d citizen:
. . . Jacpot, u are welcome on board. Am the one and only five star math general

jackpot: dear Maths generals, pls help me with this little problem.


[size=14pt]By using the Cartesian-paraboloidal coordinate transformation equations:
(x=uv sin φ, y=uv cos φ, z=¹/₂(u²-v²),
show that the 3-dimensional Laplace's equation
F_xx+F_yy+F_zz=0
reduces to
¹/_(u²+v²) (F_uu+F_vv+ ¹/_u F_u+¹/_v F_v)+¹/_(u²v²)F_φφ = 0.[/size]

johnpaul1101: goodday and happy salah 2 everyone.
Plz i could use some here:
The numerator of a fraction is 5 less than it's denominator. If 6 is added to the numerator and 4 to the denominator. The fraction is doubled. What is the fraction?
Plz solution/workings will be greatly appreciated.

Calculusf(x):
...let the denominator be x...since the numerator is 5 less than the denominator...then the original fraction is (x-5)/x...but the question continues that 6 is added to the numerator and 4 to the denominator...then (x-5+6)/(x+4)...which is equal to 2 times the original equation{(x-5)/x}...then (x+1)/(x+4)=2(x-5)/x...multiply through by x(x+4){which is the same as cross multiplication} to give x(x+1)=2(x-5)(x+4)...x^2+x=2x^2-2x-40...x^2-3x-40....x=8 or -5...since the original equation is (x-5)/x...substitute 8 which gives 3/8 OR substitute -5 which gives 2

Ortarico:

Past question, here's the solution.

Alpha Maximus: .....Voila!!! Here's the solution:
Statistics for 1992: #200,000/100 guys and #2000/each guy(don't write 'guy' for your lecturer)
Statististics for 1993: 8% pop increase and 25% taxation increase resulting in: #250,000/108 guys and #2,314.8148/each guy
(A)Objective: To find the percentage increase in taxation per guy
Change in taxation=new taxation per guy - old taxation per guy = 2,314.8148-2000= 314.8148
Percentage increase in taxation=change in taxation divided by old taxation then multiplied by 100
Thus,
(314.8148/2000)*100=15.74071%=15.7% to 3 significant figures
(B) Objective: To obtain new taxation revenue in 1993, given a 2%(stingy) discount by government
First obtain taxation per 100 guyz in 1993
Taxation per 100 guyz in 1993=(250,000/108)*100=231,481.48 per 100 guyz
Now including 2% discount
(2/100)*231,481.48=4,629.6296
New taxation revenue per 100 guyz in 1993=231,481.48- 4,629.6296=226,851.5=#226,852 to the nearest naira........hope that helped

johnpaul1101:
thanks very much bro, i really appreciate. Yea i know it's a past question but i didnt see any solution, dat's why i had 2 post it again. Have a nice day and remember 2 keep my salah meat

Alpha Maximus: That's like one of the simplest aspects of Math man!!! Its mostly statistics....if you really hate it that much, i shudder to think of your attitude toward engineering math......practice man

d citizen:
@alpha, u are not serious

Am a mechanical engineer by profession and a mathematician by passion

Olarewajub: Someöne should please expand:
(a+b+c)(a+b-c)(a-b+c)(-a+b+c).
#TeamMathematics

Alpha Maximus:
First evaluate (a+b+c)(a+b-c) and (a-b+c)(-a+b+c) seperately
First, (a+b+c)(a+b-c)
a(a+b-c)+b(a+b-c)+c(a+b-c)
=a^2+ab-ac+ab+b^2-bc+ac+bc-c^2
Collecting like terms, we have:
a^2+b^2-c^2+2ab.........(I)
Now we evaluate (a-b+c)(-a+b+c)
a(-a+b+c)-b(-a+b+c)+c(-a+b+c)
=-a^2+ab+ac+ab-b^2-bc-ac+bc+c^2
Collecting like terms, we have:
-a^2-b^2+c^2+2ab.......(II)
Now we multiply (I) by (II)
(a^2+b^2-c^2+2ab)(-a^2-b^2+c^2+2ab)
=a^2(-a^2-b^2+c^2+2ab)+b^2(-a^2-b^2+c^2+2ab)-c^2(-a^2-b^2+c^2+2ab)+2ab(-a^2-b^2+c^2+2ab)
=-a^4-a^2b^2+a^2c^2+2a^3b-a^2b^2-b^4+b^2c^2+2ab^3+a^2c^2+b^2c^2-c^4-2abc^2-2a^3b-2ab^3+2abc^2+4a^2b^2
Collecting like terms, we have a final expansion of:
-a^4-b^4-c^4+4a^2b^2-2a^2b^2+2a^2c^2+2b^2c^2........taadaa!!!

