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ALGEBRA EXPRESION ASSIGNMENT
ALGEBRA ASSIGNMENT
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In algebra, real numbers have a number of properties that enable us to simplify and solve mathematical problems. Its density property for example, implies that there is always another real number that exists between any two real numbers given. For example, between 9.1 and 9.2, there are 9.11, 9.12, 9.13 and so forth. Its identity property says that any number added to zero is equal to itself. There are a number of other properties that real numbers have including distributive, commutative, reflexive and symmetric among others. They all serve the same purpose of helping us in problem solving.
For easier computation it is always important to cluster like terms together. In more complex expressions, the like terms must have the same variable raised to the same exponent.
During the simplification of the given expressions, properties of real numbers will be utilized and identified. The mathematical workings will be aligned on the left while the right side will discuss the properties used.
2a(a-5)+4(a-5) The given expression
2a2-10a+4a-20 The parentheses are removed by use of the distributive property
2a2-6a-20 Coefficients are added to enable combination of like terms
The above is simplified fully and no more computation is needed. The like terms were already grouped together and as such there was no need to rearrange the order.
2w-3+3(w-4)-5(w-6) The given expression..
2w-3+3w-12-5w+30 Parentheses removed by distributive property.
2w+3w-5w-12+30 Commutative property of real numbers is used to arrange the like terms together. -12 and 30 are like constant terms while 2w, 3w and -5w are like variable terms. These can then all be added or subtracted.
5w-5w+18Two of both variable terms and constant terms are added.
18The remaining pair of like variable terms is added.
The expression above is fully simplified. The variable terms cancel each other out through subtraction and a single constant term remains as the simplified form.
0.05(0.3m+35n)-0.8(-0.09n-22m)The given expression
0.015m+1.75n+0.072n+17.6m Removal of parentheses using the distributive property.
0.015m+17.6m+1.75n+0.072nThe commutative property enables us arrange like terms together. Only variable terms with the same variable may be combined
17.615m+1.822n Addition of coefficients enable combination of like terms
This given problem looked complicated but it is not substantially different from the others as it simply employs the usage of the decimal numbers.
From the three expressions above it is clear that knowing the properties of real numbers is important. It is also important to arrange mathematical workings in a chronological and organized manner to enable faster understanding and conceptualization of how to tackle different mathematical problems that are encountered.
References
Poole, D. (2014). Linear algebra: A modern introduction. Cengage Learning.
Samuel, P. (2013). Algebraic Theory of Numbers: Translated from the French by Allan J. Silberger. Courier Dover Publications.
Haemophilus influenza virus normally infects the respiratory system of humans
Haemophilus influenza virus normally infects the respiratory system of humans, animals and birds. Infection by Haemophilus influenza results in fever, headache, cough, nausea, sore throat, vomiting, diarrhea and malaise, which is feeling tired and no energy in the body. Influenza infections are more fatal than most common cold infections and can result to a mortality rate of about 0.1% of people infected with influenza. Polio virus is the causative agent of poliomyelitis. Poliomyelitis is commonly known as Polio and it is an acute viral infectious disease which is spread from person to person mostly through the fecal -oral route. Transmission of polio mainly occurs through contact with stool of the infected person (Atkinson, 2006).
Babies are born with natural acquired immunity against certain diseases .They obtain the immunity through the passage of the antibodies through the mother’s placenta during birth. During breastfeeding, the babies continue getting protection against diseases but the protection is temporary. Thus, the babies need to be immunized against most diseases by being vaccinated. Vaccination is done using a small amount of a killed or weakened form of the microorganism that causes the particular disease. All babies should get vaccinated against diseases because their immune system is not well developed and this makes them vulnerable to infections.
