How does Atticus symbolize a mockingbird?

In the book "To Kill A Mockingbird,", Atticus Finch is portrayed and described as an honest innocent man.  He is a lawyer by trade and has represented Maycomb county in the state legislature.  Atticus is considered by most in the town to be an honest and virtuous man.  The book reaches an important zenith in this character portrayal when Atticus is assigned to defend Tom Robinson, a black man, accused of raping a white woman.  One of the important quotes in the book has to do with Jem and Scout receiving air rifles for Christmas.  Atticus tells them "Shoot all the blue jays you can; but don't kill a mockingbird, it would be a sin."  Mockingbirds are considered innocent, making a living by imitating all the other birds in their general locale.  The entire book is a work portraying innocence:  innocence as a virtue, as a characteristic of age, and the loss thereof by growing up and seeing the contrasting values of other people within our society.  Thus, it is fitting to symbolize Atticus with the imagery of the mockingbird itself.

`2x + 2z = 2, 5x + 3y = 4, 3y - 4z = 4` Solve the system of linear equations and check any solutions algebraically.

You may use the substitution method to solve the system, hence, you need to use the first equation to write x in terms of z, such that:

`2x + 2z = 2 => x + z = 1 => x = 1 - z`

You may now replace 1 - z for x in equation `5x + 3y = 4,` such that:

`5(1 - z) + 3y = 4 =>5 - 5z + 3y = 4 =>  - 5z + 3y = -1`

You may use the third equation, `3y - 4z = 4` , along with `-5z + 3y = -1 ` equation, such that:

`3y = 4 + 4z`

Replace 4 + 4z for 3y in equation -5z + 3y = -1, such that:

`-5z + 4 + 4z = -1 => -z = -1 - 4 => -z = -5 => z = 5`

You may replace 5 for z in equation `3y = 4 + 4z:`

`3y = 4 + 4*5 => 3y = 24 => y = 8`

You may replace 5 for z in equation `x = 1 - z:`

`x = 1 - 5 => x = -4`

Hence, evaluating the solution to the given system, yields `x = -4, y = 8, z = 5.`

`sin(2x)sin(x) = cos(x)` Find the exact solutions of the equation in the interval [0, 2pi).

`sin(2x)sin(x)=cos(x) ,0<=x<=2pi`

`sin(2x)sin(x)-cos(x)=0`

`=2sin(x)cos(x)sin(x)-cos(x)=0`

`=cos(x)(2sin^2(x)-1)=0`

`=cos(x)(sqrt(2)sin(x)-1)(sqrt(2)sin(x)+1)=0`

solving each part separately,

`cos(x)=0 , (sqrt(2)sin(x)-1)=0 , (sqrt(2)sin(x)+1)=0`

General solutions for cos(x)=0 are,

`x=pi/2+2pin , x=(3pi)/2+2pin`

solutions for the range `0<=x<=2pi`  are,

`x=pi/2 , x=(3pi/2)`

`(sqrt(2)sin(x)-1)=0`

`sin(x)=1/sqrt(2)`

General solutions are,

`x=pi/4+2pin , x=(3pi)/4+2pin`

solutions for the range `0<=x<=2pi`  are,

`x=pi/4 , x=(3pi)/4`

`sqrt(2)sin(x)+1=0`

`sin(x)=-1/sqrt(2)`

General solutions are,

`x=(5pi)/4+2pin, x=(7pi)/4+2pin`

solutions for the range `0<=x<=2pi`  are,

`x=(5pi)/4 , x=(7pi)/4`

Combine all the solutions,

`x=pi/2 ,x=(3pi)/2 , x=pi/4 , x=(3pi)/4 , x=(5pi/4) , x=(7pi)/4`

How does an imperialistic past impact the world today?

An imperialist past affects the world today. A good example of this can be seen in Latin America. The United States was heavily involved in Latin America beginning in the late 1800s or early 1900s. We indicated that we wanted Latin America to be free to develop on its own and to remain independent. Thus, we intervened in Latin American countries when we perceived there was a threat of European involvement on the horizon in Latin America. We went into the Dominican Republic and Nicaragua in the early 1900s to maintain order. When the Latin Americans understood that our involvement was mainly to protect the interests of the United States, the Latin American nations began to resent us. This resentment continues to exist today. There is a belief in Latin American countries that the United States acts as a big brother to supposedly protect them while, in reality, protecting our interests.

The imperialism of the past certainly affects the course of events today.

If a bank has a deposit of $500,000 and holds reserves of $100,000 and the central bank requires a reserve of 5%, what is (a) the excess reserve...

a) If Central Bank requires a reserve ratio of 5%, we first need to calculate the required the first required reserves. This is calculated as follows: 

Required Reserves = Deposit x Reserve Ratio 

First lets convert the reserve ratio from percentage to decimal form as follows: 

`5% = (5/100) = 0.05`

Required Reserves = `$500 000 xx 0.05 = $25 000`

Now we know the value of the required reserves, we can now determine the excess reserves: 

Excess Reserves = Total reserves - Required reserves 

Excess Reserves = `$100 000 - $25 000 = $75 000`

b) In order to determine the money supply increase, we first need to determine the multiplier. 

Multiplier = 1/(reserved ratio)

Multiplier = `1/0.05 = 20`

Money supply increase = Excess reserves x Reserved ratio 

Money supply increase = `$75000 xx 20 = $1 500 000`

SUMMARY: 

a) Excess Resevers = $75 000

b) Money Supply Increased by $1 500 00

How do you know that flammability is a chemical property ?

By definition, chemical properties are properties of a substance that can only be observed during a chemical change. Chemical changes are reactions that convert one or more substances into new substances. Therefore, chemical changes change the composition of the reactants.

Flammability is a chemical property because it can only be observed or measured during a chemical change known as combustion. Combustion is a chemical reaction that occurs when a fuel reacts with oxygen to produce light and heat.

Heat of combustion, pH, being corrosive, oxidation, and electronegativity are other examples of chemical properties.

On the other hand, physical properties of substances describe characteristics of physical states of substances. Density, melting point, boiling point, hardness, malleability, and solubility are examples of physical properties.  

When does Atticus say wise words to Scout in To Kill a Mockingbird? What are some quotes?

Whenever Scout goes to her father with a problem, he gives her wise advice.  He is consistent in his desire to instill a spirit of empathy and kindness toward others in his daughter.  Scout sometimes gets angry and wants to fight other children.  Atticus always advises her against this.

When Scout is mad at Miss Caroline because she had gotten in trouble at school for defending Walter Cunningham, Atticus encourages empathy.  He does not want his daughter to be angry with her new teacher.  He tells Scout that she should look at the situation from Miss Caroline's perspective:

Atticus said I had learned many things today, and Miss Caroline had learned several things herself.  She had learned not to hand something to a Cunningham, for one thing, but if Walter and I had put ourselves in her shoes we'd have seen it was an honest mistake on her part (To Kill a Mockingbird, Chapter 3).

Later, Scout expresses her anger toward students at school who criticize her father.  They insult Atticus because he is defending Tom Robinson, who is a black man.  Scout tries fighting them.  Atticus tells her that he does not want her to fight, and instead gives her advice:

No matter what anybody says to you, don't you let 'em get your goat.  Try fighting with your head for a change… it's a good one, even if it does resist learning" (Chapter 9).