Where does the cuckoo sing, and how do the islanders react to the maiden's song in "The Solitary Reaper"?

The cuckoo sings in the wild islands of the Hebrides off the coast of Scotland, and the traveler on the islands reacts to the break in the silence by the "melancholy strain" of the maiden.

In another of Wordsworth's poems, the cuckoo symbolizes innocence and childhood. Here in "The Solitary Reaper," the innocent cuckoo is alluded to as having broken "the silence of the seas" and the pristine forces of the rugged islands of the...

The cuckoo sings in the wild islands of the Hebrides off the coast of Scotland, and the traveler on the islands reacts to the break in the silence by the "melancholy strain" of the maiden.

In another of Wordsworth's poems, the cuckoo symbolizes innocence and childhood. Here in "The Solitary Reaper," the innocent cuckoo is alluded to as having broken "the silence of the seas" and the pristine forces of the rugged islands of the Hebrides in the "springtime." However, in the harvesting season, the cuckoo is not heard by the speaker; instead, it is the melancholy song and the "thrilling voice" of the maiden who "cuts and binds the grain" that "[B]reaks the silence of the seas" on the fossil beaches.

The song of the maiden certainly must affect those who hear her stirring and "welcome notes." While there is no specific mention of how the islanders react, the speaker is profoundly moved by "the plaintive numbers" of her song, and he feels that others are affected, as well. For, he remarks upon her sweet voice as more welcome to travelers than the song of a nightingale, and he argues that her voice is more thrilling than that of any cuckoo-bird that "[B]reak[s] the silence" on the fossil beaches of the Hebrides. So affected is the speaker by her song that he remembers the music long after he has heard her, as he interprets her song as an articulation of the spirit of the area and the universal emotions of humankind.

`y' = -sqrt(x)/(4y)` Solve the differential equation.

An ordinary differential equation (ODE)  is differential equation for the derivative of a function of one variable. When an ODE is in a form of `y'=f(x,y)` , this is just a first order ordinary differential equation. 

The given problem: `y' = -sqrt(x)/(4y)` is in a form of `y'=f(x,y)` .

 To evaluate this, we may express `y'` as `(dy)/(dx)` .

 The problem becomes:

`(dy)/(dx)= -sqrt(x)/(4y)`

We may apply the variable separable differential equation: `N(y)...

An ordinary differential equation (ODE)  is differential equation for the derivative of a function of one variable. When an ODE is in a form of `y'=f(x,y)` , this is just a first order ordinary differential equation. 

The given problem: `y' = -sqrt(x)/(4y)` is in a form of `y'=f(x,y)` .

 To evaluate this, we may express `y'` as `(dy)/(dx)` .

 The problem becomes:

`(dy)/(dx)= -sqrt(x)/(4y)`

We may apply the variable separable differential equation: `N(y) dy = M(x) d` x.

Cross-multiply `dx` to the right side:

`dy= -sqrt(x)/(4y)dx`

Cross-multiply `4y` to the left side:

`4ydy= -sqrt(x)dx`

Apply direct integration on both sides:

`int 4ydy= int -sqrt(x)dx`

Apply basic integration property: `int c*f(x)dx = c int f(x) dx` on both sides:

`4 int ydy= (-1) int sqrt(x)dx`

For the left side, we apply the Power Rule for integration: `int u^n du= u^(n+1)/(n+1)+C` .

`4 int y dy = 4*y^(1+1)/(1+1)`

               `= 4*y^2/2`

               `= 2y^2`

For the right side, we apply Law of Exponent: `sqrt(x)= x^(1/2)` before applying the Power Rule for integration: `int u^n du= u^(n+1)/(n+1)+C` .

`(-1) int x^(1/2)dx =(-1) x^(1/2+1)/(1/2+1)+C`

                       `=- x^(3/2)/(3/2)+C`

                       `=- x^(3/2)*(2/3)+C`

                       ` = -(2x^(3/2))/3+C`

Combining the results, we get the general solution for differential equation:

`2y^2= -(2x^(3/2))/3+C`

We may simplify it as:

`(1/2)[2y^2]= (1/2)[-(2x^(3/2))/3+C]`

`y^2= -(2x^(3/2))/6+C/2`

`y= +-sqrt(-(2x^(3/2))/6+C/2)`

`y= +-sqrt(-(x^(3/2))/3+C/2)` 

In the original trolley problem, a train is hurtling down a track and you see that it is going to hit a group of 5 people and will certainly kill...

