Calculusf(x):
..where 'C' represents the combination sign...n'C'r+n'C'(r+1)=(n+1)'C'(r+1)...using the formula from combination...n'C'r=n!/(n-r)!r!....n'C'(r+1)=n!/{n-(r+1)}!(r+1)!=n!/(n-r-1)!(r+1)!....and (n+1)'C'(r+1)=(n+1)!/{n+1-(r+1)}!(r+1)!=(n+1)!/(n-r)!(r+1)!...(i)..note all those...substitute them to the question...we want to prove that.n!/(n-r)!r!+n!/(n-r-1)!(r+1)!=(n+1)!/(n-r)!(r+1)!...consider the one at the left...n!/(n-r)!r!+n!/(n-r-1)!(r+1)!....which gives n!/(n-r)(n-r-1)!+n!/(n-r-1)!(r+1)(r+1)!....factorize the ones that are factorizable...n!/(n-r-1)!r!{1/(n-r)+1/(r+1)}...solve the one the the nested bracket to get (n+1)/(n-r)(r+1)....take it to where the bracket is...n!/(n-r-1)!r!*(n+1)/(n-r)(r+1)...multiply the numerator by eachother,do the same to the denominator...(n+1)n!/(n-r)(n-r-1)!(r+1)r!...[remember (n+1)!=(n+1)n!,(n-r)!=(n-r)(n-r-1)! and (r+1)!=(r+1)r!]...substitute those...to give (n+1)!/(n-r)!(r+1)!...which is the same as equation 1 above...hence equal to (n+1)'C'(r+1)...

thanks so much bro.

Solve the simultaneous equation y'=y-2x...(i) and x'=x-2y...(ii)

Solve d simultaeous equation
2 raise to power -x, 4 raise to power -y =2.......(eqn..i)
3 raise to power -x, 9 raise to power 2y =3 .........(eqn...ii) ,

Solve d simultaeous equation
2 raise to power -x, 4 raise to power -y =2.......(eqn..i)
3 raise to power -x, 9 raise to power 2y =3 .........(eqn...ii) ,

Solve d equation 3tanQ = 2secQ..

If a sequence x, 7, y, 15 is an AP find d values of X and Y..

Simplify d followin log45-log9+log20, log4+log25

Librate: Solve d simultaeous equation
2 raise to power -x, 4 raise to power -y =2.......(eqn..i)
3 raise to power -x, 9 raise to power 2y =3 .........(eqn...ii).,

...guess the question is this...2^(-x).4^(-y)=2...(eqn1) and 3^(-x).9^(2y)=3...(eqn2)...make the equation as the powers of their products...for equation 1...2^(-x).(2^2)^-y=2^1....(2^-x).2^(-2y)=2^1...using the law of indices 2^(-x-2y)=2^1...since they have the same base...-x-2y=1...multiply through by -1... x+2y=-1....(eqn3)..from equation 2...3^(-x).9^(2y)=3...3^(-x).(3^2)^(2y)=3^1...3^(-x).3^(4y)=3^1...from indices...3^(-x+4y)=3^1...since they have the same base...-x+4y=1...multiply through by -1 to get x-4y=-1...(eqn4)...consider equation 3 and 4...x+2y=-1 and x-4y=-1...subtract equation 4 from 3...x+2y-(x-4y)=-1-(-1)...x+2y-x+4y=-1+1...6y=0...therefore y=0...substitute y=0 to either of equation 3 or 4...let's use 3.x+2y=-1...x+2(0)=-1...therefore x=-1...Y=0,X=-1

Librate: Solve d equation 3tanQ = 2secQ..

If a sequence x, 7, y, 15 is an AP find d values of X and Y..

Simplify d followin log45-log9+log20, log4+log25

....for the first question 3tanQ=2secQ...remember that tanQ=sinQ/cosQ and secQ=1/cosQ....substitue those...3sinQ/cosQ=2/cosQ...multiply through by cosQ...3sinQ=2...sinQ=2/3...sinQ=0.6667...Q=arcsin(0.6667)...Q=41.8(to 1dp)...

Librate: Solve d equation 3tanQ = 2secQ..

If a sequence x, 7, y, 15 is an AP find d values of X and Y..

