∴ Avarage age of the group
\$\$eqalign{ & = left( {frac{{60 times 24 + 50 times 30 + 15 times 66}}{{120}}} right){text{ years}} cr & = left( {frac{{3930}}{{120}}} right){text{ years}} cr & = 32.75{text{ years}} cr} \$\$ | crawl-data/CC-MAIN-2023-06/segments/1674764499695.59/warc/CC-MAIN-20230128220716-20230129010716-00654.warc.gz | null |
Until 1998 the Colorado regularly flowed south along the Arizona-California border into a Mexican delta, irrigating farmlands and enriching a wealth of wildlife and flora before emptying into the Gulf of California.
But decades of population growth, climate change and damming in the American Southwest have now desiccated the river in its lowest reaches, turning a once-lush Mexican delta into a desert. The river’s demise began with the 1922 Colorado River Compact, a deal by seven western states to divide up its water. Eventually, Mexico was allotted just 10 percent of the flow.
Officials from Mexico and the United States are now talking about ways to increase the flow into the delta. With luck, someday it may reach the sea again.
It is paradoxical that the Colorado stopped running consistently through the delta at the end of the 20th century, which — according to tree-ring records — was one of the basin’s wettest centuries in 1,200 years. Now dozens of animal species are endangered; the culture of the native Cocopah (the People of the River) has been devastated; the fishing industry, once sustained by shrimp and other creatures that depend on a mixture of seawater and freshwater, has withered. In place of delta tourism, the economy of the upper Gulf of California hinges on drug smuggling operations that run opposite to the dying river. | <urn:uuid:c20408c9-28ca-4f0a-b561-0a8f3693137e> | {
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# Hot Dots® Word Problem Flash Cards Set - Grades 4-6
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# Hot Dots® Word Problem Flash Cards Set - Grades 4-6
Product Number: TB24949
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With the power of Hot Dots® technology, ordinary flash cards are transformed into individualized basic skills tutors. Use like regular flash cards, or add the Hot Dots® pen and students can drill independently with Hot Dots® instant reinforcement! Students touch the pen on the correct answer and get a positive response. The plastic storage case also makes these great send-home helpers.
CCSS Product Alignment
4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another, write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
Brand : Educational Insights Item Weight : 1.50 Manufacturer Part Number : 2766 Prop 65 :
## QUICK-TIP GUIDE
Your guide to an exceptional shopping experience. | crawl-data/CC-MAIN-2018-39/segments/1537267156252.62/warc/CC-MAIN-20180919161420-20180919181420-00327.warc.gz | null |
Learn something new every day More Info... by email
A donkey's tail, also known as a burro's tail or Sedum morganianum, is a plant with bud-like leaves along either side of a long stem. It can have bright pink or red flowers at the tips of these stalks. It grows well in warm climates and is thought to be native to Mexico and Honduras.
The leaves of a burro's tail somewhat resemble white grapes. The foliage may be light or dark green in color. It is normally very soft and smooth to the touch. The leaf stems are usually around two to four feet (.6 to 1.2 m) long, and often cascade downward. These features can make this plant a good choice for growing in a hanging basket.
Bright-colored flowers sometimes appear at the ends of the long, trailing stems. These blossoms are terminal, which means they stop the plant from growing any further while they are open. The timing of the blooms can be very unpredictable. Some plants may flower once or twice a year, while others do not bloom at all. Even so, blossoms are more likely to appear in spring or summer than during the fall or winter months.
A donkey's tail is considered to be a succulent plant, or one that retains water. This can contribute to the somewhat puffy appearance of this variety's leaves. It also helps this species to grow in hot, dry climates that may receive very little rainfall.
Although it is believed to have originated in Mexico or Honduras, it is often grown as a houseplant in many parts of the world. It can also be planted outdoors in warm areas of the United States, such as California or Florida. It should be placed in direct sunlight, if possible, but can sometimes tolerate being partially shaded.
This plant can occasionally cause an allergic reaction when it comes in contact with a person's skin. This can be especially true if the leaves of the plant are broken open. For this reason, it is often a good idea to wear latex gloves and a long-sleeved shirt when transplanting or cutting a donkey's tail. Growers may also want to leave the flowers intact rather than cutting them for a floral arrangement.
A donkey's tail is perennial, which means it has a lifespan of several years. Many gardeners find this plant to be hardy and easy to care for as long as it is protected from frost. It can be an interesting plant to decorate an office, patio, or sun room.
One of our editors will review your suggestion and make changes if warranted. Note that depending on the number of suggestions we receive, this can take anywhere from a few hours to a few days. Thank you for helping to improve wiseGEEK! | <urn:uuid:e2cc3b8f-2f53-47ec-94be-2245989febcc> | {
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# How do you simplify the expression cos^2x/(1+sinx)?
$1 - \sin x$
${\cos}^{2} \frac{x}{1 + \sin x} = \frac{1 - {\sin}^{2} x}{1 + \sin x} = \frac{\left(1 - \sin x\right) \left(1 + \sin x\right)}{1 + \sin x}$
Now we proceed to cancell $\left(1 + \sin x\right)$ in both numerator and denominator because they configure a so called avoidable discontinuity. So
${\cos}^{2} \frac{x}{1 + \sin x} = 1 - \sin x$ | crawl-data/CC-MAIN-2024-18/segments/1712296819971.86/warc/CC-MAIN-20240424205851-20240424235851-00196.warc.gz | null |
Definition of Diastole
Diastole: The time period when the heart is in a state of relaxation and dilatation (expansion).
The final letter in "diastole" is pronounced as a long "e" as in "lee." The adjective for diastole is diastolic.
The diastolic pressure is specifically the minimum arterial pressure during relaxation and dilatation of the ventricles of the heart. Diastole is the time when the ventricles fill with blood.
In a blood pressure reading, the diastolic pressure is typically the second number recorded. For example, with a blood pressure of 120/80 ("120 over 80"), the diastolic pressure is 80. By "80" is meant 80 mm Hg (millimeters of mercury).
A diastolic murmur is a heart murmur heard during diastole, the time the heart relaxes.
"Diastole" came without change from the Greek diastole meaning "a drawing apart." The term has been in use since the 16th century to denote the period of relaxation of the heart muscle.
Last Editorial Review: 6/14/2012
Back to MedTerms online medical dictionary A-Z List
Need help identifying pills and medications? | <urn:uuid:9a7ced35-a83e-490e-9ec0-0c39a55ae095> | {
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Sea Change for Sea Turtles
Sea turtles nesting in the southeastern United States are recovering, but the ancient reptiles still face formidable threats.
- Doreen Cubie
- Jul 28, 2014
BEFORE AN AUDIENCE OF MORE THAN 300 PEOPLE, a half-grown loggerhead turtle named Portsmouth scooted down a beach in Sandbridge, Virginia, near the mouth of the Chesapeake Bay. The platter-sized, brown-and-white-speckled animal had been nursed back to health at Baltimore’s National Aquarium after swallowing two fishhooks and was wasting no time hustling back to freedom. Not long after Portsmouth slipped into the sea, researchers began tracking the young turtle’s movements with the aid of a satellite transmitter they had attached to its shell. “We’re trying to learn more about where loggerheads forage in the Chesapeake,” says Gwen Lockhart, a Virginia Aquarium and Marine Science Center geographic information system specialist who is following Portsmouth and a number of other loggerheads. “We also hope to better understand turtle migration patterns in and out of the bay.”
One thing scientists already know is that the Chesapeake Bay is one of the most significant North American nurseries for juvenile sea turtles. “It is very important developmental habitat for both loggerhead and Kemp’s ridley turtles,” says Kate Mansfield, who did her doctoral research in the Chesapeake and is now an assistant professor with the University of Central Florida’s Marine Turtle Research Group. The exact number of sea turtles in the bay is not known, but the Virginia Aquarium’s preliminary estimates show that between 7,000 and 10,000 individual turtles spend the summer months there feeding on whelk, blue crabs, hermit crabs and other prey.
Although green, leatherback and hawksbill turtles also have been documented in the Chesapeake, the vast majority are juvenile loggerheads like Portsmouth. One of the world’s seven sea turtle species, the loggerhead can weigh up to 450 pounds and grow a 44-inch-long shell. Named for their big heads, these reptiles’ powerful jaws evolved to crunch and consume hard-shelled prey such as mollusks and horseshoe crabs. The species ranges throughout the Atlantic, Indian and Pacific Oceans as well as the Mediterranean Sea. But the world’s largest concentration of nesting loggerheads is found on beaches of the southeastern United States, where more and more females are coming ashore each summer to lay their eggs.
“It’s pretty thrilling,” says Mark Dodd, a biologist for the Georgia Department of Natural Resources and the state’s sea turtle program coordinator who has seen nesting loggerheads in his state hit new highs for four years straight. “We think we’re seeing the beginning of a real trend.”
Turtles on the Rebound
Loggerheads are not the only sea turtle species on the rebound. For green turtles (above), the story is even more remarkable. “They’re one of the greatest success stories in North American conservation,” says Llewellyn Ehrhart, a University of Central Florida professor emeritus who has studied green turtles since the 1970s. Like loggerheads, greens are found worldwide, but in the continental United States they nest primarily in Florida. Fifty years ago, renowned biologist Archie Carr, who almost single-handedly brought the plight of declining sea turtles to the world’s attention, estimated no more than 50 green turtle nests (laid by just five to eight individual turtles) were in the state. Even by 1989, the Florida Fish and Wildlife Conservation Commission located only 464 nests on the 26 Florida beaches it surveys each year. But by 2013, those same beaches hosted an amazing 25,553 nests. “It’s a miracle,” Ehrhart says.
