mm-4289 === Subject: Re: +1600 Solutions Manual to low cost Could you please send me Vector Mechanics for Engineers: Dynamics (8th Ed., Ferdinand P. Beer) solution manual. === Subject: Re: +1600 Solutions Manual to low cost Hey, could you email me at fdl3rd@gmail.com the solutions manual to Mechanical Behavior of Materials (3rd Ed. Dowling). === Subject: Re: Area; Integral question Bytes: 2477 > Find the area between f(x)=3x^3-x^2-10x and g(x)=-x^2+2x and prove that > the result will be the same using dx or dy. I did find the result using integrals dx (result=24) by solving two > integrals between -2 and 0, and between 0 and 2. However I don't get how > to find the solution with dy. The way I see is to find few functions > f(y) for both functions and try to integrate based on dy (?). But it > doesn't seem that easy. Any hints ? (unless I don't understand the > question) > Perhaps summer has dulled me somewhat, but your area calculation when integrating with respect to x assumes intersections of the two curves occur at +2, 0, and -2. Setting the two functions equal to each other, factoring out and dividing both sides by x, moving all terms to the left and applying the quadratic formula I get intersections at -1.69425, 0 (for the x divided out), and 2.36092. These new limits of integration give me a gross area between the curves of 25.716. As the others said, expressing each function in terms of y will be at least a bad dream. Rich === Subject: Re: Area; Integral question reply-type=response Bytes: 2656 > Find the area between f(x)=3x^3-x^2-10x and g(x)=-x^2+2x and prove that > the result will be the same using dx or dy. > I did find the result using integrals dx (result=24) by solving two > integrals between -2 and 0, and between 0 and 2. However I don't get how > to find the solution with dy. The way I see is to find few functions > f(y) for both functions and try to integrate based on dy (?). But it > doesn't seem that easy. Any hints ? (unless I don't understand the > question) Perhaps summer has dulled me somewhat, but your area calculation when > integrating with respect to x assumes intersections of the two curves > occur at +2, 0, and -2. Summer has dulled you somewhat :-) 3x^3 - x^2 - 10x + x^2 - 2x = 0 3x^3 - 12x = 0 3x(x^2 - 4) = 0 3x(x+2)(x-2)=0 x = 0, -2, 2 The 2nd part of the problem does not require actual setup of the specific integral and calculating the area. Use theorems and properties of integration here. -- Darrell === Subject: Re: Area; Integral question Bytes: 2625 > Find the area between f(x)=3x^3-x^2-10x and g(x)=-x^2+2x and prove that > the result will be the same using dx or dy. I did find the result using integrals dx (result=24) by solving two > integrals between -2 and 0, and between 0 and 2. However I don't get how > to find the solution with dy. The way I see is to find few functions > f(y) for both functions and try to integrate based on dy (?). But it > doesn't seem that easy. Any hints ? (unless I don't understand the > question) > Perhaps summer has dulled me somewhat, but your area calculation when > integrating with respect to x assumes intersections of the two curves occur > at +2, 0, and -2. Setting the two functions equal to each other, factoring out and dividing > both sides by x, moving all terms to the left and applying the quadratic > formula I get intersections at -1.69425, 0 (for the x divided out), and > 2.36092. These new limits of integration give me a gross area between the > curves of 25.716. As the others said, expressing each function in terms of y will be at least > a bad dream. Rich When I take f(x) - g(x), I get '3*x^3 - 12*x with zeros 0,2, and -2. === Subject: Re: Instructors Solutions Manual for Hayt, Engineering Electromagnetics, 7th Ed Bytes: 1396 Hey I wanted to know how the manual is presented ( pfd, etc.... ). And would you like to trade your solution manuals for other solution manuals that I have. === Subject: Need solution manual of Power Electronics: Converters, Applications, and Design Bytes: 1371 Mohan, Undeland, Robbins: Power Electronics: Converters, Applications, and Design, 3rd Edition the problem is i have to login as an instructor on the wiley website. If anybody has a login and can obtain these please help or if you already have the solutions http://bcs.wiley.com/he-bcs/Books?action=resource&bcsId=2096&itemId=04712269 39&resourceId=6730 if needed i will pay through paypal for any troubles please email me at: paulnid@optusnet.com.au === Subject: Re: Need solution manual of Power Electronics: Converters, Applications, and Design > Mohan, Undeland, Robbins: Power Electronics: Converters, Applications, and > Design, 3rd Edition the problem is i have to login as an instructor on the wiley website. If > anybody has a login and can obtain these please help or if you already > have the solutions http://bcs.wiley.com/he-bcs/Books?action=resource&bcsId=2096&itemId=04712269 3 9&resourceId=6730 if needed i will pay through paypal for any troubles please email me at: paulnid@optusnet.com.au So you can *sell it* on the internet ???? Indian students are cheating using these, and graduate substandard, cannot solve a problem, only ask for the answer on the internet! === Subject: Re: Need solution manual of Power Electronics: Converters, Applications, and Design Mohan, Undeland, Robbins: Power Electronics: Converters, Applications, and > Design, 3rd Edition There are a number of newsgroups sci.electronics.*. What makes you think that alt.math.undergrad is appropriate? > the problem is i have to login as an instructor on the wiley website. I is spelt I, Wiley is spelt Wiley. Why not enquire of Wiley how to get an instructor's login? -- Remove antispam and .invalid for e-mail address. He that giveth to the poor lendeth to the Lord, and shall be repaid, said Mrs Fairchild, hastily slipping a shilling into the poor woman's hand. === Subject: Proof matrix transpose Bytes: 909 Hi all, I need proof that a matrix A (nxn) and B(nxn): (A + B)^t = A^t + B ^t where ^t = is the matrix transpose. I very newbie in proofs, please anybody could help me with step by step. === Subject: Re: Proof matrix transpose > Hi all, I need proof that a matrix A (nxn) and B(nxn): (A + B)^t = A^t + B ^t where ^t = is the matrix transpose. I very newbie in proofs, please anybody could help me > with step by step. > 1. (A + B)^t_{ij} = (A + B)_{ji} (Def. of transpose) 2. (A + B)_{ji} = A_{ji} + B_{ji} (Def. of matrix addition) 3. A_{ji} + B_{ji} = A^t_{ij} + B^t_{ij} (Def. of transpose) 4. (A + B)^t_{ij} = A^t_{ij} + B^t_{ij} (Steps 1 - 3) 5. (A + B)^t = A^t + B^t (Def. of matrix equality) Kyle Czarnecki === Subject: Re: Proof matrix transpose On Thu, 26 Jul 2007 12:50:48 EDT, Alex If A = (a[i,j]) and B = (b[i,j]) then: 1. What is the (i,j) element of A + B? 2. So, then what is the (i,j) element of (A + B)^t? So much for the left side. Now, 3. What is the (i,j) element of A^t and of B^t? 4. What is the (i,j) element of their sum? How do your answers to 2 and 4 compare? --Lynn 2. === Subject: Re: Proof matrix transpose If A = (a[i,j]) and B = (b[i,j]) then: 1. What is the (i,j) element of A + B? Ansewer: I would say that is c[i,j] = a[i,j] + b[i,j] , then the element is c(i,j) is correct ? 2. So, then what is the (i,j) element of (A + B)^t? Ansewer: it is little hard for me... But I will try... D = (A + B) = a[i,j] + b[i,j] D^t = d[j,i] it is hard I know that Transpose Matrix a[i,j] is the matrix A^t=a[j,i], but no know how say it in formal proof. So much for the left side. Now, 3. What is the (i,j) element of A^t and of B^t? Ansewer: The element (i,j) from A^t is (j,i) and element (i,j) from B^t is (j,i) 4. What is the (i,j) element of their sum? Ansewer: I don't understand very this question... but I will try: d[j,i] = a[j,i] + b[j,i]. === Subject: Re: Proof matrix transpose On Fri, 27 Jul 2007 10:02:08 EDT, Alex Ansewer: I would say that is c[i,j] = a[i,j] + b[i,j] , then the element is c(i,j) is correct ? > Yes, assuming you are denoting A + B by C. But you call it D below. Don't call it two different things. 