Algebra II Day 1

Algebra II Day 1

An equation is a mathematical statement that asserts the equality of two expressions.

Equations often express relationships between given quantities, the knowns, and quantities yet to be determined, the unknowns. By convention, unknowns are denoted by letters at the end of the alphabet, xyzw… while knowns are denoted by letters at the beginning, abcd… The process of expressing the unknowns in terms of the knowns is called solving the equation.

In an equation with a single unknown, a value of that unknown for which the equation is true is called a solution or root of the equation. In a set simultaneous equations, or system of equations, multiple equations are given with multiple unknowns. A solution to the system is an assignment of values to all the unknowns so that all of the equations are true.

Identities

 

One use of equations is in mathematical identities, assertions that are true independent of the values of any variables contained within them. For example, for any given value of x it is true

However, equations can also be correct for only certain values of the variables. In this case, they can be solved to find the values that satisfy the equality. For example, consider the following

The equation is true only for two values of x, the solutions of the equation. In this case, the solutions are x = 0 and x = 1.

Properties

 

If an equation in algebra is known to be true, the following operations may be used to produce another true equation:

  1. Any real number can be added to both sides.
  2. Any real number can be subtracted from both sides.
  3. Any real number can be multiplied to both sides.
  4. Any non-zero real number can divide both sides.
  5. Some functions can be applied to both sides. Caution must be exercised to ensure that the operation does not cause missing or extraneoussolutions. For example, the equation y*x=x has 2 solutions: y=1 and x=0. Dividing both sides by x “simplifies” the equation to y=1, but the second solution is lost.

 

 

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Biology Chapter 1: A View of Life

Biology Chapter 1: A View of Life

 

Biology is a natural science involved with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is an extensive subject containing many subdivisions, topics, and disciplines. Among the most important topics are five principles that can be said to be the fundamental guidelines of modern biology:

 

  1. Cells are the basic unit of life
  2. New species and inherited traits are the product of evolution
  3. Genes are the basic unit of heredity
  4. An organism regulates its internal environment to maintain a stable and constant condition
  5. Living organisms consume and transform energy.

 

Cell Theory

 

Cell theory states that the cell is the fundamental unit of life, and that all living things are made up of one or more cells or the produced products of those cells. All cells arise from other cells through cell division. In multicellular organisms, every cell in the organism’s body originates from a single cell in a fertilized egg. Also, the occurrence of energy flow occurs in cells in processes that are part of the function known as metabolism. Finally, cells contain hereditary information called deoxyribonucleic acid (DNA) which is passed from cell to cell during cell division.

 

Evolution

 

A fundamental concept in biology is that life changes and develops through evolution, and that all life-forms known have a common origin. Evolution was established by Charles Darwin as a practical theory when he showed its inspiration: natural selection. Darwin theorized that species and breeds developed through the processes of natural selection and artificial selection or selective breeding.

 

Now evolution is used to explain the great variations of life found on Earth. Genetic drift was accepted as an additional means of evolutionary development in the creation of the theory.

The theory of evolution proposes that all organisms on the Earth, both living and extinct, have descended from a common ancestor or an ancestral gene pool. Biologists generally consider the universality of the genetic code as great support in favor of the theory of universal common descent for all Bacteria, Achaea, and Eukaryotes.

 

 

 

 

 

 

 

 

 

Genetics

 

Genes are the primary units of inheritance in all organisms. A gene is a unit of heredity and corresponds to a region of DNA that influences the form or function of an organism in specific ways. All organisms, from bacteria to animals, share the same basic machinery that copies and translates DNA into proteins. Cells transcribe a DNA gene into an RNA version of the gene, and a ribosome then translates the RNA into a protein, a sequence of amino acids. The translation code from RNA to amino acid is the same for most organisms, but slightly different for some. For example, a sequence of DNA that codes for insulin in humans also codes for insulin when inserted into other organisms, such as plants.

