The five star general approach to the problem: cos@+cos2@+ cos3@+

Let C = cos@ +cos2@ +cos3@+

Let S= sin@+sin2@+sin3@+ ( dat is the complex number by of the expression)

C+iS= (cos@ +isin@) (cos2@+isin2@)+ (cos3@ +isin3@)+

Thus, C+iS=e^i@+e^i2@ +ei3@+

C+iS=e^i@/(1 -ei@)(using sum to infinity)

C+is= e^i@ * (1-e^-i@)/(1-e^i@)(1-e^-i@)

C+is= e^i@-1/2-e^i@-e^-i@

C+iS=cos@+isin@-1/2(1-cos@)

Taking the real part of the expression

Cos@+cos2@+cos3@ = cos@-1/2(1-cos@)

@ generalj,

I persoanlly feel ur pain of tribalism but i wish tribalism could vanish in nigeria. But, sadly, it has come to stay. if wishes were horses, human will ride on it. Tribalism has taken deep root in nigeria. It started in 1959 but i didnot need to bore u with the activities dat happened in 1959 bt action group and ncnc. Dat was the genesis of tribalism in nigeria

Most prominenet figure in nigeria have made idols of ethnicity but anybody who try to down play it is regarded as outcast. Go and ask the zik of african his challenges and success of being a true and detribalised nationalists in the grave.

Sadly tribalism as deadly as it is has found rear its ugly head in the citadel of higher learning, u heard me, tertiary education. It is difficult for u to become a vice chancellor or rector outside ur region no matter ur level of ingenuity and sagacity. University of benin is a new casestudy where somebody has benefited frm tribalism. So, tribalism is even an elitist thing. I wonder why we are not having the replica of kenneth dike of this world, the first ingenious vice chanlcellor of univ of ibadan and the founder of national archive despite being an igboman, i also wonder why we are not having the replica of eni njoku of this world, the first vice chancellor of univ of lagos and a first class material frm university of manchester.

We have even export tribalism to advanced countries of the world. it is fashionable hearing highly educated nigerians in the dispora saying i am nigeria of yoruba decent, i am nigeria of igbo descent or i am nigeria of fulani descent to get cheap popularity for their own tribes.

we need to return to our glorious days where merit is placed above sentiment and redefined what it takes to be nigerian and down play tribalism in all its entirely .

tribalism and ethnicity have come to stay in nigeria but the right change of oreintation, true nationalism and restructure of nigeria will help to solve the problem head on.

It is sad that we are divided in the line of ethnicty and religion . The truth must be told dat the root causes of ethnicty or tribalism are injustice, lack of equity , fairness and insincerity. Can we really say that we are one in this country? If we are truly one, why deportation frm state to state, why quota system of government, why indigene and settler dichotomy, why forming a political party on tribal line? Why imposed a person as a market leader?. These are unhealthy factors dat divide us the more instead of uniting us.

We may pretend the ethnicity or tribalism donot exist but it does exist in high places even in government. Take lagos as a casestudy, i expect diversity to be in the ministries or agencies in lagos state because of the cosmopilitcan nature of the state and being a former capital; but what is on ground is the contrary. How many other tribes are represented in agencies like lasma, lawma, kai, lagos internal revenue service, which are created and run by the tax payers money from all tribes in nigeria. If diversity cannot be in such sensitive agencies, somebody, somewhere is playing the highwire or macarba scripts of tribalism, becos fair percentage of setllers in lagos are citizens by birth.

If you are putting it to me that u are a detribalised nigeria, then support the following: accepted the citizenship by birth, competition, restructuring of their nigeria state on the basis of fairness, equity and justice. democracy is about representation and constituency. The situation where some region have at most 7 states while one region has five states, is an injustice of the highest order and a murder of human conscience. The earlier we correct this social ills dat are fast tearing our society apart, the better for us all. But we cannot play an ostrich by burying our head in the sand and pretend dat nobody is seeing us.

