Nairaland Mathematics Clinic - Education (40) - Nairaland
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| Re: Nairaland Mathematics Clinic by Richiez(m): 9:41am On May 05, 2013 |
personal59: pls help me to solve this ordinary differentialsolution loading... check back by 2pm |
| Re: Nairaland Mathematics Clinic by personal59: 10:04am On May 05, 2013 |
Richiez:pls there is an error the question is (2x-4y+5)dy/dx + x-2y+3 equal0 |
| Re: Nairaland Mathematics Clinic by personal59: 10:06am On May 05, 2013 |
personal59: pls help me to solve this ordinary differential equation (2x-4y+5)dy/dx+x-2y+3 equal 0 pls d calculation (steps) is needed for self understanding thanks. |
| Re: Nairaland Mathematics Clinic by Richiez(m): 2:41pm On May 05, 2013 |
personal59: pls there is an error the question is (2x-4y+5)dy/dx + x-2y+3 equal0i think there is an error in one of the signs, but since it's for self understanding, let me solve this (2x-4y+5)dy/dx -x+2y+3 =0 (2x-4y+5)dy/dx =x-2y-3 dy/dx = (x-2y-3)/2x-4y+5 ..........(1) let us use the substitution y = v + x/2. this substitution is chosen so as to replace all y and x terms in the R.H.S with v term now let's watch out! if y= v+x/2 dy/dx = dv/dx +1/2 eqn(1) becomes dv/dx+1/2= x-2(v+x/2)-3/[2x-4(v+x/2)+5] dv/dx +1/2 = x-2v-x-3/(2x-4v-2x+5) dv/dx = -2v-3/(5-4v) -1/2 dv/dx = -4v-6-5+4v/[2(5-4v)] dv/dx = -11/(10-8v) by separating the variables, (10-8v)dv = -11dx integrating both sides 10v - 4v2 = -11x + c but recall that y= v+x/2 therefore v= y-x/2 hence the real soln to the diff eqn is 10(y - x/2) - 4(y - x/2)2 = -11x +c from here, you can expand the terms in the bracket and re-arrange 2 Likes |
| Re: Nairaland Mathematics Clinic by Richiez(m): 3:53pm On May 05, 2013 |
for others waiting for solution to their questions, just chill |
| Re: Nairaland Mathematics Clinic by personal59: 3:59am On May 06, 2013 |
Richiez:thanks a lot bro but this question is nt only for understanding is also an assignment the lecturer won't giv u d solution. This is the real question no error (2x-4y+5)dy/dx +(x-2y+3) equal 0 reforming the question won't bring the solution I can solve the one u refraim myself pls bros |
| Re: Nairaland Mathematics Clinic by Richiez(m): 6:33am On May 06, 2013 |
@personal59 just use exactly the same steps and substitution. the only difference is that the result of integration wud differ, since you need to integrate by parts 1 Like |
| Re: Nairaland Mathematics Clinic by MichaelSokoto(m): 7:46pm On May 07, 2013 |
Gboliwe:Ee be like film trick shey?  |
| Re: Nairaland Mathematics Clinic by WHees(m): 3:31pm On May 10, 2013 |
Hello, as the saying goes, understanding a question is part of answering the question, but the unfortunate thing is what i have here is something that am not familiar with. I dnt seek for answers only i also like to know how i shall work it out on my own and provide solutions[dont just give me the fish, show me how to catch it also]. Question 1; [img]http://f12.wapkafiles.com/download/d/0/e/297960_d0efe68cb55d2f5f2f7188ea.PNG/aeb99fdd70705acd7939/6.PNG[/img] Question 2; [img]http://f12.wapkafiles.com/download/7/a/f/297960_7affa0a3c7c6bc5ed401c4c5.PNG/fcc91f7c615fd4deea03/8.PNG[/img] Question 3; [img]http://f12.wapkafiles.com/download/3/f/d/297960_3fd30711fa59d6d21390969b.PNG/46a8d85f7dcfd0825b2c/9.PNG[/img] |
| Re: Nairaland Mathematics Clinic by echibuzor: 8:29am On May 12, 2013 |
WHξξ∟s: Sorry, but I cant see the picture... i am mobile... try transcribing it... |
| Re: Nairaland Mathematics Clinic by WHees(m): 9:46am On May 12, 2013 |
echibuzor: Owk boss, it is on eigen values & vectors under linear algebra & this is how they put it. If A.x=λx, where A=|2 2 -2 | |1 3 1 | |1 2 2 | determine the eigen values of the matrix A, and an eigen vector corresponding to each eigen value. If λ=1, what is a? if λ=2, what is b? and if λ=4, what is c? |
