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Nairaland Mathematics Clinic - Education (217) - Nairaland

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Re: Nairaland Mathematics Clinic by eche45(m): 6:23pm On Dec 24, 2015
Have being following this thread.
But this my 1st time of posting here.
I must say u guy are doing a great job. Watch out for my own questions o. Me too will b trying to solve some issue here.
Thanks.
Re: Nairaland Mathematics Clinic by dprinz99(m): 6:44am On Dec 25, 2015
Merry Christmas to u all
rmember why d son of man was sent to the world
celebrate with joy
Re: Nairaland Mathematics Clinic by DatechMan(m): 8:38am On Dec 25, 2015
dprinz99:
Pls can some one briefly explain to me the steps of solving partial fraction?
I have tried it my self Bt I'm gettin confused d more.
much tanks

The algorithm involved in solving partial fractions depend on the question.

It can be summarized below.

1. If power of numerator polynomial is greater than or equal to power of denominator polynomial. Divide to obtain quotient Q and Remainder R such that the question can be re-expressed as Q + R / D where D is the Denominator

2. Factorize the Denominator.
3. Create a valid template for your answer. This is the tricky part.
e.g

N / {(x + J)(x + K)} == A/(x + J) + B/(x + K)

N / {(x2 + Jx + K)(x + L)} == (Ax + B)/(x2 + Jx + K) + C/(x + L)

N / {(x + J)2(x + K)} == A/(x + J) + B/(x + J)2 + C/(x + K)


4. Solve for the unknowns, A, B, C ... Check online for more help. You can also check New School Mathematics or Project Further maths.
Re: Nairaland Mathematics Clinic by DatechMan(m): 9:19am On Dec 25, 2015
Sirneij:
1. Use the principle of mathematical induction to show that 1/ (4 x 12 - 1) + 1 / (4 x 22 - 1) +...+ 1/(4n2 - 1) = n/(2n +1).
2. Prove by mathematical induction that 1 x 20 + 2 x 21 + 3 x 22 +...+ n x 2n-1 = 1 + (n - 1)2n.

Question 1
Confirm for n=1 Valid
confirm for n =2 Valid

Assuming for n, 1/(4 x 12 - 1) + 1/(4 x 22 - 1) +...+ 1/(4n2 - 1) = n/(2n +1)

We test for n+1
It follows that

n / (2n +1) + 1/(4(n+1)2 - 1) must equal (n+1)/(2(n+1) +1)

i.e

n / (2n +1) + 1/(4(n+1)2 - 1) = (n+1)/(2(n+1) +1)

Simplifying RHS, we have

(n + 1) / (2n + 3)

Simplifying LHS, we have

n / (2n +1) + 1/(4n2 + 8n + 4 - 1)

n / (2n +1) + 1/(4n2 + 8n + 3)

n / (2n +1) + 1/(2n + 1)(2n + 3)

(n(2n+3) + 1)/(2n + 1)(2n + 3)

(2n^2 + 3n + 1) / (2n + 1)(2n + 3)

(2n +1)(n + 1) / (2n + 1)(2n + 3)

(n + 1) / (2n + 3)

Since LHS = RHS

Proved.


Not easy to type equations here o.

Eat it like that.

