People disagree about the history of Chamberlain. Some people think that his actions were wrong because he did not stop Hitler. Other people say that he gave Britain and France more time to get ready for war.
Quadratic equation
A quadratic equation is an equation in the form of formula_1, where "a" is not equal to 0. It makes a parabola (a "U" shape) when graphed on a coordinate plane.
When people work with quadratic equations, one of the most common things they do is to "solve" it. This means to find the points on a coordinate grid where the graphed equation crosses the x-axis, or the horizontal axis. These points are called the "zeroes", or "roots", of a function. In other words, to solve the equation means to find the value of "x" so that formula_1, where the coefficients, "a", "b", and "c", are all real numbers. There are different ways to find out the value of x. Plotting the function on a graph is one way. In the picture on the right, the function crosses the x-axis at the points formula_3 and formula_4.
Graphing a quadratic equation makes it is very easy to find the roots, but it is not always convenient. So there are different ways to do this using maths.
Some quadratic equations, like formula_5, can be factorized. This equation can be written as formula_6, which produces two separate equations, formula_7 and formula_8. This is because when any of the two equations is equal to zero, the original equation is equal to zero because the two equations are multiplied together to form the quadratic equation. From this equation, it is easy to use algebra to find out what the value of "x" is. In the first of the two equations, formula_9 and in the second, formula_10. This means that these two values of "x" will make the whole quadratic equation equal to zero. The y-coordinate is equal to zero at these values of x, and so the coordinates formula_11 and formula_12 are the places where the graph of the function crosses the x-axis.
Not all quadratic equations can be factorized, such as formula_13. One of the ways to solve these kinds of equations is called "completing the square". This means to find some value for ""k"" below so that:formula_14 for some "y". Since formula_15 and formula_16 this means formula_17
There are five steps to solve a quadratic equation by completing the square:
This last value for "x" has two values: formula_28 and formula_29. These are the x-coordinates at the points where the y-coordinates are equal to zero and so the function crosses the x-axis.
It is also interesting to note that the vertex of the function, formula_30, can be found from the equation in step 3 above.
Although completing the square can be used to solve many quadratic equations, it does not work with every equation. There is a way to find the value of "x" that makes the equation true by replacing the values in a formula with the coefficients from the quadratic equation. This is called the "quadratic formula", which is:
The numbers represented by "a", "b", and "c" are the same as those in the original equation, . For this formula to work properly, "a" cannot be equal to 0 for the formula (but really, when "a" = 0 in the original equation, it is not quadratic since there is no x-squared term).
The factored form of this equation is , where "s" and "t" are the zeros, "a" is a constant, and "y" and the two values of "x" are ordered pairs which satisfy the equation.
The quadratic formula can be found out, or proved, using the same "completing the square" method from above, only by using "a", "b", and "c" instead of actual values and using algebra to find the value of "x". Here is how:
Now that the value of "x" has been found out, the values of "a", "b", and "c" are replaced with the corresponding coefficients from the original equation. For example, going back to the second example, formula_13 , it can be seen that the values are formula_41, formula_42, and formula_43. By putting these values into the quadratic formula and solving, the result is:
formula_44. Solving the two square roots, the value of "x" can be either 1.148 or -0.348, which is the same as above.
Unlike the other methods described above, the quadratic equation will work with every possible value for "a", "b", and "c", even if there are no "real roots", that is, places where the graph of the function touches the x-axis.
The value inside the square root, that is, formula_45, is known as the "discriminant". It can tell whether the roots are real or Imaginary. There are three cases:
Attac (organization)
The Association pour la Taxation des Transactions pour l'Aide aux Citoyens (Association for the Taxation of Financial Transactions for the Aid of Citizens, ATTAC) is an organization that promotes a tax on foreign exchange transactions, the so-called Tobin tax.
At first Attac demanded only the introduction of the so-called Tobin tax on currency speculation. Now it fights for many issues related to globalisation. Therefore, it reports about the decisions of the World Trade Organisation (WTO), the Organisation for Economic Cooperation and Development (OECD) and the International Monetary Fund (IMF). ATTAC attends the meetings of the G8 with the goal of influencing policymakers' decisions.
Though ATTAC criticises the neoliberal ideology dominating economic globalisation, it is not "anti-globalisation". It supports globalisation policies that they characterise as sustainable and socially just. One of ATTAC's slogans is "The World is not for sale", denouncing the "merchandisation" of society.
Threat
A threat is basically a declaration of intent to inflict punishment or harm or loss on another. However, in many cases the threat is not believed, or may even be a joke. Like other communications a threat has a context, and the context decides its meaning.
A child who says "I'll tell my dad" may learn from the reply "I'm so scared!" that the threat is an idle threat: one that is promises harm that that cannot or will not actually be inflicted.
To encourage compliance, a threat to do harm may be mixed with an offer to do good, conditional upon what the recipient does. This is sometimes called a throffer. The threat part may be implied, yet effective.
Some countries, such as the United States, have a legal concept of true threat. A true threat is a threatening communication which can be prosecuted under the law.
A threat can describe a situation of danger: for example "a terrorist threat". Many countries have a system where the government can adjust its security by having official threat levels.
Promotion
Promotion means spreading information about an product, service or issue
Promotion as part of marketing means spreading information about a product, product line, brand, or company.
"Promotion" includes:
"Promotion for marketing" includes additionally:
Promotion can also happen when a marketing company is providing discounts and coupons to customers to create brand awareness.
Issue
Issue may have one of the following special meanings:
Firefly
Fireflies are a family of beetles called the Lampyridae. These beetles are special in that most of them have bioluminescence, the ability to produce light. They are sometimes called 'lightning bugs' or 'forest stars'. There are about 2000 different species, most of which are nocturnal.
Adults use flashes of light to attract mates. Also, firefly larvae flash their lights to warn predators that they are not a tasty meal. Many predators do not like the taste of firefly larvae.
A firefly is an insect, so it has an exoskeleton and three body parts. Much like an annual cicada, they are usually soft-bodied, often with the elytra (front wings) more leathery than in other beetles.
A firefly may be brown or black with yellow and red marks.
All fireflies glow as larvae. Bioluminescence serves a different function in lampyrid larvae than it does in adults. It appears to be a warning signal to predators, since many firefly larvae contain chemicals that are distasteful or toxic.