| Re: Nairaland Mathematics Clinic by johnpaul1101(m): 3:41pm On May 13, 2013 |
goodday every1, plz i need help here: in what base will 465+24+225=1050? Thanks! |
| Re: Nairaland Mathematics Clinic by Ortarico(m): 5:18pm On May 13, 2013 |
johnpaul1101: goodday every1, plz i need help here: In base seven sire I salute una oo. . . .me never reach 'A' level lyk my ogaz coz i'm still an aspirant |
| Re: Nairaland Mathematics Clinic by Nobody: 5:56pm On May 13, 2013 |
^ @Ortarico, nice one. Here is the working @johnpaul1101=>> Supposing the addition is done in base (x) to yield 1050x, then => 465x + 24x+225x =1050x To solve for x, the above can be expressed as follows=> => 4.(x)^2 + 6.(x)^1 + 5(x)^0 + 2.(x)^1 + 4.(x)^0 + 2.(x)^2 + 2.(x)^1 + 5.(x)^0 = 1.(x)^3 + 0.(x)^2 + 5.(x)^1 + 0.(x)^0 => 4x^2 + 6x + 5 + 2x + 4 + 2x^2 + 2x + 5 = x^3 + 5x. => 6x^2 + 10x + 14 = x^3 + 5x Collecting like terms yields=> x^3 - 6x^2 - 5x -14 = 0 Factorizing the above polynomial yields => (x - 7)(x^2 + x + 2) = 0 :. x - 7 = 0 or x^2 + x + 2 = 0 Since the solution to => x^2 + x + 2 = 0 will only yield complex numbers, then the answer is x = 7. Hence, the addition was done in base 7 3 Likes |
| Re: Nairaland Mathematics Clinic by Ortarico(m): 8:09am On May 14, 2013 |
^^ @Doubledx Plz i came across this challenge in one of the threads: 1. A GP of a positive terms and an AP have same first term. The sum of their first term is 3, the sum of their second term is 3/2, and the sum of their third term is 6. Find the sum of their fifth term. 2. A trader bought 30 articles, he sold 20 of them at a gain of 16% and sold the remainder at a loss of 4%. Find the percentage profit/loss on the articles. 3. Find the value of x if (x+3)^3 + (x+4)^3=(2x+7)^3 Guyz do something. . . |
| Re: Nairaland Mathematics Clinic by Afritop(m): 3:59pm On May 14, 2013 |
QUESTION: A man cycles to a village at 18km per hour and returns at 12 Km per hour. If he takes 6.25 hours for the double journey, how far does he ride altogether? NOTE: ANSWER TO THE QUESTION IS 90KM BUT I DON’T KNOW HOW TO SHOW THE WORKINGS TO THE ANSWER. I NEED PROOF IF 90KM IS REALLY THE ANSWER |
| Re: Nairaland Mathematics Clinic by Nobody: 8:52pm On May 14, 2013 |
@Ortarico, I'll post the solutions later. Kinda busy now! 1heart |
| Re: Nairaland Mathematics Clinic by Ortarico(m): 9:47pm On May 14, 2013 |
@doubleDx thanks, you're so nice |
| Re: Nairaland Mathematics Clinic by Ortarico(m): 9:53pm On May 14, 2013 |
Afritop: QUESTION: A man cycles to a village at 18km per hour and returns at 12 Km per hour. If he takes 6¼ hours for the double journey, how far does he ride altogether? Bro the question itself contradicts. As in how can one journey at different km/h but destinates at the same time? Wetin im dey do for road wey im speed at 12km/h and still got there in 6hrs 15 mins, abi e branch canteen? 1 Like |
| Re: Nairaland Mathematics Clinic by Afritop(m): 3:42am On May 15, 2013 |
I HAVE MODIFIED THE QUESTION IN MOBILE AND DECIMAL FORM. So the time he takes for the double journey is 6.25hrs OR 6 WHOLE NUMBER 1 OVER 4. The question is from new general mathematics SS1 EDITION on exercise 6D QUESTION 18 1 Like |
| Re: Nairaland Mathematics Clinic by Ortarico(m): 8:56am On May 15, 2013 |
Afritop: I HAVE MODIFIED THE QUESTION IN MOBILE AND DECIMAL FORM. So the time he takes for the double journey is 6.25hrs OR 6 WHOLE NUMBER 1 OVER 4. The question is from new general mathematics SS1 EDITION on exercise 6D QUESTION 18 Oh! Oh!! Oh!!! Now I get you bro. I thought you meant for each of the journey he cycled at different speeds the same time of 6 1/4hrs or 6hrs 15mins. . . Let the distance be x since we're looking for the distance covered. . Time taken for both journeys= d/s + d/s 6 1/4= x/18 + x/12 L.C.M is 216 and 6 1/4 is 25/4: 25/4= 12x + 18x/216: Cross multiply; it bcoms: 48x + 72x =5,400 120x=5,400 x = 45 Therefore the total distance covered = 2(x) 2(45) = 90km To check: 45/18 + 45/12 = 2.5 + 3.75 = 6.25 or 6 1/4. . . .That is the time taken at 18km/h is 2.5hrs and at 12km/h is 3.75hrs 1 Like |
