Welcome, Guest: Register On Nairaland / LOGIN! / Trending / Recent / NewStats: 3,153,776 members, 7,820,715 topics. Date: Tuesday, 07 May 2024 at 08:05 PM |
Nairaland Forum / Nairaland / General / Education / Nairaland Mathematics Clinic (480901 Views)
Mathematics Clinic / 2015 Cowbell Mathematics Champion, Akinkuowo Honoured By School. / Lead City University Clinic Welcomes First Ever Baby Since 10 Years Of Opening (2) (3) (4)
(1) (2) (3) ... (198) (199) (200) (201) (202) (203) (204) ... (284) (Reply) (Go Down)
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 12:43am On Nov 10, 2015 |
Madmathecian:QUESTION 2A x2+x>=1 x2+x-3>=0 Using quadratic formula we have; x=1.303(aprox) or x=-2.303(aprox) implies that (x-1.303)(x+2.303)>=0 using truth table or any other means of verification we have; x<=-2.303 or x>=1.303 In interval notation gives -2.303>=x>=1.303 NOW QUESTION 2B From the solution above, the function is negative if the values of x ranges between -2.303<x<1.303 QUESTION 2C(a) and 2C(b) have been solved already so no need TRY CORRECTING ME IF THERE IS ANY ERROR OR OFF POINTS. |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 1:37am On Nov 10, 2015 |
Goodyshoes:APART FROM GRAPHICAL METHOD WICH CLEARLY SHOWS THAT THE ANSWER IS 2 or 3 We can also use NEWTON-RAPHSON method i.e [img]http://web.mit.edu/10.001/Web/Course_Notes/NLAE/equation7.gif[/img] where Xi denotes first guess or initial number F(Xi) denotes d solution at Xi and F'(Xi) denote solution of the derivative at Xi F'(Xi)= 4x3+5x4-12xx(lnX+1) Now let my first guess be 2( u can use any number of ur choice) F'(2) 30.73 and F(2)=0 inserting into the formula gives X1=2-(0/30.73)=2 its obvious we going to have a reoccurring solution thus , x=2. Also doing the same for Xi=3 gives same approach. we conclude that x=2 or x=3 |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 2:17am On Nov 10, 2015 |
Karmanaut:Boss u got the answer but ur approach got error at bolded part u will get maths error(undefine) if u insert 0 in place of y for lny So will say L'HOPITAL's rule is stil d genuine way out until u proof otherwise |
Re: Nairaland Mathematics Clinic by Nobody: 2:30am On Nov 10, 2015 |
ladokuntlad:It's actually correct, you don't evaluate it directly. (ln(0) is undefined) Instead I used the standard limit: limy->0+ y*ln(y) = 0. So instead of evaluating ey*ln(y) You replace it with 0 So that it becomes e0 = 1. |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 2:49am On Nov 10, 2015 |
Karmanaut:Sighs... Okay i get |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 3:13am On Nov 10, 2015 |
House i av a cowbell question to give x+y+z=1 x2+y2+z2=35 x3+y3+z3=97 Show workings if x=-1 y=-3 and z=-3 |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 3:32am On Nov 10, 2015 |
Guys i av some maths Olympiad questions for u to solve 2 Likes
|
Re: Nairaland Mathematics Clinic by Nobody: 5:19am On Nov 10, 2015 |
ladokuntlad:In question 4, drawing the graph shows there are 6 real roots, all integers: 1, 2, 3, 4, 5, 6. Number 8: n= 836 8362 = 698,896. Number 5 is 840 whose prime decomposition is 23 * 3 * 5*7 There are a total of 32 different factors. Got using the formula: An integer n written as pa * qb * rc where p,q,r are prime factors of the integer n, and a,b,c are powers of the prime factors respectively. The number of factors of integer n will be expressed by the formula (a+1)*(b+1)*(c+1) also including 1 and the number n as factors. For example the number 36 can be written as: 22 * 32 So the number 36 has (2+1)*(2+1) factors The number 36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36. The number 840 written in its prime decomposition therefore has (3+1)*(1+1)*(1+1)*(1+1) = 4*2*2*2 = 32 factors. 1 Like |
Re: Nairaland Mathematics Clinic by Nobody: 5:20am On Nov 10, 2015 |
ladokuntlad:The question has been asked and answered in this thread Cheers. |
Re: Nairaland Mathematics Clinic by MathsChic(f): 5:55am On Nov 10, 2015 |
ladokuntlad:I solved this before. Basic algebra. |
Re: Nairaland Mathematics Clinic by MathsChic(f): 5:56am On Nov 10, 2015 |
ladokuntlad:I like this. |
Re: Nairaland Mathematics Clinic by Nobody: 6:08am On Nov 10, 2015 |
