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Re: How To Calculate Quickly And Correctly In Mathematics by Nobody: 9:14pm On Sep 24, 2013
Wow.
Re: How To Calculate Quickly And Correctly In Mathematics by Olarewajub: 11:39pm On Sep 29, 2013
Solve 2^2y + 2 = 33 X 2^y - 8
Re: How To Calculate Quickly And Correctly In Mathematics by MrCalculus(m): 8:32am On Sep 30, 2013
Olarewajub: Solve 2^2y + 2 = 33 X 2^y - 8
CROSS CHECK AND RETYPE CAUSE AM HAVIN POINT IN MY ANS
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 4:23pm On Oct 15, 2013
Where have my masters been? Pls, save the life of this great thread!
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 5:44pm On Oct 16, 2013
Ortarico: Where have my masters been? Pls, save the life of this great thread!
...my masters,it's been a while....how maths life
Olarewajub: Solve 2^2y + 2 = 33 X 2^y - 8
...i think the question is 2^(2y+2)=33*2y-8....
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 6:02pm On Oct 16, 2013
benbuks: Wow.
....my oga at the top...i respect
Re: How To Calculate Quickly And Correctly In Mathematics by koliks(m): 9:10pm On Oct 18, 2013
Gud day 2 d guruus in d auz,can any1 find d integral of dx/e^2x-2e^x
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 8:29am On Oct 29, 2013
koliks: Gud day 2 d guruus in d auz,can any1 find d integral of dx/e^2x-2e^x
...£ represents my integral sign...then £dx/(e^2x-2e^x)...let u be e^x....du=e^xdx...du=udx...dx=du/u...substitute those to get £du/u(u^2-2u)...£du/u^2(u-2)...then let's solve using integration by partial fraction...1/u^2(u-2)=A/u+B/u^2+C/(u-2)...multiply through by u^2(u-2) to get 1=A.u(u-2)+B(u-2)+Cu^2...expand the rhs to get 1=u^2A-2uA+Bu-2B+Cu^2...then 1=(A+C)u^2+(B-2A)u-2B...equate them to give,(A+C)=0,(B-2A)=0 2B=1...then,B=1/2...then 1/2-2A=0...A=1/4...1/4+C=0,then C=-1/4...substitute that,then £1/4u.du+£1/2u^2.du-£1/4(u-2).du...then 1/4lnu-1/2u+1/4ln(u-2)....then lnu^(1/4)+ln(u-2)^(1/4)-1/2u...then ln{u(u-2)}^(1/4)-1/2u...then 1/4ln(e^2x-2e^x)-1/2e^x....i'm rushing in typing,i may be wrong,but i just want you to get the steps...any criticism is allowed
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 7:33am On Nov 12, 2013
Anybody in the house?
Re: How To Calculate Quickly And Correctly In Mathematics by Nobody: 8:29am On Nov 12, 2013
Calculusf(x):
Anybody in the house?
smtyms.
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 9:32am On Nov 12, 2013
If not for these busy days, I should continue as a full time administrator. My prof, I greet you powerfully. Where is my oga @ the top, 'Mr calculus'?
Re: How To Calculate Quickly And Correctly In Mathematics by Nobody: 11:37am On Nov 12, 2013
Re-solve. y^3 -y^2 ^2 +y-1
Re: How To Calculate Quickly And Correctly In Mathematics by Prinzoladimeji(m): 12:55pm On Nov 12, 2013
Plz i want know aw to do addition and subtraction of Number bases
Re: How To Calculate Quickly And Correctly In Mathematics by rhydex247(m): 2:43pm On Nov 12, 2013
benbuks: Re-solve. y^3 -y^2 ^2 +y-1
note y^2^2 means y^4
y^3-y^4+y-1.
factor -1 out of y^3-y^4+y-1.
-(y^4-y^3+y-1).
factor terms by grouping.
-y^3+y^4-y+1=(y^4-y^3)+(1-y)=y^3(y-1)-(y-1)= -[y^3(y-1)-(y-1)].
factor -1+y from y^3(y-1)-(y-1)
we av -[(y-1)(y^3-1)]. note that y^3-1 = (y-1)(y^2+y+1).
-[(y-1)(y-1)(y^2+y+1).
-(y-1)^2(y^2+y+1). All is well.
Re: How To Calculate Quickly And Correctly In Mathematics by rhydex247(m): 3:03pm On Nov 12, 2013
Prinzoladimeji: Plz i want know aw to do addition and subtraction of Number bases
.
bring question under it. i think dat will help.
Re: How To Calculate Quickly And Correctly In Mathematics by Nobody: 3:19pm On Nov 12, 2013
rhydex 247:
note y^2^2 means y^4
y^3-y^4+y-1.
factor -1 out of y^3-y^4+y-1.
-(y^4-y^3+y-1).
factor terms by grouping.
-y^3+y^4-y+1=(y^4-y^3)+(1-y)=y^3(y-1)-(y-1)= -[y^3(y-1)-(y-1)].
factor -1+y from y^3(y-1)-(y-1)
we av -[(y-1)(y^3-1)]. note that y^3-1 = (y-1)(y^2+y+1).
-[(y-1)(y-1)(y^2+y+1).
-(y-1)^2(y^2+y+1). All is well.
...re-try.
Re: How To Calculate Quickly And Correctly In Mathematics by rhydex247(m): 3:24pm On Nov 12, 2013
TO KOLIKS QUESTION INTEGRAL dx/e^2x-e^x.

