9c, try...

...sin2x+sinx=1...find x...

Laplacian: ...sin2x+sinx=1...find x...

A graphical solution is the most accepted approach, I'll upload it when chanced. Thanks!

Ortarico:

Hmmm. . . If x is all the values satisfying the interval 0 theta 360 then;
sin2x + sinx = 1
2sinxcosx + sinx - 1 = 0
sinx(2cosx + 1) = 0
sinx = 0
x = arcsin(0)
x = 0, 180, 360

2cosx = -1
cosx = -1/2
x = arccos(-1/2)
x = 120, 240

grt solvn bro...i respect ur accuracy nd ur method nd mode of solvn dis question o...grtns 2 all maths guru in d house o.

someone shld try dis: sin$= (a-1)/x and cos$= (1-a)/x. find tan$.

Alpha Maximus: .....alright, I'm not really conversant with trigonometric equations but I'll give it a shot!
Tan ! =sin ! /cos !
Thus Tan$=sin$/cos$=((a-1)/x))/((1-a)/x))
=a-1/x*(x/1-a)
=a-1/1-a
Tan$=a-1/1-a
Multipky both sides by -1
-tan$=-a+1/1-a
-tan$=1
Divide both sides by -1
Tan$=-1
Am I right?

Yea u are 100% right.

Here is my question.
1. Suppose G is an abelian group. Show dat any factor group G/H is also abelian.

2. Suppose v=(1,3,5,7). Find the projection of v onto W or, in other words, find w€W that minimizes //v-w//, where W is d subspance of R^4 spanned by.
a) u1=(1,1,1,1) and u2=(1,-3,4,-2),
b) v1=(1,1,1,1) and v2=(1,2,3,2).
All is well.

Ortarico:

Hmmm. . . If x is all the values satisfying the interval 0 theta 360 then;
sin2x + sinx = 1
2sinxcosx + sinx - 1 = 0
sinx(2cosx + 1) = 0
sinx = 0
x = arcsin(0)
x = 0, 180, 360

2cosx = -1
cosx = -1/2
x = arccos(-1/2)
x = 120, 240

nice try bro....but ur solution is flawed

rhydex 247: Here is my question.
1. Suppose G is an abelian group. Show dat any factor group G/H is also abelian.

2. Suppose v=(1,3,5,7). Find the projection of v onto W or, in other words, find w€W that minimizes //v-w//, where W is d subspance of R^4 spanned by.
a) u1=(1,1,1,1) and u2=(1,-3,4,-2),
b) v1=(1,1,1,1) and v2=(1,2,3,2).
All is well.

Kilode.. U wan kill person??

Alpha Maximus: ah!! You chance me for this solution abi! solved like a pro! I heard you wanted to become a participabt instead of a quiz master in the Math Competition. There's yet another screening test if you are interested. 1 more page for the thread to be a CENTENOPAGERIAN!!

I feel like performing the two ni ooo but it really pains me gan that I won't be doing either. Na work cause am cause na field work. But Sir Richiez has e-mailed me again to be his assistant score keeper and will give out my contributions whenever i'm available. Shey make I help you do the correction for that your question on mixtures?

Laplacian:
nice try bro....but ur solution is flawed

Hmmmm. . . How bro?

Ortarico:

I feel like performing the two ni ooo but it really pains me gan that I won't be doing either. Na work cause am cause na field work. But Sir Richiez has e-mailed me again to be his assistant score keeper and will give out my contributions whenever i'm available. Shey make I help you do the correction for that your question on mixtures?

...Not yet, I'm saving the question for harder rounds!! No one even attempted it!! They all ran to Richiez's question!!

Alpha Maximus: ...Not yet, I'm saving the question for harder rounds!! No one even attempted it!! They all ran to Richiez's question!!

That was even one of my mine! Everybodi ja 4 the evil question!

Ortarico:

Hmmm. . . If x is all the values satisfying the interval 0 theta 360 then;
sin2x + sinx = 1
2sinxcosx + sinx - 1 = 0
sinx(2cosx + 1) = 0
sinx = 0
x = arcsin(0)
x = 0, 180, 360

2cosx = -1
cosx = -1/2
x = arccos(-1/2)
x = 120, 240

pls recheck ur soln sire...
2sinxcosx +sinx -1=0
does not reduce to
sinx(2cosx+1)=0..on factorization because the -1 is ignored by that approach.
Also chk when x=0
=>sin0+sin0=1
which is nt true.....rechk bro while i wuk on mine
but for i think of a graphical approach where
sin2x=1 +sinx
and a table for sin2x and 1+sinx are obtaind 4rm a given range f values and plotd...just finking

rhydex 247: Here is my question.
1. Suppose G is an abelian group. Show dat any factor group G/H is also abelian.

2. Suppose v=(1,3,5,7). Find the projection of v onto W or, in other words, find w€W that minimizes //v-w//, where W is d subspance of R^4 spanned by.
a) u1=(1,1,1,1) and u2=(1,-3,4,-2),
b) v1=(1,1,1,1) and v2=(1,2,3,2).
All is well.

first, i'll show that if N is a normal subgroup of G, then G/N is abelian....now, let a, b€G, then
(aN)(bN)=(ab)N=(ba)N=(bN)(aN) ...hence G/N is abelian... let H be an arbitrary subgroup of G, now since every subgroup of an abelian group is normal, [suppose otherwise, then for a, a^-1€G
H=(a*a^-1)H=(aH)(a^-1H)=aHa^-1, so that H is normal afterall] then it implies that H is normal, so G/H is abelian...

