How do you determine the number of neutrons in an atom from the mass number?

The mass number of an atom is the sum of protons and neutrons. The number of protons is an atom's atomic number and doesn't vary for a particular element. The number of neutrons can vary. When atoms with different numbers of neutrons exist for an element, they're called isotopes. To find the number of neutrons in an atom of a particular isotope you subtract the atom's atomic number from its mass number.  

Here's an...

The mass number of an atom is the sum of protons and neutrons. The number of protons is an atom's atomic number and doesn't vary for a particular element. The number of neutrons can vary. When atoms with different numbers of neutrons exist for an element, they're called isotopes. To find the number of neutrons in an atom of a particular isotope you subtract the atom's atomic number from its mass number.  

Here's an example using lead, with has four stable isotopes and an atomic number of 82:

The notation "lead-204" means the isotope of lead that has a mass number of 204. Since lead has 82 protons, the number of neutrons in an atom of lead-204 is 204-82=122. Similarly, lead-206 has 124 neutrons, lead-207 has 125 neutrons and lead-208 has 126 neutrons. 

Compare igneous and sedimentary rocks?

There are three types of rocks: igneous, sedimentary and metamorphic. Igneous rocks are the primary rocks and are formed by solidification of molten magma. Depending on whether the cooling of magma takes place above the Earth's surface or underneath it, the igneous rocks can have fine or coarse texture. Igneous rock formation involves phase change of matter: from liquid to solid. Some examples of igneous rocks are basalt, granite, etc.

In comparison, sedimentary rocks are...

There are three types of rocks: igneous, sedimentary and metamorphic. Igneous rocks are the primary rocks and are formed by solidification of molten magma. Depending on whether the cooling of magma takes place above the Earth's surface or underneath it, the igneous rocks can have fine or coarse texture. Igneous rock formation involves phase change of matter: from liquid to solid. Some examples of igneous rocks are basalt, granite, etc.

In comparison, sedimentary rocks are formed by erosion and transportation of existing rocks. Water, wind, etc., erode the existing rocks and transport the eroded material to new regions, where such material is deposited. Over time, rocks are formed by cementing of this material. Sedimentary rocks are the secondary rocks, since they are formed from existing rocks. A prominent feature of sedimentary rocks is the layering of material. Some examples of sedimentary rocks are shale, sandstone, etc.

Hope this helps. 

If asked to look at a firm’s accounting statements in order to assess the firm’s future performance and outlook, is this an effective...

In reality, a firm's accounting statements are just one of many other factors that are worthy of a full analysis in order to determine the performance of a firm. 

One of the most effective tools for analysis and prediction is the SWOT analysis. 

This tool looks for:

• S= Strengths


• W= Weaknesses


• O= Opportunities to grow


• T= Threats

The SWOT analysis was invented at the Stanford Research institute by management consultant Albert Humphrey, in the year 1960. The SWOT formula was designed with the premise that all companies, particularly those which are in the Fortune 500, need a specific way to reach financial goals in a reasonable time period. 

This can also apply to any business, or firm. The formula is universal enough to be replicated in  different business scenarios. 

In the case of the firm that you propose, the budget and accounting documents need to be analyzed as part of the process of categorizing them according to where they belong in a SWOT.

The analytical questions to be asked are:

a) Do the financial statements show organization and good documentation?  

b) Are all accounts in order?

c) Is the data matching the financial processes in place? 

Upon analyzing the accounting documents, which are also known in business jargon as "the books", there are four options as to what to do with the information you gather.

If the answer to all of the previous questions is "YES":

If the financial statements show organization and good documentation, the accounts are in order, and the data matches the financial processes already in place,  then the firm's accounting documents would be categorized as a "strength".

This means that the company can count on this process to continuously improve performance in the future. This is an easy predictor. 

If the answer is "NO":

If the books are disorganized, there is no documentation, accounts are in disarray, and the data makes no sense, then the firm's accounting statements would fall under "weakness". Immediately, the firm should consider a re-haul in financial personnel, complete with training and a new action plan. 

If the accounting books show signs of continuous improvement:

Finances are always challenging, especially when a firm is fairly new to the business. However, if the books show that a plan is in place and that there are steps being taken to make it succeed, then it would fall under " opportunities". This part of the SWOT refers to the chances that a firm or company has to improve and run the market at a given time.