Kemp’s ridleys (below), the rarest of all sea turtles, are bouncing back as well. Only 702 nests were tallied on their Tamaulipas, Mexico, nesting beaches in 1985. By 2012, there were nearly 22,000 nests, though that number dropped off to slightly more than 16,000 in 2013. Some Kemp’s ridleys also have begun nesting along the Texas coast, where the number of nests climbed from just six in 1996 to 209 in 2012. “Leatherback turtles are also doing quite well in the southeastern U.S.,” Ehrhart says. The largest of all sea turtles, these massive reptiles can weigh as much as 1,200 pounds.
Ehrhart, Dodd and other biologists believe the U.S. Endangered Species Act (ESA) has been key to the sea turtle resurgence. Once turtles were given protection under the act in the 1970s, it became illegal to catch them, sell their meat or collect their eggs. “Protection from mortality under the Endangered Species Act was a huge first step,” Dodd says.
Other simple but effective measures—such as turning down lights on nesting beaches—might not have happened without the act. Baby turtles hatch during the night and instinctively head for the brightest spot on the horizon, which historically had been the ocean. But as shorelines developed, street lamps and brightly lit buildings began to overwhelm the glow from the sea, and hatchlings often headed inland where they were crushed by cars or baked in the hot sun. Once sea turtles gained ESA protection, many coastal communities in the Southeast enacted laws eliminating or reducing beachfront lighting. “These local lighting ordinances have played a huge role in protecting sea turtles,” says Ann Marie Lauritsen, Southeast sea turtle coordinator for the U.S. Fish and Wildlife Service.
Fish and shrimp nets also used to trap and kill thousands of turtles a year off the U.S. coast. (Sea turtles must surface to breathe or they will drown.) After a long effort by NWF and other conservation groups, turtle excluder devices (TEDs)—which provide turtles an escape route if they are caught by shrimp nets—became mandatory in U.S. waters in 1993. The number of dead loggerhead and Kemp’s ridley turtles washing ashore dropped immediately and dramatically. Green turtles, which inhabit shallower water and feed primarily in seagrass beds, benefited significantly from a 1994 statewide ban on gill nets in Florida.
New Threats to Sea Turtles
“We’ll never know which conservation measure was responsible for the turnaround,” Dodd says. “It was probably all of them.” But he cautions that sea turtles are not yet out of the woods, and the list of threats remains long. Beachfront development is taking away nesting habitat. Longline fishing in the open ocean hooks and drowns many turtles. Climate change and sea-level rise lurk on the horizon. And oil spills such as the 2010 Deepwater Horizon disaster in the Gulf of Mexico are deadly to turtles.
Water pollution is also a problem, especially in estuaries like the Chesapeake Bay, where polluted runoff and sediment from eroding stream banks can smother seagrass beds crucial for juvenile turtles. Thanks to the efforts of conservationists, which have led to new laws and regulations, the bay’s water quality is slowly improving. “We have made great progress in cleaning up the Chesapeake Bay, but what we have accomplished so far is not enough,” says Hilary Falk, director of NWF’s Mid-Atlantic Regional Center. She notes that while pollution entering the bay has declined during the past decade, new stressors such as climate change and human population growth continue to impede restoration. “We must improve water quality to a level where it can sustain both wildlife and the living resources, such as crabs and oysters, that are an economic driver for the region.”
Meanwhile, polluters still challenge limits established under the Clean Water Act more than a decade ago. In 2011, the American Farm Bureau sued the U.S. Environmental Protection Agency (EPA) in an attempt to overturn a federal pollution cleanup plan for the Chesapeake, claiming the agency did not have authority under the act to establish the plan. NWF intervened on behalf of EPA to support the agency’s authority, and last year a U.S. district court judge upheld the plan. “This decision gives EPA the authority it needs to move ahead to clean up the bay,” says NWF Senior Counsel Jim Murphy. “It will have a direct, positive effect on the Chesapeake’s sea turtles.”
Despite continuing threats to sea turtles, most biologists remain optimistic. “Turtles have survived ice ages and warm periods,” Dodd says. “They’ve been on the planet a long time.” Ehrhart also is hopeful. He believes continued protection of nesting beaches is the key: “If we can keep hatchlings streaming off the beaches every year, sea turtles can survive a tremendous amount of abuse.”
Luckily, nesting turtles have an army of biologists, interns, volunteers and other seasonal workers on their side. During spring and summer, these “turtle crews” (right) fan out across beaches from Virginia’s Back Bay south to Florida and west to Padre Island, Texas, to protect and manage as many nests as possible. Some members work for national wildlife refuges, some for state agencies or town governments, and some just do it as a labor of love. Setting out on foot or all-terrain vehicles, workers patrol nesting beaches every morning looking for “turtle crawls”—distinctive tracks made by females as they laboriously pull themselves across sand to the edge of the dunes. Once there, turtles dig a hole with their rear flippers and, depending on the species, lay 60 to 220 rubbery, ping-pong-ball-sized eggs.
When crewmembers find a crawl on smaller beaches, they locate and mark the nest and keep a protective eye on it during the incubation period, which lasts 50 to 80 days. (On larger beaches, they mark only some nests.) If a nest is in a precarious location, they may dig it up and move it to safer ground. Workers often put wire cages around nests to keep raccoons, feral hogs or other predators from eating the eggs. After the young turtles have headed to sea, the crew conducts an inventory of the nest, counting the number of hatched and unhatched eggs, which helps biologists determine the success of each clutch.
Sometimes during the inventory a crewmember will pull out a live hatchling that hasn’t yet made it to the surface. One foggy morning on South Carolina’s Hilton Head Island, Dawn Brut did just that. Brut, who works for the Coastal Discovery Museum, is also a member of the island’s eight-person turtle crew. She was checking a recently hatched loggerhead nest when she unexpectedly found the baby turtle.
As she lifted the creature out of the nest, its flippers waved furiously in the air. Brut gently brushed sand off the tiny turtle and set it down on the beach. At first, it didn’t move. But when a wave washed over it, the turtle began to crawl to the sea. A second breaker upended it, but the hatchling persisted, tenaciously battling the incoming tide. Finally, it dipped under a cresting wave and disappeared into the dark ocean, one more small victory in a very big conservation success story.
Like Mother, Like Daughter
University of Georgia researchers Campbell J. Nairn and Brian Shamblin have discovered 50- to 60-year-old loggerhead mothers nest on the same beaches as their 25- to 30-year-old daughters. They’ve learned this by taking one egg from each nest laid in Georgia and the Carolinas, which enables them to analyze the mother’s DNA. With these “genetic fingerprints,” the scientists hope to identify individually every female and determine exactly how many loggerheads are nesting in the three states.
NWF Priority: Protecting the Chesapeake
NWF’s Mid-Atlantic Regional Center works to protect the natural beauty and wildlife that make the Chesapeake Bay a special place. It does this by facilitating coalitions and working with affiliates, partners and others in the region to restore and protect the bay, promote clean energy and deploy NWF’s suite of educational programming to connect people to nature through improved water quality.
Support NWF's Work to Protect Wildlife. >>
South Carolina resident Doreen Cubie visited the state’s Hilton Head Island sea turtle project while reporting this story.
Mysterious Mariners: First Australian Flatback Sea Turtle Photos
The Secret to Saving Sea Turtles
Wildlife Library: Sea Turtles | <urn:uuid:071784d9-4211-4d69-a6de-d1682e4a3691> | {
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Introduction Map Titles Compass Map Key
MAP SCALE: HOW DO I CALCULATE IT?
There are three different measuring units listed on the scale for this map. Let’s figure all three measurements.
To figure actual inches, we must use the ratio scale. According to the scale, 1 actual inch on the map is equal to 10,000 inches on the ground. We would need to multiply the measured distance, which was 8 inches, by 10,000 to calculate the actual distance on the ground in inches. The following formula calculates the distance in inches.
8 x 10,000 = 80,000 inches
To figure the distance in feet, we must use the written scale. It is figured the same way as the ratio scale. We would need to multiply the measured distance, which was 8 inches, by 833 to calculate the actual distance on the ground in feet. The following formula calculates the distance in feet.
8 x 833 = 6,664 feet
Finally, to figure the distance in miles, we must use the bar measurement. It is calculated the same way as a ratio scale and written scale. We would need to multiply the measured distance, which was 8 inches, by 1/20 to calculate the actual distance on the ground in miles. The following formula calculates the distance in miles.
8 x 1/20 = 8/20 miles = 2/5 mile
Since this scale measurement was expressed in a fraction form, it was reduced to express the distance in the simplest of terms. | crawl-data/CC-MAIN-2014-41/segments/1410657133568.71/warc/CC-MAIN-20140914011213-00316-ip-10-196-40-205.us-west-1.compute.internal.warc.gz | null |
Reading aloud to children: The evidence
- Published Online First 13 May 2008
Promoting healthy child development lies at the heart of pediatric practice, yet a major challenge facing the field is applying "evidence based standards" to our practice. In one area of this effort though, reading aloud to children, the evidence is clear. There is ample research demonstrating that reading aloud to young children promotes their development of language and other emergent literacy skills (e.g., Adams, 1990; Sénéchal & Levre, 2002; Snow, Burns, & Griffin, 1998; Storch & Whitehurst, 2001) which in turn helps children getting ready for school (e.g., Ezell & Justice, 2005; Snow, Burns, & Griffin, 1998).