Alpha Maximus:
First evaluate (a+b+c)(a+b-c) and (a-b+c)(-a+b+c) seperately
First, (a+b+c)(a+b-c)
a(a+b-c)+b(a+b-c)+c(a+b-c)
=a^2+ab-ac+ab+b^2-bc+ac+bc-c^2
Collecting like terms, we have:
a^2+b^2-c^2+2ab.........(I)
Now we evaluate (a-b+c)(-a+b+c)
a(-a+b+c)-b(-a+b+c)+c(-a+b+c)
=-a^2+ab+ac+ab-b^2-bc-ac+bc+c^2
Collecting like terms, we have:
-a^2-b^2+c^2+2ab.......(II)
Now we multiply (I) by (II)
(a^2+b^2-c^2+2ab)(-a^2-b^2+c^2+2ab)
=a^2(-a^2-b^2+c^2+2ab)+b^2(-a^2-b^2+c^2+2ab)-c^2(-a^2-b^2+c^2+2ab)+2ab(-a^2-b^2+c^2+2ab)
=-a^4-a^2b^2+a^2c^2+2a^3b-a^2b^2-b^4+b^2c^2+2ab^3+a^2c^2+b^2c^2-c^4-2abc^2-2a^3b-2ab^3+2abc^2+4a^2b^2
Collecting like terms, we have a final expansion of:
-a^4-b^4-c^4+4a^2b^2-2a^2b^2+2a^2c^2+2b^2c^2........taadaa!!!

hod898: What?! A maths thread on NL and I knew not? Great!
Alright ignore what I wrote up there--that was another me. BTW am I allowed to dine on the table of formulas wt u guys? Please?

Mikebis: i also mk use of engenrn math,buh i dnt come across any bus math,buh only statistic,nd 4 ur info,am an industrial chemistry studnt,xo we dnt make use of bus math,can u solve dis questn i gat it 4rm engr math...
If y={x + square rut of 1 +x²}³/2,shw dat 4(1 + x²)d²y/dx² +4x dy/dx - 9y=0.
I wll b apy if u do dat 4 me

Alpha Maximus: .......and i hope you dont think my answer is wrong because of the order of arrangement of the individual terms......for example, 'a' minus 'b' is the same thing as minus 'b' plus 'a'

benbuks: Hmm..@jackport..solve dat enigma u posted...2b honest..am just in 100l...i cnt solve it o..dia lots more i nid 2 kw in math..

doubleDx:

I'm on it, maybe I'll post tomorrow! Where is our 5 Star General (d citizen); I was waiting for you to post first. You are the Boss, Sire! @Jackpot, are you a Mathematician/Mathematics Student or an Engineer/Engineering Student?

rhydex 247: Breakfast questn
1. Solve. (x^2-16)(x-3)^2+9x^2=0.

muyhee: u guys should check out my post.

muyhee: guys.check d validity of dis formula.x^n=Knx-(Kn(n-1)x^2)/2!.k is a constant using d binomial powers.x is d base while n is d exponent.dis formula can b used to solve all squares.e.g5^2,16^2etc.it features:
A.diffrntiatn of trigonometric functions.B.maclaurin series(in its provin).C.binomial theorem.its nt dat we cn not easily get d answers directly bt maths finds a way dats complex to solve simple qst.example.4^2
Usin pascals triangle.we hav 1441.den take d last 4 nd 1.so x=4 n=2 K=4 K=1
So we av
4(2)4-(1(2)(2-1)(4)^2)/2!
32-1(32)/2=16.its called Adelma formula under geometries of numbas(the rules of squares).am waitim try ur own example.nd comment