The Trolley Problem was first introduced to students by Philippa Foot in 1967 and poses an interesting ethical dilemma. To answer it, you need to consider the following two questions. Firstly, is it better to sacrifice one person (the minority) in order to save the lives of the majority? Essentially, this question is asking you to reflect on the value of human life. You must think carefully about whether you believe that one life is worth more or less than the lives of many. 

Secondly, to compound the first problem, you also have to consider the physical aspects of sacrificing a life. In the original version of the Trolley Problem, for example, all you have to do is pull a switch. You are not, in any way, connected to the person who will die. But in the second version, you have to physically push over the man. This means that you are actively involved in sacrificing a life and, for some people, this is much more difficult than simply pulling a switch.

Ultimately, it is your only moral values that will help you to answer these questions. For some people, killing a person is wrong, regardless of the circumstances, while others believe that a sacrifice is sometimes worth making. 

Remember that there are no "right" or "wrong" answers here; the Trolley Problem wants you think deeply about the value of life and reflect on your own ethical code. 

For more information, please see the reference link provided.

What are the important tips of the history of Fortunato and Montresor?

Edgar Allan Poe's short story, "The Cast of Amontillado," is the story of Montresor's revenge against Fortunato. It is clear from the text that Fortunato and Montresor have a history together, and that it's been a difficult relationship, at least from Montresor's perspective. 

In the opening line, Montresor, who narrates the story,  states: "The thousand injuries of Fortunato I had borne as best I could, but when he ventured upon insult, I vowed revenge." The...

Edgar Allan Poe's short story, "The Cast of Amontillado," is the story of Montresor's revenge against Fortunato. It is clear from the text that Fortunato and Montresor have a history together, and that it's been a difficult relationship, at least from Montresor's perspective. 

In the opening line, Montresor, who narrates the story,  states: "The thousand injuries of Fortunato I had borne as best I could, but when he ventured upon insult, I vowed revenge." The reader is never told what injuries Fortunato has inflicted upon Montresor, but one can use other evidence from the text to determine the nature of insults Fortunato has likely made against Montresor.  

Later in the story, while the pair is in the catacombs, Fortunato makes a gesture that Montresor does not return. Fortunato makes the statement that Montresor does not comprehend, and this shows that he is not of the brotherhood. When Montresor replies yes, insinuating that he is a mason, Fortunato replies "You? Impossible! A mason?" This would have been insulting to Montresor. The Freemasons are a rather secretive society and an exclusive one. Anticipants, which is what a person wanting to join the organization is called, have to be recommended by someone in order to join. Often, one's family history is taken into account when a person is being considered. When Fortunato expresses disbelief that Montresor could be a part of the brotherhood, he is insinuating that he is not worthy to be a Freemason, either by his own virtues or because of his family's status, or both. Montresor insists that he is a mason. When Fortunato demands proof, he shows him his trowel. Fortunato is speaking of the secret society, and Montresor is talking about the profession in which one uses mortar and bricks or stone to build things. He is about to become that type of mason in order to exact his revenge on Fortunato. 

According to the Montresor, the two men must have been friends prior to Montresor's plot of revenge. Montresor says: "It must be understood that neither by word nor deed had I given Fortunato cause to doubt my good will. I continued, as was my wont, to smile in his face, and he did not perceive that my smile now was at the thought of his immolation." Montresor repeatedly refers to him as his friend throughout the text, both to his face and as part of the narration. This fact of friendship gives the reader questions as to the psychological health of the narrator, for what true friend carries out a plot of destruction as cruel as the one Montresor executes? 

If they were good friends, why would a mere insult cause Montresor to bury his friend alive? Aside from the questions of the narrator's psychological health, Montresor gives us one other clue as to his actions. Fortunato asks him about his family's coat of arms. Montresor describes it as an azure field with a huge human foot crushing the head of a serpent whose fangs are in its heel. Then Fortunato asks what the motto is. Montresor replies: "Nemo me impune lacessit." This is Latin for no one insults with impunity. Ironically, Fortunato does not see the connection between the insults he has hurled at Montresor and the family motto. Montresor has carefully hidden his true feelings from Fortunato. 

Another piece of textual evidence that points to the history of the two men is the dialogue between them at carnival about the Amontillado. Montresor knew Fortunato well enough to know that he considered himself a wine connoisseur and that if he told Fortunato that he'd go to Luchesi instead, Fortunato's interest would be piqued. He knew that Fortunato's pride would compel him to follow Montresor, and he uses the "carrot" of Luchesi to lure him deep into the catacombs to his doom. 

How does the eye transform light energy into neural messages?