 

A chromosome is an organized structure consisting of DNA and histones. DNA usually occurs as linear chromosomes in eukaryotes, and circular chromosomes in prokaryotes. The set of chromosomes in a cell and any other hereditary information found in the mitochondria, chloroplasts, or other locations is collectively known as its genome. In eukaryotes, genomic DNA is located in the cell nucleus, along with small amounts in mitochondria and chloroplasts. In prokaryotes, the DNA is held within an irregularly shaped body in the cytoplasm called the nuclei. The genetic information in a genome is held within genes, and the complete assemblage of this information in an organism is called its genotype.

 

Homeostasis

 

Homeostasis is the ability of an open system to regulate its internal environment to maintain stable conditions by means of multiple dynamic equilibrium adjustments controlled by interrelated regulation mechanisms. All living organisms, whether unicellular or multicellular exhibit homeostasis.

 

To maintain dynamic equilibrium and effectively carry out certain functions, a system must detect and respond to physiological disturbances. After the detection of a disturbance, a biological system normally responds through negative feedback. This means stabilizing conditions by either reducing or increasing the activity of an organ or system. One example is the release of glucagon when sugar levels are too low.

 

 

 

 

 

 

 

 

 

 

Energy

 

The survival of a living organism depends on the continuous input of energy. Chemical reactions that are responsible for its structure and function are tuned to extract energy from substances that act as its food and transform them to help form new cells and sustain them. In this process, molecules of chemical substances that constitute food play two roles; first, they contain energy that can be transformed for biological chemical reactions; second, they develop new molecular structures made up of biological molecules.

 

The organisms responsible for the introduction of energy into an ecosystem are known as producers. Nearly all of these organisms originally draw energy from the sun. Plants and other phototrophs use solar energy by a process known as photosynthesis to convert raw materials into organic molecules. Some of the captured energy is used to produce biomass to sustain life and provide energy for growth and development.

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Letter to the New King of Denmark Detailing the Story of Hamlet

It began when Hamlet met the ghost of his father. The ghost spoke to him, stating that it is his father’s spirit, and he was murdered by Claudius. Ordering Hamlet to seek revenge on the man who took over his throne and married his wife, the ghost disappears with the dawn.

Prince Hamlet devotes himself to avenging his father’s death, but, he is delayed, entering into a deep depression, and madness. Claudius and Gertrude worry about the prince’s behavior and try to find out its cause. They use a pair of Hamlet’s friends, Rosencrantz and Guildenstern, to watch him. When Polonius suggests that Hamlet may be mad with love for his daughter, Ophelia, Claudius agrees to spy on Hamlet while in conversation with the girl. Although Hamlet seems mad, he does not seem to love Ophelia: he orders her to go through a nunnery, and says that he wished to ban marriages.

A group of traveling actors came to Elsinore, and Hamlet takes advantage of the opportunity to test his uncle’s guilt. He planned to have the players perform a scene closely resembling the way Hamlet imagines his uncle to have murdered his father, so that if Claudius is guilty, he will act guilty. When the moment of the murder arrives in the theater, Claudius leaps up and leaves the room. Hamlet and I agreed that this proves he is guilty. Hamlet goes to kill Claudius but finds him praying. Since he believed that killing Claudius while in prayer would send Claudius’s soul to heaven, Hamlet thought that would be a poor way of revenge, and so he decided to wait. Claudius now frightened of Hamlet’s madness and fearing for his own safety, orders that Hamlet be sent to England at once.

Hamlet goes to meet with his mother, in whose bedroom Polonius had hidden behind a tapestry. Hearing a noise from behind the tapestry, Hamlet believes the king is hiding there. He draws his sword and stabs through the fabric, killing Polonius. For this crime, he is immediately sent off to England with Rosencrantz and Guildenstern. Yet, Claudius’s plan for Hamlet included more than banishment, as he has given Rosencrantz and Guildenstern sealed orders for the King of England demanding that Hamlet be put to death.

