How does the choice of details set the tone of the sermon?

Edwards is remembered for his choice of details, particularly in this classic sermon. His goal was not to tell people about his beliefs; he knew they already were aware of what Christianity had to say about the fate of their souls. His goal was to make them care. To that end, he focused on painting pictures with words of how dangerously close to the edge of the pit of hell they were walking, and how precarious was their foothold. Hence he begins this sermon with Deuteronomy 32:35: "Their foot shall slide in due time," breaking it down into observations about how suddenly this will happen and how no one will even need to push them; they'll fall by their own weight—all perfectly logical observations.

From there, he moves to what it means to speak of the "power of God," beginning with the observation that God can do anything at any time and we can do nothing to stop it:

Though hand join in hand, and vast multitudes of God's enemies combine and associate themselves, they are easily broken in pieces: they are as great heaps of light chaff before the whirlwind; or large quantities of dry stubble before devouring flames. We find it easy to tread on and crush a worm that we see crawling on the earth; so 'tis easy for us to cut or singe a slender thread that anything hangs by; thus easy is it for God when he pleases to cast his enemies down to hell.

Note the images of the whirlwind, the devouring flames, and the worms. The whirlwind is God, and the flames and worms are images in other scriptures depicting hell.

Edwards' tone is one of warning. He wants his congregation to picture what he describes and be afraid. If he invokes fear, he gains converts.

How is the Lord of the Flies like a devil in the novel?

One powerful literary device that William Golding uses in Lord of the Flies is the Christ-figure. Simon, the most sensitive of the boys and the only one who understands the deeper truths about "mankind's essential illness," acts as a Christ-figure. Many works of literature that contain a Christ-figure use a devil figure to reinforce the role of the Christ-figure. That is part of what Golding does with the sow's head that becomes the Lord of the Flies in Simon's vision. Several parallels to the biblical devil are apparent.

First, the devil has delusions of grandeur. In the Christian tradition, Lucifer, a being that most people believe is Satan, declares "I will be like the Most High." Thus the body-less pig has the grand title "Lord of the Flies" and claims to be "the Beast," although Simon names it for what it is: "Pig's head on a stick." "Lord of the Flies" is the translation for "Beelzebub," considered to be the chief demon or Satan himself.

Second, the devil seeks to torment those who have a special calling in their lives. Jesus said to the Apostle Peter, "Satan has desired to have you that he may sift you like wheat." The Lord of the Flies says many things to torment Simon, telling him that the other boys think he's batty, that there isn't anyone to help him, and that "we shall do you." 

Third, the devil seeks to prevent the Christ figure from fulfilling his mission. Jesus was tempted by the devil for 40 days in the wilderness. The devil tried to get Jesus to worship him and to do things contrary to his mission. The Lord of the Flies tries to get Simon to forget what he knows about how the "beast ... is only us." It tries to convince him that "it was just a joke, really" and says, "Get back to the others and we'll forget the whole thing."

Beyond the way it interacts with Simon, the Lord of the Flies is an embodiment of filth, representing evil. The disgusting flies crawl all over it; "the obscene thing grinned and dripped." It has the "infinite cynicism of the adult life." Golding's language makes the head the embodiment of evil, which is like the devil.

Because of the way the head interacts with the Christ-figure, Simon, and because of its association with evil, it is like the devil in Christian tradition.

Maya Angelou makes use of questions as a device. What is the impact of these questions in the poem, "Still I Rise"?

By addressing her reader with questions, Angelou is hoping her reader will then begin to question their own feelings and emotions on how comfortable they are that a black woman has found her self-worth. The six main questions she asks her reader are:

Does my sassiness upset you?

Why are you beset with gloom?

Did you want to see me broken?

Bowed head and lowered eyes?

Does my haughtiness offend you?

Does my sexiness upset you?

After years of misconceptions, racism, stereotyping, and lies that have been told about her and her ancestors, Angelou is ready to claim her value as a black woman.  Instead of being downtrodden and oppressed, Angelou expresses her “sassiness,” “haughtiness,” and “sexiness” throughout the poem. She says,

Up from a past that's rooted in pain

I rise

I'm a black ocean, leaping and wide,

Welling and swelling I bear in the tide.