Simplify d followin log45-log9+log20, log4+log25

...for the second question...x,7,y,15 is an a.p...x is the first term...7 is the second term...y is the third term and 15 is the fourth term...for the second term...we have already known that a=x...using the formula for a.p that a+(n-1)d...for second term.n=2... substitute that...a+d=second term...for the third term...it will be a+2d and for the third term...try yours for the fourth term...guess your answer is a+3d(great)...therefore a+d=7(second term)...a+3d=15(fourth term)...subtract the second term from the fourth term to get a+3d-(a+d)=15-7....a+3d-a-d=8...2d=8...divide through by 2...d=4...since a+d=7 then substitute for d=4...a+4=7...a=7-4=3...since x=first term(a)...therefrod x=3 and y(third term)=a+2d...y=3+2*4=3+8...y is equal to 11...therefore x=3,y=11

Guys r busy proofing.waw nice one

Some one should plz help me out with dis:::if
(x+jwL)/z=y/{k-j(1/wc)} show that
L=cyz/(w^2c^2k^2+1)

Mbahchiboy: Some one should plz help me out with dis:::if
(x+jwL)/z=y/{k-j(1/wc)} show that
L=cyz/(w^2c^2k^2+1)

where is x in the second equation

honey: where is x in the second equation

datz how d question is brb

benbuks: ok...take this....if y = X^x^x^x.... compute. dy/dx.

(3x^3x)+ln(x^3x^3x)

Hmmm...math lovers.in the house oya throw me those questions...feel like solving

Richiez: Hmmm...math lovers.in the house oya throw me those questions...feel like solving

a right circular cylinder of radius 8ft and height 16ft whose axis is horizontal is filled with water, how long will take for all the water to escape an orifice of (1/72)ft² area at the bottom of thd tank, assuming the velocity of escape v in terms of instataneous height is given by =0.6-_\(2gh)... take g=32ft/s,....... this question has given me sleepless night, and i would appreciate a correct solution.

honey: a right circular cylinder of radius 8ft and height 16ft whose axis is horizontal is filled with water, how long will take for all the water to escape an orifice of (1/72)ft² area at the bottom of thd tank, assuming the velocity of escape v in terms of instataneous height is given by =0.6-_\(2gh)... take g=32ft/s,....... this question has given me sleepless night, and i would appreciate a correct solution.

nice question.bro so no 1 has solved it...

honey: a right circular cylinder of radius 8ft and height 16ft whose axis is horizontal is filled with water, how long will take for all the water to escape an orifice of (1/72)ft² area at the bottom of thd tank, assuming the velocity of escape v in terms of instataneous height is given by =0.6-_\(2gh)... take g=32ft/s,....... this question has given me sleepless night, and i would appreciate a correct solution.

here is a little hint dat may b of help.
This is a practical question dat reflect d applicatn of diffrential eqn in chemical engineering
*Basis
volumetric rate=vol rate in-vol rate out
note dat v=dh/dt...nd dh=vdt
recall dat vol=¥(pie)r^2dh
but 4 vol out u use
area.(velocity)dt
also when height=16ft,time=0 &when height=0(since tank empties),time=?
Take dat as d integrtn boundries
....may gv d complete atempt by 2moro...sti observing,gr8 wuk gurus...

honey: a right circular cylinder of radius 8ft and height 16ft whose axis is horizontal is filled with water, how long will take for all the water to escape an orifice of (1/72)ft² area at the bottom of thd tank, assuming the velocity of escape v in terms of instataneous height is given by =0.6-_\(2gh)... take g=32ft/s,....... this question has given me sleepless night, and i would appreciate a correct solution.

Alright! Very straightforward question let me work out the answer

How can i solve polynomial questions of no simple root...

Pls house, I need solution to this questn sharpsharp:

Consider a group of 200 Nigerian made up of 50 Ibo,90 Hausa and 60 Yoruba posssessing,the entry permit into d USA.If 80 of them are Male and d rest are Female,25 of d female are Ibo,30 are Hausa and the rest are Yoruba.Find d prob that (a) An individual run at random will be a female (b) An individual run at random will be an Hausa (c) A randomly selected person frm d group will be a female given that she is Yoruba (d) A randomly selected person frm d group will be an Ibo given that he is a Male. (e) An individual randomly selected is Yoruba given that he is a Male.

Radius r=8ft
Height h=16ft
Area of orifice A=(1/72)ft²
Velocity of escape v=0.6√2gh
g=32ft/s²

Volume flow rate in m³/s = volume of water in tank/time taken to empty tank = V/t

Also, volume flow rate in m³/s = area of orifice x velocity of escape = A x v

Equating both formulas for volume flow rate in m³/s
V/t = Av
Therefore time t= V/Av
Now Volume of water in tank is given by V=II r²h
Hence t=II r²h/0.6A√2gh t=3.142 x 8²x16/(0.6(1/72)(√2x32x16))
t=12065.85 secs
Approx t=201 mins

busuyem: Pls house, I need solution to this questn sharpsharp:

Consider a group of 200 Nigerian made up of 50 Ibo,90 Hausa and 60 Yoruba posssessing,the entry permit into d USA.If 80 of them are Male and d rest are Female,25 of d female are Ibo,30 are Hausa and the rest are Yoruba.Find d prob that (a) An individual run at random will be a female (b) An individual run at random will be an Hausa (c) A randomly selected person frm d group will be a female given that she is Yoruba (d) A randomly selected person frm d group will be an Ibo given that he is a Male. (e) An individual randomly selected is Yoruba given that he is a Male.