2. So, then what is the (i,j) element of (A + B)^t? Ansewer: it is little hard for me... But I will try... D = (A + B) = a[i,j] + b[i,j] D^t = d[j,i] *** Yes, but that equals what in terms of the a and b's? When you write that down, you will know the (i,j) element of (A+B)^t and will be done with the left side of your equation. it is hard I know that Transpose Matrix a[i,j] is the matrix A^t=a[j,i], but no know how say >it in formal proof. >So much for the left side. Now, 3. What is the (i,j) element of A^t and of B^t? Ansewer: The element (i,j) from A^t is (j,i) You mean a[j,i], not just (j,i) >and element (i,j) from B^t is (j,i) You mean b[j,i] 4. What is the (i,j) element of their sum? Ansewer: I don't understand very this question... but I will try: d[j,i] = a[j,i] + b[j,i]. You can't denote it by d(j,i) yet. What you have is that the (i,j) element of A^t + B^t is a[j,i] + b[j,i]. After you answer the *** question above which tells you what the (i,j) element of (A+B)^t is, if it is the same, then you will know that (A+B)^t and A^t + B^t have the same values in their (i,j) positions, making them equal. Then you will be done. This will be my last post for a few days, so if you still need more help, others can take it from here. --Lynn === Subject: exponential functions - simplifying Here we go again ;) I am not understanding why the following simplification is wrong: (4 ^ 1 + Ì2)(4 ^ 1 + Ì2) = 16 ^ 1 - (Ì2)©Ö = 16 ^ -1 = 1/16 help? -- Any society that would give up a little liberty to gain a little security deserves neither and will lose both - Benjamin Franklin === Subject: Re: exponential functions - simplifying Bytes: 1678 > Here we go again ;) I am not understanding why the following > simplification is > wrong: (4 ^ 1 + Ì2)(4 ^ 1 + Ì2) = 16 ^ 1 - (Ì2)©Ö = 16 ^ -1 = 1/16 help? (x+y)^2 = x^2 + 2xy + y^2 [4^1+sqrt(2)]^2 = 4^2 + 8sqrt(2) + [sqrt(2)]^2 === Subject: Re: exponential functions - simplifying > Here we go again ;) I am not understanding why the following simplification is >wrong: (4 ^ 1 + ?2)(4 ^ 1 + ?2) = 16 ^ 1 - (?2)î = 16 ^ -1 = 1/16 help? Please don't use special characters, they don't display correctly in all news readers. Stick to plain ASCII text. Also, please make it clear what the problem is. Is it [4 + sqrt(2)] [4 + sqrt(2)] = 18 + 8 sqrt(2) or this ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) or something else? === Subject: Re: exponential functions - simplifying it's ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) > Here we go again ;) I am not understanding why the following simplification is > wrong: > (4 ^ 1 + ?2)(4 ^ 1 + ?2) = 16 ^ 1 - (?2)î = 16 ^ -1 = 1/16 > help? Please don't use special characters, they don't display correctly in > all news readers. Stick to plain ASCII text. Also, please make it clear what the problem is. Is it [4 + sqrt(2)] [4 + sqrt(2)] = 18 + 8 sqrt(2) or this ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) or something else? > === Subject: Re: exponential functions - simplifying reply-type=response Bytes: 1544 Base is 4, add exponents. it's > ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) === Subject: Re: exponential functions - simplifying it's > ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) Adding exponents, you have 4^[2 + 2 sqrt(2)] = (4^2)^[1 + sqrt(2)] = 16^[1 + sqrt(2)] You could also write this as (2^4)^[1 + sqrt(2)] = 2^[4 + 4 sqrt(2)] or in various other ways. I don't really know what final form is the best. >t Here we go again ;) I am not understanding why the following simplification is > wrong: (4 ^ 1 + ?2)(4 ^ 1 + ?2) = 16 ^ 1 - (?2)î = 16 ^ -1 = 1/16 help? Please don't use special characters, they don't display correctly in > all news readers. Stick to plain ASCII text. Also, please make it clear what the problem is. Is it [4 + sqrt(2)] [4 + sqrt(2)] = 18 + 8 sqrt(2) or this ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) or something else? > === Subject: Re: exponential functions - simplifying Bytes: 2359 I must have re-posted it incorrectly, it's ( 4^[1 + sqrt(2)] ) ( 4^[1 - sqrt(2)] ) > it's > ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) Adding exponents, you have 4^[2 + 2 sqrt(2)] = (4^2)^[1 + sqrt(2)] = 16^[1 + sqrt(2)] You could also write this as (2^4)^[1 + sqrt(2)] = 2^[4 + 4 sqrt(2)] or in various other ways. I don't really know what final form is the best. > > Here we go again ;) I am not understanding why the following simplification is > wrong: > (4 ^ 1 + ?2)(4 ^ 1 + ?2) = 16 ^ 1 - (?2)î = 16 ^ -1 = 1/16 > help? > Please don't use special characters, they don't display correctly in > all news readers. Stick to plain ASCII text. Also, please make it clear what the problem is. Is it [4 + sqrt(2)] [4 + sqrt(2)] = 18 + 8 sqrt(2) or this ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) or something else? > === Subject: Re: exponential functions - simplifying reply-type=response Bytes: 2951 How many times are you going to post different problems? I must have re-posted it incorrectly, it's > ( 4^[1 + sqrt(2)] ) ( 4^[1 - sqrt(2)] ) > it's > ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) > Adding exponents, you have > 4^[2 + 2 sqrt(2)] > = (4^2)^[1 + sqrt(2)] = 16^[1 + sqrt(2)] > You could also write this as > (2^4)^[1 + sqrt(2)] > = 2^[4 + 4 sqrt(2)] or in various other ways. I don't really know > what final form is the best. Here we go again ;) I am not understanding why the following > simplification is > wrong: > (4 ^ 1 + ?2)(4 ^ 1 + ?2) = 16 ^ 1 - (?2)î = 16 ^ -1 = 1/16 > help? > Please don't use special characters, they don't display correctly in > all news readers. Stick to plain ASCII text. > Also, please make it clear what the problem is. Is it > [4 + sqrt(2)] [4 + sqrt(2)] = 18 + 8 sqrt(2) > or this > ( 4^[1 + sqrt(2)] ) ( 4^[1 + sqrt(2)] ) > or something else? > === Subject: Re: exponential functions - simplifying I must have re-posted it incorrectly, it's Yes you did. 8-) >( 4^[1 + sqrt(2)] ) ( 4^[1 - sqrt(2)] ) >t > Now I think I see where you went wrong. x^a * x^b does not equal x^(a * b) It does equal x^(a + b) Adding exponents in your problem, you have 4^[ 1 + sqrt(2) + 1 - sqrt(2) ] = 4^2 = 16 === Subject: Re: exponential functions - simplifying > Here we go again ;) I am not understanding why the following > simplification is > wrong: (4 ^ 1 + ?2)(4 ^ 1 + ?2) = 16 ^ 1 - (?2)î = 16 ^ -1 = 1/16 help? well as it stands then that should be :- (4^1 + sqr(2))(4^1 + sqr(2)) = 4^2 + 8sqr(2) + (sqr(2))^2 = 18 + 8sqr(2) -- > Any society that would give up a little liberty to gain a little security > deserves neither and will lose both > - Benjamin Franklin === Subject: Re: exponential functions - simplifying Sorry, forgot some parenthesis, it's [4 ^ (1 + ?2)] [4 ^ (1 + ?2)] = 16 ^ [1 - (?2)î] = 16 ^ -1 = 1/16 > Here we go again ;) I am not understanding why the following > simplification is > wrong: > (4 ^ 1 + ?2)(4 ^ 1 + ?2) = 16 ^ 1 - (?2)î = 16 ^ -1 = 1/16 > help? well as it stands then that should be :- (4^1 + sqr(2))(4^1 + sqr(2)) = 4^2 + 8sqr(2) + (sqr(2))^2 = 18 + 8sqr(2) > -- > Any society that would give up a little liberty to gain a little security > deserves neither and will lose both > - Benjamin Franklin === Subject: Re: exponential functions - simplifying Sorry, forgot some parenthesis, it's [4 ^ (1 + ?2)] [4 ^ (1 + ?2)] = 16 ^ [1 - (?2)î] = 16 ^ -1 = 1/16 ahh well theres no room for ambiguity in the worderful world of mathematics :) guess you'll learn that alongside use of parentheses... :) Here we go again ;) I am not understanding why the following > simplification is > wrong: (4 ^ 1 + ?2)(4 ^ 1 + ?2) = 16 ^ 1 - (?2)î = 16 ^ -1 = 