Wow.

Solve 2^2y + 2 = 33 X 2^y - 8

Olarewajub: Solve 2^2y + 2 = 33 X 2^y - 8

CROSS CHECK AND RETYPE CAUSE AM HAVIN POINT IN MY ANS

Where have my masters been? Pls, save the life of this great thread!

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....

benbuks: Wow.

....my oga at the top...i respect

Gud day 2 d guruus in d auz,can any1 find d integral of dx/e^2x-2e^x

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

Anybody in the house?

Calculusf(x):
Anybody in the house?

smtyms.

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-solve. y^3 -y^2 ^2 +y-1

Plz i want know aw to do addition and subtraction of Number bases

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.

Prinzoladimeji: Plz i want know aw to do addition and subtraction of Number bases

.
bring question under it. i think dat will help.

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.

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

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

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.

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?

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

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

...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

...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

Great...kudos to everybody in the house

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...

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!

doubleDx:







Nice one generals, I greet y'all!

...master,i respect sir,welcome to the thread...

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

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......

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...