Nairaland Mathematics Clinic - Education (68)

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Re: Nairaland Mathematics Clinic by Calculusfx: 8:43pm On Sep 24, 2013

rhydex 247: 1. Solve the equation. (x-1)^4+(x+3)^4=82.
2. The real numbers a,b,c satisfy a<>b and 2009[a-b]+sqrt(2009)[b-c]+[c-a]=0. Find the value of (c-b)(c-a)/(a-b)^2.
3. Solve the systems of eqn.
x^2+xy+y^2=84...eqn 1 and x+sqrt(xy)+y=14...eqn 2.

...(1)...(x-1)^4+(x+3)^4=82...let {a be x-1}...then x+3=a+4...then a^4+(a+4)^4=82...expand to give...2a^4+16a^3+96a^2+256=82...divide through by 2...a^4+8a^3+48a^2+128a+87=0......solve the polynomial to give (a+1)(a+3)(a^2+4a+29)=0...a=-1 and -3...not that a^2+4a+29=0 gives imaginary number.....don't forget that x-1=a....when a=-1 then x=-1+1=0...when a=-3...x-1=-3...x=-3+1=-2....therefore x=0 or -2

Re: Nairaland Mathematics Clinic by rhydex247(m): 4:25am On Sep 25, 2013

well done my oga, u are great. We av two ways to solve d questn. Ur method is ok. Here is another way. let y=x+1, x=y-1. Put x=y-1 in d eqn gives (y-2)^4+(y+2)^4.
(y^2-4y+4)^2+(y^2+4y+4)^2=82. Reduces to
y^4+24y^2-25=0
(y^2+25)(y^2-1)=0.
since y^2+25>0 then y^2-1=0. So y=1 or y=-1. But recall that x=y-1. Hence x=0 or x=-2.
We are going to take mathematics to another level.

Re: Nairaland Mathematics Clinic by Calculusfx: 8:06am On Sep 25, 2013

rhydex 247: 1. Solve the equation. (x-1)^4+(x+3)^4=82.
2. The real numbers a,b,c satisfy a<>b and 2009[a-b]+sqrt(2009)[b-c]+[c-a]=0. Find the value of (c-b)(c-a)/(a-b)^2.
3. Solve the systems of eqn.
x^2+xy+y^2=84...eqn 1 and x+sqrt(xy)+y=14...eqn 2.

...(3)...x²+xy+y²=84...(i) and x+√xy+y=14...(ii)from (ii).x+y-14=√xy...square both sides...(x+y-14)²=xy...then x²+2xy+y²-28x-28y+196=xy...then x²+2xy-xy+y²-28x-28y+196=0...x²+xy+y²-28x-28y+196...don't forget that from (i)x²+xy+y²=84...substitute that to give...84-28x-28y+196=0...28x+28y=280...divide through by 28...x+y=10...{*}...don't forget that x²+y²=(x+y)²-2xy...substitute that to (i)...(x+y)²-2xy+xy=84...(x+y)²-xy=84 from (*)...x+y=10...i.e...100-xy=84...xy=16...(*')...taking * and *' x+y=10 and xy=16...solve simultaneously to give x=2,y=8 OR x=8,y=2...PLS MY GURUS,IF YOU DON'T UNDERSTAND MY EXPLANATIONS,KINDLY TELL ME TO MAKE MY EXPLANATIONS CLEAR...in my own respective,i think this thread is not for teens...

Re: Nairaland Mathematics Clinic by jackpot(f): 9:19am On Sep 25, 2013

Calculusf(x):
...try to show humility sister...i could remember a question benbuks posted,and you asked him not to post simple question again...why can't you solve this,you are just using approximate method...Try to know this that:THERE'S NO MATHS GURU...you can just know up to the level you are and the aspect you are studying......WELL SHA,you tried...

Sir, I already did. It wasn't an approximate method since the summation in my answer is still running from 1 to infinity. The fact is that I left my answer(which is very correct) in series form.