Leaving behind nights of terror and fear

I rise

These words stress that Angelou has come from a past of pain, terror, and fear; however, she has risen above that history and now loves herself for the characteristics (like haughtiness) that she possesses. Now, she is asking you if you are upset by the fact that she is no longer “broken” or shows a “bowed head.” She is asking her audience to come to grips with the new woman she has become.  

What are the key themes in the poems "Roscoe Purkaphile" and "Mrs. Purkaphile?"

The major theme in these poems is the commitment of marriage. Roscoe Purkaphile was never keen on the idea of being married, but eventually resigned himself to it. Mrs. Purkaphile, however, took her vows very seriously: "But a promise is a promise / And marriage is marriage...". The seriousness of her dedication is highlighted by the fact that she is not known by her first name, but only by her husband's surname. She is a woman who is dedicated to tradition.

Roscoe, on the other hand, comes off as a man who is constricted by social convention. He wants to "escape" from Mrs. Purkaphile. He hopes that she will divorce him, or that she will die before him so that he can be free again. He concludes, however: "But few die, none resign." Not many young women die suddenly; and none will risk the social opprobrium that comes with divorce. So, he becomes an unfaithful liar: "Then I ran away and was gone a year on a lark...I told her that while taking a row in a boat / I had been captured near Van Buren Street / By pirates on Lake Michigan..."

Mrs. Purkaphile knows better, but chooses to believe his lie so that she can keep their marriage intact. She knows that he is having an affair: "I knew very well / What he was doing, and that he met / The milliner, Mrs. Williams, now and then..." It is not out of respect for her husband, but "for [her] own character" that she refuses to divorce. She made a promise; marriage is a vow for life. If she cannot keep this promise, then she is not true. She contrasts her own character with her husband's: "I refused to be drawn into a divorce / By the scheme of a husband who had merely grown tired / Of his marital vow and duty." She trivializes his feelings with the phrase "merely grown tired," and asserts her own moral superiority. 

Though marriage is the main, overarching theme, there are also the peripheral themes of infidelity, morality, existential boredom (Roscoe wants to be with other women because people often grow bored living with the same person), and the place of God in marriage. Much of what Mrs. Purkaphile believes about marriage is probably rooted in religious faith. Ironically, Roscoe comes to agree with her side of things: "I then concluded our marriage / Was a divine dispensation / And could not be dissolved, / Except by death. / I was right." Due to his wife's earnestness, only death allowed them to part.

What is DMT?

History of Use

Europeans who first arrived in the Caribbean and in Central and South America came into contact with indigenous peoples who used DMT derived from plants to induce hallucinations as part of their religious experience. The explorers tried to suppress these practices, which persisted, often in secretive settings.

DMT was first synthesized in a laboratory in 1931 by chemist Richard Manske. It
gained popularity as a drug of abuse in the counterculture of the 1960s. In 2006,
the US Supreme Court ruled in Gonzales v. O Centro Espirita Beneficiente
Uniao Do Vegetal that a Brazilian church in the United States could
import and use hoasca, a tea containing DMT, for their religious ceremonies,
saying that the practice is protected by the 1993 Religious Freedom Restoration
Act. According to the US National Survey on Drug Use and Health, the use of DMT in
the United States has increased from roughly 688,000 users in 2006 to more than
1.4 million in 2012.

Effects and Potential Risks

DMT is the shortest-acting of commonly abused hallucinogens. Its effects are evident within ten minutes, peak at about thirty minutes, and usually end within an hour. Hence the street name businessman’s special.

Physical effects of DMT abuse include increased blood pressure and heart rate,
agitation, dizziness, nystagmus (involuntary, rapid eye movement), and loss of
coordination. At high doses, seizures and respiratory arrests have occurred.
Psychological effects of DMT abuse include intense visual hallucinations,
depersonalization, auditory distortions, and altered sense of time and body image.
DMT causes anxiety attacks far more frequently than does the hallucinogen
LSD (acid).

Bibliography

Abadinsky, Howard.
Drug Use and Abuse: A Comprehensive Introduction. 8th
ed. Belmont: Wadsworth, 2013. Print.

Julien, Robert M.,
Claire D. Advokat, and Joseph E. Comaty. A Primer of Drug
Actions. 12th ed. New York: Worth, 2010. Print.

Kuhn, Cynthia, Scott
Swartwelder, and Wilkie Wilson. Buzzed: The Straight Facts About the
Most Used and Abused Drugs from Alcohol to Ecstasy. 4th ed. New
York: Norton, 2014. Print.