Babies should get immunization against polio virus by administration of the polio vaccine which is called the Inactivated Polio Vaccine (IPV). Children should get four doses of the polio vaccine which should be properly spaced. The first dose should be administered at 2 months, the second dose at 4 months, and the third dose at 6-18 months and a booster dose at 4-6 years of age. IPV is very effective in preventing polio, but only when all recommended doses are completed. A single dose of IPV provides little or no immunity against polio. It is thus important for babies to be immunized against polio virus when they are still young to prevent contracting polio. Polio can cause paralysis of the muscles that help one to breathe thus it can lead to death. (Atkinson, 2006).
Babies should also get immunized against Haemophilus influenza virus because it can cause fatal meningitis, epiglottitis and other invasive diseases. The vaccine against Haemophilus influenza is Haemophilus influenza serotype b (Hib). The widespread use of Hib vaccines in infants has led to a significant decline in the incidences of invasive Hib disease in children. The vaccine is normally administered in four doses. The first dose is given at 2 months, the second dose at 4 months, and the third dose at 6 months. A booster dose is given at 12-15 months of age. Young children are at risk of severe or complicated influenza infection. Immunization against influenza is recommended for all persons older than 6 months (Yogev, 1990).
Therefore, it is very important that babies are immunized against Haemophilus Influenza and Polio viruses because these diseases can be fatal or can cause serious complication if one contracts the disease later in life due to lack of immunization.
Alexis de Tocqueville Democracy in America
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Alexis de Tocqueville Democracy in America
Alexis de Tocqueville’s Democracy in American is considered as one of the greatest works of political writing of the nineteenth century. The text’s daring conjectures, formidable length, narrative complexity, and elegant prose make it a masterpiece. However, these qualities have over time made sure that opinions differ greatly when it comes to the roots of greatness. Alexis de Tocqueville was a French political theorist and sociologist who went to the United States in 1831 to study prison systems. As a result of his trip, he returned to France with a wealth of broad observations which he coded in the book Democracy in America. In the text, he makes trenchant observations about individualism and equality, and his work remains to be a valuable explanations of Americans to each other and America to Europeans.
His book revealed Tocqueville’s position on equality. Tocqueville opined that equality was the greatest social and political idea of his era and was convinced that the US provided the most advanced example of equality in motion at the time. While he admired American individualism, he warned that society could become paradoxically uniform and easily atomized when each citizen that is being incorporated into the rest gets lost in the crowd. In his opinion, a section of society did not have intermediate social structures like those provided by traditional systems to mediate relations with the state. He warned that the result would be a democratic tyranny of majority where individual rights were compromised. Tocqueville was impressed by what he saw in American society and admired the stability of the economy and popularity of the churches. He also marveled at the nation’s embrace of slavery and the country’s irony of the mistreatment of Native Americans.
Tocqueville’s arguments concerning the direction of American democracy are accurate. His arguments about American democracy beg the question of whether democracies are safe. From my standpoint, democracies are not as safe as we might view them. The text showcases fresh insights on important perennial themes such as the liberty of the press and tyranny of civil societies and majorities. Tocqueville’s findings reveal why modern democracies remain susceptible to commercial panics. His main concern was having a democracy where the individual rights of the people would be compromised. True to his word, it is evidenced in how modern democracies value equality, have grown complacent, and curtailed the treat of a revolution.
Undoubtedly, the contemporary political order has worked out exactly as predicted by Alexis de Tocqueville. During his visit to America, he was impressed by a lot of things, including the thriving economy and the wandering popularity of churches. Besides that, he found it ironic how despite claiming to be a freedom-loving nation, they embraced slavery and mistreated Native Americans. This goes to show that society was not as equal as it purported to be and if not careful, democracy would be feasible on paper and not implementable. He predicted there was a possibility that democracy would become compromised with time. He noted that to caution society from tyranny, there was a need to institute intermediate social structures like the ones that existed in traditional hierarchies to control relations in the state. His fears about inequality reflect in the current American society, where like most countries continues to be watered down. The reality is that democracies are not safe and there are a lot of divisions that are going on in the systems and the societies at large.