With my method, there is the temptation to conclude that I can integrate just any function! wink

Re: Nairaland Mathematics Clinic by jackpot(f): 9:29am On Sep 25, 2013

where my fellow Maths generals at? Help me solve this:

[size=14pt]let a, b and c be real numbers selected randomly from the interval (0,1). What is the probability that the equation ax^2+bx+c=0 has at least one real solution x?[/size]

Re: Nairaland Mathematics Clinic by Nobody: 9:56am On Sep 25, 2013

jackpot: where my fellow Maths generals at? Help me solve this:

[size=14pt]let a, b and c be real numbers selected randomly from the interval (0,1). What is the probability that the equation ax^2+bx+c=0 has at least one real solution x?[/size]

forgıve my basıc knowledge of mathematıcs............ the three coeffıcıents could all be 0s or 1s havıng (000) (111), and we could have two 1s wıth a sıngle zero, or two 0s wıth a sıngle one...... two 1s wıth a sıngle zero can arranged ın 3 ways, and two 0s wıth a sıngle 1 can be arranged ın 3 ways gıvıng the arrangementr (000) (111) (110) (101) (011) (100) (001) (010), gıvıng a total of 8 ways, out of these arrangements the quadratıc equatıon wıthout real roots ınclude (x²+x+1) and (x[sup]2[/]+1), meanıng the remaınıng 6 arrangements have real roots...... therefore the probabılıty of havıng a quadratıc wıth real roots becomes 6/8 =3/4

Re: Nairaland Mathematics Clinic by jackpot(f): 11:43am On Sep 25, 2013

honey: forgıve my basıc knowledge of mathematıcs............ the three coeffıcıents could all be 0s or 1s havıng (000) (111), and we could have two 1s wıth a sıngle zero, or two 0s wıth a sıngle one...... two 1s wıth a sıngle zero can arranged ın 3 ways, and two 0s wıth a sıngle 1 can be arranged ın 3 ways gıvıng the arrangementr (000) (111) (110) (101) (011) (100) (001) (010), gıvıng a total of 8 ways, out of these arrangements the quadratıc equatıon wıthout real roots ınclude (x²+x+1) and (x[sup]2[/]+1), meanıng the remaınıng 6 arrangements have real roots...... therefore the probabılıty of havıng a quadratıc wıth real roots becomes 6/8 =3/4

but Sir,
a, b and c are all real numbers and such they are not limited to integer values. For example, a can be log2=0.301029995. . ., because 0<log2<1.

Also Sir,
a, b and c lies inbetween the open interval (0,1) which means the set {x: 0<x<1}. Thus, a, b and c can not admit any integer values (in particular, a, b and c cannot take 0 or 1).

Re: Nairaland Mathematics Clinic by Nobody: 12:25pm On Sep 25, 2013

jackpot: Sir, I already did. It wasn't an approximate method since the summation in my answer is still running from 1 to infinity. The fact is that I left my answer(which is very correct) in series form.

With my method, there is the temptation to conclude that I can integrate just any function!

....ok try this dear....integrate (x^x^x^x....to infinity.)dx

Re: Nairaland Mathematics Clinic by Calculusfx: 2:10pm On Sep 25, 2013

2004^2004

Re: Nairaland Mathematics Clinic by Esji80(m): 2:34pm On Sep 25, 2013

Helo maths gurus.

I am a graduate of Information Technology.I rili love maths.I want to do my masters in maths edu.

Itz it possible for me 2 go 4 Msc. ed Maths?

I need your advces please. . .thanks

Re: Nairaland Mathematics Clinic by jackpot(f): 4:11pm On Sep 25, 2013

benbuks: ....ok try this dear....integrate (x^x^x^x....to infinity.)dx

is this a function? No

for example, if f(x)=x^x^x^x. . ., then you'll agree with me that f(x) forall x>1 doesn't exist.

By the way, power series representation is only valid for analytic functions.

Re: Nairaland Mathematics Clinic by Nobody: 4:22pm On Sep 25, 2013

jackpot: is this a function? No

for example, if f(x)=x^x^x^x. . ., then you'll agree with me that f(x) forall x>1 doesn't exist.

By the way, power series representation is only valid for analytic functions.

..av u heard of sophomore's dream?

Re: Nairaland Mathematics Clinic by Richiez(m): 4:28pm On Sep 25, 2013

Esji80: Helo maths gurus.

