How did humanist ideals change the world of art in terms of the artists themselves and their artwork?

Humanist ideals came to the forefront in Europe during the Renaissance, roughly the fifteenth and sixteenth centuries. This period saw a burst of renewed interest in the classical literature of Greek and Roman authors. Humanism, which grew out of an interest in the classics, is, as the name indicates, a form of thought that places emphasis on the importance of humankind and human reason. Humanism shifted thinking away from the prior emphasis on God and faith, though these elements remained important.
Humanism brought themes from classical literature into art. Instead of art wholly concerned with Christian subjects, artists began painting stories from Greek and Roman literature. For example, Botticelli painted the birth of Venus, a Greco-Roman goddess. This was a significant shift in artistic sensibility.
Further, artists moved from being anonymous artisans imitating and reproducing conventional images. Instead, they became creative artists as we understand them today, producing unique works. As a result, artists themselves, like Botticelli and Michelangelo, began to be celebrated as stars and to sign their work.

5^(2x)+20*5^x-125=0 Solve the equation.

We are asked to solve 5^(2x)+20*5^x-125=0 :
Rewrite as (5^x)^2+20*5^x-125=0 and let y=5^x to get
y^2+20y-125=0 and
(y+25)(y-5)=0 so y=-25 or y=5.
y cannot be -25 as 5^x>0 for all real x.
If y=5 then x=1. If x=1 then 25+20(5)-125=0.
x=1 is the solution.
The graph:

 

How does William Golding depict the loss of the "lawful world"? What results from a loss of civility on the island?

William Golding illustrates the loss of a "lawful world" by depicting the boys' gradual descent into savagery. At the beginning of the novel, the boys democratically elect Ralph as their leader and work together to complete various tasks. They are still influenced by civilization and treat one another with considerable respect. As the novel progresses, the boys begin to neglect their agreed-upon duties, and their belief in a beast drastically affects the stability of the entire group. Jack gradually uses his position to influence the hunters and encourages their violent behavior. The hunters experience bloodlust after killing their first pig and begin to favor Jack over Ralph. After Jack attempts to usurp power from Ralph, the majority of the boys choose to join Jack's tribe at the other end of the island. Ralph, Piggy, Samneric, and Simon are the only boys who do not capitulate to Jack's rule. Toward the end of the novel, the boys brutally murder Simon after mistaking him for the beast, and Roger purposely kills Piggy. Brutality, savagery, and immorality take the place of civility on the island. Jack then commands his tribe of savages to hunt Ralph as the novel comes to an end. Fortunately, Ralph is able to survive and is saved when a British officer arrives on the beach. Golding's use of symbols also reveals the loss of civility throughout the novel. The conch symbolizes civilization, democracy, and order. Initially, the boys obey the conch by allowing the person holding it to speak without interrupting them. As the novel progresses, Jack begins to break the rules regarding the conch by speaking out of turn. Eventually, Jack and his hunters reject the power of the conch and move to the other end of the island. Toward the end of the novel, the conch breaks when Piggy is brutally murdered. The broken conch symbolizes the complete destruction of civilization on the island. In addition to the conch, Golding also uses the signal fire, clothing, and the length of the boys' hair to represent the loss of a "lawful world." The signal fire also represents civilization, hope, and rescue. As the novel progresses, the boys struggle to maintain the fire, and it eventually goes out. Similar to the broken conch, the inability to maintain a signal fire represents the boys' descent into savagery. The boys also begin to neglect their clothing, a remnant of their civilized past, and their hair begins to grow. Shaggy, unkempt hair symbolizes their developing savagery. Jack and the hunters also neglect their clothing and choose to paint themselves in tribal patterns. Clothing is a symbol of civilization, and the boys' decision to discard their clothes represents their deteriorating civility.

What is the difference between "character" and "characterization" according to the paragraph below? Character is essential to plot. Without characters Burroughs’s Tarzan of the Apes would be a travelogue through the jungle and Faulkner’s “A Rose for Emily” little more than a faded history of a sleepy town in the South. If stories were depopulated, the plots would disappear because characters and plots are interrelated. A dangerous jungle is important only because we care what effect it has on a character. Characters are influenced by events just as events are shaped by characters. Tarzan’s physical strength is the result of his growing up in the jungle, and his strength, along with his inherited intelligence, allows him to be master there. The methods by which a writer creates people in a story so that they seem actually to exist are called characterization. Huck Finn never lived, yet those who have read Mark Twain’s novel about his adventures along the Mississippi River feel as if they know him. A good writer gives us the illusion that a character is real, but we should also remember that a character is not an actual person but instead has been created by the author. Though we might walk out of a room in which Huck Finn’s Pap talks racist nonsense, we would not throw away the book in a similar fit of anger. This illusion of reality is the magic that allows us to move beyond the circumstances of our own lives into a writer’s fictional world, where we can encounter everyone from royalty to paupers, murderers, lovers, cheaters, martyrs, artists, destroyers, and, nearly always, some part of ourselves. To understand our response to a story, we should be able to recognize the methods of characterization the author uses.