In the aftermath of her father’s death, Ophelia went mad with grief and drowns in the river. Polonius’s son, Laertes, who had been staying in France, returns to Denmark in rage. Claudius convinces him that Hamlet is to blame for his father’s and sister’s deaths. When Horatio and the king receive letters from Hamlet indicating that the prince has returned to Denmark after pirates attacked his ship while traveling to England, Claudius makes up a plan to use Laertes’ desire for revenge to secure Hamlet’s death. Laertes will fence with Hamlet, but Claudius will poison Laertes’ blade so that if he draws blood, Hamlet will die. As a backup plan, the king decides to poison a goblet, which he will give Hamlet to drink should Hamlet score the first or second hits of the match. Hamlet returned to the area of Elsinore just as Ophelia’s funeral is taking place. Stricken with grief, he attacked Laertes and declared that he had always loved Ophelia. Back at the castle, he tells me that he thinks one must be prepared to die, since death can come at any time. A courtier named Osric arrived on Claudius’s orders to arrange the fencing match between Hamlet and Laertes.

 

As soon as the sword-fighting began, Hamlet scored the first hit. The king then offered the poisoned goblet, but Hamlet rejected the drink. Instead, Gertrude takes a drink from it and is killed by the poison. Laertes succeeds in cutting Hamlet, though Hamlet does not die of the poison instantly. After an accidental switch of swords, Laertes is cut by his own poisoned sword blade, and, after telling Hamlet that Claudius is responsible for the queen’s death, he dies from the blade’s poison. Hamlet then stabs Claudius with the poisoned sword and forces him to drink down the rest of the poisoned wine. Claudius dies, and Hamlet dies right after getting his revenge.

It began when Hamlet met the ghost of his father. The ghost spoke to him, stating that it is his father’s spirit, and he was murdered by Claudius. Ordering Hamlet to seek revenge on the man who took over his throne and married his wife, the ghost disappears with the dawn.

Prince Hamlet devotes himself to avenging his father’s death, but, he is delayed, entering into a deep depression, and madness. Claudius and Gertrude worry about the prince’s behavior and try to find out its cause. They use a pair of Hamlet’s friends, Rosencrantz and Guildenstern, to watch him. When Polonius suggests that Hamlet may be mad with love for his daughter, Ophelia, Claudius agrees to spy on Hamlet while in conversation with the girl. Although Hamlet seems mad, he does not seem to love Ophelia: he orders her to go through a nunnery, and says that he wished to ban marriages.

A group of traveling actors came to Elsinore, and Hamlet takes advantage of the opportunity to test his uncle’s guilt. He planned to have the players perform a scene closely resembling the way Hamlet imagines his uncle to have murdered his father, so that if Claudius is guilty, he will act guilty. When the moment of the murder arrives in the theater, Claudius leaps up and leaves the room. Hamlet and I agreed that this proves he is guilty. Hamlet goes to kill Claudius but finds him praying. Since he believed that killing Claudius while in prayer would send Claudius’s soul to heaven, Hamlet thought that would be a poor way of revenge, and so he decided to wait. Claudius now frightened of Hamlet’s madness and fearing for his own safety, orders that Hamlet be sent to England at once.

Hamlet goes to meet with his mother, in whose bedroom Polonius had hidden behind a tapestry. Hearing a noise from behind the tapestry, Hamlet believes the king is hiding there. He draws his sword and stabs through the fabric, killing Polonius. For this crime, he is immediately sent off to England with Rosencrantz and Guildenstern. Yet, Claudius’s plan for Hamlet included more than banishment, as he has given Rosencrantz and Guildenstern sealed orders for the King of England demanding that Hamlet be put to death.

In the aftermath of her father’s death, Ophelia went mad with grief and drowns in the river. Polonius’s son, Laertes, who had been staying in France, returns to Denmark in rage. Claudius convinces him that Hamlet is to blame for his father’s and sister’s deaths. When Horatio and the king receive letters from Hamlet indicating that the prince has returned to Denmark after pirates attacked his ship while traveling to England, Claudius makes up a plan to use Laertes’ desire for revenge to secure Hamlet’s death. Laertes will fence with Hamlet, but Claudius will poison Laertes’ blade so that if he draws blood, Hamlet will die. As a backup plan, the king decides to poison a goblet, which he will give Hamlet to drink should Hamlet score the first or second hits of the match. Hamlet returned to the area of Elsinore just as Ophelia’s funeral is taking place. Stricken with grief, he attacked Laertes and declared that he had always loved Ophelia. Back at the castle, he tells me that he thinks one must be prepared to die, since death can come at any time. A courtier named Osric arrived on Claudius’s orders to arrange the fencing match between Hamlet and Laertes.

