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

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

Calculusf(x):
.hmmm,here is my own approach to it...sin2x+sinx=1...2sinxcosx+sinx=1...2sinx.sqrt(1-sin^2x)+sinx=1...{let sinx be a...(i)}...2a.sqrt(1-a^2)+a=1...2a.sqrt(1-a^2)=1-a...square both sides...4a^2(1-a^2)=1-2a+a^2...4a^2-4a^4=1-2a+a^2...4a^4-3a^2-2a+1=0,it's obvious that a=1(one of the four roots) then we divide 4a^4-3a^2-2a+1 by a-1 to give 4a^3+4a^2+a-1=0...then transform the equation to reduced cubic equation to get by representing a as y-1/3...(ii) to give y^3-y/12-7/27...you can use any method for solving cubic polynomial to do it but for me,i used tartaglia's method for finding real root of a cubic equation and got y as 0.68114(approximated),don't forget that a=y-1/3 and by substituting that a=0.34781(the first root of the cubic polynomial)...to get the other two roots...from relationship between the co-efficients and roots of a polynomial...a1+a2+a3=-1 a1.a2.a3=0.25(from the polynomial 4a^3+4a^2+a-1=0)...let a1 be 0.34781,by solving a2+a3=-1.34781 and a2.a3=0.7188 and by solving the simultaneous equation a={-1.34781±j1.0287}/2...with all we have done so far,the two real roots got were a=1 and a=0.34781,don't forget that sinx=a...let a be 1,then sinx=1 and x=90 and if a=0.34781,sinx=0.34781 and x=20.35...i rest my case

Laplacian:
...the indomitable f(x)...nice wrk...

Calculusf(x):
.hmmm,here is my own approach to it...sin2x+sinx=1...2sinxcosx+sinx=1...2sinx.sqrt(1-sin^2x)+sinx=1...{let sinx be a...(i)}...2a.sqrt(1-a^2)+a=1...2a.sqrt(1-a^2)=1-a...square both sides...4a^2(1-a^2)=1-2a+a^2...4a^2-4a^4=1-2a+a^2...4a^4-3a^2-2a+1=0,it's obvious that a=1(one of the four roots) then we divide 4a^4-3a^2-2a+1 by a-1 to give 4a^3+4a^2+a-1=0...then transform the equation to reduced cubic equation to get by representing a as y-1/3...(ii) to give y^3-y/12-7/27...you can use any method for solving cubic polynomial to do it but for me,i used tartaglia's method for finding real root of a cubic equation and got y as 0.68114(approximated),don't forget that a=y-1/3 and by substituting that a=0.34781(the first root of the cubic polynomial)...to get the other two roots...from relationship between the co-efficients and roots of a polynomial...a1+a2+a3=-1 a1.a2.a3=0.25(from the polynomial 4a^3+4a^2+a-1=0)...let a1 be 0.34781,by solving a2+a3=-1.34781 and a2.a3=0.7188 and by solving the simultaneous equation a={-1.34781±j1.0287}/2...with all we have done so far,the two real roots got were a=1 and a=0.34781,don't forget that sinx=a...let a be 1,then sinx=1 and x=90 and if a=0.34781,sinx=0.34781 and x=20.35...i rest my case

jackpot: Hi all, please solve this.

If three fair dice are rolled simultaneously ONCE, what is the probability of getting:
(i) a sum of 11?
(ii) a sum of 12?



Show FULL working

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

jackpot: Hi all, please solve this.

If three fair dice are rolled simultaneously ONCE, what is the probability of getting:
(i) a sum of 11?
(ii) a sum of 12?



Show FULL working

Laplacian: ...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...

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

smurfy:

Okay.

Here goes...

0.977777... =
0.9 + (0.07 + 0.007 + ...) = 9/10 + (0.07 + 0.007 + ...)
Using sum to infinity for expression in the bracket: a = 0.07, r = 1/10.
Sum to infinity = a/(1-r)
= 0.07/(1-1/10)
= 7/100 * 10/9
= 7/90
So we have 9/10 + 7/90
= 880/900
= 44/45

