For exponential equation: `5^(6x)= 8320` , we may apply the logarithm property:
`log(x^y) = y * log (x).`
This helps to bring down the exponent value.
Taking "log" on both sides:
`log(5^(6x))=log(8320)`
`6x * log (5) = log(8320)`
Divide both sides by log (5) to isolate "6x":
`(6x * log (5)) /(log(5))= (log(8320))/(log(5))`
`6x=(log(8320))/(log(5))`
Multiply both sides by `1/6` to isolate x:
`(1/6)*6x=(log(8320))/(log(5))*(1/6)`
`x =(log(8320))/(6log(5))`
`x=0.935`
According to the Bureau of Statistics, the unknown citizen was a model worker who served the greater community well.
He was a good worker who never got fired, and he "satisfied his employers" immensely as an employee. According to the Bureau, the unknown citizen was socially popular, fully insured, and resistant to extreme or unpopular convictions. By all indications, the unknown citizen adhered to socially-accepted views about popular life and culture. He was said to have bought a paper everyday while he lived and to have reacted to advertisements predictably.
The unknown citizen was also regarded by the Bureau as the stereotypical model citizen who never veered from the truths his government expected him to adhere to: "That he held the proper opinions for the time of year;/ When there was peace, he was for peace: when there was war, he went."
Last, but not least, the unknown citizen was said to have had five children, the "right number for a parent of his generation." He was also said to never have interfered in his children's education, a fact that the Bureau finds especially commendable. In all, the Bureau views the unknown citizen as the ideal citizen.
It is both a moral and a legal issue.
The story of the Wellton 26 began in May 2001. Twenty-six men and teenage boys from the Mexican state of Veracruz, located in southeastern Mexico, attempted to cross the United States-Mexico border into Arizona. They were led by a "coyote," or someone who helps desperate people cross into the United States illegally in exchange for a fee. The coyote was Jesus Lopez Ramos who, before becoming a coyote, also lived in poverty.
Sometime between May 22 and May 24, 2001, fourteen members of the group died, while the other twelve barely escaped with their lives. Unfortunately, Ramos and the migrants had not brought along enough food and water to sustain them during the long trip in the harsh desert climate. They are named the Wellton 26 after Wellton, Arizona, which is the border station nearest to the place where the survivors were found by Border Patrol agents.
The story of the Wellton 26 is, unfortunately, not unusual. Desperate people from Mexico and Central America frequently die trying to reach the United States. They are fleeing from poverty and violence in their home countries, and toward relative safety and economic opportunity. This story made news because of the high number of casualties in this single trek.
The issue of illegality is inextricable from the issue of morality. Many, if not all, of the men and boys in the Wellton 26 were probably entering the United States with the hope of getting jobs as farm laborers, or perhaps, in construction.
Farm labor -- e.g., picking oranges or tomatoes -- pays very little and requires one to work long hours in uncomfortable conditions. Americans, typically, do not perform this work. Certain positions in construction which require hard, manual labor are very similar. Therefore, supervisors seek out illegal immigrants whom they can pay meager wages in exchange for many hours of labor. They can also avoid subsidizing certain benefits, such as health insurance. Thus, because the migrants are illegal, they can be exploited. If they complain about their treatment or their wages, they can be expelled from their jobs and possibly threatened with deportation.
The American desire to "protect our borders" is often at odds with the economic desire for cheap labor. Illegal immigration is undeniably a problem. People who are undocumented have not undergone background checks. Some of these people have criminal records in their home countries. Being undocumented poses an even greater risk for the immigrants. If they are victims of a crime they are less likely to report it out of fear that they will reveal their undocumented status and be deported. For those who have lived in the United States for years and have native-born children, this is a major risk.
Undocumented immigrants also perform a great deal of domestic labor. They are gardeners, nannies, and housekeepers. Again, their illegal status can allow their employers to pay them far less than their labor is worth, while threatening to have them deported if they complain about their wages or responsibilities.
Undocumented immigrants, as previously stated, are fleeing from desperate circumstances. American employers who use their undocumented status to exploit their labor are not only guilty of disobeying the law but are also guilty of treating others inhumanely.
One educated guess about the story's moral is that an obsession with money and material things can be destructive. Mathilde is frustrated with how her life has turned out. She had envisioned herself living among the wealthier, upper class. Instead of making the best of her lower class life, Mathilde spends lots of time daydreaming about that "better" life.
Her husband is comfortable with his life and he does whatever he can to make Mathilde happy. He sacrifices his own savings to buy her a dress. Mathilde is a hit at the party, but this probably has more to do with her positive attitude than it does with her gown and the necklace. When she loses the necklace, she works incredibly hard to repay the loan. Essentially, she works very hard to pay for something she never needed.
It turns out that the necklace was not that expensive. Mathilde had only thought that the necklace was extremely valuable. She was popular at the party because her behavior reflected her pride in how she looked. This is the other moral of the story. Your happiness in life (upper or lower class) depends upon your attitude. Imagine you are "rich," in any sense of the word, and you will feel rich. Imagine you are happy, and your behavior will reflect that positive outlook.
Hello!
Let's set up the problem with the variables. Besides the given height `H = 10 ft,` a rectangular prism also has a length `L` and a width `W` (both in feet). Of course we know that the volume of the rectangular prism is `V = H*L*W ft^3 = 10L*W ft^3,` and we need to maximize it.