1/16 help? > well as it stands then that should be :- > (4^1 + sqr(2))(4^1 + sqr(2)) = 4^2 + 8sqr(2) + (sqr(2))^2 = 18 + 8sqr(2) > -- > Any society that would give up a little liberty to gain a little > security > deserves neither and will lose both > - Benjamin Franklin > === Subject: Please help me with formual for calculating Hi Guys Sorry if this is the wrong group (you guys all seem way too smart for this question) if it is please point me in right direction.. Basically, i plot a series of X Y coordinates. I need to know the formuala for calcluating the x value where y=60 and also the x value where y =10, on the same set. Then divide one by the other to give me my answer. I'll explain.. Example 1. X Y 100 100 75 89 63 80 50 70 37.5 60 28 50 20 40 14 30 10 25 6.3 21 5 20 3.35 18 2 15 1.18 13 0.6 10 0.3 7 0.15 5 0.063 2 So the x value where y=60 is 37.5, the x value where y=10 is 0.6 therefore my answer is 37.5/0.6=62.5. but, example 2 X Y 100 99 75 88 63 80 50 72 37.5 65 28 55 20 50 14 46 10 42 6.3 38 5 30 3.35 27 2 20 1.18 15 0.6 8 0.3 5 0.15 3 0.63 1 So the x value where y=60 is somewhere between 37.5 and 28, the x value where y=10 is somewhere between 1.18 and 15 therefore my answer is *roughly* 32 / *roughly* 0.7. Problems. - I need the PC to automatically calculate these values, i cant just type them in as estimates - Even if i could type them in, that would only work if i had exactly 60 and exactly 10 (which never happens) - Does the log graph on the x-axis make it easier or impossible - I do all my work on excel so feel free to not only tell me how to do it, but to put it on excel formaula as well as a mathematical answer. Ta === Subject: Re: Please help me with formual for calculating Bytes: 1461 >Hi Guys >Sorry if this is the wrong group (you guys all seem way too smart for >this question) if it is please point me in right direction.. >Basically, i plot a series of X Y >coordinates. I need to know the formuala for calcluating the x value >where y=60 Calculate the regression line, and use the resulting equation. Since you are already in Excel, look up regression in the help file. bob === Subject: Simplify cos(x+pi) Simplify cos(x+pi) How do I do this with the addition/subtraction formula? === Subject: Re: Simplify cos(x+pi) >Simplify cos(x+pi) How do I do this with the addition/subtraction formula? The sum of two angles formula is cool, but here is another method. cos(x + pi) = cos[(x + pi/2) + pi/2] = - sin(x + pi/2) = - cos x This only works for specific angles because cosine is complementary sine. Brian === Subject: Re: Simplify cos(x+pi) >Simplify cos(x+pi) How do I do this with the addition/subtraction formula? The sum of two angles formula is cool, but here is another method. cos(x + pi) = cos[(x + pi/2) + pi/2] = - sin(x + pi/2) = - cos x You may find that the op wants to apply the addition formula to cos[(x + pi/2) + pi/2]! -- Remove antispam and .invalid for e-mail address. He that giveth to the poor lendeth to the Lord, and shall be repaid, said Mrs Fairchild, hastily slipping a shilling into the poor woman's hand. === Subject: Re: Simplify cos(x+pi) On Thu, 26 Jul 2007 20:33:05 -0700, in alt.math.undergrad: > Simplify cos(x+pi) > How do I do this with the addition/subtraction formula? The sum formula for the cosine is cos(x + y) = cos(x) cos(y) - sin(x) sin(y), so cos(x + pi) = cos(x) cos(pi) - sin(x) sin(pi). You know what cos(pi) and sin(pi) are, so you can substitute those values into this formula to complete the simplification. Brian === Subject: Re: Simplify cos(x+pi) Thu, 26 Jul 2007 23:48:32 -0400 from Brian M. Scott : > On Thu, 26 Jul 2007 20:33:05 -0700, > in alt.math.undergrad: Simplify cos(x+pi) How do I do this with the addition/subtraction formula? cos(x + pi) = cos(x) cos(pi) - sin(x) sin(pi). And you can check your work by thinking about what relation cos(x+pi) must bear to cos(x). Since an angle of pi is half a circle, what geometrical relationship do you see between cos(x+pi) and cos(x)? Work this out on your own, and then jave a look at my less-than- beautiful diagram at http://oakroadsystems.com/twt/refangle.htm#RelatedIdentities -- The internet is famously powered by the twin engines of bitterness and contempt. -- Nathan Rabin, /The Onion/ Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ === Subject: Maximum value Bytes: 1158 Help on this one please Find maximum value of C = 2x + y on the region determined by the constraints x + y <= 6 0 <= x <= 4 0 <= y <= 4 === Subject: Re: Maximum value Bytes: 2211 > Help on this one please Find maximum value of C = 2x + y on the region determined by the > constraints > x + y <= 6 > 0 <= x <= 4 > 0 <= y <= 4 > Methods to answer such questions fall under the category of linear programming. In this case, since you only have two variables, just graph the region in the x,y plane. The answer is simply the greatest y-value of the region, and as already stated will occur at a vertex of the region. For n variables, such linear programming problems can be solved analytically with algorithms such as the Simplex Method and others. Geometrically interpreted, such solutions are found by following each edge to each vertex of an n-dimensional hyper tetrahedron until the optimal vertex is achieved. -- Darrell === Subject: Re: Maximum value Bytes: 1481 ... since you only have two variables, just graph > the region in the x,y plane. The answer is simply the greatest y-value of > the region, Greatest x (which is x = 4), and on that edge greatest y (which is y = 2), unless I've misunderstood. -- Remove antispam and .invalid for e-mail address. He that giveth to the poor lendeth to the Lord, and shall be repaid, said Mrs Fairchild, hastily slipping a shilling into the poor woman's hand. === Subject: Re: Maximum value Bytes: 2018 Frederick Williams ... since you only have two variables, just graph > the region in the x,y plane. The answer is simply the greatest y-value > of > the region, Greatest x (which is x = 4), and on that edge greatest y (which is y = > 2), unless I've misunderstood. It doesn't ask which x yields the maximum value of C. It asks for the maximum value of C. Clearly, y >= 2 if x =< 4. Equally clear is y=4 when x=0. -- Darrell === Subject: Re: Maximum value > Help on this one please Find maximum value of C = 2x + y on the region determined by the > constraints > x + y <= 6 > 0 <= x <= 4 > 0 <= y <= 4 Note that C is monotonically increasing as either variable increases. Thus, if x1 > x0, and (x0,y) and (x1,y) are both in the region, the latter has a larger value. Thus, the maximum must be on the edge of the region. Moreover, it must be a point which cannot increase in x or y and stay in the region. Graphing will show that the only points that satisfy the restriction I listed are along the line-segment from (2,4) to (4,2). By inspection, it is obvious that you want x as large as possible, so the point (4,2) is the maximum of C. You can do this analytically as well by noting that on this line, x=6-y, and so C=12-y. Finding the maximum of C on the domain 2<=y<=4 is a trivial matter (and can be done in several ways) === Subject: Re: Maximum value Bytes: 2414 > Help on this one please Find maximum value of C = 2x + y on the region determined by the > constraints > x + y <= 6 > 0 <= x <= 4 > 0 <= y <= 4 Note that C is monotonically increasing as either variable increases. > Thus, if x1 > x0, and (x0,y) and (x1,y) are both in the region, the > latter has a larger value. Thus, the maximum must be on the edge of > the region. Moreover, it must be a point which cannot increase in x or > y and stay in the region. Graphing will show that the only points that satisfy the restriction I > listed are along the line-segment from (2,4) to (4,2). > By inspection, it is obvious that you want x as large as possible, so > the point (4,2) is the maximum of