I am a graduate of Information Technology.I rili love maths.I want to do my masters in maths edu.

Itz it possible for me 2 go 4 Msc. ed Maths?

I need your advces please. . .thanks

I think you should start with PGD before going for Msc

Re: Nairaland Mathematics Clinic by Richiez(m): 4:29pm On Sep 25, 2013

@benbuks and jackpot let me sit back, relax and learn a bit from you both...cheers!

1 Like

Re: Nairaland Mathematics Clinic by Esji80(m): 6:09pm On Sep 25, 2013

Richiez:
I think you should start with PGD before going for Msc

Ok,PGD in whc course? Education?

Thanks

Re: Nairaland Mathematics Clinic by busuyem: 9:08pm On Sep 25, 2013

busuyem: [color=#550000][/color]

Pls house, I'm planning 2 go 4 my MSc. in Maths. Which option is the best in Maths to study. I'm contemplating on which to choose considering the future advantages.
Need ur advice.

Re: Nairaland Mathematics Clinic by jackpot(f): 9:11pm On Sep 25, 2013

benbuks: ..av u heard of sophomore's dream?

yeah. I doubt it'll ever have application.

Well, that thing you gave as f(x)=x^x^x^x^x^. . ., let's take a bit look at it.

f(0)=0^0^0^0^. . .which you may argue as undefined since even 0^0=0^(1-1)=0/0 is undefined.

What is f(0.1)?

f(0.1)=0.1^0.1^0.1^0.1^. . .which remains undefined [compute a few terms, maybe up to 15, monitor ir's behaviour and convince yourself that it is undefined]

what is f(2)?

f(2)=2^2^2^2^. . . = infinity.

f(3)= ?

f(3)=3^3^3^3^. . ., which as you already knew, blows up too!

Thus, why bother yourself by integrating what doesn't make sense?

Re: Nairaland Mathematics Clinic by jackpot(f): 9:34pm On Sep 25, 2013

busuyem: Pls house, I'm planning 2 go 4 my MSc. in
Maths. Which option is the best in Maths to
study. I'm contemplating on which to choose
considering the future advantages.
Need ur advice.

in case you intend lecturing after the M.Sc, I suggest you do Pure Maths(that's take courses like General Topology, Abstract Algebra, Functional Analysis, Measure Theory).

If you are still thinking about lecturing or may wish to work elsewhere after doing your M.Sc, then choose Applied Maths(that's take courses like Advanced Optimization, Numerical Analysis, Operations Research).

Note however that list of courses available at M.Sc differs university-wise.

Re: Nairaland Mathematics Clinic by yat11: 9:56pm On Sep 25, 2013

Re: Nairaland Mathematics Clinic by Nobody: 10:14pm On Sep 25, 2013

jackpot: yeah. I doubt it'll ever have application.

Well, that thing you gave as f(x)=x^x^x^x^x^. . ., let's take a bit look at it.

f(0)=0^0^0^0^. . .which you may argue as undefined since even 0^0=0^(1-1)=0/0 is undefined.

What is f(0.1)?

f(0.1)=0.1^0.1^0.1^0.1^. . .which remains undefined [compute a few terms, maybe up to 15, monitor ir's behaviour and convince yourself that it is undefined]

what is f(2)?

f(2)=2^2^2^2^. . . = infinity.

f(3)= ?

f(3)=3^3^3^3^. . ., which as you already knew, blows up too!

Thus, why bother yourself by integrating what doesn't make sense?

..nice 1 dear...i remove my cap 4u,....kip rollin...

Re: Nairaland Mathematics Clinic by Nobody: 10:22pm On Sep 25, 2013

yat@11:
Hi house, pls wld really appreciate any help as regards dis simple logarithm problem
Log₄ (x² + x + 10) = ¹/₂ + Log ₄ (x² + x - 5)
Thanks in advance.

..x^2+x+10=2(x^2+x-5)....x^2+x-20=0....x=4 or -5....

1 Like

Re: Nairaland Mathematics Clinic by jackpot(f): 10:49pm On Sep 25, 2013

^good job benbuks.

Final thing to note is that, generally, Log doesn't take negative bases, and as such, we discard the value x=-5.