 

As soon as the sword-fighting began, Hamlet scored the first hit. The king then offered the poisoned goblet, but Hamlet rejected the drink. Instead, Gertrude takes a drink from it and is killed by the poison. Laertes succeeds in cutting Hamlet, though Hamlet does not die of the poison instantly. After an accidental switch of swords, Laertes is cut by his own poisoned sword blade, and, after telling Hamlet that Claudius is responsible for the queen’s death, he dies from the blade’s poison. Hamlet then stabs Claudius with the poisoned sword and forces him to drink down the rest of the poisoned wine. Claudius dies, and Hamlet dies right after getting his revenge.

It began when Hamlet met the ghost of his father. The ghost spoke to him, stating that it is his father’s spirit, and he was murdered by Claudius. Ordering Hamlet to seek revenge on the man who took over his throne and married his wife, the ghost disappears with the dawn.

Prince Hamlet devotes himself to avenging his father’s death, but, he is delayed, entering into a deep depression, and madness. Claudius and Gertrude worry about the prince’s behavior and try to find out its cause. They use a pair of Hamlet’s friends, Rosencrantz and Guildenstern, to watch him. When Polonius suggests that Hamlet may be mad with love for his daughter, Ophelia, Claudius agrees to spy on Hamlet while in conversation with the girl. Although Hamlet seems mad, he does not seem to love Ophelia: he orders her to go through a nunnery, and says that he wished to ban marriages.

A group of traveling actors came to Elsinore, and Hamlet takes advantage of the opportunity to test his uncle’s guilt. He planned to have the players perform a scene closely resembling the way Hamlet imagines his uncle to have murdered his father, so that if Claudius is guilty, he will act guilty. When the moment of the murder arrives in the theater, Claudius leaps up and leaves the room. Hamlet and I agreed that this proves he is guilty. Hamlet goes to kill Claudius but finds him praying. Since he believed that killing Claudius while in prayer would send Claudius’s soul to heaven, Hamlet thought that would be a poor way of revenge, and so he decided to wait. Claudius now frightened of Hamlet’s madness and fearing for his own safety, orders that Hamlet be sent to England at once.

Hamlet goes to meet with his mother, in whose bedroom Polonius had hidden behind a tapestry. Hearing a noise from behind the tapestry, Hamlet believes the king is hiding there. He draws his sword and stabs through the fabric, killing Polonius. For this crime, he is immediately sent off to England with Rosencrantz and Guildenstern. Yet, Claudius’s plan for Hamlet included more than banishment, as he has given Rosencrantz and Guildenstern sealed orders for the King of England demanding that Hamlet be put to death.

In the aftermath of her father’s death, Ophelia went mad with grief and drowns in the river. Polonius’s son, Laertes, who had been staying in France, returns to Denmark in rage. Claudius convinces him that Hamlet is to blame for his father’s and sister’s deaths. When Horatio and the king receive letters from Hamlet indicating that the prince has returned to Denmark after pirates attacked his ship while traveling to England, Claudius makes up a plan to use Laertes’ desire for revenge to secure Hamlet’s death. Laertes will fence with Hamlet, but Claudius will poison Laertes’ blade so that if he draws blood, Hamlet will die. As a backup plan, the king decides to poison a goblet, which he will give Hamlet to drink should Hamlet score the first or second hits of the match. Hamlet returned to the area of Elsinore just as Ophelia’s funeral is taking place. Stricken with grief, he attacked Laertes and declared that he had always loved Ophelia. Back at the castle, he tells me that he thinks one must be prepared to die, since death can come at any time. A courtier named Osric arrived on Claudius’s orders to arrange the fencing match between Hamlet and Laertes.