C. You can do this analytically as > well by noting that on this line, x=6-y, and so C=12-y. Finding the > maximum of C on the domain 2<=y<=4 is a trivial matter (and can be > done in several ways) There is a general theorem that a linear expression varying over a finite region bounded by linear inequalities, will have its extrema at corner points of the region. === Subject: Re: Maximum value Bytes: 2952 > Help on this one please > Find maximum value of C = 2x + y on the region determined by the > constraints > x + y <= 6 > 0 <= x <= 4 > 0 <= y <= 4 Note that C is monotonically increasing as either variable increases. > Thus, if x1 > x0, and (x0,y) and (x1,y) are both in the region, the > latter has a larger value. Thus, the maximum must be on the edge of > the region. Moreover, it must be a point which cannot increase in x or > y and stay in the region. Graphing will show that the only points that satisfy the restriction I > listed are along the line-segment from (2,4) to (4,2). > By inspection, it is obvious that you want x as large as possible, so > the point (4,2) is the maximum of C. You can do this analytically as > well by noting that on this line, x=6-y, and so C=12-y. Finding the > maximum of C on the domain 2<=y<=4 is a trivial matter (and can be > done in several ways) There is a general theorem that a linear expression varying over a > finite region bounded by linear inequalities, will have its extrema at > corner points of the region I am aware of that, but I wanted only to use tools that I was fairly certain the OP already had (assuming your comment was directed at me and not the OP, of course). For this particular problem, since the region is so simple, it could be solved by inspection anyway. === Subject: Re: Maximum value Help on this one please Find maximum value of C = 2x + y on the region determined by the > constraints > x + y <= 6 > 0 <= x <= 4 > 0 <= y <= 4 10. -- Remove antispam and .invalid for e-mail address. He that giveth to the poor lendeth to the Lord, and shall be repaid, said Mrs Fairchild, hastily slipping a shilling into the poor woman's hand. === Subject: Re: Maximum value Bytes: 1539 > Help on this one please Find maximum value of C = 2x + y on the region determined by the > constraints > x + y <= 6 > 0 <= x <= 4 > 0 <= y <= 4 Draw the allowed area on grid paper and draw a few lines corresponding do various values of C, e.g. 2x+y=0, 2x+y=2, 2x+y=4. What can you see from the picture? === Subject: Re: Math Wars, reconsidered > Those who read my math blog may have noticed I now have an explanation Good for you ! > for this situation where I say I have major mathematical discoveries > and others work diligently to fight that claim where I speculate that > members of the lower class in Britain fleeing to the Americas to > create this country so many hundreds of years ago, came with some > baggage about their noble class. so, were all these dudes were British lower-class mathematicians ? didn't wear wigs? > Some of the history of this country is well-known, of course, and I > don't think it odd to suggest that those colonists who turned to > slavery were trying to create a permanent underclass with themselves > as a permanent upper class--they were trying to make themselves > nobility. that is right out, most blacks that came over from Africa *wanted to be slaves*, and not have to live in the jungle eating bugs and pooping on the ground. No chance to learn Math in Africa, even to this very day for advanced math. The Hollywood image of all this has misled you. > So what does any of that have to do with math? I suggest to you that some of them haven't quite stopped and that > descendants of those British lower classes not only continue to try at > times to turn themselves into something of an upper class in the > United States, but they follow bizarre and twisted rules which are > THEIR interpretations of upper class behavior. descendants of those British lower classes => Punk Rockers ? > They believe that upper class members are above the law, will win at > any cost, and exploit the people beneath them with no mercy, and that > denial of this reality is just a sign of a lack of education and lower > class status. Just like in Nigeria. > I ran into this kind of behavior years ago when I graduated from high > school with the highest SAT of my graduating class and there was an > award for that, which by the rules I had won. What was your SAT score ? 600 ? Perhaps you went to a lower class school and didn't know it. Like by the rules I had a paper published in a peer reviewed > mathematical journal. no you did not, it was rejected, because it was garbage, show me a real printed copy of the journal with your paper in it. Can't do that can you? Was NOT published. > The school changed the rules so that you had to have the highest SAT > score and be in the top 10% by grades, which I was not, so they didn't > give me the award and gave it instead to some white kid. JSH is a Bigot. What award was it ? The I just made this stuff up award ? > And he was so proud. As he should be, because he was in the top 10% and you are not. Were you in the top 70% ? > In this reality of a bizarre class war that has spanned centuries > where the British nobles that those colonists were--I'd say--fleeing, > long dead, you have a modern society with some people fighting ghosts. bigot, ghosts = blacks And their twisted interpretation of what it means to be upper class as > seen by those from the bottom has created a group of very dangerous > people capable of just about anything believing that is what a > nobility does. Like Mathematitions ? On one of my blogs I have contrasted George W. Bush avoiding serving > in combat in the Vietnam War with Prince Harry, an actual British > royal, trying to get INTO war in Iraq. But he did not. There is one view of what people in an upper class always do, and > there is the reality of a mixed bag of behaviors from those who read > the histories of classed societies around the world. You are saying you are confused again ? Yes, I'm saying that there are a lot of people needlessly being evil > who follow naive interpretations they inherited from their ancestors > who were on the bottom. How is this going to justify your math is correct ? People on the bottom in a classed society rarely rave about those on > the top. This is high school stuff, are you taking a history class in High School ? has not upper class. BS, idealistic moron. But some people here don't quite get it as they follow some wicked > programming from past ages. you are projecting again, wiki for it. You see, as they lie, cheat and steal, doing anything to grasp for > meaningless power--they think they're being, noble. A good statement about yourself and your goals on sci.math. Or maybe I should say, they think they are noble, British style. Why do you *hate* the British ? They love your stinking math. They teach it to the lower class kids. That way they stay lower class forever. James Harris > === Subject: Re: Math Wars, reconsidered <46aa32b0$0$97267$892e7fe2@authen.yellow.readfreenews.net Those who read my math blog may have noticed I now have an explanation Good for you ! for this situation where I say I have major mathematical discoveries > and others work diligently to fight that claim where I speculate that > members of the lower class in Britain fleeing to the Americas to > create this country so many hundreds of years ago, came with some > baggage about their noble class. so, were all these dudes were British lower-class mathematicians ? didn't > wear wigs? Some of the history of this country is well-known, of course, and I > don't think it odd to suggest that those colonists who turned to > slavery were trying to create a permanent underclass with themselves > as a permanent upper class--they were trying to make