`int 5^t sin(5^t) dt` Evaluate the indefinite integral.

You need to use the following substitution  `5^t=u` , such that:

`5^t=u=>5^t*ln 5 dt = du => 5^t*dt= (du)/(ln 5)`

`int5^t*sin(5^t) dt = (1/(ln 5))*int sin u du`

`(1/(ln 5))*int sin u du = -(1/(ln 5))*cos u + c`

Replacing back  `5^t ` for u yields:

`int5^t*sin(5^t) dt = (-cos(5^t))/(ln 5)+c`

Hence, evaluating the indefinite integral, yields `int5^t*sin(5^t) dt = (-cos(5^t))/(ln 5)+c.`

You need to use the following substitution  `5^t=u` , such that:

`5^t=u=>5^t*ln 5 dt = du => 5^t*dt= (du)/(ln 5)`

`int5^t*sin(5^t) dt = (1/(ln 5))*int sin u du`

`(1/(ln 5))*int sin u du = -(1/(ln 5))*cos u + c`

Replacing back  `5^t ` for u yields:

`int5^t*sin(5^t) dt = (-cos(5^t))/(ln 5)+c`

Hence, evaluating the indefinite integral, yields `int5^t*sin(5^t) dt = (-cos(5^t))/(ln 5)+c.`

Why do our cells need to do cellular respiration in order to survive?

All the cellular functions require energy and cells have no direct way of getting energy. Similar to us, cells also need to consume food and then obtain energy out of it. Cellular respiration is the process by which we all get energy. This process can be represented by the following chemical reaction:

`C_6H_12O_6 + 6 O_2 -> 6 CO_2 + 6 H_2O + ATP`

In this process, glucose is broken down in presence of oxygen...

All the cellular functions require energy and cells have no direct way of getting energy. Similar to us, cells also need to consume food and then obtain energy out of it. Cellular respiration is the process by which we all get energy. This process can be represented by the following chemical reaction:

`C_6H_12O_6 + 6 O_2 -> 6 CO_2 + 6 H_2O + ATP`

In this process, glucose is broken down in presence of oxygen and the resultant products are carbon dioxide, water and energy (in the form of ATP or adenosine triphosphate molecules). ATP molecules further break down into ADP (or adenosine diphosphate) along with the release of energy. It is this energy that cells use to carry out their operations. Thus, cellular respiration is essential for cells' survival and functioning.

Hope this helps. 

From what point of view is this story told?

Shirley Jackson's short story "Charles" is told from the point of view of the mother. This point of view is third-person limited. 

This particular point of view is perfectly suited to the dramatic irony that is the main literary feature of the narrative. For, while the mother narrates the story, it becomes apparent to the reader that the "sweet-voiced, nursery-school tot" as she calls Laurie, her son, who says good-bye to her on the first...

Shirley Jackson's short story "Charles" is told from the point of view of the mother. This point of view is third-person limited. 

This particular point of view is perfectly suited to the dramatic irony that is the main literary feature of the narrative. For, while the mother narrates the story, it becomes apparent to the reader that the "sweet-voiced, nursery-school tot" as she calls Laurie, her son, who says good-bye to her on the first day of school is not what his mother believes him to be. For instance, when he tells her that his teacher said they were not to take the name of the Lord in vain, the mother does not ask Laurie what he has said that has prompted the teacher to this admonition; instead, she herself is "mindful of the Lord's name" when she exclaims, "Good heavens" in response to Laurie's tales of Charles's getting spanked two consecutive days.

While Laurie may have exaggerated some of the exploits of Charles, he is obviously not a respectful or well-behaved little boy as there is certainly language that he uses when he speaks to his parents that indicates his disrespect. For example, while he tells his mother of Charles's misbehavior, he turns to his father and says, "Hi, Pop, y'old dust mop." (The father says nothing, nor does the mother comment on Laurie's disrespectful name for his father.) Nevertheless, it is not until the mother accompanies Laurie to the PTA meeting that she discovers there is no Charles in the kindergarten. It is then that she learns that her perspective of her son has been very subjective and her point of view quite limited.

Ionic bonds form between ions that have ________.

Ionic bonds occur between ions that have opposite charges. An ionic bond is the electrostatic force that holds ionic compounds together. When a metal reacts with a non-metal, electrons are transferred from the metal which forms a postive ion to the nonmetal which forms a negative ion. The positive and negatve ions are then attracted to each other. 

An example is the reaction between sodium and chlorine. Sodium is a very reactive metal and chlorine...

Ionic bonds occur between ions that have opposite charges. An ionic bond is the electrostatic force that holds ionic compounds together. When a metal reacts with a non-metal, electrons are transferred from the metal which forms a postive ion to the nonmetal which forms a negative ion. The positive and negatve ions are then attracted to each other. 

An example is the reaction between sodium and chlorine. Sodium is a very reactive metal and chlorine is a very reactive nonmetal. Each sodium atom loses an electron to form Na+ and each chlorine atom gains an electron to form Cl-. The resulting sodium and choride ions form a crystal lattice (three-dimenional structure) with a ratio of one Na+ to one Cl-. The formula of an ionic compound always represents the lowest whole-number ratio of ions, but the substance isn't in the form of individual molecules.