The thing here is that, when all stockholders buy into a plan and work for it, the chances for success are extremely high. This is what the Association of Supervision and Curriculum Development (ASCD) has called a "shared vision". 

Another way to demonstrate opportunity is showing how much better the books in this one firm fare, compared to those of other firms. Any chance to get ahead, is an opportunity. 

If the accounting books show that only a few people know how to truly operate "the books"...,

If the books are only ran by a few people who refuse to share or disclose essential information to stockholders, then the books may pose to be a threat to the firm that could ruin its reputation. This lack of organization would be considered a "threat" as well as a "weakness" that could ruin the enterprise due to its lack of transparency. This makes it hard to show validity and reliability as it is. 

As you can see, the financial statements of a firm can fall under any of the analytical categories addressed by the SWOT. Numbers alone do not tell the story of what is going on in a firm. The way that the firm reaches the numbers, and the correlations made between data, process, and productivity are much more important than to observe "the books" in isolation. 

`y = sqrt(x), y = 0, x = 1` Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given...

With the method of cylindrical shells we sum up the volumes of thin cylinders.

The volume of a cylinder is

`2pi*r*h*dr,`

where `h` is the height (the value of a function), `r` is the radius of a cylinder (the distance from the axis of rotation to the argument) and `dr` is the thickness.

Here this is `2pi*(x+1)*sqrt(x)dx` and the volume is

`2pi int_0^1 (x+1)sqrt(x) dx=2pi int_0^1 (x^(3/2)+x^(1/2)) dx =`

`=2pi(2/(5)x^(5/2)+2/(3)x^(3/2))_0^1=2pi(2/5+2/3)=32/(15)pi.`

With the method of cylindrical shells we sum up the volumes of thin cylinders.

The volume of a cylinder is

`2pi*r*h*dr,`

where `h` is the height (the value of a function), `r` is the radius of a cylinder (the distance from the axis of rotation to the argument) and `dr` is the thickness.

Here this is `2pi*(x+1)*sqrt(x)dx` and the volume is

`2pi int_0^1 (x+1)sqrt(x) dx=2pi int_0^1 (x^(3/2)+x^(1/2)) dx =`

`=2pi(2/(5)x^(5/2)+2/(3)x^(3/2))_0^1=2pi(2/5+2/3)=32/(15)pi.`

How has Macbeth murdered sleep in act 2 of Macbeth?

In Act 2 of Macbeth, Macbeth recounts his act in murdering Duncan and explains: 

Methought I heard a voice cry “Sleep no more!/Macbeth does murder sleep”—the innocent sleep,/ Sleep that knits up the raveled sleave of care,/ The death of each day’s life, sore labor’s bath,/ Balm of hurt minds, great nature’s second course,/ Chief nourisher in life’s feast.

In this quotation we can take sleep to mean two things.  First, the act of committing...

In Act 2 of Macbeth, Macbeth recounts his act in murdering Duncan and explains: 

Methought I heard a voice cry “Sleep no more!/Macbeth does murder sleep”—the innocent sleep,/ Sleep that knits up the raveled sleave of care,/ The death of each day’s life, sore labor’s bath,/ Balm of hurt minds, great nature’s second course,/ Chief nourisher in life’s feast.

In this quotation we can take sleep to mean two things.  First, the act of committing murder is ultimately putting someone to sleep permanently.  Here sleep is portrayed as "innocent," a "cleave of care," and a "bath" as well as a "balm."  All of these things highlight the nourishing and healing powers of sleep, which Macbeth has ultimately corrupted for his own purposing in committing murder.  In this way, Macbeth has robbed Duncan of this healing power by murdering him in his sleep.  Moreover, Macbeth continues in the act saying: 

Still it cried “Sleep no more!” to all the house. “Glamis hath murdered sleep, and therefore Cawdor Shall sleep no more. Macbeth shall sleep no more.”