HERE IS THE SOLUTION.
I'm taking my integral sign to be $.
divide through by e^x we ave
$e^-x/e^x-2 dx
let u=e^x..... du/dx=e^x...... dx=du/e^x
$1/(u-2)u^2 du.
using partial fraction
$(-1/2u^2 - 1/4u +1/4(u-2))du
integrating term by term
-1/2$1/u^2du +1/4$1/(u-2)du - 1/4$1/udu.
1/2u+1/4ln(u-2)-1/4lnu +C.
put u=e^x.
1/2e^x+1/4ln(e^x-2)-1/4lne^x+C.
By simplifying we av this as final answer.
1/4[2e^-x+ln(1-2e^-x)]+C. All is well
Re: How To Calculate Quickly And Correctly In Mathematics by Nobody: 3:31pm On Nov 12, 2013
Mayb sm of u kw dis
multplyin any integer by 6 without using calculator

e.g 6 x 3 =18

put a zero in front of '3'
(30) then divide by '2' (15) then add the number (3) to the answer you got (15+3)=18

also
6x4 =40/2 =20+4 =24
6x5=50/2=25+5=30
6x6=60/2=30+6=36


nb: (works for all integers)

hence
6x n= n0/2 =m+n,

.just my lit2 discovery

1 Like

Re: How To Calculate Quickly And Correctly In Mathematics by rhydex247(m): 4:11pm On Nov 12, 2013
benbuks: ...re-try.
There is nothing to re try. becos from my answer
-(y-1)^2(y^2+y+1) implies -(y^2-2y+1)(y^2+y+1)
(-y^2+2y-1)(y^2+y+1) gives back the question y^3-y^4+y-1. Hence my answer and my working they KAMPE.
Re: How To Calculate Quickly And Correctly In Mathematics by Nobody: 4:29pm On Nov 12, 2013
rhydex 247:
There is nothing to re try. becos from my answer
-(y-1)^2(y^2+y+1) implies -(y^2-2y+1)(y^2+y+1)
(-y^2+2y-1)(y^2+y+1) gives back the question y^3-y^4+y-1. Hence my answer and my working they KAMPE.
...here is the solution,

y^3 -y^2 +y -1
=(y^3-y^2) + (y-1)
=y^2(y-1) +(y-1)

==>y^3-y^2 +y-1
=(y^2 +1)(y-1)

got that?
Re: How To Calculate Quickly And Correctly In Mathematics by rhydex247(m): 4:40pm On Nov 12, 2013
benbuks: ...here is the solution,

y^3 -y^2 +y -1
=(y^3-y^2) + (y-1)
=y^2(y-1) +(y-1)

==>y^3-y^2 +y-1
=(y^2 +1)(y-1)

got that?
bro abeg check the question again.
the question is y^3-y^2^2+y-1 which implies y^3-y^4+y-1 not y^3-y^2+y-1
Re: How To Calculate Quickly And Correctly In Mathematics by Laplacian(m): 9:52pm On Nov 13, 2013
benbuks: Mayb sm of u kw dis
multplyin any integer by 6 without using calculator

e.g 6 x 3 =18

put a zero in front of '3'
(30) then divide by '2' (15) then add the number (3) to the answer you got (15+3)=18

also
6x4 =40/2 =20+4 =24
6x5=50/2=25+5=30
6x6=60/2=30+6=36


nb: (works for all integers)

hence
6x n= n0/2 =m+n,

.just my lit2 discovery
here's a simple proof justifying your assertion
6*n=(5+1)*n=5n+n=10n/2+n....
Nice work bro, keep it up, dis is exactly wat dis thread is all about...
Direct extension of ur propsition shows that;
4*n=(5-1)*n=5n-n=10n/2-n
e.g 4*7=70/2-7=35-7=28