This article provides an overview of the research on reading aloud to young children and the impact on children's language and literacy development. We will discuss both the impact of frequency as well as the quality of parent-child bookreading, the impact of socio-economic status and race/ethnicity on these factors, and its influence on early language and literacy development. | <urn:uuid:b7b16e23-ae57-4363-be32-2aff81b25067> | {
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Student Center
GED Practice Test Formulas Alternate Grids Calculator Directions GED Score Glossary Math Handbook GED Links Choose a ChapterChapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 9Chapter 10Chapter 11 Chapter Overview Chapter Outline Chapter Review Quiz GED Practice Quiz Web Links FeedbackHelp Center
Contemporary's GED Mathematics
Ratio and Proportion
# Chapter Review Quiz
## Directions:
Choose the best answer to each problem. You may refer to pages 137–148 in Contemporary’s GED Mathematics if you need additional help. You may NOT use a calculator for problems 1–6. When you have finished the quiz, click on Submit Answers to receive feedback and results. You may also choose to e-mail your results to your instructor.
1 Which of the following ratios is equal to the ratio 8:22? A) 4:11 B) 22:36 C) 2:16 D) 11:25 E) 22:8 2 Simplify the ratio 1.2:6. A) 3:4 B) 2:5 C) 1:5 D) 1:4 E) 1:3 3 On a quiz in her driver education class, Kim got 4 questions wrong and 16 questions right. What was the ratio of the number of questions Kim got right to the total number of questions on the quiz? A) 1:5 B) 1:4 C) 4:1 D) 4:5 E) 5:4 4 Solve for n in n/3 = 7/10. A) 3.3 B) 2.1 C) 1.3 D) 0.7 E) 0.48 5 Which of the following represents the two cross products in the proportion 9:15 = 12:20? A) 9 x 20 = 15 x 12 B) 9 x 15 = 12 x 20 C) 9 x 12 = 15 x 20 D) 9 x 9 = 12 x 12 E) 15/15 = 12/12 6 Which of the following represents a solution to 5/9 = 8/x? A) x = (8 x 9)/5 B) x = 5/(8 x 9) C) x = (5 x 9)/8 D) x = (5 x 8)/9 E) x = 8/(5 x 9)
You may use a calculator for problems 7–10.
7 St. Louis and Kansas City are 253 miles apart. To the nearest tenth of an inch, how far apart are the two cities on a map with a scale of 1 inch = 30 miles? A) 2.5 inches B) 4.3 inches C) 6.1 inches D) 7.2 inches E) 8.4 inches 8 For every 5 regular tickets that were sold for a matinee movie, 1 senior discount ticket was sold. All together 342 people bought tickets for the movie. How many senior discount tickets were sold? A) 48 tickets B) 57 tickets C) 69 tickets D) 273 tickets E) 285 tickets 9 For every dollar that the Vega family takes in at their luncheonette, they spend \$0.40 in rent. The Vegas pay \$2,580 a month for rent for the luncheonette. How much money do they take in in a year? A) \$10,320 B) \$30,960 C) \$46,440 D) \$77,400 E) \$103,200 10 In a factory that makes plastic containers, an average of 3 out of every 1,000 containers has to be discarded because of some flaw. In a week when the factory has produced 54,216 containers, approximately how many containers had to be discarded? A) 50 to 100 B) 100 to 150 C) 150 to 200 D) 200 to 250 E) 250 to 300 | crawl-data/CC-MAIN-2018-17/segments/1524125936981.24/warc/CC-MAIN-20180419150012-20180419170012-00057.warc.gz | null |
Student Teaming Tips for Your STEM Classroom
The ways in which [students] are involved in problem-solving activities is as important to the design of integrated STEM education as the problems themselves. – STEM Integration in K-12 Education, The National Academies
STEM classes feature collaboration and teamwork – 21st century skills that all students need, no matter what their career paths. Preparing kids to work together successfully in teams plays a critical role in today’s STEM classes.
Students will work together in teams during each STEM lesson. To be productive, team members will need to understand the value and purpose of working in teams, and develop a sense of being part of a team. They should begin building the skills needed to collaborate successfully and be responsible and accountable for their work.
Setting your students up for successful teaming will help the activities go smoother and increase the learning value for students. Consider three initial tips to get your STEM teaming venture off to a smooth start:
- Make teaming an ongoing part of your classroom practice. This gives students multiple opportunities to develop needed behaviors and skills.
- Set students up in teams ahead of time. On the day of the STEM lesson they should be ready to get in teams and begin work when class begins.
- Provide teaming tips as needed throughout the lesson. Give students opportunities to self-assess their teamwork regularly.
Written by Anne Jolly as a free supplement to her book STEM by Design (2016), the Student Teaming Tips Handbook is a starter set of ideas you may find useful for priming kids to work creatively and productively in STEM teams.
“As you go about the task of establishing productive student teams in your classroom you will encounter both obstacles and successes,” Anne writes. “Be persistent and committed to making teams work and your students will reap valuable rewards in learning, social skills, and preparation for both life and work.” | <urn:uuid:3f0602a4-639b-48ce-86b6-281d1b525e6e> | {
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In this chapter, we provide NCERT Exemplar Problems Solutions for Class 11 Physics Chapter 10 Thermal Properties of Matter for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Exemplar Problems Solutions for v pdf, free NCERT Exemplar Problems Solutions for Class 11 Physics Chapter 10 Thermal Properties of Matter book pdf download. Now you will get step by step solution to each question.
|Chapter Name||Thermal Properties of Matter|
NCERT Exemplar Class 11 Physics Chapter 10 Thermal Properties of Matter
Q1. A bimetallic strip is made of aluminium and steel (aAI > astee|) On heating, the strip will
(a) remain straight (bj get twisted
(c) will bend with aluminium on concave side.
(d) will bend with steel on concave side
Key concept: Bi-metallic strip-. Two strips of equal lengths but of different materials (different coefficient of linear expansion) when join together, it is called “bi-metallic strip”, and can be used in thermostat to break or make electrical contact. This strip has the characteristic property of bending on heating due to unequal linear expansion of the two metal. The strip will bend with metal of greater a on outer side, i.e. convex side.
On heating, the metallic strip with higher coefficient of linear expansion (∝Al) will expand more.
According to the question, ∝AI > ∝steel, so aluminum will expand more. So, it should have larger radius of curvature. Hence, aluminium will be on convex side. The metal of smaller ∝ (i.e., steel) bends on inner side, i.e., concave side.
Q2. A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly
(a) its speed of rotation increases
(b) its speed of rotation decreases
(c) its speed of rotation remains same
(d) its speed increases because its moment of inertia increases
Sol: (b) When the rod is heated uniformly to raise its temperature slightly, it expands. So, moment of inertia of the rod will increase.
Moment of inertia of a uniform rod about its perpendicular bisector
If the temperature increases, moment of inertia will increase.
No external torque is acting on the system, so angular momentum should be conserved.
Q3. The graph between two temperature scales A and B is shown in figure between upper fixed point and lower fixed point there are 150 equal division on scale A and 100 on scale B. The relationship for conversion between the two scales is given by
Sol: Key concept: Temperature on one scale can be converted into other scale by using the following identity.
Reading on any scale – LFP /UFP – LFP = Constant for all scales
where, LFP —> Lower fixed point
UFP —>Upper fixed point
From the graph it is clear that the lowest point for scale A is 30° and highest point for the scale A is 180°.
Lowest point for scale B is 0° and highest point for scale B is 100°. Hence, the relation between the two scales A and B is given by
Q4. An aluminium sphere is dipped into water.
Which of the following is true?
(a) Buoyancy will be less in water at 0°C than that in water at 4°C.
(b) Buoyancy will be more in water at 0°C than that in water at 4°C.
(c) Buoyancy in water at 0°C will be same as that in water at 4°C.
(d) Buoyancy may be more or less in water at 4°C depending on the radius of the sphere.
Key concept: Liquids generally increase in volume with increasing temperature but in case of water, it expands on heating if its temperature is greater than 4°C. The density of water reaches a maximum value of 1.000 g/cm3 at 4°C.
This behaviour of water in the range from 0°C to 4°C is called anomalous expansion.
Q5. As the temperature is increased, the period of a pendulum
(a) increases as its effective length increases even though its centre of mass still remains at the centre of the bob
(b) decreases as its effective length increases even though its centre of mass ‘ still remains at the centre of the bob
(c) increases as its effective length increases due to shifting to centre of mass below the centre of the bob
(d) decreases as its effective length remains same but the centre of mass shifts above the centre of the bob
Sol: (a) A pendulum clock keeps proper time at temperature θ0. If temperature is increased to θ (>θ 0), then due to linear expansion, length of pendulum increases and hence its time period will increase
So, as the temperature increases, length of pendulum increases and hence time period of pendulum increases. Due to increment in its time period, a pendulum clock becomes slow in summer and will lose time.
Q6. Heat is associated with
(a) kinetic energy of random motion of molecules
(b) kinetic energy of orderly motion of molecules
(c) total kinetic energy of random and orderly motion of molecules
(d) kinetic energy of random motion in some cases and kinetic energy of orderly motion in other
Sol: (a) When a body is heated its temperature rises and in liquids and gases vibration of molecules about their mean position increases, hence kinetic energy associated with random motion of molecules increases.
So, thermal energy or heat associated with the random and translatory motions of molecules.
Q7. The radius of a metal sphere at room temperature Tis Rand the coefficient of linear expansion of the metal is .The sphere heated a little by a temperature ∆Tso that its new temperature is T + ∆T.The increase in the volume of the sphere is approximately.
ρ = mass / volume
So, the volume of all object will also be same.
Here the cooling will be done in the form of radiations that is according to Stefan’s law. Since, emissive power is directly proportional to the surface. Here, for given volume, sphere has least surface area and circular plate of greatest surface area.
As thickness of the plate is least, hence surface area of the plate is maximum. According to Stefan’s law, heat loss (cooling) is directly proportional to the surface area.
Hsphere : Hcube: Hplate = Asphere : Acube: Aplate
As Aplate is maximum, hence the plate will cool fastest.
As the sphere is having minimum surface area, hence the sphere cools slowest.