Ruiz, Pedro, and Eric
Strain. Lowinson and Ruiz's Substance Abuse: A Comprehensive
Textbook. 5th ed. Philadelphia: Lippincott, 2011.
Print.

What will cause an increase in the period of a simple pendulum that is swinging with small amplitude?

The time period of a simple pendulum which is oscillating is given by the following equation:

`T = 2pi sqrt(L/g)`

where, T is the time period of oscillations, L is its length and g is the acceleration due to gravity. 

Thus, the time period is directly proportional to the square root of the pendulum length. That is,

`T alpha sqrtL`

This means that in order to increase the time period of a simple pendulum, we have to increase its length. If the length of the pendulum is increased by a factor of 4, the time period increases by a factor of 2. 

That is, `T' alpha sqrt(L')`

`T' alpha sqrt(4L)`

`T' alpha 2sqrt(L)`

`T' = 2T`

The change in the mass of a pendulum will not have any effect on the time period of the pendulum. 

Thus, pendulum length is the only variable on which the time period of a simple pendulum depends.

Hope this helps.

What are three talking points that provide information about how humor heals?

Evidence supports the use of humor in healing because it has the ability to provide a growth in meaningful relationships, and an increase in mental and physical health benefits. Three talking points could address these issues: mental health benefits, physical health benefits, and increasing the development of relationships that cultivate humor. 

Belief that humor aids the healing process comes from a variety of medical specialties including psychotherapy, oncology, and pain management. Humor is beneficial in the treatment of chronic pain syndromes and pain from procedures and surgeries.

It is believed that humor and laughter increase the chemicals in the brain that are responsible for many bodily functions including those that control heart rate and emotional reactions.  Studies point to laughter in the reduction of heart disease by reducing stress and regulating the heart rate.

Humor that leads to laughter can reduce a patient’s response to pain by creating a diversion while regulating the biological substances that modulate pain. Medical professionals encourage patients with pain to watch funny movies or find a way to integrate humor into their lives.

Humor plays a role in mental health, in part by changing a person’s point of view so they are able to see they have the ability to adapt to difficult situations by maintaining a more positive outlook in the face of adversity. Again, there is evidence that humor increases endorphins and hormones that are responsible of feelings of well-being.

Why does Bud keep the extra trousers from the Sleet family in Bud, Not Buddy?

There is a fairly simple answer to your question found in chapter 11 in Bud, Not Buddy.   Bud keeps the extra trousers that the Sleet family gives him because he is sick of wearing short pants that he calls “knickers.”  “Trousers” and “knickers” are typical words in the 1930s to describe long pants and short pants. 

This scene happens when Mr. Lefty Lewis takes Bud to his daughter’s house.  After Lefty Lewis introduces his grown daughter as Mrs. Sleet, Bud is given a pair of pants used by Mrs. Sleet’s son.  Because Mrs. Sleet’s son has grown too old for the trousers, they are the perfect set of pants for Bud.  Bud is ten years old now and considers knickers to be for a small child.  As a result, he is tired of wearing them all the time.  Therefore, Bud is happy to receive the hand-me-down pants.  Bud is invited downstairs to breakfast after he exclaims, “No more knickers!”

What is von Hippel-Lindau (VHL) disease?

Related conditions:

Renal cysts; clear cell form of renal cell carcinoma; hemangioblastomas of the brain, spinal cord, and retina; pheochromocytoma; endolymphatic sac tumors

Definition:
A hereditary cancer syndrome, von Hippel-Lindau (VHL) disease is associated with renal cell carcinoma (kidney cancer); pheochromocytoma (an adrenal gland tumor that releases stress hormones); catecholamine-secreting paraganglioma (a tumor that releases stress hormones like a pheochromocytoma but is located outside the adrenal gland); hemangioblastomas (blood vessel tumors) of the brain, spinal cord, and retina; neuroendocrine tumors (nerve-cell tumors that may produce hormones) of the pancreas; and endolymphatic sac tumors (inner ear tumors). For individuals with VHL, the lifetime risk of developing renal cell carcinoma—the leading cause of VHL-associated death—is approximately 70 percent, as E. R. Maher, H. P. H. Neumann, and S. Richard reported in their 2011 European Journal of Human Genetics review. Several distinct clinical presentations of VHL have been described based on the risk for pheochromocytoma and renal cell carcinoma. The types of tumors and the severity of the disease vary within and between families.