themselves > nobility. that is right out, most blacks that came over from Africa *wanted to be > slaves*, and not have to live in the jungle eating bugs and pooping on the > ground. No chance to learn Math in Africa, even to this very day for > advanced math. > The Hollywood image of all this has misled you. So what does any of that have to do with math? I suggest to you that some of them haven't quite stopped and that > descendants of those British lower classes not only continue to try at > times to turn themselves into something of an upper class in the > United States, but they follow bizarre and twisted rules which are > THEIR interpretations of upper class behavior. descendants of those British lower classes => Punk Rockers ? They believe that upper class members are above the law, will win at > any cost, and exploit the people beneath them with no mercy, and that > denial of this reality is just a sign of a lack of education and lower > class status. Just like in Nigeria. I ran into this kind of behavior years ago when I graduated from high > school with the highest SAT of my graduating class and there was an > award for that, which by the rules I had won. What was your SAT score ? 600 ? > Perhaps you went to a lower class school and didn't know it. Like by the rules I had a paper published in a peer reviewed > mathematical journal. no you did not, it was rejected, because it was garbage, show me a real > printed copy of the journal with your paper in it. > Can't do that can you? Was NOT published. The school changed the rules so that you had to have the highest SAT > score and be in the top 10% by grades, which I was not, so they didn't > give me the award and gave it instead to some white kid. JSH is a Bigot. What award was it ? The I just made this stuff up award > ? And he was so proud. As he should be, because he was in the top 10% and you are not. Were you in the top 70% ? In this reality of a bizarre class war that has spanned centuries > where the British nobles that those colonists were--I'd say--fleeing, > long dead, you have a modern society with some people fighting ghosts. bigot, ghosts = blacks And their twisted interpretation of what it means to be upper class as > seen by those from the bottom has created a group of very dangerous > people capable of just about anything believing that is what a > nobility does. Like Mathematitions ? On one of my blogs I have contrasted George W. Bush avoiding serving > in combat in the Vietnam War with Prince Harry, an actual British > royal, trying to get INTO war in Iraq. But he did not. There is one view of what people in an upper class always do, and > there is the reality of a mixed bag of behaviors from those who read > the histories of classed societies around the world. You are saying you are confused again ? Yes, I'm saying that there are a lot of people needlessly being evil > who follow naive interpretations they inherited from their ancestors > who were on the bottom. How is this going to justify your math is correct ? People on the bottom in a classed society rarely rave about those on > the top. This is high school stuff, are you taking a history class in High School ? has not upper class. BS, idealistic moron. But some people here don't quite get it as they follow some wicked > programming from past ages. you are projecting again, wiki for it. You see, as they lie, cheat and steal, doing anything to grasp for > meaningless power--they think they're being, noble. A good statement about yourself and your goals on sci.math. Or maybe I should say, they think they are noble, British style. Why do you *hate* the British ? They love your stinking math. They teach it to the lower class kids. That > way they stay lower class forever. James Harris And here's the punchline: JSH himself acknowledges that he got into Vanderbilt due to affirmative action. (I don't know how someone *knows* he gets into a post-secondary institution due to affirmative stupid to meet our normal requirements for matriculation to Vanderbilt. Fortunately for your dumb, lazy ass that does not appreciate the educational opportunities afforded to you in this country, we are going to deny an otherwise legitimate applicant who is white, admission because of your skin color. I am sure you and parents must be very proud of you.). But I digress ;>).... Whatever the case, JSH admits to being proud of an accomplishment he did not legitimately earn (wow how much have things changed, huh?) He has *never* addressed this issue. But he *is* thinking about it. He is thinking of some spin or rationalization he can make-up to explain this away/attack those who bring up this perfectly legitimate true statement that he made. But this is good, because while he is thinking about a rationalization, I want him to realize that he *IS* making up a rationalization. I want him to understand and reflect upon the fact that he is having to lie. He will never admit it, but he *will* know it. M === Subject: Re: JSH: Math Wars, reconsidered > So what does any of that have to do with math? > to get you. Actually they are, we have been assigned to monitor him at all times, if his technology gets out, China will take over and we will have no teeth because of bad toothpaste. > The faculties of major universities are not out to get > you. Yes they are, JSH can make inquires if he is on the black list at any of them. >None of these people even know who you are. Wrong, one person does know who JSH is, but he left. >Whatever epic or > titanic struggle you imagine yourself to be engaged in exists only in > your own demented, paranoid imagination -- it has no basis in reality. Wrong, a delusion is a delusion. > I've said it before and I will say it again: you need to see a > psychiatrist, you need to be on medication, and you need serious > counseling. He is all troll, he is simply counting the number of replies he gets off one post of his stupidity. === Subject: A nice succession. 1) Consider a,b E R,a0,whatever x part of ]a,b[.Prove that if f(a)=f(b) therefor f has one extreme in ]a,b[ and tell if it's a maximum or a minimum. 2) Calculate Limit of x tending to 1 for the real function of real variable y(x) = [(x/(x+1)) - (1/(ln x))] 3)Calculate the limit of n index root for fn. fn = n!/[(n+1)(n+2)...(2n)] 3.a] Calculate the limit of wn = cos (n).tan (1/n) === Subject: Re: A nice succession. Bytes: 1107 > 2) Calculate Limit of x tending to 1 for the real function of real variable > y(x) = [(x/(x+1)) - (1/(ln x))] > -oo Any other orders besides the ones I've refused? === Subject: Re: A nice succession. ok 1+1 . 2+2 . ... . 2n ... Is it introductory??? Perhaps it is,i don't care === Subject: Re: A nice succession. hummm..too good to be real..in fact another introduction of a waco's nonsense...I haven't seen that succession..and believe me when i say i've seen some. Well,it could be a series of numbers..ok... 1.3.5.7 ... (2n-1)..or 2.4.8.32. ... . (2^n) .Indeed it could be this and much more. I wonder what it is ... evol introduction??What is then.. Yes,take my advise don't tell granny how to suck eggs cause they 've been sucked too long ago... === Subject: Re: A nice succession. 3) fn = n!/(n+1)(n+2)...(2n) The given limit is Lim (n+1)!/(n+2)(n+3)...(2n+2)/n!/(n+1)(n+2)...(2n) = Lim (n+1)!(n+1)(n+2)...(2n)/n!(n+2)(n+3)...(2n+2) = Lim (n+1)!/n! * * Lim (n+2)(n+3)...(2n+2)/(n+3)(n+4)...(2n+6)/ /(n+1)(n+2)...(2n)/(n+2)(n+3)...(2n+6) = Lim (n^3-n)!/(n^2-1)!