More Than One Correct Answer Type
Q9. Mark the correct options.
(a) A system X is in thermal equilibrium with Y but not with Z. The systems Y and Z may be in thermal equilibrium with each other.
(b) A system X is in thermal equilibrium with Y but not with Z. The systems Y and Z are not in thermal equilibrium with each other.
(c) A system X is neither in thermal equilibrium with Y nor with Z. The systems Y and Z must be in thermal equilibrium with each other.
(d) A system X is neither in thermal equilibrium with Y nor with Z. The systems Y-and Z may be in thermal equilibrium with each other.
Sol: (b, d)
Key concept:Two bodies are said to be in thermal equilibrium with each other, when no heat flows from one body to the other. That is when both the bodies are at the same temperature.
Q10. Gulab jamuns (assumed to be spherical) are to be heated in an oven. They are available in two sizes, one twice bigger (in radius) than the other. Pizzas (assumed to be discs) are also to be heated in oven. They are also in two sizes, one twice bigger (in radius) than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following.
(a) Both size gulab jamuns will get heated in the same time
(b) Smaller gulab jamuns are heated before bigger ones
(c) Smaller pizzas are heated before bigger ones
(d) Bigger pizzas are heated before smaller
Sol: (b, c) Between these four which has the least surface area will be heated first because of less heat radiation. So, smaller gulab jamuns are having least surface area, hence they will be heated first.
Similarly, smaller pizzas are heated before bigger ones because they are of small surface areas.
Q11. Refer to the plot of temperature versus time (figure) showing the changes in the state if ice on heating (not to scale). Which of the following is correct?
(a) The region AB represents ice and water in thermal equilibrium
(b) At B water starts boiling
(c) At C all the water gets converted into steam
(d) C to D represents water and steam in equilibrium at boiling point
Sol: (a, d) During phase change process, temperature of the system remains constant.
(a) In region AB, a phase change takes place, heat is supplied and ice melts but temperature of the system is 0°C. it remains constant during process. The heat supplied is used to break bonding between molecules.
(b) In region CD, again a phase change takes place from a liquid to a vapour state during which temperature remains constant. It shows water and steam are in equilibrium at boiling point.
Q12. A glass full of hot milk is poured on the table. It begins to cool gradually. Which of the following is correct?
(a) The rate of cooling is constant till milk attains the temperature of the surrounding.
(b) The temperature of milk falls off exponentially with time.
(c) While cooling, there is a flow of heat from milk to the surrounding as well as from surrounding to the milk but the net flow of heat is from milk to the surrounding and that is why it cools.
(d) All three phenomenon, conduction, convection and radiation are responsible for the loss of heat from milk to the surroundings.
Sol: (b, c, d) When hot milk spread on the table heat is transferred to the surroundings by conduction, convection and radiation. Because the surface area of poured milk on a table is more than the surface area of milk filled in a glass. Hence, its temperature falls off exponentially according to Newton’s law of cooling. Heat also will be transferred from surroundings to the milk but will be lesser than that of transferred from milk to the surroundings. So, option (b), (c) and (d) are correct.
Very Short Answer Type Questions
Q13. Is the bulb of a thermometer made of diathermic or adiabatic wall?
Sol: The bulb of a thermometer is made up of diathermic wall because diathermic walls allow exchange of heat energy between two systems but adiabatic walls do not. So it receives heat from the body to measure the temperature of body.
Q14. A student records the initial length l , change in temperature ∆ T and change in length ∆ l of a rod as follows:
|1.||2||10||4 x 10-4|
|2.||1||10||4 x 10-4|
|3.||2||20||2 x 10-4|
If the first observation is correct, what can you say about observations 2, 3 and 4.
Sol: If the first observation is correct, hence from the 1st observation we get the coefficient of linear expansion
For 4th observation, ∆l = ∝l∆T
= 2 x 10-5 x 3 x 10 = 6 x 10-4 m [i.e., observed value is correct]
Q15. Why does a metal bar appear hotter than a wooden bar at the same temperature? Equivalently it also appears cooler than wooden bar if they are both colder than room temperature.
Key concept: Kirchhoffs Law:
The ratio of emissive power to absorptive power is same for all surfaces at the same temperature and is equal to the emissive power of a perfectly black body at that temperature.
Now since (Eλ)Black is constant at a given temperature, according to this law if a surface is a good absorber of a particular wavelength it is also a good emitter of that wavelength.
This in turn implies that a good absorber is a good emitter (or radiator).
The conductivities of metals are very high compared to wood. Due to difference in conductivity, if one touch the hot metal with a finger, heat from the surrounding flows faster to the finger from metals and so one feels the heat.
Similarly, when one touches a cold metal the heat from the finger flows away to the surroundings faster. So we can say that a good radiator can be a good absorber.
Q16. Calculate the temperature which has numeral value on Celsius and Fahrenheit scale.
Sol: To construct a scale of temperature, two fixed points are taken. First fixed point is the freezing point of water, it is called lower fixed point. The second fixed point is the boiling point of water, it is called upper fixed point. Temperature on one scale can be converted into other scale by using the following identity.
Q17. These days people use steel utensils with copper bottom. This is supposed to be good for uniform heating of food. Explain this effect using the fact that copper is the better conductor. Junction
Sol: The copper bottom of the steel utensil gets heated quickly.
Because of the reason that copper is a good conductor of heat as compared to steel. But steel does not conduct as quickly, thereby allowing food inside to get heated uniformly.
Short Answer Type Questions
Q18. Find out the increase in moment of inertia I of a uniform rod (coefficient of linear expansion a) about its perpendicular bisector when its temperature is slightly increased by ∆T.
Sol: Moment of inertia of a uniform rod of mass M and length l about its perpendicular bisector
Q19. During summers in India, one Of the common practice to keep cool is to make ice balls of crushed ice, dip it in flavored sugar syrup and sip it. For this a stick is inserted into crushed ice and is squeezed in the palm to make it into the ball. Equivalently in winter in those areas where it snows, people make snow balls and throw around. Explain the formation of ball out of crushed ice or snow in the light of p-T diagram of water.
Sol : Given diagram shows the variation of pressure with temperature for water. When the pressure is increased in solid state (at 0°, 1 atm), ice changes into liquid state while decreasing pressure in liquid state (at 0°, 1 atm), water changes to ice.
When crushed ice is squeezed, some of it melts, filling up the gap between ice flakes upon releasing pressure. This water freezes, binding all ice flakes and making the ball more stable.
Q20. 100 g of water is super cooled to -10°C. At this point, due to some disturbance mechanised or otherwise some of it suddenly freezes to ice. What will be the temperature of the resultant mixture and how much mass would freeze?
Q21. One day in the morning Ramesh filled up 1/3 bucket of hot water from geyser, to take bath. Remaining 2/3 was to be filled by cold water (at room temperature) to bring mixture to a comfortable temperature. Suddenly Ramesh had to attend to something which would take some times, say 5-10 min before he could take bath. Now, he had two options (i) fill the remaining bucket completely by cold water and then attend to the work, (ii) first attend to the work and fill the remaining bucket just before taking bath. Which option do you think would have kept water warmer? Explain
Sol:According to the Newton’s law o‘f cooling, the rate of loss of heat is directly proportional to the difference of temperature. Or we can say which gives a consequence about rate of fall of temperature of a body with respect to the difference of temperature of body and surroundings.
The first option would have kept water warmer because by adding hot water to cold water, the temperature of the mixture decreases. Due to this temperature difference between the mixed water in the bucket and the surrounding decreases, thereby the decrease in the rate of loss of the heat by the water.
In second option, the hot water in the bucket will lose heat quickly. So if he first attend to the work and fill the remaining bucket with cold water which already lose much heat in 5-10 minutes then the water become more colder as comparison with first case.
Long Answer Type Questions
Q22. We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their length B remain constant. If αiron = 1.2 x 10 -5/K and αbrass = 1.8xl0-5/K, what should we take as length of each strip?
Sol: According to the problem, L1-Lb = 10 cm where,
L1 = length of iron scale
Lb = Length of brass scale
This condition is possible if change in length both the rods is remain same at all temperatures.
Q23. We would like to make a vessel whose volume does not change with temperature (take a hint from the problem above). We can use brass and iron (βvbrass = 6 x 10 5 / K and βviron = 3.55 x 10-5/K) to create a volume of 100 cc. How do you think you can achieve this?
Sol:Here we are making a vessel whose Brass volume does not change with temperature.
To make the desired vessel, we should have an iron vessel with a brass rod inside as shown in the diagram.
Therefore, an iron vessel with a volume of 249.9 cm3 fitted with a brass rod of volume 144.9 cm3 will serve as a vessel of volume 100 cm3, which will not change with temperature.
- Solids can expand in one dimension (linear expansion), two dimensions (superficial expansion) and three dimensions (volume expansion) while liquids and gases usually suffers change in volume only.
- Thermal expansion is minimum in case of solids but maximum in case of gases because intermoleeular force is maximum in solids but minimum in gases.
Q24. Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of 57°C is drunk. You can take body (tooth) temperature to be 37°C and a = 1.7x 10-5/°C bulk modulus for copper = 140x 109N/m2.
This is about 103 times of atmospheric pressure
Q25. A rail track made of steel having length 10 m is clamped on a railway line at its two ends (figure). On a summer day due to rise in temperature by 20°C. It is deformed as shown in figure. Find x (displacement of the centre) if27
Q26. A thin rod. having length L0 at 0°C and coefficient of linear expansion α has its two ends maintained at temperatures θ1, and θ2, Find its new length.