Next, the constraint relating to the walls surface. It is not clear whether "walls" means four side walls excluding both the ceiling and the floor. I suppose walls are four vertical walls only. There are two walls of the dimensions `L xx H` and two walls `W xx H,` so their total area is `2*L*H + 2*W*H,` and this is equal to `S = 2000 ft^2.`
This equation, `2*L*H + 2*W*H = 2*L*10 + 2*W*10 = 2000,` gives us the simple constraint `L + W = 2000/20 = 100,` so `L = 100 - W.` The function we need to maximize becomes `V = V(W) = 10(100-W)W = -10W^2 + 1000W.`
It is the quadratic function of `W` with the negative factor `a = -10` at `W^2` and the factor `b=1000` at `W^1.` Its graph is a parabola branches down and it has the only maximum. The point where it is reached is `W_0 = -b/(2a) = -1000/(-20) = 50 (ft).`
Thus `L_0 = 100 - W_0 = 50 (ft),` and the volume they give is `V = 10*50*50 = 25000 (ft^3).`
The answer: the (horizontal) dimensions of the room that give a maximum volume are 50 ft and 50 ft. The maximum volume is `25000 ft^3.`
(if we have to take the ceiling and/or the floor with the area `L*W` each into account, the function remains quadratic and the solution remains similar)
Sam Westing and Bertha Crow’s daughter Violet died.
Even though she never appears in the book, Violet Westing heavily influences events. Her death devastates her mother and father. It is the cause of Crow’s alcoholism and mental health issues, and Sam Westing’s bizarre eccentricities. Neither parent recovers.
Violet Westing was supposed to be married. She was young, and had her whole life in front of her.
The paper king’s later years were marred by tragedy. His only daughter, Violet, drowned on the eve of her wedding, and two years later his troubled wife deserted their home. Although Mr. Westing obtained a divorce, he never remarried. (Ch. 4)
The mystery of who killed Sam Westing stems from his daughter’s death. Westing writes a will and concocts an elaborate game to find out which of his heirs is worthy of his fortune, but he is never actually dead. Westing is there the whole time in his various disguises as Barney Northrup and Sandy McSouthers.
Sam Westing has his fun, and finds that not all of his heirs are hopeless.
His watery blue eyes stared at her over his rimless half-glasses. Hard eyes. His teeth were white, not quite even (no one would ever guess they were false). He was smiling. He wasn’t angry with her, he was smiling.
“Hi, Sandy,” Turtle said. “I won!" (Ch. 27)
Eventually, Sam Westing does die. He dies of old age, with Turtle by his side.
So while there are a lot of explosions and questions about who killed Sam Westing, the only real deaths in this novel are of natural causes. Sam Westing’s daughter drowned, and Sam Westing died of old age. Before he died, he got to know all of his relatives a lot better.
Both the Space Race and the Arms Race were part of the Cold War struggle between the United States and its market-driven, democratic ideology, and the Soviet Union, with its communist, totalitarian ideology. Both races were bound up in the struggle for technological supremacy that came to define post-World War Two foreign policy for the two superpowers. The Arms Race shifted the balance of power back and forth several times in the late 1950s and early 1960s, when the United States and Soviet Union were trying to build up their nuclear arsenals so that each could claim nuclear superiority, and maintain their so-called First Strike Capability, in the event of a nuclear war.
While the United States was ahead of the Soviet Union in enlarging its arsenal of nuclear weapons and miniaturizing warheads to place on top of Intercontinental Ballistic Missiles (ICBMs), the Soviet Union stunned the Americans in 1957 by launching Sputnik, the first man made satellite to enter Earth's orbit. This launch was deeply unsettling and embarrassing for the Eisenhower administration and for the United State's public relations, which aimed to convince unaligned countries that it was the better ally to have.
For the United States, at least up until the launch of Sputnik, building up its nuclear capabilities and containing the spread of communism through proxy war, both overt and covert, was the main priority. Once the Soviets beat the United States into space, however, and showed that they weren't a second rate technological innovator, the Space Race became a main forum for the United States and the USSR to wage their ideological and public relations battles.
The fear on both sides that other country would colonize space first and weaponize it led to a massive outlay in spending from the pentagon, and when JFK announced his intention to land a man on the moon within ten years, the real competition began. The Space Race was not just a race into space, but a race between two diametrically opposed ideological forces who wanted to prove their supremacy to the world. Both sides understood that whoever got a manned mission into space first would claim bragging rights for eternity, and that kind of propaganda victory could win or lose the Cold War. Whoever won the space race would likely win struggle, and export its ideology and power around the globe. As it happened, the United States landed its astronauts on the Moon in 1969 and went on to win the Cold War, proving this thesis.
Finally, the Space Race and the Arms Race were not separate races, but rather, they became conflated when the United States and Soviet Union realized that the military applications of space technology such as communication satellites could determine which side had more effective nuclear arsenals. Both sides used their space technology for missile guidance and detection of enemy missiles and enemy positions. The ability to place spy satellites in space and to use low orbiting ICBMs to launch nuclear attacks changed the face of warfare forever. Once the United States and Soviet Union realized that they could launch missiles with nuclear warheads from the other side of the world and have those missiles hit their targets in 35 minutes, instead of the hours it took for bombers to deliver their payloads from nearby bases, the idea of having first strike capability became a moot point. Both sides used their space satellites to set up missile shields, that could detect incoming missiles and self-launch a so-called Massive Retaliation, which would ensure that a nuclear war, regardless of who started it, would end with the destruction of human civilization.
This realization brought about the notion of Mutually Assured Destruction, and convinced both the United States and the Soviet Union that nuclear weapons had no practical use except as deterrents. In some ways, the Space Race actually brought the two countries closer together, making both of them realize that treaties such as Open Skies, SALT (The Strategic Arms Limitation Treaty) and a ban on weaponizing and colonizing outer space exclusively, was the best way to avoid a nuclear holocaust. The Space Race also brought about unprecedented cooperation between the two countries, who finally understood from the vantage point of outer space that they shared a planet, and needed to learn how not to destroy it, even as they both sought to defeat on another.