Risk factors: Because von Hippel-Lindau disease is hereditary, the main risk factor is having a family history of this syndrome. Each child of a person with von Hippel-Lindau disease has a 50 percent chance of inheriting the disease.

Etiology and the disease process: The underlying genetic cause of von Hippel-Lindau disease is a mutation, or a genetic change, in the VHL gene. Normally, the protein made by the VHL gene acts as a tumor suppressor, which means that it helps stop uncontrolled cell growth and proliferation. Mutations in the VHL gene either prevent the protein from being made or cause the protein to be made incorrectly, which leads to the multistep process of tumorigenesis (formation or production of tumors).

Usually, each person has two normal copies of the VHL gene. A mutation in one copy of the gene is sufficient to cause von Hippel-Lindau disease, which is why this condition is referred to as autosomal dominant (autosomal means the VHL gene is located on one of the twenty-two pairs of autosomes, which are the non-sex chromosomes). A person with von Hippel-Lindau disease has a VHL gene mutation from the time of conception in the womb; however, symptoms of the disease may not manifest until later in life. Symptoms can occur before the age of five, and nearly all people with a VHL gene mutation have symptoms of the disease by the age of sixty-five, as reported by endocrinologists C. Frantzen and T. P. Links and nephrologist R. H. Giles in GeneReviews (2012).

Different types of mutations in the VHL gene lead to different clinical presentations. Therefore, a person with von Hippel-Lindau disease may be more likely to have pheochromocytoma, renal cell carcinoma, or both.

Incidence: According to the US National Library of Medicine's Genetic Home Reference (2012), approximately 1 in 36,000 people has von Hippel-Lindau disease. Some 80 percent of people with von Hippel-Lindau disease inherit the disease from a parent, but 20 percent of people with the disease have a new gene mutation, meaning the mutation occurs for the first time in that individual.

Symptoms: Symptoms depend on where the tumors are located. Hemangioblastomas of the brain or spinal cord can cause headaches, vomiting, coordination problems, and walking difficulties. Retinal (eye) hemangioblastomas can lead to vision problems. Pheochromocytomas and catecholamine-secreting paragangliomas release catecholamines (stress hormones) that can cause dangerously high blood-pressure levels. Neuroendocrine tumors of the pancreas usually do not produce hormones and may have no associated symptoms. Tumors of the endolymphatic sac can result in deafness, which may occur suddenly and be severe to profound.

Screening and diagnosis: Von Hippel-Lindau disease is clinically diagnosed in a person who has two or more tumors associated with this condition. However, if a person has a family history of the disease, just one of the characteristic findings is needed to make a diagnosis. Tools used to check for disease include computed tomography (CT) or magnetic resonance imaging (MRI) to look for pheochromocytomas, endolymphatic sac tumors, or tumors of the brain and spinal cord. Ultrasound or CT may be used to examine the kidneys and pancreas, and urine testing may be done to check for catecholamines and metanephrines released by pheochromocytomas or paragangliomas. Ophthalmologic examination (an eye exam) is performed to check for retinal hemangioblastomas.

Because von Hippel-Lindau disease is caused by mutations in the VHL gene, genetic testing is a valuable tool to confirm a suspected diagnosis or to test a family member who is at risk for the disease but has no symptoms. Genetic testing detects 90 to 100 percent of VHL gene mutations, according to Frantzen, Links, and Giles.

Treatment and therapy: The main focus of treatment for von Hippel-Lindau disease is surgery to remove tumors. Early surgery offers the best outcome for most of the tumors associated with von Hippel-Lindau disease, including renal cell carcinoma. Renal cell carcinoma may also be treated with chemotherapy, radiation therapy, ablation therapy (using probes to destroy the tumor with heat or cold), biological therapy (using the patient’s immune system to fight the cancer), and targeted therapy (using drugs that attack cancer cells without damaging normal cells).

Prognosis, prevention, and outcomes: Because von Hippel-Lindau disease is a genetic condition, its manifestations cannot be prevented. However, monitoring of individuals who are at risk for the disease based on their family history or who are known to have a VHL gene mutation can detect problems early and lead to more effective treatment and better outcomes. Such monitoring includes yearly ophthalmologic screening, yearly blood pressure checks, yearly urine testing for catecholamines and metanephrines, yearly abdominal ultrasounds, periodic MRI of the brain and spinal cord, and hearing evaluation if symptoms of hearing loss are present. The medical team caring for patients decides the age at which monitoring should start.