According to this paragraph, a character is a person in a story whereas characterization is a device used to create a character and make him or her seem vivid and real.
A character is literally just a figure in a story whose actions drive the plot. A character need not be a person—it can be an animal or even an object. All that matters is that the character provides a reason for a plot to occur.
Characterization usually occurs through dialogue, action, and what the author tells us outright about a character. These elements make a character seem like a real person. This keeps the reader invested and interested in the story.
So according to this paragraph, character and characterization are quite interrelated. One cannot exist without the other. Characterization cannot exist without character, and a character lacking characterization is nothing but an emotionless puppet the reader will be unable to care about.

The paragraph states that any person who appears in a story is a character. Without characters there would be no real story, the writer argues, because it is characters that make the plot of a story come alive. A character, however, doesn't have to have much of a role in a story nor does the character have to be very well rounded.
Characterization, on the other hand, is the process of making a character in a a story seem real. The author uses the example of Huckleberry Finn, a boy who might seem alive to us. A good writer like Mark Twain can create characters who seem like real people, but we need to remember that these figures are merely fictional constructs.
A story needs characters, whether they are one-dimensional or well-rounded. A good story, however, includes characters who are so well-characterized that they fell alive to us.

While considering the idea of "character," you may wish to also consider stock characters, archetypes, and stereotypes.
You can find information on stock characters here.
You can find information on archetypes here.
You can find information on stereotypical characters here.

Based on the included paragraph, it is a bit tough to specifically nail down the definition of "character" because the paragraph doesn't include a definition.  The paragraph states that characters are "essential to plot" and "influenced by events," but that doesn't concretely tell readers what a character is.  The Merriam-Webster dictionary defines a character as follows:

one of the persons of a drama or novel

That works okay, but I believe that the definition should be expanded a little bit.  The above definition seems a bit too limited to me because it gives the connotation that a character must be human.  I like to define a character as follows: a character is a person, an animal, or an imaginary being that participates in the action of a story.  
Characterization is what makes a character feel real and alive.  Characterization is the tool that authors use to make a character something more than a proper noun.  The paragraph that the question provides ends with a statement about authors using various characterization methods to build a character.  
The two methods of characterization are direct and indirect characterization.  Direct characterization happens when the narrator or another character directly tells readers information about a character.  This kind of characterization usually occurs early in a story.  The narrator will tell readers that a particular character has blond hair and blue eyes.  There isn't anything for a reader to deduce about the character.  That's what indirect characterization requires.  A reader or viewer must deduce the characteristics of a character based on that character's behavior, speech, appearance, etc.   
https://literarydevices.net/characterization/

What were some changes in American foreign policy from 1898 to 1953?

1898 marked a significant change in the foreign policy of the United States. It was in that year that the country began growing its overseas holdings and projecting its power around the world. Much of this was the result of the modernization of the US Navy. Adopting the principles laid out by Captain Alfred Thayer Mahan that a strong navy ensured a strong nation, the United States began building more modern warships. To support a steamship navy, the country needed coaling stations strategically placed around the globe. As such, the US gained control of ports in Puerto Rico, Guam. Hawaii, and the Philippians for this purpose.
Also, at the end of the nineteenth century, the United States had very little experience in diplomatic foreign policy. There were very few professional diplomats in the State Department. President Theodore Roosevelt sought to change this. He recruited a number of statesmen to add to the diplomatic core and actively sought out new talent.
Another major change in foreign policy occurred in 1904 when President Roosevelt issued the Roosevelt Corollary to the Monroe Doctrine. This states that the United States was retaining the right to get involved in the affairs of unstable nations in the Western Hemisphere in order to keep European nations uninvolved.
Roosevelt also supported what he called "Big Stick Diplomacy." Essentially the United States would act as an international police force to put an end to unrest in the hemisphere. In practice, this heavy-handed foreign policy also served the needs of the United States, such as in issues of the canals in Panama and Nicaragua, the blockade of Venezuela, and the Spanish-American War in Cuba.
In the second decade of the twentieth century, American foreign policy took a shift towards neutrality and non-interference. President Woodrow Wilson set this isolationist agenda in an attempt to keep the country out of the conflicts that were consuming the great powers of Europe. Circumstances, particularly the repeated destruction of American ships by German U-boats, prevented the country from staying neutral and the United States did take up arms in WWI in 1917. This ended nearly a decade of non-martial foreign policy. However, the United States did not formally take up alliances with Great Britain and France.
The 1920s saw a more subtle approach to foreign policy. The United States did not enter into any formal political alliances with other countries and had little contact with the League of Nations. However, the country did use its financial influence to set a number of international agendas. The United States was particularly concerned with changing some of the practices resulting from the Treaty of Versailles and used its importance as a trade partner to achieve these ends.
Franklin Roosevelt's early presidency was characterized by the "Good Neighbor Policy." In a radical shift from the more heavy-handed policies of the past, Roosevelt pledged not to interfere militarily in the affairs of Latin American nations. This did a lot to repair the strained relations between the United States and many other countries in the hemisphere.
Roosevelt also tried to keep the country out of the Second World War while supporting Great Britain through the lend-lease program. The attack on Pearl Harbor and the declaration of war by the Axis Powers brought the country reluctantly into the conflict. The country threw itself wholesale into defeating the Axis. Unlike WWI, the United States became a fully fledged member of the Allied forces and worked closely with Great Britain and the Soviet Union to defeat their common enemies.
The post-war period was mostly concerned with issues relating to the Cold War. The United States was mostly concerned with containing the influence of the Soviet Union and preventing the spread of communism. This included programs such as the Marshall Plan which provided economic aid to rebuild Western Europe. The thinking was that economically robust nations would better be able to withstand the influence of the USSR.
In 1950, the United States and its NATO allies attempted to stop the spread of communism on the Korean Peninsula in the three-year-long Korean War. This was just the first of a series of proxy wars between the two world powers for global influence.
In short, foreign policy from the end of the nineteenth century to the mid-twentieth century went through periods of isolationism and periods broader global outlook. The United States started the period as an emerging global player just learning to flex its muscles. Fifty years later, the US was one of the most influential countries in the world with a well-defined foreign policy.
https://history.state.gov/departmenthistory/short-history/development