1 Like

Re: How To Calculate Quickly And Correctly In Mathematics by Laplacian(m): 11:07pm On Nov 13, 2013
...d square of any number can be computed easily...from d relation;
(x-y)^2=x^2-2xy+y^2 we have x^2=(x-y)^2+2xy-y^2
e.g
17^2=(17-1)^2+2*17*1-1^2=256+34-1=289

again
27^2=625+100-4=721

1 Like

Re: How To Calculate Quickly And Correctly In Mathematics by Laplacian(m): 11:22pm On Nov 13, 2013
...easy steps to multiplication...
x*y=(x-a+a)*y=(x-a)y+ay
in particular if a=y, then
x*y=(x-y)y+y^2
e.g
6*3=(6-3)*3+3^2=9+9=18

17*24=(24-4)*17+4*17=
20*17+68=340+68=408
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 11:31pm On Nov 13, 2013
Great...kudos to everybody in the house
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 11:34pm On Nov 13, 2013
To square anything which comes between 25-50...say 46...just say 46 minus 25...to give 21,keep that,say 50 minus 46 to give 4(square the 4 to give 16)...take the 16 to 21 and write together...so that answer for 46^2 is 2116...just other ones and ask me questions on the ones that seems to be difficult between 25-50...but note this,it works for all numbers in that range...

1 Like

Re: How To Calculate Quickly And Correctly In Mathematics by Nobody: 12:47am On Nov 14, 2013
Laplacian: ...easy steps to multiplication...
x*y=(x-a+a)*y=(x-a)y+ay
in particular if a=y, then
x*y=(x-y)y+y^2
e.g
6*3=(6-3)*3+3^2=9+9=18

17*24=(24-4)*17+4*17=
20*17+68=340+68=408

benbuks: Mayb sm of u kw dis
multplyin any integer by 6 without using calculator

e.g 6 x 3 =18

put a zero in front of '3'
(30) then divide by '2' (15) then add the number (3) to the answer you got (15+3)=18

also
6x4 =40/2 =20+4 =24
6x5=50/2=25+5=30
6x6=60/2=30+6=36


nb: (works for all integers)

hence
6x n= n0/2 =m+n,

.just my lit2 discovery


Calculusf(x):
To square anything which comes between 25-50...say 46...just say 46 minus 25...to give 21,keep that,say 50 minus 46 to give 4(square the 4 to give 16)...take the 16 to 21 and write together...so that answer for 46^2 is 2116...just other ones and ask me questions on the ones that seems to be difficult between 25-50...but note this,it works for all numbers in that range...


Nice one generals, I greet y'all!
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 1:14am On Nov 14, 2013
doubleDx:







Nice one generals, I greet y'all!
...master,i respect sir,welcome to the thread...
Re: How To Calculate Quickly And Correctly In Mathematics by Laplacian(m): 7:22am On Nov 14, 2013
Calculusf(x):
To square anything which comes between 25-50...say 46...just say 46 minus 25...to give 21,keep that,say 50 minus 46 to give 4(square the 4 to give 16)...take the 16 to 21 and write together...so that answer for 46^2 is 2116...just other ones and ask me questions on the ones that seems to be difficult between 25-50...but note this,it works for all numbers in that range...
nice work bro...its a special case of what i showed earlier...here's a simple proof;
(x-y)^2=x^2-2xy+y^2....let x=50, then,
(50-y)^2=2500-100y+y^2 from here we get;
y^2=(50-y)^2+100(y-25)....finally,

y^2=(y-25)0(50-y)^2....that's d digit of d number...
E.g
48^2=(48-25)0(50-48)^2
=2304
....once again, nice work...
I must comment that ur restriction that; 25<y<50 is unnecessary....it works for all numbers greater than 25, that is y>25...
E.g
Let y=51 then,
51^2=(51-25)0(50-51)^2
=2601

1 Like

Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 9:02am On Nov 14, 2013
Laplacian:
nice work bro...its a special case of what i showed earlier...here's a simple proof;
(x-y)^2=x^2-2xy+y^2....let x=50, then,
(50-y)^2=2500-100y+y^2 from here we get;
y^2=(50-y)^2+100(y-25)....finally,

y^2=(y-25)0(50-y)^2....that's d digit of d number...
E.g
48^2=(48-25)0(50-48)^2
=2304
....once again, nice work...
I must comment that ur restriction that; 25<y<50 is unnecessary....it works for all numbers greater than 25, that is y>25...
E.g
Let y=51 then,
51^2=(51-25)0(50-51)^2
=2601
.you are one of my ogas bro.so,i can't quote you wrong.but there are still better and faster ways i've got of calculating faster and easier than that.you can even calculate some faster than someone with calculator(believe me,i'm not joking o)...let's play with one more for this morning.here we go......
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 9:05am On Nov 14, 2013
To square anything which comes between 51-60...say 57...the unit is 7...add the 7 to 25 to give 32...keep that and square that 7 to give 49..write it together to give 3249...

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