Notes, abstracts, papers, exams and problems of Greek

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Derivatives and Limits: Rules, Properties, and Common Identities

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Derivadas

derivative rules

der(xa) = a . xa-1

der(a) = 0

(f+-g)' = f' + g'

(a.f)' = a .f'

(f/g)' = ((f'.g-g'.f)/g2)

der( ln(x) ) = 1/x

der( ln|x| ) = 1/x

der( ex) = ex

der( log(x) ) = 1/(x.ln(10))

der( loga(x) ) = 1/(x.ln(a))

common limits

limx->cf(x) = ∞

limx->cg(x) = L

limx->c[f(x) +- g(x)] = ∞

limx->c[f(x) . g(x)] = ∞, L>0

limx->c[f(x) . g(x)] = - ∞, L<0

limx->∞(1 + k/x)x = ek

limx->∞[axn] = ∞, 0

limx->0(1 +x)1/x = e

Trigonometria

basic identities

tan(x) = sin(x)/cos(x)

cot(x) = cos(x)/sin(x)

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

pythagorean identities

sin(2x) = 2 sin(x)cos(x)

cos(2x) = 1 - 2.sin2(x)

tan(2x) = 2tan(x) / 1-tan2(x)

sin(x) | -1<= y <= 1 | arcsin(x) | - (π/2) <= y <= π/2

cos(x) | -1<= y <= 1 | arccos(

... Continue reading "Derivatives and Limits: Rules, Properties, and Common Identities" »

Current Events & Headlines: A Collection of News Summaries

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NOW TEACHERS ARE ORDERED:

1-

  1. p1
  2. p3

2-

  1. F: Staff have also - is too hard
  2. F: Yesterday the mail - to senior staff
  3. T: Some schools - are going

3-

  1. a staff
  2. feedback
  3. incident
  4. panel

4-

  1. b
  2. c
  3. a

HOW FIVE YEARS OF YOUTUBE:

1-

  1. 1p
  2. p3

2-

  1. F: never before - by accident
  2. T: it's an illuminating - good bet
  3. F: what many - in history

3-

  1. generated
  2. accident
  3. choice
  4. dismissed

4-

  1. b
  2. c
  3. a

SHOPPERS GO GREEN:

1-

  1. p1
  2. p5

2-

  1. F: the privacy - different behavior
  2. F: celebrities - a prius
  3. T: the study - to be caring

3-

  1. concerned
  2. privacy
  3. purchased
  4. prime

4-

  1. a
  2. b
  3. b

SCIENTISTS CALL FOR RESEARCH:

1-

  1. p1
  2. p3

2-

  1. F: It was previously - events more likely
  2. T: melting glaciers - the ground
  3. T: studies point - warmer world

3-

  1. likely
  2. rise
  3. link
  4. distant

4-

  1. b
  2. c
  3. c

ARE YOUR KIDS AWAKE?:

1-

  1. p4
  2. p5

2-

  1. F: the average young - to a new study
  2. T: and because so many - a half hours
  3. T:
... Continue reading "Current Events & Headlines: A Collection of News Summaries" »

Projected Financial Statements and Budgets

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 Presupuesto de Venta

 Septiembre  Octubre 
 Unidades                     6.000                      7.000  
 Precio Unitario                   53.400                    54.000  
Presupuesto de Produccion  
 Unidades  Vender                     6.000                      7.000  
 Inventario Inicial                            -                        7.000  
 Inventario Final                     7.000                      8.000  
 Unidades a Producir                   13.000                     
... Continue reading "Projected Financial Statements and Budgets" »

Chemical Reactions and Thermodynamics

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Written at on English with a size of 2.59 KB.

Termoquimica:

-Reacciones electroquimicas: intercambio de energia interna en forma de trabajo electrico./ -Reacciones termoquimicas: intercambio de energia interna mediante calor y trabajo mecanico./ -Reacciones fotoquimicas: intercambio de energia interna en forma de radiacion electromagnetica.