2nioshine: pls recheck ur soln sire...
2sinxcosx +sinx -1=0
does not reduce to
sinx(2cosx+1)=0..on factorization because the -1 is ignored by that approach.
Also chk when x=0
=>sin0+sin0=1
which is nt true.....rechk bro while i wuk on mine
but for i think of a graphical approach where
sin2x=1 +sinx
and a table for sin2x and 1+sinx are obtaind 4rm a given range f values and plotd...just finking

Oops, Thanks a lot bro, that part was truly an error. I have modified my answer. I'll upload the new solution when chanced. Thanks!

Alpha Maximus: ...Not yet, I'm saving the question for harder rounds!! No one even attempted it!! They all ran to Richiez's question!!

Deal, thank you!

rhydex 247: Here is my question.
1. Suppose G is an abelian group. Show dat any factor group G/H is also abelian.

2. Suppose v=(1,3,5,7). Find the projection of v onto W or, in other words, find w€W that minimizes //v-w//, where W is d subspance of R^4 spanned by.
a) u1=(1,1,1,1) and u2=(1,-3,4,-2),
b) v1=(1,1,1,1) and v2=(1,2,3,2).
All is well.

let x, y€R then for each w€W...we have
w=xu1+yu2
=(x+y, x-3y, x+4y, x-2y)...so that
w-v
=(x+y-1, x-3y-3, x+4y-5, x-2y-7)...
Now define the norm of v-w to be....//w-v//=|w-v|=d...from calculus we know that if an abscissa optimizes the square of a function, then it also optimizes that function: proof y^2=f(x), then 2yy'=f'(x)...it follows that, from
d^2=(x+y-1)^2+(x-3y-3)^2+(x+4y-5)^2+(x-2y-7)^2, differentiatin partially wrt x & y and solvin gives d solution when their values are substituted in d vector eqn for w...

Laplacian:
let x, y€R then for each w€W...we have
w=xu1+yu2
=(x+y, x-3y, x+4y, x-2y)...so that
w-v
=(x+y-1, x-3y-3, x+4y-5, x-2y-7)...
Now define the norm of v-w to be....//w-v//=|w-v|=d...from calculus we know that if an abscissa optimizes the square of a function, then it also optimizes that function: proof y^2=f(x), then 2yy'=f'(x)...it follows that, from
d^2=(x+y-1)^2+(x-3y-3)^2+(x+4y-5)^2+(x-2y-7)^2, differentiatin partially wrt x & y and solvin gives d solution when their values are substituted in d vector eqn for w...

hmmmm. Bro u tried sha buh d major issue is d answer nd d steps. I will b glad if dat can b done.

the sum of the first two terms of a g.p is x and the sum of last two terms is y .If there are n terms.
Find common ratio in terms of x , y and n

...a two digit number is divisible by 4, if d unit digit is also divisible by 4, show that d tens digit MUST be even...

...a two digit number is divisble by 4 prove that d unit digit MUST be even...

benbuks: the sum of the first two terms of a g.p is x and the sum of last two terms is y .If there are n terms.
Find common ratio in terms of x , y and n

.the first two terms are a and ar,the last two terms are ar^(n-2)+ar^(n-1)...from the question a+ar=x...(i) and ar^(n-2)+ar^(n-1)=y...(ii).from (ii)factorize r^(n-2) to give r^(n-2){a+ar}=y...(iii).divide iii by 1 to give r^(n-2)=y/x...then r={y/x}^{1/(n-2)}

@Richiez, i will like to participate in the quiz. What are the requirements?

0.977777. . .
=x
express x in fraction

benbuks: 0.977777. . .
=x
express x in fraction

where ... Represents continuity to infinity.0.9+0.0777...then take 0.0777...and let's work on it.0.07...*10-0.07...=0.77...-0.07...then 0.07(10-1)=0.7 then 0.07=0.7/9 which is equal to 7/90 and don't forget we had 0.9+0.07... same as 9/10+7/90 which now equals to 44/45...i rest my case

Laplacian: ...sin2x+sinx=1...find x...

@ laplacian here is my solution.
sin2x+sinx=1.
Subtract 1 4rm bth sides. We av -1+sinx+sin2x=0.
Substitute y=tan(x/2). Then sinx=2y/y^2+1 and cosx=1-y^2/y^2+1.
-1+4y/(y^2+1)^2-4y^3/(y^2+1)^2+2y/y^2+1 =0
takin d lcm nd simplifyin we av
-y^4-2y^3-2y^2+6y-1=0.
-(y-1)(y^3+3y^2+5y-1)=0.
multiply thru by -1.
y-1=0 or y^3+3y^2+5y-1=0.
y=1. Recal dat y=tan(x/2).
tan(x/2)=1. x/2=tan^-1.
x/2=45. Finally x=90. For the y^3+3y^2+5y-1=0. I will leave dat to my fellow maths general. All is well. I'm off to MARINA.

benbuks: 0.977777. . .
=x
express x in fraction

Here goes...

x = 0.977777... (eqn 1).
Multiply eqn 1 by 10:
10x = 9.77777... (eqn 2)
Multiply eqn 1 by 100:
100x = 97.77777... (eqn 3)
eqn 3 - eqn 2 gives
100x - 10x = 97.77777... - 9.77777...
90x = 88
x = 44/45

^ 9c Try guys, bt they gat 2b anoda method....mayb 'series'

Calculusf(x):
.the first two terms are a and ar,the last two terms are ar^(n-2)+ar^(n-1)...from the question a+ar=x...(i) and ar^(n-2)+ar^(n-1)=y...(ii).from (ii)factorize r^(n-2) to give r^(n-2){a+ar}=y...(iii).divide iii by 1 to give r^(n-2)=y/x...then r={y/x}^{1/(n-2)}

...rectitudiously indomitable.