Sol. When temperature of a rod varies linearly, then average temperature of the middle point of the rod can be taken as mean of temperatures at the two ends. According to the diagram,
All Subject NCERT Exemplar Problems Solutions For Class 11
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THE CURRENT MONETARY SYSTEM BEFORE THE VOTE
December 23, 2013 marked the 100th Anniversary of the Federal Reserve Act, which created the Central Bank for the United States. The Federal Reserve is called a central bank. Other important central banks are: The Bank of Japan, The Bank of England, and the European Union’s Central Bank. These central banks are basically the fourth branch of government, which has more influence on the economy than tax and spend (fiscal policy).
The Federal Reserve is NOT a federal agency. It is primarily a private agency that regulates commercial banks. These commercial banks generate the majority of our money in circulation. The Federal Reserve is NOT a reserve; it directly creates the rest of our money supply by a stroke of a computer key.
In its 100 years of existence, we have had 16 recessions, the Great Depression, the Great Recession, and excess inflationary periods creating extensive human hardships. It is time to end these extreme downturns or at least make them less severe.
Increasing and/or changing banking regulations and breaking up or nationalizing the banks is not a substitution for reform, as it does not alter the unsustainable system by leaving monetary creation with the banks. In fact, there have been many government owned banks that experience the same failures as privately owned banks. Many central banks are actually owned by the government such as the Bank of Japan and the Bank of England. We need a 21st Century, modern monetary system to create a quality Win-Win economy!
The major source of new money in an economy is generated by the commercial banking system, i.e. Wells Fargo, Citibank, Bank of America, Chase, and the smaller local banks. They don’t loan out your deposits. They loan out far more. This excess is new money created out of thin air! This is a very important concept to understand. This is called “debt” money—where new money is created and distributed by only a loan.
Congress gave the power to the Federal Reserve in 1913, to operate the monetary system. This system creates new money only by issuing debt – private and government. Private debt-money is only created by the commercial bank loans under the regulation of the Federal Reserve. Government debt money is only created directly by the Federal Reserve’s open market operations, at the Fed’s bank in New York.
The Fed gradually buys U.S Treasuries from the banks with newly created money. This is forced money creation by issuing Treasuries to fund deficit spending. This is called, “Monetization of the Debt.”
Basically, someone—or government—has to go into debt to release new money into the economy.
This is the main reason you see a very slow recovery and growth when we have a financial collapse like 2008. In reality, there is no cost of creating new money except for creating too much in circulation, thus creating excess or hyperinflation. Creating too little with narrow circulation severely costs the economy in recessions, depressions, and extreme human hardships. In reality, there should be no cost for creating new money; there should only be the nominal cost for distribution.
When commercial banking lending slows down or freezes up, as in 2008, new money ceases to be issued and is reduced at the same time, whereby the lesser system of money creation takes over. This lesser system is deficit spending by the Federal government. Yes, deficit spending forces the Federal Reserve to create money by monetizing the debt. They digitally create money (a touch of the computer keys) and buy Treasuries and other assets from commercial banks. No, it is not all borrowed from China.
The newer policy of buying other assets from commercial banks started as a result of the 2008 crash. This is called quantitative easing, which basically creates new money by buying the suspect mortgages that the banks still hold. This process of monetizing the debt is a substitute or an addition for the lack of money in circulation from the banking system. Federal spending is also more diversified in its distribution. Deficit spending has kept us out of severe depression! There was no fiscal spending in 1929 and the Federal Reserve tightened money, which caused the Great Depression.
The next question is: When do you reduce this substantial deficit spending? If reduced too early, as Japan did in 1997 and the U.S. did in 1937, the country goes back into recession. This
reduction of deficit spending is labeled “austerity”.
The following example gives you a brief overview of the steps involved in creating money under our current system of government debt. The U.S. Government needs $1,000 to pay the salary of a federal employee. The U.S. Treasury issues a $1,000 Treasury Note, Bill, or Bond to the private government bond brokers for sale. This note is then purchased by commercial banks. The check is recorded by the Fed as a liability against the government, and the Note becomes an asset of the Fed.
The Fed has created the $1000 check with simple keystrokes on their computer without actually getting the money from any specific place. In other words, the Fed issued this money against no funds of its own. Thus we see why many call this money creation process “money created out of nothing or thin air”. This is also called “fiat money”, which all countries use. It is in reality, debt money, debt backed money or bank money.
The process for making a loan by commercial banks, which is the largest source of new money, is called a fractional reserve system. This system allows a bank to create new money on a fraction of deposits made with that bank. This fraction is determined by the Federal Reserve Board, as part of its monetary policy, and is called the reserve requirement. If the reserve requirement is 10%, then the banking system can loan $900 from the deposit of the $1000 salary check or 90% of the value of the $1000.
This new $900 loan is then deposited in another bank, which can make another $810 loan. This process repeats itself until a maximum of $9000 is loaned out by the commercial banks from the initial deposit of $1000. All the new money created was created out of nothing; or to describe the process more correctly, it was created using debt. Therefore, it can be labeled debt backed money. (With the merger of commercial and investment banks and loans driving the creation process, the supposed restrictions provided by the reserve requirement are very limited.)
In other words, every loan or overdraft creates money and every repayment of these financial instruments destroys money.
In reality, banks issue the loans first, creating deposits in the process, and then they look for reserves by raising capital, deposits, or borrowing from the Federal Reserve. Therefore, it is almost pure credit money, not fractional reserve creation, much of which was created for themselves for their trading departments —investment banks attached to their commercial banks—because of the cancellation of the Glass-Steagall Act, which separated the commercial banks from the investment banks. In other
words, they violate their own rules.
This process is intentionally kept invisible! There is no reason for you to comprehend all the lingo and complicated operations of the Federal Reserve System. It is just the gyrations of a faulty, incomplete and monopolistic system to issue and control the supply of money in circulation. The point is that you know about its basic function of “new” money creation and distribution.
The big questions are: If all money is created through debt principle, where does the money come from to pay the compound interest charges by these banks? Where is it written that we have to create and distribute money only through debt? Nowhere! This debt system of money creation and distribution has been going on since about the 12th Century.
My audiences have always asked me, “Why have they not changed this unsustainable system by now?” There are many reasons:money only through debt? Nowhere! This debt system of money creation and distribution has been going on since about the 12th Century. My audiences have always asked me, “Why have they not changed this unsustainable system by now?” There are many reasons:
• People are reluctant to change• The banking system is very opaque and politically powerful• The academic world is dominated by the neoclassical philosophy, which has money as a minor or neutral factor in their theories and formulas; but in reality, it is the major factor• “Illusion of reality”, coined byDaniel Kahneman, is the irrational behavior of doing the same thing over and over and expecting different results Because the debt money system has been around since the 12th century, it has become a religious beliefTruths about MoneyDebt (loans) is the only way we currently get new money into circulationMoney is not scarce! | <urn:uuid:fd50aa21-b3c6-4a63-ad80-05b5b69d4860> | {
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The history of ancient Greek aesthetics spans centuries. Philosophical theories of beauty through this era are proportion, functionality and form.
What are the three main aesthetic?
The three aesthetic theories of art criticism are most commonly referred to as Imitationalism, Formalism, and Emotionalism. on realistic representation. of art using the principles of art.
What are the principles of Greek art?
They established them as being: unity, duality, polarity, equilibrium, and proportion. The Greeks believed these creative principles were of universal origin, and by understanding them, they could complement the beauty of nature in their art and architecture.
What are the three types of Greek art?
There are three scholarly divisions of the stages of later ancient Greek art that correspond roughly with historical periods of the same names. These are the Archaic, the Classical and the Hellenistic.
What are the 4 main points of Greek art?
What Are The 4 Main Points Of Greek Art? There are four distinct periods in ancient Greek art: geometric, archaic, classical, and hellenistic.
What are the main types of aesthetics?
- art hoe. This style is heavily based on one’s love for art and their connection to nature, with key items such as famous paintings and sunflowers. …
- baddie. …
- cottagecore. …
- dark academia. …
- light academia. …
- ethereal. …
- fairycore. …
What are the 5 aesthetics?
- Art and Technology. Making a movie requires expert ability, in both the technical and the artistic sense, because it takes both of these skills for a movie to come out just right. …
- Frame, Flux, and Sound. …
- Mise-en-Scene. …
- Point of View. …
- Pastoral. …
- Sensibility. …
- The Beautiful. …
- The Gothic.
What are the 3 types of art that were created in Rome?
The art of Ancient Rome, its Republic and later Empire includes architecture, painting, sculpture and mosaic work.
What are the three phases of the classical period in Greek art?
List the three phases of the Classical Period in Greek art, including dates and important events. 480-450 BCE: Early Classical – Marked by the defeat of Persians in 480 BCE. 450-400 BCE: High Classical – Marked by the Pericles and the Golden Age. 400-323 BCE: Late Classical – Marked by the death of Alexander the Great.
What are the most common methods of Greek painting?
Painting Materials and Methods
On walls the methods of painting were tempera and fresco; on wood and marble, tempera and encaustic – a technique in which the colours were mixed with wax, applied to the surface and then `burnt in’ with a red-hot rod.
What makes Greek art unique?
Ancient Greek art emphasized the importance and accomplishments of human beings. Even though much of Greek art was meant to honor the gods, those very gods were created in the image of humans. Much artwork was government sponsored and intended for public display.
What are the four periods of Greek civilization?
Their general, Epaminondas, crushed Sparta at the Battle of Leuctra in 371 BC, inaugurating a period of Theban dominance in Greece. to the first century B.C., Greek art can be broken down into four periods: geometric, archaic, classical and Hellenistic.
What are the 3 Greek styles of sculpture?
Modern scholarship identifies three major stages in monumental sculpture in bronze and stone: the Archaic (from about 650 to 480 BC), Classical (480–323) and Hellenistic.
What is color of Greek painting?