Alpha Maximus: Finally!!! The clinic is a CENTENOPAGERIAN!!! *pops mathematical bottle of champagne* I wanna give a shoutout to Sivasubramaniam, the author of SS Further Math textbooks and Co-author Tuttuh Adegun,Leonhard Euler(who discovered the Euler's constant, is the Father of Mathematics) , Euclid(the Prince Of Math) , Pythagoras Of Samos(triangles would have been a pain in the calculator if not for this guy), Rene Descartes for his beautiful work which gave birth to Cartesian Planes, Blaise Pascal( a true prodigy, made his own formulae at 20 or younger), Isaac Newton( laid the foundation for Albert Einstein's works and published the single most important document in Mathematics- Principia de Mathematica), Pierre de Fermat(constructed Fermat's last conjecture:stating that no 3 positive integers a, b and c can satisfy a^n+b^n=c^n for positive integer values of n which are equal to or greater than 3, which was disproven by Andrew Wiles who worked on this for 7 years!!), Andrew Wiles, British mathematician who solved Fermat's notorious Conjecture and rejected the 1 million dollar prize money, Chike Obi of Nigeria who showed that whites were not the only capable problem-solvers, Grace Alele, pioneer of Nigerian female mathematicians, Albert Einstein( E=mc^2 says it all), the author's of new general mathematics for preparing the Nigerian youth for WAEC, KA Stroud for his insightful Advanced Engineering Math textbook and all other great mathematician whom I have failed to mention. We can't do without math in life! Even space is made up of numbers! Mathematics is the very back-bone of all sciences, the blood that pumps through the veins of engineers! Indeed what would we be without math? Merry solving and cheers to the Nairaland Mathematics Clinic on its 100 page anniversary *moonwalks on stage*

smurfy:

Here goes...

(a) Sample space = 6^3 = 216

Set of combinations which gives a sum of 11 include:
164, 146, 461, 416, 641, 614, 155, 515, 551, 245, 254, 425, 452, 524, 542, 236, 263, 326, 362, 623, 632, 344, 434, 443, 335, 353, 533.

That's 27 ways of getting the sum 11. So answer to question (a) is 27/216 = 3/24

(b) Set of combination which gives the sum 12 include:
156, 165, 516, 561, 615, 651, 246, 264, 426, 462, 624, 642, 255, 525, 552, 336, 363, 633, 345, 354, 435, 453, 534, 543, 444.

That's 25 ways of getting the sum of 12. That gives 25/216.

jackpot: Nice!!!

Cashio: And this thread just made a century of pages!!!
Pls if x is a positive integer divisible by 3 but less than 100,what are the possible square roots of x

smurfy:

Really? I thought my method was watery and was expecting some rebukes from thee followed by a grandiose way of solving it.

Is there another method?

Alpha Maximus: Finally!!! The clinic is a CENTENOPAGERIAN!!! *pops mathematical bottle of champagne* I wanna give a shoutout to Sivasubramaniam, the author of SS Further Math textbooks and Co-author Tuttuh Adegun,Leonhard Euler(who discovered the Euler's constant, is the Father of Mathematics) , Euclid(the Prince Of Math) , Pythagoras Of Samos(triangles would have been a pain in the calculator if not for this guy), Rene Descartes for his beautiful work which gave birth to Cartesian Planes, Blaise Pascal( a true prodigy, made his own formulae at 20 or younger), Isaac Newton( laid the foundation for Albert Einstein's works and published the single most important document in Mathematics- Principia de Mathematica), Pierre de Fermat(constructed Fermat's last conjecture:stating that no 3 positive integers a, b and c can satisfy a^n+b^n=c^n for positive integer values of n which are equal to or greater than 3, which was disproven by Andrew Wiles who worked on this for 7 years!!), Andrew Wiles, British mathematician who solved Fermat's notorious Conjecture and rejected the 1 million dollar prize money, Chike Obi of Nigeria who showed that whites were not the only capable problem-solvers, Grace Alele, pioneer of Nigerian female mathematicians, Albert Einstein( E=mc^2 says it all), the author's of new general mathematics for preparing the Nigerian youth for WAEC, KA Stroud for his insightful Advanced Engineering Math textbook and all other great mathematician whom I have failed to mention. We can't do without math in life! Even space is made up of numbers! Mathematics is the very back-bone of all sciences, the blood that pumps through the veins of engineers! Indeed what would we be without math? Merry solving and cheers to the Nairaland Mathematics Clinic on its 100 page anniversary *moonwalks on stage*

jackpot: well, you could have used permutations anyway.

Like arrangement of 6,5, 1 is 3P3=6
then, do the same for all and add.