In this instance, Macbeth is exclaiming that all of his territories and all of those in his house will sleep no more.  And ultimately he will not be able to sleep any longer.  In this sense of the term we see that Macbeth will "lose sleep" over the heinous act that he has committed. In this way, Macbeth has murdered his own sleep because he will never be able to rest given the terrible things that he has done and the resulting remorse that he feels. Given these two quotations taken together, Macbeth has murdered sleep because one cannot rest in his presence (given that he is a dangerous person) and Macbeth will not be able to sleep given the remorse and guilt that he feels from the murder that he has committed.   

In what ways is the word "Nevermore" related to emotional changes in the narrator?

The narrator in Edgar Allan Poe's "The Raven" has a wide variety of emotional reactions to the Raven's saying "Nevermore" and to other uses of the word in the poem. One can follow at least eight separate emotional reactions to the word.

1. Amazement: in stanza 9, after the narrator hears the bird say the word for the first time, he marvels at the bird's ability to speak "so plainly."

2. Surprise: in stanza 11,...

The narrator in Edgar Allan Poe's "The Raven" has a wide variety of emotional reactions to the Raven's saying "Nevermore" and to other uses of the word in the poem. One can follow at least eight separate emotional reactions to the word.

1. Amazement: in stanza 9, after the narrator hears the bird say the word for the first time, he marvels at the bird's ability to speak "so plainly."

2. Surprise: in stanza 11, the narrator, after having said something to himself, is startled when the bird answers with the same word.

3. Empathy: also in stanza 11, the narrator begins to sympathize with the bird's former owner, from whom it must have learned the word by imitation.

4. Curiosity: in stanza 12, the man is first intrigued even to the point of smiling, but as he begins to wonder more about the bird, his curiosity turns "ominous."

5. Grief: in stanza 13, the narrator considers "nevermore" as it applies to his lost love, Lenore, and falls into deep sorrow.

6. Anger: in stanzas 14 - 16, the narrator becomes angry at the bird for saying that he will not see Lenore in Heaven.

7. Pain: in stanza 16, the narrator tells the bird to "take thy beak from out my heart."

8. Depression: in the final stanza, the narrator laments that his soul will never be able to escape the shadow of the raven, signifying the deep depression he has sunk into. 

Thus the single word "nevermore" leads the narrator on an exhausting emotional journey as the poem progresses.

How is the theme of children portrayed in the Brothers of Karamazov?

What an interesting idea for a simplistic theme for this very deep Russian novel.  I agree that "children" could definitely be a very simple theme in The Brothers Karamazov by Fyodor Dostoevsky, especially when considering the family of Fyodor Karamazov (who, of course, is murdered). Even the title lends itself to this simple theme in labeling the sibling relationship immediately.

The original children involved here are, in fact, these brothers of the Karamazov family: Dmitri Karamazov,...

What an interesting idea for a simplistic theme for this very deep Russian novel.  I agree that "children" could definitely be a very simple theme in The Brothers Karamazov by Fyodor Dostoevsky, especially when considering the family of Fyodor Karamazov (who, of course, is murdered). Even the title lends itself to this simple theme in labeling the sibling relationship immediately.

The original children involved here are, in fact, these brothers of the Karamazov family: Dmitri Karamazov, Ivan Karamazov, and Alyosha Karamazov. The Brothers Karamazov by Fyodor Dostoevsky focuses on the differences between children in the same family and, specifically, the differences between the three brothers.  Each of the three boys has one trait in their personality that hovers over the others.  In other words, each child has one personality trait that is dominant. 

For example, the first-born, Dmitri (who is often given the nickname of Mitya), is labeled by to have "broad passions."  This simply means that Dmitri is very excitable with strong feelings and impulsiveness that makes him be quick to action on any of his passions (whether it be love or antagonism).

The second child in The Brothers Karamazov by Fyodor Dostoevsky, named Ivan, has the opposite trait of the first-born.  Ivan, then, is absolutely not excitable.  He is cool and aloof, with a tendency towards intellectualism.Finally, there is the baby of the family:  Alyosha.  Different from the other children, Alyosha has a tendency towards the spiritual.

In conclusion, The Brothers Karamazov by Fyodor Dostoevsky can be labeled with the theme of "children" due to the different personalities of the three brothers.  Whether it be passion, intellectualism, or spirituality, children of any family can be vastly different.  The Karamazov family is no exception.