Abstract. Pliny the Elder and Cicero state that during Classical period the palette of Greek painters was limited to four basic colours: white, black, red and yellow. Indeed, some mosaics considered as copies of the lost paintings have neither blue nor green.
What are examples of aesthetics?
Aesthetic is defined as a concept of what is visually acceptable, in trend or expected at the time. An example of an aesthetic is minimalism. Aesthetic means the pleasant, positive or artful appearance of a person or a thing. An example of the word is aesthetic is to say that a particular car is beautiful.
What is the Y2K aesthetic?
Y2K (also known as Kaybug) is an aesthetic that was prevalent in popular culture from roughly 1995 to 2004. Named after the Y2K Bug, it is characterized by a distinct aesthetic period, encapsulating fashion, hardware design, music, and furnishings shining with tech optimism — sometimes literally.
What aesthetic is preppy?
Often referred to as Prep or “preppie”, The Preppy aesthetic is an American sub-culture. The term stereotyped students that went to old private Northeastern university-preparatory schools. This aesthetic is characterized by upper-class upbringing and often reflects values such as narcissism, snootiness, or elitism.
What was the basic principle of Roman law?
Roman law, like other ancient systems, originally adopted the principle of personality—that is, that the law of the state applied only to its citizens. Foreigners had no rights and, unless protected by some treaty between their state and Rome, they could be seized like ownerless pieces of property by any Roman.
What is Kant’s theory of aesthetics?
Kant believes he can show that aesthetic judgment is not fundamentally different from ordinary theoretical cognition of nature, and he believes he can show that aesthetic judgment has a deep similarity to moral judgment. …
What is aesthetics theory?
Aesthetics may be defined narrowly as the theory of beauty, or more broadly as that together with the philosophy of art. The concepts of expression, representation, and the nature of art objects will then be covered. …
What are the characteristics of classical Greek and Roman art?
The elements of Greek sculpture – realism, idealism, harmony of form – held a great appeal to the Romans. The Romans may also have borrowed inspiration from the Etruscans, who had an artistic tradition all their own, including sculptures and murals.
What are the function of Greek paintings?
The chapter highlights the function of Greek art primarily in public spaces, both to visualize the divine and to commemorate humans and also to embellish sacred architecture.
What core beliefs from Greek culture are shown in the vase?
Picture 2: This is a funerary vase. Funerary art reflected the belief that the dead could continue to enjoy their favorite activities even in death. On the vase, you can see abstract forms of both humans and animals.
What are the qualities of Greek literature?
- Qualities of Greek Literatu re.
- Permanence and universalit y.
- Permanence and Universality it has an enduring quality.
- Permanence and Universality it was read and admired by all nations of the world regardless of race, religion,
- Essentially full of artistry.
What are the main characteristics of the Geometric period in art?
The Geometric period was the first specifically Greek style of vase painting. It was characterized by linear motifs such as spirals, diamonds, and cross-hatching. Abstract forms were used to represent human figures.
What do you call the 3 orders of the Greek architectural style?
At the start of what is now known as the Classical period of architecture, ancient Greek architecture developed into three distinct orders: the Doric, Ionic, and Corinthian orders.
What were the principal characteristics of classical Greek sculpture?
The Classical period of Ancient Greece produced some of the most exquisite sculptures the world has ever seen. The art of the Classical Greek style is characterized by a joyous freedom of movement, freedom of expression, and it celebrates mankind as an independent entity (atomo).
What are characteristics of Greek architecture?
Greek architecture is known for tall columns, intricate detail, symmetry, harmony, and balance. The Greeks built all sorts of buildings. The main examples of Greek architecture that survive today are the large temples that they built to their gods.
Why do Greek statues have no eyes?
Originally Answered: Why were the Roman statues depicted without pupil in the eye? They were, in paint. The paint has since faded. The old Greek Roman statues were NOT unpainted white statues, they were mostly painted.
What are the 4 common shapes of Kerch style?
The Kerch style.
The shapes most commonly found are the pelike, the lekanis, the lebes gamikos, and the krater.
How is Greek art different from Roman art?
In conclusion the difference between Greek and Roman art is revealed in a comparison of the sculpture created by each culture. While the Greeks were content to idealize their images, the Republic Romans preferred representations in stone and bronze that emphasized the reality of the person being portrayed.
What are the elements of Greek?
The ancient Greeks believed that there were four elements that everything was made up of: earth, water, air, and fire. This theory was suggested around 450 BC, and it was later supported and added to by Aristotle.
What is the most common form of Greek art Why?
Sculpture became one of the most important forms of expression for the Greeks. The Greek belief that “man is the measure of all things” is nowhere more clearly shown than in Greek sculpture. The human figure was the principal subject of all Greek art.
What are the stages of Greek civilization?
- Neolithic Period (6000-2900 BC) …
- Early Bronze Age (2900 – 2000 BC) …
- Minoan Age (2000-1400 BC) …
- Mycenaean Age (1100 – 600 BC) …
- The Dark Ages (1100 – 750 BC) …
- Archaic Period (750 – 500 BC) …
- Classical Period (500 – 336 BC) …
- Hellenistic Period (336 – 146 BC)
What is Greek period?
2-Min Summary. ancient Greek civilization, the period following Mycenaean civilization, which ended about 1200 bce, to the death of Alexander the Great, in 323 bce. It was a period of political, philosophical, artistic, and scientific achievements that formed a legacy with unparalleled influence on Western civilization …
Was the Trojan War real?
For most ancient Greeks, indeed, the Trojan War was much more than a myth. It was an epoch-defining moment in their distant past. As the historical sources – Herodotus and Eratosthenes – show, it was generally assumed to have been a real event.
Why are Greek statues white?
What this means is that the sculpture and architecture of the ancient world was, in fact, brightly and elaborately painted. The only reason it appears white is that centuries of weathering have worn off most of the paint.
What is the Greek art style?
The art of ancient Greece is usually divided stylistically into four periods: the Geometric, Archaic, Classical, and Hellenistic. … Forms of art developed at different speeds in different parts of the Greek world, and as in any age some artists worked in more innovative styles than others.
What are Greek statues made of?
The Greeks used a variety of materials for their large sculptures: limestone, marble (which soon became the stone of choice- particularly Parian marble), wood, bronze, terra cotta, chryselephantine (a combination of gold and ivory) and, even, iron. | <urn:uuid:792bf619-af9d-407d-bfe2-e10d3e19283d> | {
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Marine debris is an environmental problem of global importance, enlisting the concern and action of scientists, policy makers, as well as the general public. This three-lesson kit focuses primarily on plastic marine debris. Students critically examine data and samples and take part in activities that explore the causes, geographical distribution, and biological impacts of marine debris. Each lesson can be completed in about 50–60 minutes, but many of the activities are discrete and can be easily rearranged to fit various curricular objectives and time constraints.
By clicking any of the links to download the lesson materials, you acknowledge that C-MORE educational materials may be reproduced for educational, non-commercial purposes only. Please contact us at [email protected] or (808) 956-7739 to request teacher answer keys for this kit.
NOTE: If you have trouble downloading a file, please first try using a different browser (FireFox, Internet Explorer, Safari, Chrome, Opera, etc.) Still having problems? Contact [email protected].
For more information and lesson plans on ocean stewardship, seabirds and marine debris, check out Oikonos.
Jump to the other science kits we offer: | <urn:uuid:d29ab495-cbe6-41ef-a56e-548a3ea20408> | {
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Corn’s unique biology encouraged diversity beginning with peoples’ selections of its desirable characteristics over its history. It continues to carry the essential C4 photosynthesis mechanisms attributed to its origin in a tropical environment and the separation of male and female flowers allowing the easy cross pollination with other corn plants.
The C4 photosynthesis system allowed large potential for converting light energy into carbohydrates. Separation of male and female flowers allowed the diversity and ultimately the broad genetic base and adaptation by humans to their use of corn. Being an annual plant also allowed quick adaptation to diverse environments as humans distributed the seed with their desired attributes. This happened long before humans were describing and understanding of genetics and biology.
As people started more intense farming methods, they increased their efforts to select corn seed with desirable characteristics adapted to their environments. The broad genetic base encouraged by its separation of sexes, allowed selection of plants with flowering and grain maturity appropriate for the frost-free season. They also selected seed from their crop with desired grain hardness and volume. Eventually multiple farmers selected their own seed from many areas of the earth. In North America, the soft starch form in the grain was desired whereas in the northeast states those with hard endosperm starch was selected. These two extremes in starch were also selected elsewhere corn was distributed.
Diversity of genetics within Zea mays also allowed selection of plants with root growth appropriate for the local soils and water supplies. Also selected were genetics that allowed close timing for emergence of female flowers and pollen resulting in successful grain development. Plants with desirable resistance to local pathogens and insects were selected by individual farmers.
This selection of genetics within regions resulted in some restriction of genetic diversity within that region and eventual limits in grain production to only to a small fraction of what is expected by today’s corn growers. That began to change in the late 1930’s and continues today. That phenomenon will be discussed in the next Corn Journal issue.
About Corn Journal
The purpose of this blog is to share perspectives of the biology of corn, its seed and diseases in a mix of technical and not so technical terms with all who are interested in this major crop. With more technical references to any of the topics easily available on the web with a search of key words, the blog will rarely cite references but will attempt to be accurate. Comments are welcome but will be screened before publishing. Comments and questions directed to the author by emails are encouraged. | <urn:uuid:90d3f48f-5ed2-4461-9053-a35050847542> | {
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# To solve:|3x+1| \leq 13.General strategy to solve the inequaliti
To solve:
$$\displaystyle{\left|{3}{x}+{1}\right|}\leq{13}$$.
General strategy to solve the inequalities that involve absolute value:
Absolute value inequalities deal with the inequalities $$\displaystyle{\left({<},{>},\leq,{\quad\text{and}\quad}\ \geq\right)}$$ on the expressions with absolute sign.