Ley de hess:

El calor absorbido o desprendido por una reaccion quimica a presion constante es siempre el mismo, independientemente de si el proceso se lleva en una o varias etapas.

Espontaneidad:

-Proceso espontaneo: Aquel que se produce sin la necesidad de exponentes externos./ -Proceso no espontaneo: Aquel que se puede llevar a cabo gracias a la accion de agentes externos./ -Procesos imposibles: aquel que no se puede llevar a cabo de ninguna manera ni... Continue reading "Chemical Reactions and Thermodynamics" »

English Vocabulary for Crime and Law

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Crime and Law Vocabulary

Crimes

  • Burgle: to enter a building illegally and steal things
  • Mug: to attack someone in a public place and steal their money
  • Steal: to take something that does not belong to you
  • Rob: to steal from a person or place, often using violence or threats
  • Murder: to kill someone illegally and intentionally
  • Kidnap: to take someone away illegally and keep them as a prisoner

People Involved in Crimes

  • Witness: someone who sees a crime happen
  • Culprit: someone who is responsible for a crime
  • Suspect: someone who is thought to be guilty of a crime
  • Victim: someone who has been harmed by a crime

Legal Proceedings

  • Arrest: to take someone into custody because they are suspected of a crime
  • Judge: a person who presides over a court of law
  • Statement: a formal
... Continue reading "English Vocabulary for Crime and Law" »

Interest Groups in Politics: A Glossary of Terms

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Written at on English with a size of 6.97 KB.

A

527 Organization

A political group organized under section 527 of the IRS.

Amicus Curiae Brief

Literally, a "friend of the court" brief, filed by an individual or organization to present arguments in addition to those presented by the immediate parties to a case.

B

Boycott

A form of pressure or protest – an organized refusal to purchase a product or service.

Bundling

A tactic in which PACs collect contributions from like-minded individuals (each limited by campaign finance laws) and present them to a candidate or political party as a "bundle," thus increasing the PAC's influence.

C

Campaign Assistance

Interest groups have additional strategies to use in campaigns, including recruiting and training candidates, and getting out the vote.

Climate Control

The... Continue reading "Interest Groups in Politics: A Glossary of Terms" »

Untitled 1

Classified in Greek

Written at on English with a size of 1.67 KB.

10560 (572) a (440) 560

11 300 (170) A (520) 3000

122315 (173) a (523) 2315

13

8605 (477) A (472) 5762

                   (4750) 2843

14  900 (610) a (610) 900

1650 (300) a (610) 1650

(129) GASTOS 41531

708 i 6 a gastos

Impost benefici

antes:

resultado*%(630) a (473) si hayenelbalance

                             (4752) resultado 630 o restar el 473

despues:

(630) a (473) o (4752) resultado 630

x

resultado 630 (129) a (630) resultado 630

Total 129 restar: benefico antes impuesto - importe 630

G

BENEFICIO DEL 129 ANTERIOR (129) A (112) %*129

                                                         (1141) %*129

                                                        ... Continue reading "Untitled 1" »

The Scarlet Letter: Chapters 9-12 Summary and Analysis

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Chapter 9: Hester's Plea

Hester speaks with Roger and insists that he reveal his true identity to Dimmesdale. Believing it's time to unburden Dimmesdale, she reveals Roger's secret. Meanwhile, Pearl questions her mother about the scarlet letter, but Hester tells her that some things are beyond a child's understanding.

Chapter 10: A Secret Revealed

Determined to help Dimmesdale, Hester arranges a meeting in the forest. There, she reveals Roger's true identity as her husband.

Chapter 11: A Moment of Freedom

During their conversation, Hester removes the scarlet letter, feeling a sense of liberation. She introduces Pearl to Dimmesdale as her father, expressing her love for him. They plan to escape to Bristol by ship. Dimmesdale, though unwell, refuses... Continue reading "The Scarlet Letter: Chapters 9-12 Summary and Analysis" »