* *Lim 2n+2/2n+6 = +oo * 1 = +oo === Subject: Re: A nice succession. Yes,yes it's the mean average theorem,and another nonsense..As I reformulated the question..neither Lagrange Nor even rolle have proven that in this conditions the expressed real function of real variable has only one and just one extreme in that part of R. In fact,it's the intruduction of another waco's nonsense.And by the way,if f'(c) = 0 according to Lagrange ...humm well it's a condition proven by Rolle's theorem but .. no one can tell that there is not another extreme ... grrrr .. It's necessary that the second derivative is positive to prove that the minimum is the only one.... ok..is it absolute or local?? I haven't even introduced trojans in matrices..ehehe And this quesion of derivatives...a high risk ...ye..litigation at the barrister..ok...I give it up..but i've won this time.Or is it solid waco transcendental derivative?? === Subject: Re: A nice succession. 1) f(x) is continuous in [a,b] f(x) has finite derivative until n order in all numbers of ]a,b[ According to Lagrange, f'(x)*(b-a) = f(a)-f(a) I guess that it's the mean average theorem of Lagrange. So in this way,theres at least one zero of the derivative in ]a,b[,cause f'(x) = 0/(b-a). If the derivative has at least one zero,it has in this subset of R an extreme. As d^2f/dx^2 is greater than zero,this extreme is a minimum. === Subject: Re: A nice succession. Stay tuned , don't miss .. the succession parts II and III. === Subject: Re: A nice succession. There was a fellow in athens that was very interested in rectangular trangules and in circles,too. f(x) : R -é [-1,1] x -é Y=cos x Co-sines,sines,tangents and co-tangents are to be expressed in pi radians.Indeed.. ch ^2 x+ sh^2 x = 1 ...truly and that .. y=sh^-1 x = ln ( x + sq rt(1+x^2)).. they truly did.. and that the limit of x wenting to minus infinitive of sh^-1 x = - infinitive...truly.. But have these guys told to us if this is to be expressed in pi rads??In fact it's open wide public.. f(x):R-é]-pi/2,pi/2[ x -é y = tan^-1 x ...?? I guess it was that guy from athens ,too. It seems that the cos 1 in the scientific calculator returns a result.In the waco's mind that's the get away ... to trade pi rads for natural numbers..Well if it was cos (1.bc).. could be true...I guess it's the first successive aspect...then. === Subject: Re: A nice succession. Bytes: 978 On the other hand. Cos (n)= cos (1),cos (2),cos (3) ,..., Cos (n),cos(n+1),... * tan 0 pi rad.... The success is the succession. In this way.. that's a complet piece of a nonsence. === Subject: Re: A nice succession. 3.a) Lim cos(n).tan(1/n) = Lim [(1-tan^2 (n/2))/(1+tan^2(n/2))] * *[[(2tan(1/2n))/(1+tan^2(1/2n))]/(cos (1/n))] = without limit (Oscilant divergency) === Subject: Re: Complete electronic solution manual in pdf ! Get it in hours! Can you send me the Physics, 5th Edition, Vol 2 by Halliday, Resnick, Krane (Chap 25-52). much appreciated, Alina > I have the complete electronic SOLUTION MANUAL in PDF format > containing ALL (odd and even - except where noted) solutions for the > books listed below. These are not paper books, they are ebooks and > most are only $12.00 each - paypal accepted. If you do not see a solution on my list, email me and I will see if I > can locate it, but no guarantees, but I will try! Books for which I have electronic solution manual: A Course in Game Theory by Osborne, Rubinstein > A Course in Algebraic Number Theory by Cohen > Adaptive Filter Theory, 4th Edition, by Haykin > Adaptive Control, 2nd. Ed., by Astrom, Wittenmark > Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even > solutions) > Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even > solutions) > Advanced Macroeconomics, David Romer > Advanced Mathematical Concepts Precalculus With Applications by > Holliday [ISBN: 0028341759] > Advanced Modern Engineering Mathematics, 3rd Ed., by G. James > A First Course In Differential Equations, 7th Edition, by Zill, Cullen > Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray, > Hurst, Lewis, Meyer > Analytical Mechanics, 7th Edition, by Fowels, Cassiday > An Interactive Introduction to Mathematical Analysis, by Jonathan > Lewin > An Introduction to the Mathematics of Financial Derivatives, 2nd Ed., > by Neftci [ISBN: 0125153929] > Antenna Theory, 2nd Ed., by Balanis > Antennas for all Applications, 3rd Edition, Kraus, Marhefka > Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) > Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley > Applied Numerical Methods with MATLAB for Engineers and Scientists, > 1st Ed,. by Chapra > Applied Statistics and Probability for Engineers, 3rd Ed., by > Montgomery, Runger (Selected Solutions) > Applied Strength of Materials, 4th Edition, by Mott > A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen, > Andre > Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi Basic Business Statistics: Concepts and Applications, 10th Ed., by > Berenson, Krehbiel, Levine (chap1-18) > Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin > Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms > (Missing a chapter or 2) > Bioprocess Engineering Principles by Doran Calculus Early Transcendental, 5th Ed., by James Stewart > Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis > Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney, > Demana, Kennedy > Calculus: Multivariable, 5th Edition, by James Stewart > Calculus: Single Variable, Early Transcendental, 5th Edition, by James > Stewart > Calculus, Single and Multivariable, 3rd Ed., by Hughes-Hallett, > McCallum > Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson, > Hostetler, Edwards > Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler > Chemical Engineering Volume 1, Sixth Edition, by Richardson, Coulson, > Backhurst, Harker > Thornton > College Physics, Volume 1: 7th Edition, by Serway, Faugh > College Physics, Volume 2: 7th Edition, by Serway, Faughn > Communications Systems, 4th Ed., by Haykin > Communications Systems Engineering, 2nd Edition, by Proakis > Computational Techniques for Fluid Dynamics by Srinivas, Fletcher > Computer Networks, 4th Ed., by Andrew S. Tanenbaum > Computer Networks: A Systems Approach, 3rd Edition, by Davie > Control Systems Engineering, 4th Ed., by Norman Nise > Corporate Finance, 6th Edition, by Ross > C++ How to Program: Intro Object-Oriented Design with the UML, 3rd > Ed., by Deitel, Nieto Data and Computer Communications, 8th Edition by Stallings > Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke (Sol. > for Chapters 2-21, odd only) > Design of Analog CMOS Integrated Circuits, 1st Edition, by Razavi > Design of Analysis of Experiments, 6th Edition, Montgomery (missing > chapter 6-8) > Design of Machinery, 3rd Ed by Robert L. Norton > Design With Operational Amplifiers and Analog Integrated Circuits, 2nd > Ed., by Sergio Franco > Design With Operational Amplifiers and Analog Integrated Circuits, 3rd > Ed., by Sergio Franco > Device Electronics for Integrated Circuits 3rd Edition by Muller > Differential Equations with Boundary Value Problems, 2nd Ed., by > Polking, Arnold > Digital And Analog Communication Systems 7th Ed., Leon W. Couch > Digital Communications, 4th Edition, by Proakis > Digital Communications: Fundamentals and Applications, 2nd Ed, Skylar > Digital Design, 4th Edition, by Mano, Ciletti > Digital Image Processing, 2nd Edition, by Gonzalez, Woods > Digital Integrated Circuits, 2nd Ed., by Rabaey (Solutions ONLY for > Chapters 3, 5, 6, 10) > Digital Signal Processing: A Computer Based Approach, 1st Ed., by > Mitra > Digital Signal Processing: A Computer Based Approach, 2nd Ed., by S. > Mitra > Digital Signal Processing: A Computer Based Approach, 3rd Ed., by S. > Mitra > Digital Signal Processing: Priciples, Algorithms and Applications, 3rd > Edition, by Proakis > Discrete Time Signal Processing, 2nd Edition, Oppenheim > Dynamics of Mechanical Systems by C.T.F. Ross Econometric Analysis, 5th Edition, by Greene > Wooldridge > Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, > Viceira > Electrical Properties of Materials, 7th Ed., by D. Walsh, L. Solymar > Electric Circuits 6th Ed. by Nilsson > Electric Circuits 7th Ed. by Nilsson > Electric Machinery, 