"Brain and Spinal Cord Tumors in Adults." Cancer.org. Amer. Cancer Soc., 5 Mar. 2014. Web. 29 Oct. 2014.

Frantzen, Carlijn, Thera P. Links, and Rachel H. Giles. "Von Hippel-Lindau Disease." GeneReviews. Ed. Roberta A. Pagon et al. Seattle: U of Washington, Seattle, 1993–2014. NCBI Bookshelf. Natl. Center for Biotechnology Information, 21 June 2012. Web. 29 Oct. 2014.

Linehan, W. M., B. Zbar, and D. R. Klausner. “Renal Carcinoma.” The Metabolic and Molecular Bases of Inherited Disease. Ed. Charles R. Scriver, Arthur L. Beaudet, David Valle, and William S. Sly. 8th ed. New York: McGraw-Hill, 2001. Print.

Maher, Eamonn R., Hartmut P. H. Neumann, and Stéphane Richard. "Von Hippel–Lindau Disease: A Clinical and Scientific Review." European Journal of Human Genetics 19.6 (2011): 617–23. PDF file.

Molino, D., J. Sepe, P. Anastasio, and N. G. De Santo. “The History of Von Hippel-Lindau Disease.” Journal of Nephrology 10 (2006): S119–23. Print.

"Von Hippel-Lindau Syndrome." Genetics Home Reference. US Natl. Lib. of Medicine, July 2012. Web. 29 Oct. 2014.

Woodward, E. R., and E. R. Maher. “Von Hippel-Lindau Disease and Endocrine Tumour Susceptibility.” Endocrine Related Cancer 32 (2006): 415–25. Print.

How do you measure a dip angle with a protractor?

The key is that you need some way of knowing which way is down---and for that, we use gravity, using either a level (perpendicular to gravity) or a plumb bob (parallel to gravity).

Once you have clearly determined which way is down, simply use the protractor to measure the angle between the surface that you want the dip angle for and the straight downward direction. Remember that a flat, level surface has zero dip; so the dip is not the angle with the plumb bob, but 90 degrees (`pi/2 ` radians) minus that angle.

In practice, there is a tool called a Brunton compass that contains a compass, a level, and a protractor, which can be directly used to measure dip angles.

How are music and culture connected?

The easiest answer to this is that music is part of a society's culture. 

The term culture refers to the accumulated body of knowledge and traditions possessed by a society. While not every person in a society will be familiar with all aspects of a society's culture. In the aggregate, culture is what a society teaches its children and hands down to future generations. It is what binds a society together with shared bonds of customs and knowledge and ways of thinking. 

Performance is a means by which a society shares its culture among its members. Even purely instrumental music can be a shared bond among members of a society, as in Beethoven's Ode to Joy, which for many people expresses the spirit of the European Union, even if unaccompanied by the words of Schiller.

Musical performance can often convey a society's traditions to people who are not literate, as is the case with traditional bardic performance. 

What is bypass surgery?

Indications and Procedures

Coronary artery bypass surgery
is needed when angiography reveals a narrowing or blockage in heart
arteries causing angina that cannot be controlled by medication or relieved by angioplasty. The traditional method of open chest
bypass surgery, which first became popular in the 1970s, requires that the patient be fully anesthetized. The surgeon cuts open the patient’s chest, saws through the breastbone, and spreads the halves of the ribcage to expose the heart. The heart is stopped and cooled, and the major heart vessels are attached to a heart-lung machine, which oxygenates and circulates the blood. At the same time, another surgeon removes a leg vein and prepares grafts to be sewn around blockages in the heart arteries. Mammary arteries are also employed to redirect blood flow around obstructed arteries. After the bypasses are satisfactorily implanted, the heart-lung machine is disconnected and the heart resumes pumping on its own. The two halves of the breastbone are reattached with stainless steel wire, and the incision is sewn closed. Patients are taken to a cardiac intensive care unit overnight and are normally discharged from the hospital within a week. They recover fully in one to three months.

Bypass surgery of the peripheral arteries, usually those of the legs, is indicated when ischemia
causes severe pain. Sections of leg veins and grafts made of synthetic material, such as Dacron, are used to bypass obstructions and to open blood flow to the legs.

