Humphrey77: state and prove LAGRANGE THEOREM ( ABSTRACT ALGEBRA)

hmmmm.
dis is my best course
here the soln goes.
langrange theorem states that for any finite group G, the order number of element of every sub group H of G divides the order of G. The theorem is named after joseph louis langrange.

now the prove.
this can be shown using the concepts of left cosets of H in G. the left cosets are the equivalence classes of a certain equivalence relation on G and therefore form a partition of G. Specifically, x and y in G are related if and only if there exists h in H such that x=yh . If we can show dat all cosets of H av d same number of elements, then each coset of H has precisely /H/ elements. We are den done since the order of H times the number of cosets is equal to the no of elements in G, thereby proving that the order of H divides the order of G. Now, if aH and bH are two left cosets of H. We can define a map. f:aH--->bH. by setting f(x)=ba^-1x. This map is bijective because its inverse is given by f^-1 y=ab^-1(y).

Alpha Maximus: *flies into Math Clinic clad in state-of-the-art Iron Man Suit Version Hyper Velocity* I have a confession and you gotta listen(in D'Banj's voice). My evil question posted above is not really a question at all! I just came up with a demonic-looking word problem which was not valid at all and decided to post it here to see who would claim to have a solution! I hope nobody's brain underwent hydrolysis in an attempt to solve my 'question'!! *increases Iron Man armour's strength to resist stones being thrown by Math Doctors in the house and uses uni-beam to blow up mountain thrown by who-ever suffered in an attempt to solve it* Cheers!!

Is that fair? Is it fair to post an invalid question? Don't you think people may treat your future (wp) questions with levity?

I suggest you take off your Iron Man's suit and prostrate and ask for forgiveness, especially from whoever attempted your 'question'.

How many integers between 1 and
1,000,000 contain the digit 5 at least
twice?

hardedeji1: How many integers between 1 and
1,000,000 contain the digit 5 at least
twice?

Here goes...

2-Digit Numbers: 1 way (i.e. 55).

3-Digit Numbers: 555, 55* (9 ways), 5*5 (9 ways), *55 (8 ways, we can't start with 0). Total: 27 ways.

4-Digit Numbers: Three cases.
Two 5's: 55** (81 ways), *5*5 (72 ways, we can't start with 0), *55* (72 ways), **55 (72 ways), 5*5* (81 ways), 5**5 (81 ways).

Three 5's: 555*(9 ways), 55*5 (9 ways), 5*55 (9 ways), *555 (8 ways). Total =

Four 5's: 5555 (1 way)

5-Digit Numbers
Two 5's: 55***, 5*5**, 5**5*, 5***5, *55**, *5*5*, *5**5, **55*, **5*5, ***55
Three 5's: 555**, 55*5*, 5*55*, *555*, *55*5, *5*55, **555, 55**5, 5*5*5, 5**55,
Four 5's: 5555*, 555*5, 55*55, 5*555, *5555
Five 5's: 55555 (1 way)

6-Digit Numbers
Two 5's: 55****, 5*5***, 5**5**, 5***5*, 5****5, *5*5**, *5**5*, *5***5, **55**, **5*5*, **5**5, ***55*, ***5*5, ****55, *55***, **55**, ***55*, ****55
Three 5's: 555***,
Four 5's: 5555**, 555*5*, 55*55*, 5*555*, *5555*, *555*5, *55*55, *5*555, **5555, 5**555, 55**55, 555**5
Five 5's: 55555*, 5555*5, 555*55, 55*555, 5*5555, *55555
Six 5's: 55555 (1 way)

Stll loading...

Wat r d criteria needed in statin d properties of a differential equation, ie how do I identify d order, degree, linearity and homogenity of a DE

Humphrey77: MY QUEEN GAVE ME THIS QUESTION YESTERDAY AND AS ME TO COMPLETE IT : I said to my self what am i going to do ? told her that am going to post it to my oga on top : complete these : 6,__,204__,__,25779. (hint they are multiple of 3) : HAPPY

The formula for the nth term of your sequence may be given by

x_n = (8426n²-33209n+24813)/₅.

It is easy to verify that:
x₁ = 6
x₃= 204
x₆=25779

and as such, we have

x₂= - ⁷⁹⁰¹/₅
x₄=²⁶⁷⁹³/⁵
x₅=⁶⁹⁴¹⁸/₅

Use these numbers to fill in the gaps you gave. There you have it, bro.

jackpot:
The formula for the nth term of your sequence may be given by

x_n = (8426n²-33209n+24813)/₅.