Good Morning Nigeria.
#GodBlessNigeria
Re: Nairaland Mathematics Clinic by Ayomide002: 7:52pm On Dec 25, 2015
When will I ever have time to be active as I used to long time ago on this thread...?
Anyways,kudos to the gurus in the house.......calculusf(x)
Re: Nairaland Mathematics Clinic by Sirneij(m): 9:33am On Dec 26, 2015
No one to address these?
c DatechMan
cc Richiez
Sirneij:
1. Use the principle of mathematical induction to show that the arithmetic mean is always greater than or equal to the geometric mean.
2. Prove that (3 + square root5)n + (3 - square root5)n is an even integer for all natural numbers n using the principle of mathematical Induction.
3. Use the principle of Mathematical Induction to Prove that 2002n +2 + 20032n + 1 is divisible by 4005.
4. Prove by Mathematical Induction that 1/2 + cosx + . . . + cos(n - 1)x = sinx/2(2n - 1)/2sinx/2
Re: Nairaland Mathematics Clinic by Hadampson(m): 5:07pm On Dec 28, 2015
y=lnx(tanx)^4 .. plz help me wit dz questn
Re: Nairaland Mathematics Clinic by Meel: 5:27pm On Dec 28, 2015
Someone should help me with dis mth102 question. A particle is Moving in a straight line and a time T sec its acceleration is (6-kt)ms-2 where k is a constant. When t=9 the acceleration of the particle is zero and its velocity is 30ms-2.
1): find the numerical value of the velocity when t= 0 and the distance between its positions when t=0 and t=9.
Re: Nairaland Mathematics Clinic by GreatYinkus(m): 8:00pm On Dec 28, 2015
Meel:
Someone should help me with dis mth102 question. A particle is Moving in a straight line and a time T sec its acceleration is (6-kt)ms-2 where k is a constant. When t=9 the acceleration of the particle is zero and its velocity is 30ms-1.
1): find the numerical value of the velocity when t= 0 and the distance between its positions when t=0 and t=9.

Given a = 6-kt, substituting t = 9 into the eqn.,
6-9k=0, => k= 2/3;
=> a = 6-(2/3)t
v = $adt = $6dt-(2/3)$tdt;
=> v = 6t - (1/3)t² + c, where c is a constant. [I suppose you know how to integrate]
when t = 9, v = 30 m/s, subtituting t = 9 into v, we have;
30 = 54 - 27 + c, => c = 3.
=> v = 6t - (1/3)t² + 3.
1). Put t = 0 in v, we have; v = 3 m/s.
2). x = $vdt = 6$tdt - (1/3)$t²dt + 3$dt; we have,
x = 3t² - (1/9)t³ + 3t + c ,

Let the distance at t = 0 and t = 9 be rep as x(0) and x(9) respectively.
x(0) = c (substituting t as 0 into x) and x(9) = 243 - 81 + 27 + c = 189 + c.

Therefore distance between its positions is
x(9) - x(0) = 189 + c - c = 189m.
Re: Nairaland Mathematics Clinic by GreatYinkus(m): 8:03pm On Dec 28, 2015
Hadampson:
y=lnx(tanx)^4 .. plz help me wit dz questn
[size=15pt]What should we do sir?[/size]
Re: Nairaland Mathematics Clinic by Hadampson(m): 3:11pm On Dec 29, 2015
GreatYinkus:
[size=15pt]What should we do sir?[/size]
plz solve it 4 me. find the differentiation of the function
Re: Nairaland Mathematics Clinic by Mathemagician1(m): 3:44pm On Dec 29, 2015
Hadampson:
y=lnx(tanx)^4 .. plz help me wit dz questn

Here you go.

Re: Nairaland Mathematics Clinic by GreatYinkus(m): 4:13pm On Dec 29, 2015
Hadampson:
plz solve it 4 me. find the differentiation of the function
[size=15pt]Ok. Mathemagician has solved it.[/size]
Re: Nairaland Mathematics Clinic by Sarmosky: 4:34pm On Dec 29, 2015
Sirneij:
No one to address these?
c DatechMan
cc Richiez

Omo FUTA, I get u die... MTS101 assignment. God dei my brother, Mr Afolabi no go kill us
Re: Nairaland Mathematics Clinic by skuribeebo: 6:03pm On Dec 29, 2015
Calebsworld:
@ Richiez,my question,is how can I become a mathematician,as in having distinctions in the subject.God bless u.
do you reside in Ibadan? If yes, I am a mathematician who can give you the best of mathematical knowledge .Call mr lecturer on 07087531126.
Re: Nairaland Mathematics Clinic by skuribeebo: 6:05pm On Dec 29, 2015
Mathemagician1:

Here you go.
This is elementary maths.
Re: Nairaland Mathematics Clinic by Olarewajub: 6:37pm On Dec 29, 2015
Compliment of the season guys. Please does any one know the Principles of mathematical induction, sets, and venn diagram?
Re: Nairaland Mathematics Clinic by Mathemagician1(m): 6:41pm On Dec 29, 2015
skuribeebo:
This is elementary maths.