We can use the property $$\displaystyle{\left|{x}\right|}{<}{k}$$ is equivalent to $$\displaystyle{x}\succ{k}\ {\quad\text{and}\quad}\ {x}{<}{k}$$, where k is a positive number and we can write a conjuction such as $$\displaystyle{x}\succ{k}\ {\quad\text{and}\quad}\ {x}{<}{k}$$ in the compact form.
$$\displaystyle-{k}{<}{x}{<}{k}$$.
For example, $$\displaystyle{\left|{x}\right|}{<}{2}\ {\quad\text{and}\quad}\ {\left|{x}\right|}{>}{2}$$.
$$\displaystyle{\left|{x}\right|}{<}{2}$$, represents the distance between x and 0 that is less than 2.
Whereas $$\displaystyle{\left|{x}\right|}{>}{2}$$, represents the distance between x and 0 that is greater than 2.
We can write an absolute value inequality as a compound inequality $$\displaystyle{\left({i}.{e}.\right)}-{2}{<}{x}{<}{2}$$.
When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.
$$\displaystyle{\left|{a}{x}+{b}\right|}{<}{c}$$, where $$\displaystyle{c}{>}{0}$$
$$\displaystyle=-{c}{<}{a}{x}+{b}{<}{c}$$
$$\displaystyle{\left|{a}{x}+{b}\right|}{>}{c}$$, where $$\displaystyle{c}{>}{0}$$
$$\displaystyle={a}{x}+{b}{<}-{c}\ {\quad\text{or}\quad}\ {a}{x}+{b}{>}{c}$$
We can replace > above with $$\displaystyle\geq\ {\quad\text{and}\quad}\ {<}\ {w}{i}{t}{h}\ \leq$$.
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Calculation:
To solve: $$\displaystyle{\left|{3}{x}+{1}\right|}\leq{13}$$
Let's continue to think in terms of distance on a number line. The number, $$\displaystyle{3}{x}+{1}$$, must be less than or equal to 13 units away from zero.
$$\displaystyle{\left|{3}{x}+{1}\right|}\leq{13}$$ is equivalent to $$\displaystyle-{13}\leq{3}{x}+{1}\leq{13}$$
By using the property $$\displaystyle{\left|{x}\right|}{<}{k}$$ is equivalent to $$\displaystyle{x}\succ{k}\ {\quad\text{and}\quad}\ {x}{<}{k}$$, where k is positive number,
We can write $$\displaystyle-{13}\leq{3}{x}+{1}\leq{13}\ {a}{s}\ {3}{x}+{1}\geq-{13}\ {\quad\text{and}\quad}\ {3}{x}+{1}\leq{13}$$.
Now we have to solve this conjunction.
First we have to isolate the absolute value expression on one side of the inequality before solving the inequality, so we have to subtract 1 from both sides.
$$\displaystyle{3}{x}+{1}\geq-{13}$$
$$\displaystyle{3}{x}+{1}-{1}\geq-{13}-{1}$$
$$\displaystyle{3}{x}\geq-{14}$$
Divide both sides by 3, we get
$$\displaystyle{\frac{{{3}{x}}}{{{3}}}}\geq-{\frac{{{14}}}{{{3}}}}$$
$$\displaystyle{x}\geq-{\frac{{{14}}}{{{3}}}}$$
And $$\displaystyle{3}{x}+{1}\leq{13}$$
$$\displaystyle{3}{x}+{1}-{1}\leq{13}-{1}$$
$$\displaystyle{3}{x}\leq{12}$$
Divide both sides by 3, we get
$$\displaystyle{\frac{{{3}{x}}}{{{3}}}}\leq{\frac{{{12}}}{{{3}}}}$$
$$\displaystyle{x}\leq{4}$$
We can write an absolute value inequality as a compound inequality (i.e.)
$$\displaystyle{\frac{{-{14}}}{{{3}}}}\leq{x}\leq{4}$$
The solution set is $$\displaystyle{\left[{\frac{{-{14}}}{{{3}}}},{4}\right]}$$
Conclusion: The solution set is $$\displaystyle{\left[{\frac{{-{14}}}{{{3}}}},{4}\right]}$$ | crawl-data/CC-MAIN-2022-05/segments/1642320301730.31/warc/CC-MAIN-20220120065949-20220120095949-00362.warc.gz | null |
- Bully Prevention
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Wraparound Service and Positive Behavior Support
What is Wraparound?
Wraparound is a philosophy of care with defined planning process used to build constructive relationships and support networks among students and youth with emotional or behavioral disabilities (EBD) and their families. It is community based, culturally relevant, individualized, strength based, and family centered. Wraparound plans are comprehensive and address multiple life domains across home, school, and community, including living environment; basic needs; safety; and social, emotional, educational, spiritual, and cultural needs. Another defining feature of wraparound is that it is unconditional; if interventions are not achieving the outcomes desired by the team, the team regroups to rethink the configuration of supports, services, and interventions to ensure success in natural home, school, and community settings. In other words, students do not fail, but plans can fail. Rather than forcing a student to fit into existing program structures, wraparound is based on the belief that services and supports should be flexibly arranged to meet the unique needs of the students and their families.
Wraparound distinguishes itself from traditional service delivery in special education and mental health with its focus on connecting families, schools, and community partners in effective problemsolving relationships. Unique implementation features include (a) family and youth voice guide the design and actions of the team; (b) team composition and strategies reflect unique youth and family strengths and needs; (c) the team establishes the commitment and capacity to design and implement a comprehensive plan over time; and (d) the plan addresses outcomes across home, school, and community through one synchronized plan.
Although on the surface wraparound can be seen as similar to the typical special education or mental health treatment planning process, it actually goes much further as it dedicates considerable effort on building constructive relationships and support networks among the youth and his or her family (Burchard, Bruns, & Burchard, 2002; Eber, 2005). This is accomplished by establishing a unique team with each student and the student’s family that is invested in achieving agreed-on quality-of-life indicators. Following a response to intervention (RTI) model in which problem-solving methods become more refined for smaller numbers of students, these more intensive techniques for engagement and team development are needed to ensure that a cohesive wraparound team and plan are formed.
The concept of wraparound has been operationalized in numerous forms (Bruns, Suter, Force, & Burchard, 2005; Burchard et al., 2002; Burns & Goldman, 1999; Miles, Bruns, Osher, Walker, & National Wraparound Initiative Advisory Group, 2006). In fact, the absence of an established theoretical framework has contributed to the lack of consistency regarding procedural guidelines for wraparound (J. S. Walker & Schutte, 2004). Arguably, the two theories that are most compatible with wraparound are ecological systems theory (Bronfenbrenner, 1979) and environmental ecology theory (Munger, 1998). Both theories stress the influence of various systems (e.g., schools, health care, etc.) on the level of functioning for children and their families. Two related theories reflect the family-centered (Allen & Petr, 1998), strengths-based approach (Saleebey, 2001) of wraparound. The consistent underlying philosophy of wraparound is a change from “expert-driven” models as it places the family, not a mental health agency or the school, in the leadership role within the team process. Furthermore, the wraparound process emphasizes that services are identified and designed based on the needs of the families and youth rather than what the system has available and is experienced with providing. The ultimate goal is success for the youth within the context of their families and their home schools. These characteristics are what make wraparound a unique, family and community-based process that is often experienced as antithetical to traditional mental health treatment planning or IEP procedures (Burchard et al., 2002). The spirit of wraparound and its elements were summarized by Burns and Goldman (1999) with 10 guiding principles:
- Strength-based family leadership.
- Team based.
- Flexible funding/services.
- Outcome focused.
- Community based.
- Culturally competent.
- Natural supports.
Procedure and components
A key component in the wraparound process is the development of a rich and deep strength profile that identifies very explicit strengths across settings (e.g., home, school, community) and life domains (i.e., social, cultural, basic living skills, academics, etc.). Big needs in wraparound can be defined as follows:
- The needs are big enough that it will take a while to achieve, such as “James needs to feel respected at school.”
- There is more than one way to meet it; for example, “Hector needs to feel competent/able about learning” instead of “Hector will complete his assignments.”
- The need will motivate the family to want to participate on the team. For instance, Maria’s mother needs to feel confident that Maria will get treated fairly at school
- If met, the need will improve quality of life for the youth or those engaged with the youth on a regular basis (e.g., the family, the teacher).
The wraparound process includes specific steps to establish ownership, and therefore investment, of people who spend the most time with the student (i.e., family, teacher). This creates an environment in which a range of interventions, including behavioral supports, are more likely to be executed with integrity. For example, a wraparound team may solicit involvement from the community to assist a family with accessing stable housing and other basic living supports as parents may be better able to focus on a home-based behavior change plan for their child if stress about being evicted from an apartment is alleviated. Other examples include teams facilitating transportation, recreation opportunities, and social supports. Teams can also tailor supports for teachers who may be challenged with meeting the unique needs of a student. For example, a plan to change problem behavior at school may be more likely to succeed if the teacher has a trusted colleague of choice who models the instruction of the replacement behavior or how to naturally deliver the reinforcement in the context of the classroom.
The wraparound process delineates specific roles for team members, including natural support persons (Eber, 2003), and detailed conditions for interventions, including specifying roles each person will play in specific circumstances. The role of a designated team facilitator is critical to ensure the process is adhered to and that the principles of the strength-based person-/family-centered approach are held fast. The wraparound facilitator, often a school social worker, counselor, or school psychologist, guides the team through the phases of wraparound, ensuring a commitment to “remain at the table,” despite challenges and setbacks, until the needs of the youth and family are met and can be sustained without the wraparound team.