Our eyes belong to a special set of eyes called "camera-type eyes". Light comes in via our lenses and focuses on a light-sensitive membrane in the back of the eye called the retina. This works similarly to how a camera focuses light onto film, thus the name. 

The retina is made up of millions of light sensitive cells. These cells come in two varieties: rods and cones. Cones are used for seeing color and fine...

Our eyes belong to a special set of eyes called "camera-type eyes". Light comes in via our lenses and focuses on a light-sensitive membrane in the back of the eye called the retina. This works similarly to how a camera focuses light onto film, thus the name. 

The retina is made up of millions of light sensitive cells. These cells come in two varieties: rods and cones. Cones are used for seeing color and fine details, while rods are used for vision in poor lighting. Rods are found more towards the outside of the retina, while cones can be found in the center of the eye. When light strikes these cells, it excites them into sending electrical signals through the optic nerve to the brain. 

It is not yet fully understood how exactly our brains process these messages into images, but the most recent research suggests that there are three different processing centers in the brain. One works with shape, one deals with color, and the last is responsible for spatial location and movement. These can all be found in the primary visual cortex, which is in the back of the brain (occipital lobe).

How does the narrator describe herself as phenomenal in Maya Angelou's poem "Phenomenal Woman"?

As explanation for men's attraction to her, Maya Angelou's speaker describes the movements of her individual features and the poetry of her motions. These, she declares, are the reasons for her being a "phenomenal woman."

In the first stanza, the speaker notes that pretty women are curious about her secret and ask her how she is able to be so attractive to men. However, when she explains that it is not just her features, "They...

As explanation for men's attraction to her, Maya Angelou's speaker describes the movements of her individual features and the poetry of her motions. These, she declares, are the reasons for her being a "phenomenal woman."

In the first stanza, the speaker notes that pretty women are curious about her secret and ask her how she is able to be so attractive to men. However, when she explains that it is not just her features, "They think I'm telling lies." Nevertheless, she says that her "certain something" that is indefinable is found in the style of her movements and the grace of these movements:

It's in the reach of my arms,
The span of my hips,
The stride of my step,
The curl of my lips...
The swing in my waist

Then, too, she employs imagery to describe the unique features of her body:

It's the fire in my eye,
And the flash of my teeth

The speaker then further explains that she has an inner mystery reflected by her body and movements, which she describes in metaphoric terms:

It's in the arch of my back,
The sun of my smile...
The grace of my style.

Calling herself "a woman / Phenomenally," the speaker adds that men cannot define what it is that draws them to her. For she has an inner mystery, and even when she makes an effort to show it to them, the men say that they still cannot see from what features come her mysterious attractiveness. While the men in the poem look for something concretely physical as the cause of the speaker's attractiveness, the speaker understands that her feminine power comes from an inner source reflected in a combination of physical attributes.

5. You throw a golf ball straight up at 10 meters per second. a. What is the velocity when you catch the golf ball after its return trip? b. How...

When you throw a golf ball straight up, assuming that wind and air resistance are irrelevant, it is pulled back down by gravity, which decelerates it by 9.8 meters/second every second. That deceleration is constant through its rise and fall, creating a parabolic arc when considering its speed graphically.

The answer to part a) is 10m/s. No calculation is necessary. Acceleration curves are symmetrical; in the absence of air resistance, a rising and...

When you throw a golf ball straight up, assuming that wind and air resistance are irrelevant, it is pulled back down by gravity, which decelerates it by 9.8 meters/second every second. That deceleration is constant through its rise and fall, creating a parabolic arc when considering its speed graphically.

The answer to part a) is 10 m/s. No calculation is necessary. Acceleration curves are symmetrical; in the absence of air resistance, a rising and falling object will always land at the same speed at which it was launched.

To answer part b), we can do a simple calculation involving the gravitational constant. Gravity robs the golf ball of speed at its constant rate, so it will take 10 / 9.8 = ~1.02 seconds for the golf ball's velocity to reach zero at the apex of its flight. Because rise and fall are symmetrical, we do not need calculations to know that it will take another 1.02 seconds for the upward motion to reverse, reaching your hand once again. The total time the golf ball travels is 2 * ~1.02 = ~2.04 seconds

Finally, part c) is once again fairly simple. Because acceleration is constant, the average velocity of a fall is always equal to exactly half the final velocity. Because of the symmetry of physics, the acceleration upwards perfectly mirrors the fall back down. Since the golf ball started and ended its flight at 10 m/s, its average speed is 5 m/s, meaning it traveled a total distance of 5 * 2.04 = 10.08 meters.