An obstruction in the intestines can be treated surgically by removing the blocked region and sewing together the healthy portions of the gut. Severe problems may require creating an opening for the digestive tract through the abdominal wall, called a stoma, through which its contents can empty into a removable plastic bag. The procedure may be permanent or temporary, to allow the affected gut to heal. After successful healing, the bypass and bag are removed and the intestine segments are reattached.

Removal of part of the stomach or small intestine is sometimes used to treat cases of extreme obesity. The operation improves the patient’s quality of life and may also extend its duration.

Uses and Complications

Traditional coronary artery bypass surgery is profoundly invasive. The heart-lung machine can create problems, even though newer machines are less stressful than the original models. The action of the pump is more powerful than that of a normal heart and can generate turbulence that damages blood cells and other organs. The machines have been blamed for blood clot formation, causing strokes and heart attacks during an operation. Patients, especially the elderly, often experience memory loss and confusion following surgery; though usually temporary, the problem can last for years. Surgeons, therefore, have been seeking less stressful and invasive methods of treating coronary artery disease.

Neither peripheral artery surgery nor intestinal bypass surgery involves using heart-lung machines, but the large incisions commonly used in such operations can also lead to complications by exposing extensive body areas to possible infection. Although traditional surgery is highly successful, innovators continue to seek the development of less invasive procedures.

Perspective and Prospects

The goal of research is minimally invasive surgery. Intestinal surgeons led the way with the development of laparoscopic
gallbladder and kidney stone surgery in the 1980s. Only small circular incisions are needed to insert a fiber-optic instrument that transmits enlarged images of the surgical site to a screen. Laparoscopic tools are introduced though several additional small incisions. Segments of bowel can then be removed though tubes and their ends joined without opening the abdomen. The use of laparoscopic techniques reduces the tissue damage caused by traditional surgery. The patient feels less pain after the operation, experiences a shorter hospitalization, returns to normal activity sooner, and develops a smaller scar.

To avoid use of the heart-lung machine, and its medical complications, cardiac surgeons have experimented with open chest surgery on a beating heart. This very delicate operation involves temporarily immobilizing the area of the heart where the surgeon intends to attach a graft, slowing the heartbeat with drugs, and stitching the bypass into place between heartbeats. Only the most skilled surgeons succeed in mastering this difficult technique.

In the 1990s, cardiac surgeons, following intestinal surgeons, adopted the use of fiber-optic tubes that permit so-called keyhole surgery. Incisions of 3.0 inches in the chest and holes 0.5 inch in diameter under the armpit are sufficient to gain entry to the heart, thereby eliminating any need to open the chest cavity. Immobilizing segments of the heart and sewing grafts to the rhythm of the heartbeat, however, is considerably more difficult when done through a tube while viewing a television screen. In the twenty-first century, surgeons have begun using computer-controlled robots to carry out the intricate maneuvers needed to repair ailing hearts.

In May 2013, a study published in the Annals of Thoracic Surgery
suggested that short-term use of antidepressant medications aid in mental and emotional recovery following bypass surgery.

Bibliography

"Coronary Artery Bypass Grafting." Health Library, September 26, 2012.

Doherty, Gerard M., and Lawrence W. Way, eds. Current Surgical Diagnosis and Treatment. 12th ed. New York: Lange Medical Books/McGraw-Hill, 2006.

Emery, Robert W., ed. Techniques for Minimally Invasive Direct Coronary Artery Bypass (MIDCAB) Surgery. Philadelphia: Hanley & Belfus, 1997.

Klaidman, Stephen. Saving the Heart: The Battle to Conquer Coronary Disease. New York: Oxford University Press, 2000.

Pittman, Genevra. "Heart bypass surgery or stents? Depends on patient." MedlinePlus, April 22, 2013.

Preidt, Robert. "Antidepressants May Hasten Bypass Recovery, Study Finds." MedlinePlus, May 1, 2013.

Youngson, Robert. The Surgery Book: An Illustrated Guide to Seventy-three of the Most Common Operations. New York: St. Martin’s Griffin, 1997.

`1^3 + 2^3 + 3^3 + 4^3 + n^3 = (n^2(n + 1)^2)/4` Use mathematical induction to prove the formula for every positive integer n.

