The equation of a line L is y= -3x - 14. Find the coordinates of th.pdf

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The equation of a line L is y= -3x - 1/4. Find the coordinates of the point of intersection of L with the x-axis. Solution We have to find the point of intersection of the line L which has an equation y= -3x - 1/4 with the x-axis. On the x-axis the y coordinate is 0 Solving 0 = -3x - 1/4 => 3x = -1/4 => x = -1/12 The required point at which the line intersects the x-axis is (-1/12, 0).

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The field of quotients of any fieldDis isomorphic toD.Why? Solution Let K be the field of quotients of D. Define the following function f: D --> K such that f(x)=x First this is clearly a ring homomorphism: f(x+y)=x+y=f(x)+f(y) f(xy)=xy=f(x)f(y) f(1)=1 It is also easily seen to be one to one: if f(x)=f(y) then x=y So far all this is saying is that D is contained in its field of quotients. But this is true for any integral domain. Next we show f is onto which will say that F and K are actually the same field. In other words the field of quotients of a field is just the field itself. Let x be in K. Now by definition x=a/b for some elements a and b in D such that b is nonzero. But if b is nonzero then since D is a field, b has a multiplicative inverse 1/b in D. Then a*(1/b)=a/b is in D and f(a/b)=a/b=x. So f is onto. In short, the field of quotients of an integral domain is the smallest field in which the integral domain can be embedded. So if D is a field then it\'s field of quotients must be at least as big as D (since D has to be embedded into it). But D is a field so it is thus the smallest field in which D can be embedded. In other words, the field of quotients of a field F is just F. Now of course you could say that they are not exactly the same field since the field of quotients is actually comprised of equivalence classes of elements a/b where b is nonzero. But if D is a field and a,b are elements of F with b nonzero then what is the equivalence class of a/b? Well, suppose c/d is in the same equivalence class, then ad=bc. But b is nonzero so since we are in a field we can multiply by its inverse to obtain. (ad)/b = c But d is also nonzero so multiplying by its inverse gives a/b=c/d (now we are talking about elements of D and not equivalence classes) So the equivalence class of a/b is really just a/b. So D and its field of quotients really are the same field..

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The feeding habits of two-species of net-casting spiders, DEINOPIS and MENNEUS, are studied. They both coexist in eastern Australia. The following summary statistics were obtained on the size, in millimeters, of the prey of the two species: Adult DINOPIS Adult MENNEUS Assume that the populations of both species have relative frequency distributions that are approximately normal and the samples are selected in an independent manner from two populations. Estimate, with 95% confidence, the ratio of the two population variances. Adult DINOPIS Adult MENNEUS n_1= 10 n_2=10 X(bar)=10.30 y(bar)=9.06 S(x)^2= (2.50)^2 S(Y)^2=(1.95)^2 Solution Test of equality of variances: H0: S1^2 = S1^2 (equal population variance) H1: S1^2 is not equal to S1^2 test statistic, F = s1^2 / s2^2 test statistic, F = 1.643 degree of freedom,df = n1-1,n2-1 = 9,9 P-value = 0.207 Statistical conclusion: since P-value>0.05 hence we fail to reject H0 Practical conclusion:so we conclude that population variances are equal.

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The Erie Canal has been called America’s first school of engineering. How successful do you think it was as a “school”? What would you identify as its major strengths as a school? What would you identify as its most significant limitations as a school? The Erie Canal has been called America’s first school of engineering. How successful do you think it was as a “school”? What would you identify as its major strengths as a school? What would you identify as its most significant limitations as a school? Solution There were no civil engineers in the United States. Erie Canals was a great pioneer work of American engineering, where the engineers, without previous training, learned in the hard school of experience, and conquering by courage, persistence and force of character, became famous in their profession and spent lives of usefulness in their country’s welfare. The engineers showed great sagacity in beginning their work on the middle section, the least difficult and costly, and advancing in both directions. In this way they gradually prepared the people for greater expense and at the same time gave them encouragement by showing them steady progress; and all the while they were learning and feeling their way along, making everything sure, and never sacrificing accuracy. They used such discretion and wisdom in the selection of their assistants that the many enemies of the enterprise made no political capital out of their errors and defects, nor did the State suffer from any want of fidelity and ability in the discharge of their arduous and important duties Many of the distinctive characteristics of American engineering originated with those Erie canal engineers. Limitation of Erie Canal School:.

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The engineering profession is similar to medicine and law in that engineers are required to assimilate a large quantity of specialized knowledge that they then apply to the solution of specific problems. The application of knowledge is often bound by an extensive set of standards and practices that specify \"accepted methods and norms\". You will note that creative individuals are those that \"think outside the box\" or violate accepted norms of the field in order to bring a creative solution into being (e.g. Einstein\'s theory of relativity). They are often described as \"mavericks\". Thus, you might think that creativity and engineering are in some sense incompatible. Yet, when we look at innovative firms in complex industries, engineers are in the forefront of achieving creative solutions that drive innovation. In fact, they are necessary in many industries since modern business requires extensive technical knowledge to drive new solutions. How can this seeming paradox be explained? What factors separate the engineer who applies existing solutions to problems from the engineer who pioneers creative solutions? In your opinion, is it individual differences or can the difference be explained by organizational or environmental characteristics? Solution 1) As the asked question is based on the engineering students. 2) it is quiet different from any other branches because this is the only field that a student must think individually. 3) Not only individualy but also innovatively in many ways that can be applied. 4) And the most important thing in thid field is that learning of applications in theory and applying them in practical. 5) In many ways a student can make his subject more intersting by understading what he was learning. 6) The only subject that a student can easily understand and apply his thoughts to it. 7) In the pressent scenario engineering studies are more helpful in this fast running world. 8) You will note that creative individuals are those that \"think outside the box\" or violate accepted norms of the field in order to bring a creative solution into being (e.g. Einstein\'s theory of relativity). 9) The application of knowledge is often bound by an extensive set of standards and practices that specify \"accepted methods and norms\" 10) Generally, Science is the study of the physical world, while Engineering applies scientific knowledge to design processes, structures or equipment. 11) Both Engineers and Scientists will have a strong knowledge of science, mathematics and technology, but Engineering students will learn to apply these principles to designing creative solutions to Engineering challenges. 12) Engineering is a design process, combining knowledge of the properties of materials, models that predict how these behave, and innovative thinking, to create often-novel solutions to human needs. 13) In contrast, it may be helpful to think of technology as the process of making things, using tools, materials, and process skill.

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