The ratio of ions in a formula is related to the charges of the ions. For example, Magnesium chloride has the formula MgCl2. Magnesium loses two electrons to form a +2 ion, so there must be two Cl- ions for every Mg(2+) ion to have a neutral compound.

In this story the Civil War serves as a backdrop; Bierce's main intent is to examine the psychology of someone in a life-or-death situation. What...

Ambrose Bierce implies several things about the psychology of the human mind in "An Occurrence at Owl Creek Bridge". One is that the mind essentially creates its own reality, especially in a moment of great stress. Nothing that Peyton thinks is happening actually is. Although the entire episode Peyton imagines takes place in a fraction of a second, in his mind he travels quite far after the miraculous breaking of the hangman's noose. Even though...

Ambrose Bierce implies several things about the psychology of the human mind in "An Occurrence at Owl Creek Bridge". One is that the mind essentially creates its own reality, especially in a moment of great stress. Nothing that Peyton thinks is happening actually is. Although the entire episode Peyton imagines takes place in a fraction of a second, in his mind he travels quite far after the miraculous breaking of the hangman's noose. Even though there are logical inconsistencies in what he imagines he sees in the forest, such as the timing being off on how long a journey should take, or being able to see a spectrum of light  in "all the dewdrops upon a million blades of grass", his mind accepts all of it at face value. 

Bierce also shows that a mind will reject a subject it perceives as too unpleasant. It is impossible for Peyton to accept that he is really about to die, and his mind creates a much happier outcome for him. He escapes, and will live! The reader is fooled as well, as maybe the happier outcome is one we would also prefer.

From the short story "Rappaccini's Daughter," what inferences can you make about Beatrice and the garden?

Both Beatrice and the garden are poisonous. This much is obvious. But both are also innocent. The garden is clearly not a conscious being with malicious intent. It just happens to be beautiful and deadly. Beatrice is also innocent. She has no malicious intent. She just happens to be beautiful and deadly, like the garden, through no fault of her own. 

Rappaccini has created what we might call a reverse Garden of Eden. Instead of...

Both Beatrice and the garden are poisonous. This much is obvious. But both are also innocent. The garden is clearly not a conscious being with malicious intent. It just happens to be beautiful and deadly. Beatrice is also innocent. She has no malicious intent. She just happens to be beautiful and deadly, like the garden, through no fault of her own. 

Rappaccini has created what we might call a reverse Garden of Eden. Instead of healthy plants as God had created, Rappaccinni has created poisonous ones. Instead of starting with a man (Adam), Rappaccinni has started with a woman. And Rappaccinni is in opposition to a benevolent God. Rappaccinni has not created a paradise for his daughter. He's created a prison; therefore, something more like Hell in the disguise of a Heavenly garden. The narrator makes it clear that the garden (flower in particular) and Beatrice are similar: 

Flower and maiden were different, and yet the same, and fraught with some strange peril in either shape. 

Beatrice refers to the shrubs and flowers as "sisters." She seems to have sympathy and/or empathy with these beautiful and deadly plants because they share the same predicament. She and the garden are marked by these paradoxical notions of immortal beauty and death. So, there is this sense of evil juxtaposed to heavenly beauty. But neither Beatrice nor the garden are inherently evil. They represent the folly of a man who tries to be God. Beatrice and the garden are Rappaccinni's creations. He has endeavored to be like God in creating an immortal and beautiful world for his daughter. Beatrice and the garden are symbols of temptation, but both are innocent in and of themselves. It is Rappaccinni that imbues them with evil and death. 

What is the author's message in the story "The Third and Final Continent"?

I'd say that Jhumpa Lahiri’s message in "The Third and Final Continent" is that friendship can really help ease a difficult transition. But you can find other messages in the story, too, such as the need to bravely forge ahead even when you're in an unfamiliar situation.

You can read more about possible messages, or themes, in the story .

How did I come up with these ideas for the story's message?

One...

I'd say that Jhumpa Lahiri’s message in "The Third and Final Continent" is that friendship can really help ease a difficult transition. But you can find other messages in the story, too, such as the need to bravely forge ahead even when you're in an unfamiliar situation.

You can read more about possible messages, or themes, in the story .

How did I come up with these ideas for the story's message?

One way to identify the author's message in any story is to look at what the problem is, how it gets solved, and what that whole process seems to say about the nature of the problem or the way to solve the problem.

Here, the problem seems to be that the narrator feels awkward and uncomfortable in his new country and with his new wife. The solution is that Mrs. Croft offers friendship to the narrator, easing his transition. She also helps the narrator and Mala (his new wife) find something to laugh about together. In this way, her friendship helps the narrator feel more comfortable in both American society and in his new arranged marriage. He truly falls in love with his wife, and they go on to lead a happy life and have a son who goes to an elite college.

So, by looking at how the main problem is resolved, I was able to make a good guess (an inference) about the author's message.

The next step, of course, would be to apply that message to our lives. In this case, we could offer our own friendship to someone going through a difficult transition; or, if we're in a difficult transition ourselves, we could reach out for someone's friendship.

However, not all stories have a happy ending. If you’re looking for the author’s message in a story that ends in tragedy, you might look at how the problem failed to be solved, and what that failure seems to be saying about the nature of the problem or how the problem should have been solved.