 

As soon as the sword-fighting began, Hamlet scored the first hit. The king then offered the poisoned goblet, but Hamlet rejected the drink. Instead, Gertrude takes a drink from it and is killed by the poison. Laertes succeeds in cutting Hamlet, though Hamlet does not die of the poison instantly. After an accidental switch of swords, Laertes is cut by his own poisoned sword blade, and, after telling Hamlet that Claudius is responsible for the queen’s death, he dies from the blade’s poison. Hamlet then stabs Claudius with the poisoned sword and forces him to drink down the rest of the poisoned wine. Claudius dies, and Hamlet dies right after getting his revenge.

It began when Hamlet met the ghost of his father. The ghost spoke to him, stating that it is his father’s spirit, and he was murdered by Claudius. Ordering Hamlet to seek revenge on the man who took over his throne and married his wife, the ghost disappears with the dawn.

Prince Hamlet devotes himself to avenging his father’s death, but, he is delayed, entering into a deep depression, and madness. Claudius and Gertrude worry about the prince’s behavior and try to find out its cause. They use a pair of Hamlet’s friends, Rosencrantz and Guildenstern, to watch him. When Polonius suggests that Hamlet may be mad with love for his daughter, Ophelia, Claudius agrees to spy on Hamlet while in conversation with the girl. Although Hamlet seems mad, he does not seem to love Ophelia: he orders her to go through a nunnery, and says that he wished to ban marriages.

A group of traveling actors came to Elsinore, and Hamlet takes advantage of the opportunity to test his uncle’s guilt. He planned to have the players perform a scene closely resembling the way Hamlet imagines his uncle to have murdered his father, so that if Claudius is guilty, he will act guilty. When the moment of the murder arrives in the theater, Claudius leaps up and leaves the room. Hamlet and I agreed that this proves he is guilty. Hamlet goes to kill Claudius but finds him praying. Since he believed that killing Claudius while in prayer would send Claudius’s soul to heaven, Hamlet thought that would be a poor way of revenge, and so he decided to wait. Claudius now frightened of Hamlet’s madness and fearing for his own safety, orders that Hamlet be sent to England at once.

Hamlet goes to meet with his mother, in whose bedroom Polonius had hidden behind a tapestry. Hearing a noise from behind the tapestry, Hamlet believes the king is hiding there. He draws his sword and stabs through the fabric, killing Polonius. For this crime, he is immediately sent off to England with Rosencrantz and Guildenstern. Yet, Claudius’s plan for Hamlet included more than banishment, as he has given Rosencrantz and Guildenstern sealed orders for the King of England demanding that Hamlet be put to death.

In the aftermath of her father’s death, Ophelia went mad with grief and drowns in the river. Polonius’s son, Laertes, who had been staying in France, returns to Denmark in rage. Claudius convinces him that Hamlet is to blame for his father’s and sister’s deaths. When Horatio and the king receive letters from Hamlet indicating that the prince has returned to Denmark after pirates attacked his ship while traveling to England, Claudius makes up a plan to use Laertes’ desire for revenge to secure Hamlet’s death. Laertes will fence with Hamlet, but Claudius will poison Laertes’ blade so that if he draws blood, Hamlet will die. As a backup plan, the king decides to poison a goblet, which he will give Hamlet to drink should Hamlet score the first or second hits of the match. Hamlet returned to the area of Elsinore just as Ophelia’s funeral is taking place. Stricken with grief, he attacked Laertes and declared that he had always loved Ophelia. Back at the castle, he tells me that he thinks one must be prepared to die, since death can come at any time. A courtier named Osric arrived on Claudius’s orders to arrange the fencing match between Hamlet and Laertes.

 

As soon as the sword-fighting began, Hamlet scored the first hit. The king then offered the poisoned goblet, but Hamlet rejected the drink. Instead, Gertrude takes a drink from it and is killed by the poison. Laertes succeeds in cutting Hamlet, though Hamlet does not die of the poison instantly. After an accidental switch of swords, Laertes is cut by his own poisoned sword blade, and, after telling Hamlet that Claudius is responsible for the queen’s death, he dies from the blade’s poison. Hamlet then stabs Claudius with the poisoned sword and forces him to drink down the rest of the poisoned wine. Claudius dies, and Hamlet dies right after getting his revenge.