https://www.foreignaffairs.com/history-foreign-affairs

What are the essential features of lipids?

Lipids are naturally occurring organic compounds that include fats, oils, and certain steroids. They are present in almost all living organisms in this ecosystem. They play immense roles in the cells of living organisms. Almost all lipids are insoluble in water and are known as hydrophobic since they are water-repellent.
They have many important roles. The most important function lipids perform is serving as the building blocks of cell membranes. Other functions include energy storage, insulation, and cellular communication and protection. Lipids also allow for the absorption of fat-soluble vitamins like A, D, E, and K, which are very much essential for the body.
Cell membranes are made up of a double layer of lipids known as phospholipids. This phospholipid layer creates a barrier for substances moving in and out of a cell, thus providing a protection.
Fat (lipid) molecules can store very high amounts of energy, which is needed for the body to perform day-to-day activities. Fats are important for insulating the body from outer temperatures, especially in the case of some marine animals. In order to prevent themselves from freezing water, they have a thick layer of fat to keep them warm. Fats also provide a protective layer around important organs like the liver and kidneys.
Steroids are a group of lipids that are involved in cell-to-cell communication. Most steroids are hormones and are important for many processes in the body, including growth, sexual development, regulating metabolism, and immune defense.
https://basicbiology.net/micro/biochemistry/lipids

Is Zeus mortal or immortal?

Zeus is the Greek sky god, ruler of Olympus, and supreme arbiter among the gods, so he is most certainly immortal, and there are definitely stories that demonstrate this quality. To begin with, you might consider looking into the story of the birth of Athena, by which she emerges out of his head fully formed.
As an additional example, I would refer to a particular variation on the story of Zeus's battle with Typhoeus, sometimes referred to as Typhon, as related by Apollodorus (as cited in Barry B. Powell, Classical Myth, 4th Ed., Upper Saddle River, New Jersey: Pearson Education, 2004, pp. 92–93). This particular version of the story is interesting because in it, Typhon is actually able to defeat Zeus, and even cripple him, after which he hides Zeus in a cave, under guard by a dragon. But it's notable, as far as this answer is concerned, that, while he has defeated Zeus, he can't actually kill Zeus, and that this injury, while severe, is not itself permanently impairing. Hermes proceeds to sneak into the cave and assist his father, after which Zeus emerges healed. The fight with Typhon resumes, with Zeus victorious this time.
The one caveat you should be aware of, however, is that Greek mythology tends to be variable. Different places had their own traditions and stories, so we should expect a certain element of variance to emerge within the mythology. Nevertheless, I'd hope that, as far as this answer is concerned, these examples give some idea as to the vast degree of separation the Greeks understood as existing between mortals and the gods.

Zeus is immortal. This simply means that he cannot die, as opposed to mortals, who can. He is the god of sky and thunder, as well as lightning, law, order, and justice. He's the father of the gods in the Greek pantheon, the one whom all the other gods fear and respect. He's also the object of veneration from human beings, or mortals, who honor him with countless sacrifices and rituals. Zeus, like all the gods, regularly intervenes in human affairs—taking sides in conflicts, sending down bolts of thunder to destroy those mortals foolish enough to defy him, taking on the form of animals to allow him to mate with mortal females. He's certainly not someone to be trifled with, by either god or man. He is truly the first of the gods.
https://www.theoi.com/Olympios/Zeus.html