So?

If your math is that great why not join the train and help solve some problems. I don't see how your bravado is helping out on this thread.

Cheers.
Re: Nairaland Mathematics Clinic by DatechMan(m): 7:27pm On Dec 29, 2015
Sirneij:
No one to address these?
c DatechMan
cc Richiez

Been busy lately.

I will try to crush those questions soonest
أ

#GodBlessNigeria
Re: Nairaland Mathematics Clinic by skuribeebo: 8:54pm On Dec 29, 2015
Mathemagician1:


So?

If your math is that great why not join the train and help solve some problems. I don't see how your bravado is helping out on this thread.

Cheers.
Eyaaa, you don vex be that, pele bro. Bravado ke jooor ooo.
Re: Nairaland Mathematics Clinic by Madmathecian(m): 1:26am On Dec 30, 2015
Solve the following system of equations:
x+y+z = a,
x2+y2+z2 = b2,
xy = z2


where a and b are given real numbers. What conditions must hold on a and b for the solutions to be positive and distinct?
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 3:44am On Dec 30, 2015
Madmathecian:
Solve the following system of equations:
x+y+z = a,
x2+y2+z2 = b2,
xy = z2


where a and b are given real numbers. What conditions must hold on a and b for the solutions to be positive and distinct?




I did dis in my final year

hopefully i will get back to u
Re: Nairaland Mathematics Clinic by ElDeeVee(m): 4:58am On Dec 30, 2015
Anyone here knows Lebesque measure?

1 Like

Re: Nairaland Mathematics Clinic by DatechMan(m): 10:27am On Dec 30, 2015
Sirneij:
1. Use the principle of mathematical induction to show that the arithmetic mean is always greater than or equal to the geometric mean.
2. Prove that (3 + square root5)n + (3 - square root5)n is an even integer for all natural numbers n using the principle of mathematical Induction.
3. Use the principle of Mathematical Induction to Prove that 2002n +2 + 20032n + 1 is divisible by 4005.
4. Prove by Mathematical Induction that 1/2 + cosx + . . . + cos(n - 1)x = sinx/2(2n - 1)/2sinx/2

Kindly write the questions on a paper and snap. The trig question is not clear
Re: Nairaland Mathematics Clinic by oluwasammy(m): 12:18pm On Dec 30, 2015
Pls i need good explanation nd step to follow for me to have good grade in REAL ANALYSIS nd LINEAR ALGEBRA
Re: Nairaland Mathematics Clinic by ElDeeVee(m): 12:34pm On Dec 30, 2015
oluwasammy:
Pls i need good explanation nd step to follow for me to have good grade in REAL ANALYSIS nd LINEAR ALGEBRA
These are pure mathematical courses. You need to dedicate time to understand the processes. Some cramming skills may be needed too.
Re: Nairaland Mathematics Clinic by Nobody: 2:51pm On Dec 30, 2015
i hereby register my interest in maths. I wish to become a wizard
Re: Nairaland Mathematics Clinic by ElDeeVee(m): 10:49pm On Dec 30, 2015
ElDeeVee:
Anyone here knows Lebesque measure?
Re: Nairaland Mathematics Clinic by Madmathecian(m): 4:06am On Dec 31, 2015
Let p be the polynomial defined by

p(x) = x5 − 99999x4 − 9999x3 − 999x2 − 99x − 9.



Is p(x) positive or negative for x near ∞?

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