6th Ed., Fitzgerald, Kingsley, Umans > Electric Machinery Fundamentals, 4th Ed by Chapman > Electromagnetic Fields and Waves by Iskander (...) > Electronic Circuit Analysis, 2nd Ed., by Donald Neamen > Electronics, 2nd Ed., by Allan R. Hambley > Elementary Differential Equations, 8th Edition, by Boyce, DiPrima > (some odd/even) > Elements of Chemical Reaction Engineering, 3rd Ed., by H. Scott Fogler > Engineering and Chemical Thermodynamics, by Koretsky [ISBN: 0471385867] > (No sol. for chapt 6) > Engineering Circuit Analysis, 6th Edition, Hyat > Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck > Engineering Fluids Mechanics 7th Edition by Crowe > Engineering Fluids Mechanics 8th Edition by Crowe > Engineering Mathematics, 4th Ed., by John Bird > Engineer Mechanics: Dynamics, 4th Ed., by Bedford > Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler > Engineering Mechanics: Dynamics 11th Ed. by Hibbeler > Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige > Engineering Mechanics: Statics, 4th Edition - A. Bedford, Wallace > Fowler > Engineering Mechanics: Statics, 5th Ed., Meriam > Engineering Mechanics: Statics, 6th Ed., Meriam > Engineering Mechanics: Statics, 10th Ed., by Russell C. Hibbeler > Engineering Mechanics: Statics 11th Ed. by Hibbeler > Experiments with Economic Principles by Bergstrom, Miller Feedback Control of Dynamic Systems, 4th Edition, by Powell, Emami- > Naeini > Financial Accounting, 4th Ed., by Libby, Short (Chap1-14) > Financial Accounting: An International Introduction, 2nd Ed., by > Alexander, Nobes > Finite Element Techniques in Structural Mechanics by Ross > Fluid Mechanics - 5th Edition by Frank M. White > Fluid Mechanics and Thermodynamics of Turbomachinery, 5th Ed., by S. > L. Dixon [ISBN: 0750678704] > Essentials of Fluid Mechanics: Fundamentals and Applications, 1st Ed., > by Cengel & Cimbala > Fluid Mechanics with Engineering Applications, 10th Edition, by > Finnemore > Fundamentals of Aerodynamics, 3rd Edition, by J. D. Anderson, Jr. > Fundamentals of Aerodynamics, 4th Edition, by Anderson > Fundamentals of Applied Electromagnetics, 2001 Media Edition, by Ulaby > Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition, > by Ulaby > Fundamentals of Digital Logic with Verilog Design, 1st Edition, by > Brown, Vranesic > Fundamentals of Digital Logic with VHDL Design by Stephen Brown, > Zvonko Vranesic > Fundamentals of Electric Circuits, 2nd Edition, by Alexander > Fundamentals of Electromagnetics with Engineering Appls by Wentworth > Fundamentals of Fluid Mechanics, 5th Ed. by Munson, Young.. > Fundamentals of Heat and Mass Transfer, 4th Ed by Incropera... > Fundamentals of Heat and Mass Transfer, 5th Ed by Incropera... > Fundamentals of Heat and Mass Transfer, 6th Ed by Incropera... > Fundamentals of Logic Design, 5th Ed., by Roth Jr. > Fundamentals of Machine Component Design, 3rd Ed., by Juvinall > Fundamentals of Machine Component Design, 4th Ed., by Juvinall > Fundamentals of Machine Elements, 2nd Ed., Hamrock, Jacobson, Schmid > Fundamentals of Physics by Halliday, 7th Ed., Walker, Resnick > Fundamentals of Semiconductor Devices, 1st Edition by Anderson > Fundamentals of Structural Analysis, 2nd Ed., Chia-Ming Uang, Kenneth > Leet > Fundamentals of Thermal-Fluid Sciences, 2nd Ed. by Cengel > Fundamentals of Thermal-fluid Sciences, Int'l 2nd Ed. by Cengel > Fundamentals of Engineering Thermodynamics, 5th Ed. by Shapiro > Fundamentals of Thermodynamics, 5th Ed., by Sonntag, Borgnakke... > Fundamentals of Thermodynamics, 6th Ed., by Sonntag Geometry, 04 Edition, by McGraw-Hill [ISBN: 0078296374] > Guide to Energy Management, 5th Edition, by Pawlik Heat Transfer: A Practical Approach - 2nd Edition by Cengel > Hydraulics in Civil and Environmental Engineering, 4th Ed., by Andrew > Chadwick Introduction to Algorithms, 2nd Ed by Cormen, Leiserson (Selected > Sol.) > Introduction To Chemical Engineering Thermodynamics, 7th Ed., by Van > Ness, Smith, Abbott > Introduction To Chemical Engineering Thermodynamics, 7th Ed., by Van > Ness, Smith, Abbott > Introduction to Electric Circuits, 6th Ed., by Dorf, Svoboda > Introduction to Electric Circuits, 7th Ed., by Dorf, Svoboda > Introduction to Electrodynamics, 3rd Ed. by David Griffiths > Introduction to Fluid Mechanics - 5th Ed. by Fox.. > Introduction to Fluid Mechanics - 6th Ed by Fox, McDonald... > Introduction to Linear Algebra, 3rd Ed., by Gilbert Strang > Introduction to Linear Algebra, 5th Ed., Arnold, Johnson, Riess > Introduction to Quantum Mechanics, 2nd Ed. by Griffiths > Introdution to Solid State Physics, 8th Edition by Kittel > Intro to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, > and Heat Transfer by Moran, Shapiro, Munson, DeWitt Introduction to Thermal Systems Engineering, by Moran, Shapiro Linear Algebra, by J. Hefferon > Linear Algebra And Its Applications, 3rd Ed., by David C. Lay > Linear Algebra with Applications, 2nd Edition - by Otto Bretscher > Linear Algebra with Applications, 3rd Edition - by Otto Bretscher > Linear Circuit Analysis: Time Domain, Phasor and Laplace.., 2nd Ed, > Lin Machine Design: An Integrated Approach, 2nd Ed., by Robert L. Norton > (same problems as third edition except for last 2-4 problems per > chapter that were added to the third edition) > Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton > Managerial Accounting, 11th Ed., by Noreen, Brewer, Garrison > Materials Science and Engineering: An Introduction, 6th Ed. by > Callister > Matrix Analysis and Applied Linear Algebra by Carl Meyer > MC68HC11: An Introduction: Software/Hardware Interf, 2nd Ed, by Huang > Mechanical Engineering Design, 7th Ed. by Mischke, Shigley Mechanical Vibrations, 3rd Edition, by S. S. Rao (99% same as 4th > Edition, No Solutions for Chapters 6, 9, and 12) > Mechanics of Fluids, 8th Ed., by Bernard Massey > Mechanics of Fluids, 4th Ed., Irving H. Shames > Mechanics of Fluids, 8th Ed., by Bernard Massey > Mechanics of Materials - 3rd Ed. by Beer, Johnston, Dewolf > Mechanics of Materials - 4th Ed. by Beer, Johnston, Dewolf > Mechanics of Materials - 6th Ed. by Hibbeler > Mechanics of Materials, 6th Edition by James M. Gere (missing small > portion, section 8.5) > Mechanics of Materials, 6th Ed., by Sturges, Morris, Riley (part of > Chapt 2 is missing but only #1 thru #60) > Mechanics of Solids by C.T.F. Ross > Microeconomic Analysis, 3rd Ed., by H. Varian (Ans. to Exercises: Ch.1- > Ch.25) > Microeconomic Theory, by Mas-Colell, Whinston, Green > Microelctronic Circuits, 5th Ed. by Sedra and Smith > Microelectronic Circuit Design, 2nd Edition by Jaeger, Blalock > Microelectronics: Digital and Analog Circuits and Systems by Millman > Microwave and Rf Design of Wireless Systems, 1st Edition, by Pozar > Miller & Freund's Probability and Statistics for Engineers, 7th > Edition, Johnson, Miller > Modern Compressible Flow, 3rd Edition, by Anderson > Modern Control Engineering, 3rd Edition, by Ogata > Modern Control Engineering, 4th Edition, by Ogata > Modern Digital and Analog Communication Systems, 3rd Ed., by Lathi > Modern Control Systems, 9th Ed., by Richard C. Dorf, Robert H Bishop > Modern Operating Systems,2nd Ed., by Andrew Tanenbaum > Modern Physics 4th Edition by Tipler > Monetary Theory and Policy, 2nd Edition, by Walsh > Multivariable Calculus, 5th Edition, by James Stewart Numerical Methods, 3rd Ed., by J. Douglas Faires, Richard L. Burden > (Selected Solutions) Operating Systems: Internals and Design Principles, 4th Edition, by > Stallings > Options, Futures and Other Derivatives, 5th Ed., by John Hull > (Chapters 1 thru 18 ONLY) > Orbital Mechanics: For Engineering Students by Howard Curtis (includes > matlab scripts) > Organic Chemistry, 4th Ed., by Carey, Atkins (Student Study Guide and > Sol. Man.) Partial Differential Equations with Fourier Series and Boundary Value > Problems, 2nd Ed., by Asmar (Student Solutions Manual) > Physical Chemistry - 7th Edition - by Julio de Paula, Peter Atkins > Physics, 6th Edition, by John Cutnell > Physics, 5th Edition, Vol 2 by Halliday, Resnick, Krane (Chap 25-52) > Physics for Scientist and Engineers by Knight (No Chapt 36-42) > Physics for Scientist and Engineers, 6th Ed., by Serway > Physics for Scientists and Engineers-Vol 1, 5th Edition, Serway, > Beichner (Chap. 1 - 22) > hysics for Scientists and Engineers-Vol 2, 5th Edition, Serway, > Beichner (Chap. 23 - 46) > Physics for Scientists and Engineers, 3rd Ed., by Douglas C. Giancoli > Physics for Scientist and Engineers, 5th Edition, by Tipler, Mosca > Physics: Principles with Applications, 6th Ed. by Giancoli > Power System Analysis and Design, 3rd Ed., by Glover, Sarma > Principles and Applications of Electrical Engineering 4th (Revised) Ed > by Rizzoni > Principles of Communication: Systems, Modulation Noise, 5th Ed., > Ziemer > Principles of Physics, 3rd Edition, by Serway > Principles of Statics, 10th Ed., by Russell C. Hibbeler [ISBN: > 0131866745] > Probability and Statistics for Engineers and Scientists, 3rd Edition, > Hayter > Probability and Statistics for Engineering and the Sciences, 6th Ed., > by Jay L. Devore > Probability Random Variables, and Stochastic Processes, 4th Ed., by > Papoulis, Pillai (..) 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Parr > (No Solutions for Chap 9-12) > Shigley's Mechanical Engineering Design, 8th Ed. by Budynas, Nisbett > (No Sol. for Chapt 18 & 19) Simply C#: An Application-Driven Tutorial Approach, by Deitel, Hoey... > (Chapters 1-32) > Soil Mechanics: Concepts and Applications, 2nd Ed., by Powrie > Solid State Electronic Devices - 5th Ed by Streetman > Solid State Electronic Devices - 6th Ed by Streetman > Statics and Mechanics of Materials: An Integrated Approach, 2nd Ed., > by Riley, Sturges, Morris > Structural Analysis, 5th Edition, by Hibbeler > System Dynamics, 3rd Edition, by Ogata Theory and Design for Mechanical Measurements, 4th Ed., Beasley, > Figliola > Thermal Physics, 2nd Edition, by Charles Kittel > Thermal Physics, by Ralph Baierlein > Thermodynamics: An Engineering Approach by Cengel, Boles (Missing > solutions #118-149 of Chapter 7) > The Science and Engineering of Materials, 4th Ed., by Donald R. > Askeland, Pradeep P. Phule Thomas' Calculus, Early Trans., Part 1, 10th Ed. by Thomas, Weir, > Hass, Giordano > Thomas' Calculus: Part 2, 10th Ed. (Multivariable, chs. 11-16), by > Thomas, Weir, Hass, Giordano > Thomas' Calculus, Early Trans., Part 1, 11th Ed. by Thomas, Weir, > Hass, Giordano > Thomas' Calculus: Part 2, 11th Ed. (Multivariable, chs. 11-16), by > Thomas, Weir, Hass, Giordano > Transport Phenomena, 1st Edition, by R. Byron Bird University Physics 11th Edition by Young.. Vector Calculus, Linear Algebra and Differential Forms: A Unified > Approach, 2nd Ed., by Hubbard > Vector Mechanics: Statics 7th Edition by Beer > Vector Mechanics: Dynamics, 7th Ed., by Beer, Johnston, Staab, Clausen > Vibrations and Stability: Advanced Theory, Analysis, and Tools, 7th > Ed., by Thomsen Wireless Communications: Principles and Practice, 2nd Ed, by Rappaport === Subject: Re: Complete electronic solution manual in pdf ! Get it in hours! Can you send me the Physics, 5th Edition, Vol 2 by Halliday, Resnick, > Krane (Chap 25-52). much appreciated, Alina I have the complete electronic SOLUTION MANUAL in PDF format > containing ALL (odd and even - except where noted) solutions for the > books listed below. These are not paper books, they are ebooks and > most are only $12.00 each - paypal accepted. If you do not see a solution on my list, email me and I will see if I > can locate it, but no guarantees, but I will try! Three points: (1) Don't top post. (2) Snip the irrelevant parts of what you're replying to. (3) Read what you're replying to before you reply to it. In this case note the op's request to be e-mailed. -- Remove antispam and .invalid for e-mail address. He that giveth to the poor lendeth to the Lord, and shall be repaid, said Mrs Fairchild, hastily slipping a shilling into the poor woman's hand. === Subject: AC method of factoring polynomials Summary: How well known and/or frequently taught is the AC method of factoring, sometimes called factoring by grouping. Factoring of polynomials often seemed like an art to me. For example, consider 18x^2 + 7x - 30. I used to consider all possible pairs of factors of 18 and of 30 until I found the right coefficients. Considering placement of thes factors, that's 24 possible combinations, though with intuition (hence the art), I might be able to narrow down the search. learned a method the book calls factoring by grouping. The client's professor calls it the AC method, from consideration of polynomials of the type Ax^2 + Bx + C. Here's how it works in the above example: - Multiply the leading coeffiecient 18 = 2 x 3^2 and the constant term -30 = -2 x 3 x 5, getting -540 = -2^2 x 3^3 x 5. - Find a pair of factors of -540 such that their sum is the middle coefficient 7. That is equivalent to findiing factors of 540 whose difference is 7. Either by listing all the factors or by looking at the prime factorization, we find 20 = 2^2 x 5 and 27 = 3^3 as these factors. I prefer the prime factorization way, in which case I didn't even need the fact that the product was 540. - Rewrite the polynomial by splitting up the middle term: 18x^2 +27x - 20x + 30. (-20x + 27x will work as well.) - Factor by grouping: 9x(2x + 3) - 10(2x + 3) = (9x -10) (2x + 3). Voil`a! (grave accent) - If no pair of factors of AC (the product of the leading coefficient and the constant term) sum to the middle coefficient B, then the polynomial is irreducible. When A > 1, this approach seems in general a lot easier to me than searching pairs of factors of A and C individually. If you haven't seen this before, try it on some examples yourself, such as 6x^2 + 13x y + 6y^2 16a^4 - 24a^2 b + 9b^2 12x^2 - 29x + 15 6b^2 + 13b - 28 10m^2 -13m n - 3n^2 I don't think it is the case that I learned this method once long ago and subsequently forgot it, so I am surprised I never saw it before. How well known is this method? Is it taught much? I don't find it in my favorite College Algebra text (by C.H. Lehmann), and it doesn't show up in the first three pages from Googl(R)ing polynomial factor. At least one of my more advanced clients had never seen it before either. -- Stephen J. Herschkorn sjherschko@netscape.net Math Tutor on the Internet and in Central New Jersey and Manhhattan === Subject: clarification on power series expansion I got confused for a minute: Power series expansion in 2 variables is defined as sum_{n,p} a_{n,p} x^n y^p Does it mean it is equal to: a00 + a10 x + a01 y +a11 xy + a12 xy^2+ a21 x^2y + a22x^2y^2+ a23 x^2y^3 + a32 x^3y^2+... or to a00+ a01 y + a02 y^2 + a03 y^3 +..... === Subject: Re: clarification on power series expansion > I got confused for a minute: Power series expansion in 2 variables is defined as > sum_{n,p} a_{n,p} x^n y^p Does it mean it is equal to: a00 + a10 x + a01 y +a11 xy + a12 xy^2+ a21 x^2y + a22x^2y^2+ a23 x^2y^3 + a32 x^3y^2+... > No. Here are the first four parts with n + p = 0,1,2 & 3 (a_00) + (a_10 x + a_01 y) + (a_20 x^2 y + a_11 xy + a_02 y^2) + (a_30 x^3 + a_21 x^2 y + a_12 xy^2 + a_03 y^3) + ... x^2y looks like x^(2y) instead of the intended x^2 y = (x^2)y. > or to a00+ a01 y + a02 y^2 + a03 y^3 +..... > That is sum_j a_0j y^j. === Subject: Re: clarification on power series expansion === Subject: Why this is approximately? If = 2 and p = 24, then the decimal number 0.1 cannot be represented exactly, but is approximately 1.10011001100110011001101 '.84 2-4. How come 0.1 cannot be represented by base 2 and precsion of 24..but 0.1 is not a recurring number Jack begin 666 beta.gif