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| 3. |
Mathematician Leonhard Euler’s Refutation of Pierre de Fermat’s Conjecture
(3 Pages, 35.85 $ (USD) )
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This is a 3 page paper discussing Euler’s refutation of Fermat’s conjecture. In 1637, French lawyer Pierre de Fermat wrote that he had “discovered a truly marvelous proof which this margin is too narrow to contain” in regards to a mathematical statement which had been unproven for over 1000 years. The basis of Fermat’s (“Last”) theorem or conjecture began with that of the Pythagoras equation [x.sup.2] + [y.sup.2] = [z.sup.2] which he proved “had an infinite set of whole number solutions” which related to the lengths of the sides of a right-angled triangle. Pythagoras did not know “how many solutions existed if the exponent in his equation were a number greater than 2”. Fermat claimed that “for any exponent greater than 2, there were no solutions at all”. During his lifetime however, Fermat often did not supply “proofs” of many of his theorems but many mathematicians since his time have been able to prove his claims to be correct except for that in relation to the Pythagoras equation. Swiss mathematician Leonard Euler (1707-1783) did however work further on many of Fermat’s theorems and “later proved that there are no solutions when the exponent is 3” and “unfortunately, an infinite number of cases remained and the case-by-case method was doomed to fail”. While Fermat’s Last Theorem proved to be difficult to prove, Euler managed to disprove and refute other assertions such as “2^(2^n) = p, where p is a prime number” and found that it is only true for the first four cases provided by Fermat. Bibliography lists 4 sources.
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| 4. |
Parenting Problems
(5 Pages, 59.75 $ (USD) )
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A 5 page research paper that offers discussion and solution to 4 different parenting scenarios. The writer for offers personal observations about the scenario and then discusses the solution offered by Bigner (2006), as well as problems implementing the solution. Scenarios address problems with toddlers, young children and adolescents. Bibliography lists 1 source.
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| 5. |
Leases R Us
(2 Pages, 23.9 $ (USD) )
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A 2 page solution to a problem determining the lease payment for a piece of machinery with a functional life of 5 years. The solution provides the present value of the lease allowing for the depreciation tax shield and real salvage value to determine the annual lease payment, adjusted for tax effects. An additional 3 page section includes a partial solution to another problem involving finding standard deviation, correlation and beta in preparation for determining whether the CAPM equation results in accurate pricing of several securities. Bibliography lists 1 source.
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| 6. |
What is the Cost of Reducing Medical Care?
(5 Pages, 59.75 $ (USD) )
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A 5 page paper discussing the inevitable decline in health care and the cost of that reduction. Opinions vary from consumer to HMO provider to physician to hospital. There is perhaps no one solution to the problem but rather it is compromise in many instances which appears to offer the best solution to the problems facing the medical industry. Varying opinions are offered in addition to a theorized solution. Bibliography lists 4 sources.
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