a)- p(f) = 120/200 = 0.6

B) P(H) = 90/200 = 0.45

C) p(Fy) = (120-55 = 65/200= 0.325

D) P (Im) = 25/200

I will leave the last one for you to solve

hmmm, long time! General Biolabee, I've also missed the likes of Generals Ositadima, Doubledx, our gurus echibuzor, ghetoguru and the rest.
but it seems like we have new forces in the house like ; calculus f(x), 2nionshine, honey, benbuks e.t.c
greetings to you all

How did u arive at this? Ur solutions are different frm what others solve around me here, espectially ur answere c and d. Explain better.

Richiez: hmmm, long time! General Biolabee, I've also missed the likes of Generals Ositadima, Doubledx, our gurus echibuzor, ghetoguru and the rest.
but it seems like we have new forces in the house like ; calculus f(x), 2nionshine, honey, benbuks e.t.c
greetings to you all

oga mi sir.. i dey oooo

you guys are doing excellently

@busuyem.. put the answers you have up.. here
lets discuss

Calculusf(x):
How can i solve polynomial questions of no simple root...

Were u ƌ guy dah had Ă small passport on ur print out during ƌ putme 4 uniben??

Calculusf(x):
How can i solve polynomial questions of no simple root...

Post a sample question let's see

Pls help me wif dis Oº°˚˚°º..
1.Find ƌ equ of Ă circle passin tru points (2,3),(3,2),(-4,3)
2.Find ƌ equ of hyperbola passin tru points (4,6) nd whose asymptotes are y=±square root of 3..

busuyem: Pls house, I need solution to this questn sharpsharp:

Consider a group of 200 Nigerian made up of 50 Ibo,90 Hausa and 60 Yoruba posssessing,the entry permit into d USA.If 80 of them are Male and d rest are Female,25 of d female are Ibo,30 are Hausa and the rest are Yoruba.Find d prob that (a) An individual run at random will be a female (b) An individual run at random will be an Hausa (c) A randomly selected person frm d group will be a female given that she is Yoruba (d) A randomly selected person frm d group will be an Ibo given that he is a Male. (e) An individual randomly selected is Yoruba given that he is a Male.

I am still expecting more solutions on this question, pls.

busuyem: Pls house, I need solution to this questn sharpsharp:

Consider a group of 200 Nigerian made up of 50 Ibo,90 Hausa and 60 Yoruba posssessing,the entry permit into d USA.If 80 of them are Male and d rest are Female,25 of d female are Ibo,30 are Hausa and the rest are Yoruba.Find d prob that (a) An individual run at random will be a female (b) An individual run at random will be an Hausa (c) A randomly selected person frm d group will be a female given that she is Yoruba (d) A randomly selected person frm d group will be an Ibo given that he is a Male. (e) An individual randomly selected is Yoruba given that he is a Male.

Total =200.,,,T(I)=50,T(H)=90,T(Y)=60,T(M)=80,T(Ƒ)=120,T(FnI)=25,T(FnH)=30,T(FnY)=65...Ă)P(Ƒ)=120/200,ß)P(H)=90/200,,C)P(FnY)=65/200,,D)P(MnI)=25/200,,

2nioshine: here is a little hint dat may b of help.
This is a practical question dat reflect d applicatn of diffrential eqn in chemical engineering
*Basis
volumetric rate=vol rate in-vol rate out
note dat v=dh/dt...nd dh=vdt
recall dat vol=¥(pie)r^2dh
but 4 vol out u use
area.(velocity)dt
also when height=16ft,time=0 &when height=0(since tank empties),time=?
Take dat as d integrtn boundries
....may gv d complete atempt by 2moro...sti observing,gr8 wuk gurus...

plz y dont my soln reflect sir richez..av done this twice yet can find it.
In summary i wuk at mine in term of instantenous time
since water fills d tank
vol rate in =vol rate out
pie*64*dh=1/72*0.6*(_/2*32*h)dt
hence
201.088dh=0.067_/h dt
By applyin method f integratn by seperatn variable gvs
3001.3 integra(1/root h)dh =integra dt

at boundaries h=16 t=0, and h=0 t=t
solving this gvs
3001.3*2h^1/2=t
imputing values gvs h=16 and t=t
we have
3001.3*8=t
:-
t=24010.4sec or 400mins aprox

lavosier:
Total =200.,,,T(I)=50,T(H)=90,T(Y)=60,T(M)=80,T(Ƒ)=120,T(FnI)=25,T(FnH)=30,T(FnY)=65...Ă)P(Ƒ)=120/200,ß)P(H)=90/200,,C)P(FnY)=65/200,,D)P(MnI)=25/200,,

Thanks alot.