| Re: Nairaland Mathematics Clinic by Afritop(m): 9:55am On May 15, 2013 |
THANKS A LOT. I PRAY YOU WILL EXCEL IN EVERYTHING YOU DO. Very soon, i will give you a token of my appreciation |
| Re: Nairaland Mathematics Clinic by Ortarico(m): 10:17am On May 15, 2013 |
Amen! Bro, that's the token, I also really appreciate |
| Re: Nairaland Mathematics Clinic by 2nioshine(m): 11:33am On May 15, 2013 |
Ortarico: ^^ @Doubledx..... Lets go...(1) Let their ist term b 'a'... Hence...a+a=3 2a=3.. =>a=3/2....* their sec term=> (a+d)+ar=3/2 a+ar=3/2-d a(1+r)=3/2-d multiply tru by 2 2a(1+r)=3-2d but a=3/2 simplifying gives 3+3r=3-2d 3r=-2d d=-3r/2......** dia 3rd term gives a+2d+ar2=6 simplifyn gvs... a(1+r2)=6-2d giving 3/2(1+r2)=6-2d this reduces to ie mutply 2ru by 2.. 3r2=9-4d but d=-3r/2 subtitutn gvs 3r2-6r-9=0 r2-2r-3=0 r=3 or-1...but r =3 since terms r positiv hence a=3/2,r=3 and d=-9/2 hence d sum of dia 5th term=>a+4d+ar4=122....rechk solvin coz am on mobile nd somewot busy wil asist wt odas shortly...4 my boss 2 Likes |
| Re: Nairaland Mathematics Clinic by 2nioshine(m): 12:03pm On May 15, 2013 |
Ortarico: ^^ @Doubledx..4(2) tips....d 16%profit implies116 of 20. 4%loss of rem=>96 of 10...aply d knowledge of proft nd loss..if sti confuse then ask.... No 3.. Nb:a3+b3=(a+b)3-3ab(a+b) sum of powers of 3 let a=x+3 and b=x+4 substitutn gvs (x+3)^3+(x+4)^3=(2x+7)^3-3(x+3)(x+4)(2x+7) ==> (2x+7)^3-3(x+3)(x+4)(2x+7)=(2x+7)3 =>3(x+3)(x+4)(2x+7)=0 solving d above gives x=-3,-4 or-7/2 3 Likes |
| Re: Nairaland Mathematics Clinic by 2nioshine(m): 12:07pm On May 15, 2013 |
WHξξ∟s:i wil assist wt d tip soon....kinda busy now |
| Re: Nairaland Mathematics Clinic by WHees(m): 12:41pm On May 15, 2013 |
2nioshine: i wil assist wt d tip soon....kinda busy now Anytime boss.. |
| Re: Nairaland Mathematics Clinic by Richiez(m): 7:54pm On May 15, 2013 |
@General Doubledx, 2nioshine and ortarico, thanks for contributing on this thread 3 Likes |
| Re: Nairaland Mathematics Clinic by Ortarico(m): 8:57pm On May 15, 2013 |
@2nioshine, thanks for shedding light and to all maths-gurus in the house i'm grateful as well. 2 Likes |
| Re: Nairaland Mathematics Clinic by Nobody: 3:14pm On May 16, 2013 |
@2nioshine, nice work; welcome back on board! |
| Re: Nairaland Mathematics Clinic by Mbahchiboy(m): 9:05pm On May 16, 2013 |
if y=x^1/3 find dy/dx using first principle? 1 Like |
| Re: Nairaland Mathematics Clinic by Nobody: 9:34pm On May 16, 2013 |
Mbahchiboy: plz i cant understand ur solution@mathefaro Here is your solution: By first principle: If y = x(1/3) Then dy/dx = {f(x + dx) - f(x)}/dx lim as dx→0 Where f(x) = x(1/3) Then, establishing a function, f(x + dx) = (x + dx)(1/3) So that, {f(x + dx) - f(x)} lim dx→0 = (x + dx)(1/3) - x(1/3) Applying binomial theorem to: (x + dx)(1/3) yields=> x(1/3) + (1/3)dx(1/x)(2/3) - 9(dx)2(1/x)(5/3) + (5/81)(dx)3(1/x)(8/5).... => {f(x + dx) - f(x)} = x(1/3) + (1/3)dx(1/x)(2/3) - 9(dx)2(1/x)(5/3) + (5/81)(dx)3(1/x)(8/5) - x(1/3) => {f(x + dx) - f(x)} = => {f(x + dx) - f(x)} = (1/3)dx(1/x)(2/3) - 9(dx)2(1/x)(5/3) + (5/81)(dx)3(1/x)(8/5) Dividing both sides by dx yields => {f(x + dx) - f(x)}/dx = (1/3)(1/x)(2/3) - 9(dx)(1/x)(5/3) + (5/81)(dx)2(1/x)(8/5) Taking lim as dx→0 yields : dy/dx = (1/3)(1/x)(2/3) - 9(0)(1/x)(5/3) + (5/81)(0)2(1/x)(8/5) dy/dx = (1/3)(1/x)(2/3) dy/dx = 1/3x(2/3) dy/dx = 1/(3³√x2) OR y = x^(1/3) By chain rule, dy/dx = (1/3).(x)^(1/3 - 1) . {d/dx}(x) dy/dx = (1/3).(x)^(-2/3). 1 dy/dx = (1/3).(1/x)^(2/3) dy/dx = 1/(3³√x^2) 1 Like |
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