ladokuntlad:Why are you using a sledge hammer to crack an egg? Na wa for you. The graph shows the roots are integers, leave Newton for irrational numbers. |
Re: Nairaland Mathematics Clinic by Nobody: 6:23am On Nov 10, 2015 |
As an alternative to the graphical method for question 4. We're trying to see how many integer solutions the equation (x2-5×+5)x[sup]2-11×+30[/sup] = 1 has. Consider the equation ab = 1. The roots of this equation are a=1, b=0, a=1, b=1 also satisfies it. Or if a=-1, and b is an even number. Now let the base x2 -5× +5 = a, and the power x2-11×+30 = b. Case 1: a= 1 x2 -5× + 5 = 1 The solutions are: x= 4, x=1. We have gotten 2 valid answers. Next: b=0 x2-11×+30=0 The roots are: x=6, x=5. Two more valid solutions. Case II: b=1 ×2 -11× + 30 = 1 Here we get two floating point solutions: x=6.61... and x= 4.38... We discard them as they're not valid. Case III: a=-1 ×2-5×+5=-1 The roots are: x=3, x=2. We have two more valid solutions totalling 6. Next: b is even, let's start with 2. x2 -11×+30 = 2 The solutions are: x=7, x= 4 7 is not a valid solution as it is odd. Only 4 satisfies the equation and we've gotten it before. So it has 6 integer solutions: x=1,2,3,4,5,6. |
Re: Nairaland Mathematics Clinic by agentofchange1(m): 7:11am On Nov 10, 2015 |
MathsChic: hmmm, really don't know what to say know , maybe later .. |
Re: Nairaland Mathematics Clinic by agentofchange1(m): 7:14am On Nov 10, 2015 |
see mathematicians abeg .. greetings. all . |
Re: Nairaland Mathematics Clinic by jackpot(f): 7:18am On Nov 10, 2015 |
MathsChic:elementary |
Re: Nairaland Mathematics Clinic by jackpot(f): 7:20am On Nov 10, 2015 |
agentofchange1:Hey agentofchange |
Re: Nairaland Mathematics Clinic by agentofchange1(m): 7:34am On Nov 10, 2015 |
jackpot:hey , buddy , howdy ? |
Re: Nairaland Mathematics Clinic by shaboti: 7:53am On Nov 10, 2015 |
MathsChic:thank you |
Re: Nairaland Mathematics Clinic by jackpot(f): 8:04am On Nov 10, 2015 |
agentofchange1:fine. Hope you're good? |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 9:42am On Nov 10, 2015 |
Karmanaut:Didnt see any workings all i see is final answer. Dats y am bringing it back here SHOW WORKINGS AND NOT FINAL ANSWERS |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 9:44am On Nov 10, 2015 |
agentofchange1:Boss u av some of my questions to answer naaa. Oya kindly giv me solutions to it |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 9:47am On Nov 10, 2015 |
Karmanaut :
|
Re: Nairaland Mathematics Clinic by agentofchange1(m): 9:47am On Nov 10, 2015 |
ladokuntlad:where ? |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 9:50am On Nov 10, 2015 |
agentofchange1:Scroll up maths olympiad questions |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 10:23am On Nov 10, 2015 |
Masperano u av some cakes to eat ooo. scrol up and solve dose maths olympiad questions |
Re: Nairaland Mathematics Clinic by agentofchange1(m): 10:29am On Nov 10, 2015 |
ladokuntlad:oh , really ? like for. how much are we talking about here ? |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 10:31am On Nov 10, 2015 |
. |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 10:32am On Nov 10, 2015 |
agentofchange1:Go meet d Australians dat set d questions. Dey ar secondary school maths oooo |
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 10:39am On Nov 10, 2015 |
CONTINUATION OF THE AFOREMENTIONED QUESTIONS
|
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 10:43am On Nov 10, 2015 |
. |
Re: Nairaland Mathematics Clinic by agentofchange1(m): 10:58am On Nov 10, 2015 |
ladokuntlad:oh..i see , guess my boss above has done(is doing) justice already .. |
(1) (2) (3) ... (198) (199) (200) (201) (202) (203) (204) ... (284) (Reply)
DIRECT ENTRY Admission. / Mastercard Foundation Scholarship, Enter Here / 2016/2017 University of Ibadan Admission Thread Guide.
(Go Up)
Sections: politics (1) business autos (1) jobs (1) career education (1) romance computers phones travel sports fashion health religion celebs tv-movies music-radio literature webmasters programming techmarket Links: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Nairaland - Copyright © 2005 - 2024 Oluwaseun Osewa. All rights reserved. See How To Advertise. 48 |