1: emeka anyaku
2: charles soludo
3: dora akunyilli
6; ngozi okonjo iweala
5: rochas okorocha

The math general in the house,

Nobody has done justice to the third question posed by mikebis on page 57

I believe dat he extracted the question from a textbook called bouday

u^2/v + v^2/u =12

1/v + 1/u = 1/3.

Alpha, u again. U want to pick issue with a female general becos she constructively criticise ur approach to the problem. You need to take it easy. We are all here to learn but u need to becareful about ur working to a problem to prevent misinforming young aspiring mathematicians in the house. There is no point engaging a supremacy tussle with with jackpot or throwing tandrums at her. Jackpot as a female math general according to my assessment is quite intelligent and forward-looking . Also, u need to be humble and learn from her becos she has lived above board. Her math ingenuity, intellectual sagacity and prowess are what have won for her the general esteem and the confidence of others

@jackpot, u use lagrange multipler to solve the problem posted by laplacian

Let me use simple differentiation to solve it

Let p = xy

Sum of the digit,

X+ y = 12
Y= 12-x

P= x(12-x)
P=12x -x^2

dp/dx=12 -2x
d^2p/dx^2 = -2

It implies dat the function is maximum

for thr number to be maximum, dp/dx=0
2x=12
X=6

thus, y=6

The number=10x+y
=10(6)+6= 66

@ laplacian,

Relationship bt Ux and xu derivative can be obtained by jacobian method. I know dat the problem posed by jackpot involved jacobian method. That is why i am yet to provide a detailed solution to the problem. I am even planning to go to ikeja library if i am on night shit to get input from engineering math to deal with the problem. Jackpot, u are welcomed on board and i are very happy dat we are having a sound female mathematician in the house. Jackpot, u must be possessed with 7 golden spirits of math, lol. Math goes beyond the physical realm becos it is a tool dat help us to understand the physical and abstract world. It is a driving force behind civilisation. It is practically impossible to imagine civilization dat is worth sacrifices and dreams without a sound intellectual framework in math. Jackpot, once again, u are welcome on board. To laplacian, i salute ur math ingenuity and astuteness. The five star general

Solution to integral square root x2-36

Y=integral sqr x2-36 dx
Let x = 6cosht

dx/dt=6sinht
dx=6sinht dt

Thus, y= integral sqr((6cosht)^2 -36)dx

Y=integral sqr(36(cosh^2t -1))dx

Y=6integral sqr(cosh^2 -1)dx

y=6 integral sinhtdx

But x=6cosht
dx/dt=6sinht
dx=6sinhtdt

Thus,y= integral 36sin^2htdt

Y=36integral sin^2htdt

Y=36 integral (cosh2t-1/2)dt

Y=18 integral (cosh2t -1)dt


Y= 9sinh2t -18t c

Y= xsqr(x2-36)/2 -18cosh-1(x/6) c

. Five star math genral

@jackpot

Ur question is about partial differential equation and laplace equation. It has been long i lay my hands on engineering mathematics becos i graduated in 2007 but presently working as a production officer in a reputable company. I am jst using my residual knowledge in basic mathematics especially pure math to deal with problems posed by contributors in the house though i have a mechanical engineering background.i may not be able to make contributions on problem relating to higher matrixes e.g upper n lower triangular matrix, guassian jordan elimination matrices, row transformation matrix, fourier series, numerical analysis particularly, runge kuta, power n fiuboren series, simplex tableau, green n stoke theorem, laplace transformation and partial differentiation and ode. Operador d method, jacobian method -all which i consider as engineering math. U can referred ur problems to laplacian, doubledx, benbuck, calculus and jackpot (our one and only female fermat in d house) and others. i admired their ingenuity and sagacity in math. I believe dat they will pave way for the design of underground satellite tru their math ingenuity. If i can lay my hands on borrowed engineering math on schaum outline on pde or a canders or k.a stroud textbook, i will give u answer to ur problem. Ur question u posted was quite simple, i must confess. Single out. Five star math general

The five star general back online.
Thank God dat i have jst fully recovered from acute fever and fully ready to make contributions
I have gone through series of post by the math generals in the house and i noticed unhealthy verbal attacks between doubledx and alpha maxius. i want to believe that this thread is meant for matured math generals and there is no point throwing tandrums at our colleagues on the basis of correction. We are all here to learn from each other.