Phase I: Engagement and Team Preparation
During Phase I, the facilitator works closely with the family, student, and teacher to build trust and ownership of the process.
The first step is to reach out to the family and arrange a time and place to have an “initial conversation” with them to hear their story and begin the process of building a relationship and a team.
The family is encouraged to tell “their story” by articulating their perception of the strengths, needs, and experiences of their child and family. This initial contact should be a low-key conversational discourse with the goals of:
(a) developing a trusting relationship,
(b) establishing an understanding of the process and what they can expect, and
(c) seeking information about potential team members, strengths, and big needs.
Phase II: Initial Plan Development
During Phase II, the facilitator moves from engagement and assessing strengths and needs with the family and other potential team members to guiding the team through the initial wraparound meetings. This shift into team meetings needs to occur as quickly as possible, typically within 2 weeks from the initial Phase I conversations. Baseline data reflecting youth, family, and teacher perception of strengths and needs are shared and used to guide team consensus on and commitment to quality-of-life indicators (the big needs). During Phase II, facilitators share the strengths and needs data with the team. Needs are prioritized, and action planning begins as the facilitator guides team members to brainstorm strategies to increase strengths and meet needs. As strategies are developed, tasks and roles for all team members are clarified. A safety plan for school or home is developed if team members feel this to be an imminent need.
Phase III: Ongoing Plan Implementation and Refinement
During Phase III, data-based progress monitoring is used to review initial plans and revise interventions in response to ongoing efforts. The facilitator ensures a regular meeting schedule for the team and continuous data collection and review of results so that data informs the team when things are/not working, thus sustaining objectivity among team members.
Phase IV: Transition From Wraparound
The final phase of the wraparound process marks the formal point of transition when frequent/regular meetings are not needed. During this phase, accomplishments are reviewed and celebrated, and a transition plan is developed. The family may elect at this stage to share their experience with other families who are currently participating in the wraparound process.
Wraparound and SW-PBS
It is useful to broaden this framework and view the secondary and tertiary tiers of SW-PBS as a continuum of interventions that progress through a “scaling up” of supports with a broader range of delineated steps or stages. The following figure depicts the secondary-to-tertiary continuum, moving (a) small-group interventions, to (b) a small-group intervention with a unique feature for an individual student (i.e., a unique reinforcement schedule), to (c) an individualized function-based behavior support plan for a student (typically focused on one specific problem behavior), to (d) behavior support plans that cross settings (i.e., home and school), to (e) more complex and comprehensive (wraparound) plans that address multiple life domains (i.e., safety, basic needs, behavioral, emotional, medical cultural, etc) across home, school, and community.
Wraparound can be integrated into school-based planning for students with special needs, regardless of special education label or agency involvement. Bringing families, friends, and other natural support persons together with teachers, behavior specialists, and other professionals involved with the student and family can be done for students at the first indication of need (Scott & Eber, 2003). The wraparound approach is a critical part of the SW-PBS system as it offers a means for schools to succeed with the 1–2% of students whose needs have become so complex that starting with an FBA/BIP process for one selected problem behavior is not efficient, effective, or enough to improve quality-of-life issues for all those affected.
The benefits that SW-PBS offer to the highest level of support on the continuum (wraparound) include experience with a problem-solving approach and using data to guide decisions. Also, full implementation of SW-PBS at the universal level provides a solid base of lower-level interventions (e.g., primary and secondary) to build on and more effective and supportive environments in which to implement wraparound plans. Within a three-tier system of behavioral support, students who need tertiary-level supports also have access to and can benefit from universal and secondary supports. Each level of support in SW-PBS is “in addition to” the previous level. In other words, no student only needs wraparound as the wraparound plan, with its multiple life-domain and multiple-perspective focus, often makes the universal and secondary supports available in the school effective for the student.
Allen, R. I., & Petr, C. G. (1998). Rethinking family-centered practice. American Journal of Orthopsychiatry, 68, 196–204.
Brofenbrenner, U. (1979). The ecology of human development. Cambridge, MA: Harvard University Press.
Bruns, E. J., Suter, J. C., Force, M. M., & Burchard, J. D. (2005). Adherence to wraparound principles and association with outcomes. Journal of Child and Family Studies, 14, 521–534.
Burchard, J. D., Bruns, E. J., & Burchard, S. N. (2002). The wraparound approach. In B. Burns & K. Hoagwood (Eds.), Community treatment for youth: Evidence-based interventions for severe emotional and behavioral disorders. New York: Oxford University Press.
Burns, B. J., & Goldman, S. K. (Eds.). (1999). Promising practices in wraparound for children with serious emotional disturbance and their families. Systems of Care: Promising Practices in Children’s Mental Health, 1998 Series (Vol. 4). Washington, DC: Center for Effective Collaboration and Practice, American Institutes for Research.
Eber, L. (2003). The art and science of wraparound: Completing the continuum of schoolwide behavioral support. Bloomington, IN: Forum on Education at Indiana University.
Miles, P., Bruns, E. J., Osher, T. W., Walker, J. S., & National Wraparound Initiative Advisory Group. (2006). The wraparound process user’s guide: A handbook for families. Portland, OR: National Wraparound Initiative, Research and Training Center on Family Support and Children’s Mental Health, Portland State University.
Munger, R. L. (1998). The ecology of troubled children. Cambridge, MA: Brookline Press.
Saleebey, D. (2001). The strengths perspective in social work practice (2nd ed.). New York: Longman.
Scott, T., & Eber, L. (2003). Functional assessment and wraparound as systemic school processes: Primary, secondary, and tertiary systems examples. Journal of Positive Behavior Supports, 5, 131–143.
Walker, J. S., & Schutte, K. M. (2004). Practice and process in wraparound teamwork.Journal of Emotional and Behavioral Disorders, 12, 182–192.
The wraparound cotent is extracted from ‘Chapter 27: Completing the Continuum of Schoolwide Positive Behavior Support: Wraparound as a Tertiary-Level Intervention’ by Eber, L., Hyde, K., Rose, J., Breen, K., McDonald, D., & Lewandowski, H. (in press) in W. Sailor, G. Dunlap, G. Sugai, R. Horner, (Eds.) Handbook of Positive Behavior Supports & ‘Wraparound: Description and Case Example’ by Eber, L. (2005) in George Sugai & Rob Horner (Eds.) Encyclopedia of Behavior Modification and Cognitive Behavior Therapy: Educational Applications, (pp. 1601-1605).
The newsletter article provides research base, relevant target population, case example, and suggested readings for wraparound service.
Describes a process, wraparound planning, for extending educational services to students with emotional and behavioral disorders (EBD) and their families. A merger of community and school-based wraparound is being implemented in pilot school districts in Illinois. Guidelines for implementing school-based wraparound for students with EBD are provided and implications for school organization are drawn.
Initial Training Activities for Core Elements of Wraparound from Illinois PBIS - PBIS Intensive Level: Integrating Wraparound in Schools
This is a training manual which provides information on how to integrate Wraparound Approaches in PBIS Schools.
Illinois Statewide Technical Assistance Center (ISTAC) Systematic Information Management for Educational Outcomes (SIMEO) Big Behavior Tool (BB-T)
This is a checklist which reflects the caregiver/facilitator/team's rating of a student's externalized, internalized and expressive behavior.
Illinois Statewide Technical Assistance Center (ISTAC) Systematic Information Management for Educational Outcomes (SIMEO) Educational Information Tool (EI-T)
This is a questionnaire in which a teacher rates a student's classroom functioning and his/her academic performance.
Illinois Statewide Technical Assistance Center (ISTAC) Systematic Information Management for Educational Outcomes (SIMEO) Family/Caregiver Satisfaction Tool (FS-T)
This is a checklist in which parent's/caregiver's rate their experience in working with teams (i.e., IEP Team).
Illinois Statewide Technical Assistance Center (ISTAC) Systematic Information Management for Educational Outcomes (SIMEO) Home, School, Community Tool (HSC-T)
This is a questionnaire in which a teacher, parent/caregiver, and youth's facilitator complete in order measure a student's needs and/or strengths.
Illinois Statewide Technical Assistance Center (ISTAC) Systematic Information Management for Educational Outcomes (SIMEO) Referral/Disposition Tool (RD-T)
This tool is useful for tracking referral on individual student's.
Illinois Statewide Technical Assistance Center (ISTAC) Individual Student Evaluation System (ISES) Wraparound Integrity Tool (WIT)
This is a tool that describes activities involved in Phases I through IV of the Wraparound intervention.
Illinois Statewide Technical Assistance Center (ISTAC) Systematic Information Management for Educational Outcomes (SIMEO) Youth Satisfaction Tool (YS-T)
This survey is intended to reflect youth’s experience with a previous team (if any) such as a special education IEP team.
This is a powerpoint presentation that is a 2-Day training for schools implementing School-Wide PBIS. The goals of the training are to: proivide Understand about key features of wraparound value base and process, have participants Gain experience with components of the wraparound process, and Learn to apply data-based decision-making, self-assessment and monitoring procedures to ensure effectiveness of practices.
This document provides a description of what steps are involved in the Four Phases of Wraparound Implementation.
Functional assessment and wraparound as systemic school processes: Primary, secondary, and tertiary systems examples
This article proposes a framework for expanding the traditional presentation of wraparound and FBA to (a) view wraparound and FBA as concepts that are inextricably linked at the core of each level of the proactive systemic process of PBS and (b) understand how wraparound and FBA are critical features of prevention as well as intervention for creating safer schools for all students.
This training resource guide provides: 1) training course materials, 2) initial & advanced training activities, 3) evaluation tools, 4) wraparound, 5) team development and action planning strategies, 6) crisis planning, and 7) team planning tools for tertiary level support. | <urn:uuid:e29c7565-6507-4255-a54c-90384a45d5bd> | {
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