Thus, the only answer is x=4.

1 Like

Re: Nairaland Mathematics Clinic by yat11: 10:53pm On Sep 25, 2013

@benbuks & jackpot, Thanks.

Re: Nairaland Mathematics Clinic by busuyem: 10:39am On Sep 26, 2013

jackpot: in case you intend lecturing after the M.Sc, I suggest you do Pure Maths(that's take courses like General Topology, Abstract Algebra, Functional Analysis, Measure Theory).

If you are still thinking about lecturing or may wish to work elsewhere after doing your M.Sc, then choose Applied Maths(that's take courses like Advanced Optimization, Numerical Analysis, Operations Research).

Note however that list of courses available at M.Sc differs university-wise.

Thanks dear. God bless u.

Re: Nairaland Mathematics Clinic by jackpot(f): 11:31am On Sep 26, 2013

Richiez: @benbuks and jackpot let me sit back, relax and learn a bit from you both...cheers!

*blushes*

hi Richiez

are you sure it shouldn't be the other way round? wink

Lol.

Re: Nairaland Mathematics Clinic by rhydex247(m): 12:27pm On Sep 26, 2013

the real numbers a,b,c satisfy a nt equal to b and 2009(a-b)+ sqrt 2009(b-c)+(c-a)=0. Find the value of (c-b)(c-a)/(a-b)^2.
Solution.
Let x= sqrt 2009. Also x^2= 2009.
puttin it in the eqn gives x^2(a-b+x(b-c)+(c-a)=0.
a nt equal to b => this eqn is a quadratic eqn. Obviously x=sqrt 2009 and 1 are the two root of this quadratic eqn. Nw recall dat.
sum of x =-b/a
product of root =c/a. Sum of x.
=> sqrt 2009 +1=c-b/a-b. Also
product of root
=> sqrt 2009*1= c-a/a-b. Hence (c-b)(c-a)/(a-b)(a-b).
=>(sqrt 2009 +1)(sqrt 2009)
=2009+sqrt 2009.

Re: Nairaland Mathematics Clinic by Nobody: 12:36pm On Sep 26, 2013

Richiez: @benbuks and jackpot let me sit back, relax and learn a bit from you both...cheers!

.ahh..master Richiez.am just a baby mathematician oo...u r d bozz....kip rollin..

Re: Nairaland Mathematics Clinic by MrCalculus(m): 2:49pm On Sep 26, 2013

....

Re: Nairaland Mathematics Clinic by Nobody: 4:31pm On Sep 26, 2013

.manage this cake pls..find the co-ordinates of the points on the curve ,.y=3x^-3 -3/2 x^2 -3x +5 where the tangent makes an angle of 45¤ with the positive direction of the x-axis.....i kw dis z 4 kids lyk me.

Re: Nairaland Mathematics Clinic by jackpot(f): 8:29pm On Sep 26, 2013

^
let the required point(s) be (a,b). Then, note that the slope of any line making an angle of 45^o with the positive x-axis is tan 45^^o=1.

Then, obtain dy/dx. Substitute x=a and in the equation and equate to 1. Solve to get the value of a.

Next, to obtain b, note that the point (a,b) lies on the curve y=f(x). Set b=f(a). Substitute the value of a, to obtain b.

Write the coordinate of the point(s) as the pair (a,b).

Thats all!

Re: Nairaland Mathematics Clinic by Mikebis(m): 8:50pm On Sep 26, 2013

Pls ma oga at d top help me wt dis little questn..(2y+3)^-5.its a binomial questn

Re: Nairaland Mathematics Clinic by Nobody: 9:16pm On Sep 26, 2013

jackpot: ^
let the required point(s) be (a,b). Then, note that the slope of any line making an angle of 45^o with the positive x-axis is tan 45^^o=1.

Then, obtain dy/dx. Substitute x=a and in the equation and equate to 1. Solve to get the value of a.

Next, to obtain b, note that the point (a,b) lies on the curve y=f(x). Set b=f(a). Substitute the value of a, to obtain b.

Write the coordinate of the point(s) as the pair (a,b).

Thats all!

..nice 1 but i will prefer u solvin rada dan explainin.

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