A@alpha maxiud,

Your solution to 2^x = 4x is wrong even if u get the answer right. What i am interested in is ur working. U show a total disregard to the basic law of logarithm.

Here is ur working:

2^x = 4x

Take log of both sides:

Xlog2 = log 4x
Xlog2=log4 +logx (since loga +logb=logab)
right up to this extend but here is where u get it all wrong and show a total disregard to basic law of logarithm

Xlog2 -log4=logx

Cancel out the logarithm of both sides:

2x-4=x
X=4. U have violated the law of basic mathematics and u are sentenced to 10years in imprisonment with hard labour by the math military police. Lol.

Simple rule of logarithm:

Loga +logb =logc
a+b is not equal to c

But logab=logc,

Only then, u can cancel out
ab=c.

Hope u get that.

Another common mistake again

Xloga=logb

xa is not equal to b

But loga^x=logb
a^x=b

@ adewasco2kYes, dat is exactly what i intend to achieve. I will like you to help me out

Thanks adewasco2k,

I get ur hint dat u have given to me but i will try and learn more on mysql database.

I need more help. I want you to guide me in creating a php code for a registration form dat extend to two page or more pages with next on each page and with submit button on last page. But i want the data to be submitted to a table in the data base register. Need ur insight pls.

@ adewasco2k,

Thank you so much but i will like u to send me a format for the table and php based on what i required to my email: francisakwari@hotmail.com. Thanks once again. I look forward to ur response.

@ adewasco2k,

How will i display the subjects and respective grade of each student.

Let me give u a hint of the broadsheet

Id name reg eng mth phy chem govt leng
1 ab 02 a1 b2 c4 b1 nil nil

2 kb 05 b2 c2 nil nil b3 nil

3 ch 07 a1 c1 nil nil b2 a1

I want the table of this result to be query using the reg to display as follow:

Ab

Eng: a1


Mth: b2

Phy: c4
Chem: b1

@ adewasco2k

have u seen a waec broadsheet. It contains result of students dat offer science, commercial and art based subject togther.

I need a clue on how to extract the result of each student without including other subject
. It is not compulsory for all science student or commercial or art to offer the same subject.

. I need a guide pls. i donot need separate table for science, commercial and art students result

If the table contain the following subjects and grade by various student from science, commercial and art , how will i display the result of a student only dat offer science subject and grade. Hope u get me

Example,

Table contain the following field

English: A1

Math

Crk

Accounting:

Physics

And i want to query result for a science student without including the subject for commercial and art student. How will i go by it? Pls, i need ur help

@alpha, u are not serious

Am a mechanical engineer by profession and a mathematician by passion

It is really painful for math generals in the house to make simple mistake in mathematics and failing to learn the right correction

Pls, take note

Log (a b) is not equal to log ab

So if u are given such expression as

a b = c

Introduce log to bothside cannot mean the following:

Log a log b = log c

Math general, pls take note. I wasnot able to provide solutions to questions posted becos i was down with fever. Once my recovery, i will be very active again. Your and only five star general

It is really painful for math general in the house for misrepresenting the simple law of logarithm

Log a + log b = logab

There is no validity for the following

Log (a+ b) = logab

Log (a-b) = log a/b

So if u are given an expression as follow:

a + b = c

Introducing log to both side do not mean

Log a + logb = log c ( never, there is no such law in logarithm)

My fellow, math general, let us post realistic problem and learn the correction of common and silly error in math be it pure, applied and engineering mathematics

@ mbachiboy,

I have provided a clue to ur problem especially x5 -32 =0. Check my post. Am down with fever. Sorry for not proviving answers to engineering mathematics problem. Jacpot, u are welcome on board. Am the one and only five star math general