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My Last Lecture

 

My Last Lecture

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My First Japanese Lesson

Japanese is a language spoken by over 130 million people in Japan and in Japanese emigrant communities. It is a member of the Japonic  language family, which has a number of proposed relationships with other languages, none of which has gained wide acceptance among historical linguists.

Japanese word order is classified as Subject Object Verb. However, unlike many Indo-European languages, the only strict rule of word order is that the verb must be placed at the end of a sentence; other elements in the sentence may be in various orders for emphasis, or possibly omitted. This is because the Japanese sentence elements are marked with particles that identify their grammatical functions.

In Japanese, the subject or object of a sentence need not be stated if it is obvious from context. In addition, it is commonly felt, particularly in informal spoken Japanese, that the shorter a sentence is, the better.As a result of this grammatical permissiveness, there is a tendency to gravitate towards brevity; Japanese speakers tend to omit pronouns on the theory they are inferred from the previous sentence, and are therefore understood. In the context of the above example, hana-ga nagai would mean “their noses are long,” while nagai by itself would mean “they are long.” A single verb can be a complete sentence: Yatta! (やった!)”They  did it!”.

Japanese has an extensive grammatical system to express politeness and formality. The Japanese language can express differing levels in social status. The differences in social position are determined by a variety of factors including job, age, experience, or even psychological state. The person in the lower position is expected to use a polite form of speech, whereas the other might use a more plain form. Strangers will also speak to each other politely. Japanese children rarely use polite speech until they are teens, at which point they are expected to begin speaking in a more adult manner.

Most Japanese sentences contain both kanji and hiragana. Kanji is used for nouns  and the stems of verbs, and hiragana for the endings of verbs and for grammatical particles. Foreign borrowings are normally spelled in katakana. Some Japanese words are written with different kanji depending on the specific usage of the word—for instance, the word naosu  is written 治す when it refers to curing a person, and 直す when it refers to fixing an object.

Traditionally, Japanese is written in a format called tategaki, which copies the traditional Chinese system. In this format, the characters are written in columns going from top to bottom, with columns ordered from right to left. After reaching the bottom of each column, the reader continues at the top of the column to the left of the current one. Modern Japanese also uses another writing format, called yokogaki. This writing format is horizontal and reads from left to right, just like English. A book printed in tategaki opens from what a Westerner would call the back, while a book printed in yokogaki opens from what traditionally in Japan would have been considered the back.

Japanese has five vowels, and vowel length is phonemic, with each having both a short and a long version. Elongated vowels are usually denoted with a macron over the vowel in rōmaji, or a chōonpu succeeding the vowel in Japanese.

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First Synthetic Cell Created

Synthetic Cells

Blue colonies indicate a successfully transplanted genome.

Craig Venter and team make a historic announcement: they’ve created the first fully functioning, reproducing cell controlled by synthetic DNA.

Here is the video announcement from Washington D.C.:

For the first time, to a degree scientists have created life. Craig Venter’s team at the J. Craig Venter Institute in Rockville, Maryland, and San Diego, California, have made a bacterial genome from smaller DNA subunits, and then transplanted the whole string into another cell. So what exactly is the science behind this, and what are its broader applications to this discovery?

The cell was created by stitching together the genome of a pathogen called Mycoplasma mycoides from smaller pieces of DNA synthesised in the lab, and inserting the genome into the empty cytoplasm of a related bacterium. The transplanted gene booted up in its host cell, and then divided over and over to make billions of M. mycoides cells.

Venter and his team added a bunch of representative markers into their synthesised genome. All of them were found in the synthetic cell when it was sequenced.

These markers do not make any proteins, but they contain the names of 46 scientists on the project and several quotations written out in a secret code. The markers also contain the key to the code.

Venter’s work was just proof of what could be done in the future, future synthetic cells could be used to create drugs, bio-fuels and other useful products. He is expected to join up with with Exxon Mobil to produce biofuels from algae and with Novartis to create vaccines.

But such advances come with uncertainty, Robert Field, professor of Law and Health Management and Policy at Drexel University said: “The ability to create new life forms may be emerging from the world of science fiction; but will everything we create be benign, or is Frankenstein now in the realm of possibility?”

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