You need to use mathematical induction to prove the formula for every positive integer n, hence, you need to perform the two steps of the method, such that:

Step 1: Basis: Show that the statement P(n) hold for n = 1, such that:

`1^3 = 1^2(1+1)^2/4 => 1 = 1*4/4 => 1=1`

Step 2: Inductive step: Show that if P(k) holds, then also P(k + 1) holds:

`P(k): 1^3 + 2^3 + .. + k^3 = (k^2(k+1)^2)/4` holds

`P(k+1):  1^3 + 2^3 + .. + k^3 + (k+1)^3 = ((k+1)^2(k+2)^2)/4`

You need to use induction hypothesis that P(k) holds, hence, you need to re-write the left side, such that:

`(k^2(k+1)^2)/4 + (k+1)^3 = ((k+1)^2(k+2)^2)/4`

`k^2(k+1)^2 + 4(k+1)^3 = (k+1)^2(k+2)^2`

Factor out `(k+1)^2` to the left side:

`(k+1)^2(k^2 + 4k + 4) = (k+1)^2(k+2)^2`

Notice that `k^2 + 4k + 4` is a perfect square, such that:

`k^2 + 4k + 4 = (k+2)^2`

`(k+1)^2(k+2)^2 = (k+1)^2(k+2)^2`

Notice that P(k+1) holds.

Hence, since both the basis and the inductive step have been verified, by mathematical induction, the statement `P(n):1^3 +2^3 +3^3 + ... + n^3 = (n^2(n+1)^2)/4`  holds for all positive integers n.

What is fifth disease?

Causes and Symptoms

Fifth disease is caused by
infection with the human parvovirus (HPV) B19. The disease is more prevalent during late winter or early spring. Fifth disease is most commonly observed in young children, with the peak attack rate between five and fourteen years of age. Adults may become infected, but they rarely show evidence of disease.

The virus is spread from person to person through nasal secretions or sneezing. Following an incubation period of several days, a rash develops on the face, which has the appearance of slapped cheeks. The bright red color fades as the rash spreads over the rest of the body. An erythematous, pimply eruption may also appear on the trunk or extremities. A mild fever, sore throat, and nasal stuffiness may also be apparent. The rash generally lasts from ten days to two weeks. Often, it will fade only to reappear a short time later. Sunlight may aggravate the skin during this period, also causing a reappearance of the rash.

The diagnosis of fifth disease is primarily clinical, based on the symptoms. Laboratory tests for the virus are generally not performed.

Treatment and Therapy

No antiviral medication is available for fifth disease. Since the disease is rarely serious, treatment is mainly symptomatic, including medications for fever, pain, and itchiness. Bed rest and the administration of liquids, as commonly used in treating mild illness in children, are generally sufficient. Isolation is unnecessary since transmission is unlikely following appearance of the rash.

Perspective and Prospects

Fifth disease was first described during the late nineteenth century as the fifth in the series of erythematous illnesses often encountered by children; the others are measles, mumps, chickenpox, and rubella. HPV B19 was isolated in 1975 and shown to be the etiological agent of the disease in the mid-1980s.

The disease is common and generally benign. HPV B19 has been implicated, however, in certain forms of hemolytic anemias and arthritis in adults, and research continues on the virus.

Bibliography:

Kliegman, Robert, and Waldo E. Nelson, eds. Nelson Textbook of Pediatrics. 19th ed. Philadelphia: Saunders/Elsevier, 2011.

Burg, Fredric D., et al., eds. Treatment of Infants, Children, and Adolescents. Philadelphia: W. B. Saunders, 1990.

"Fifth Disease." MedlinePlus, May 2, 2013.

Kemper, Kathi J. The Holistic Pediatrician: A Pediatrician’s Comprehensive Guide to Safe and Effective Therapies for the Twenty-five Most Common Ailments of Infants, Children, and Adolescents. 2d ed. New York: HarperCollins, 2007.

Kumar, Vinay, Abul K. Abbas, and Nelson Fausto, eds. Robbins and Cotran Pathologic Basis of Disease. 8th ed. Philadelphia: Saunders/Elsevier, 2010.

McCoy, Krisha, and Michael Woods. "Fifth Disease." Health Library, Sept. 26, 2012.

"Parvovirus B19 and Fifth Disease." Centers for Disease Control and Prevention, Feb. 14, 2012.

Sompayrac, Lauren. How Pathogenic Viruses Work. Boston: Jones and Bartlett, 2002.