It is easy to verify that:
x₁ = 6
x₃= 204
x₆=25779

and as such, we have

x₂= - ⁷⁹⁰¹/₅
x₄=²⁶⁷⁹³/⁵
x₅=⁶⁹⁴¹⁸/₅

Use these numbers to fill in the gaps you gave. There you have it, bro.

Confirmed! But can you explain how you arrived at that formula?

@ ,MADAM jackpot the solution to the sequence ; 6,__,204,__,__,25779 - IS 6,39,204, 1029,5154, 25779.
THE RULE IS : muitiply the previous number by5 and add 9. HAPPY

doubleDx:

Her formula explains everything bruv!

APPLICATION
THE SEQUENCE 6,39,204,1029,5154,25779 ARE MULTIPLE OF 3 . :*HAPPY

rhydex 247:
hmmmm.
dis is my best course
here the soln goes.
langrange theorem states that for any finite group G, the order number of element of every sub group H of G divides the order of G. The theorem is named after joseph louis langrange.

now the prove.
this can be shown using the concepts of left cosets of H in G. the left cosets are the equivalence classes of a certain equivalence relation on G and therefore form a partition of G. Specifically, x and y in G are related if and only if there exists h in H such that x=yh . If we can show dat all cosets of H av d same number of elements, then each coset of H has precisely /H/ elements. We are den done since the order of H times the number of is equal to the no of elements in G, thereby proving that the order of H divides the order of G. Now, if aH and bH are two left cosets of H. We can define a map. f:aH--->bH. by setting f(x)=ba^-1x. This map is bijective because its inverse is given by f^-1 y=ab^-1(y).

GOOD

Humphrey77: @ ,MADAM jackpot the solution to the sequence ; 6,__,204,__,__,25779 - IS 6,39,204, 1029,5154, 25779.
THE RULE IS : muitiply the previous number by5 and add 9. HAPPY

Her formula explains everything bruv!

jackpot:
The formula for the nth term of your sequence may be given by

x_n = (8426n²-33209n+24813)/₅.

It is easy to verify that:
x₁ = 6
x₃= 204
x₆=25779

and as such, we have

x₂= - ⁷⁹⁰¹/₅
x₄=²⁶⁷⁹³/⁵
x₅=⁶⁹⁴¹⁸/₅

Use these numbers to fill in the gaps you gave. There you have it, bro.

Alpha Maximus: Confirmed! But can you explain how you arrived at that formula?

since d sequence is too scanty to admit a rule she approximtd
let
x_n=a+bn+cn²
substitut 4 each of x₁, x₃ and x₆
she obtained three equtns in which she solved simultaneously for a, b, and c...& i agree with her

doubleDx:

Her formula explains everything bruv!

WE HAVE 6,39,204,1029,5154,25779. MULTIPLE OF 3 ; JACKPOT FORMULA IS WRONG

rhydex 247:
hmmmm.
dis is my best course
here the soln goes.
langrange theorem states that for any finite group G, the order number of element of every sub group H of G divides the order of G. The theorem is named after joseph louis langrange.

now the prove.
this can be shown using the concepts of left cosets of H in G. the left cosets are the equivalence classes of a certain equivalence relation on G and therefore form a partition of G. Specifically, x and y in G are related if and only if there exists h in H such that x=yh . If we can show dat all cosets of H av d same number of elements, then each coset of H has precisely /H/ elements. We are den done since the order of H times the number of cosets is equal to the no of elements in G, thereby proving that the order of H divides the order of G. Now, if aH and bH are two left cosets of H. We can define a map. f:aH--->bH. by setting f(x)=ba^-1x. This map is bijective because its inverse is given by f^-1 y=ab^-1(y).

GREAT! WHAT ARE MONIC EQUATION?

jackpot:
The formula for the nth term of your sequence may be given by

x_n = (8426n²-33209n+24813)/₅.

It is easy to verify that:
x₁ = 6
x₃= 204
x₆=25779

and as such, we have

x₂= - ⁷⁹⁰¹/₅
x₄=²⁶⁷⁹³/⁵
x₅=⁶⁹⁴¹⁸/₅

Use these numbers to fill in the gaps you . There you have it, bro.

.NICE , (:THE SEQUENCE IS A MULTIPLE OF 3 WE HAVE THE SEQUENCE AS 6,39,204,1029,5154,25779. ( RULE MULTIPLY 5 TO THE PREVIOUS TERM AND ADD 9 , TO GET THE NEXT TERM @ ,MADAM JACKPOT YOUR FORMULA DID NOT SATISFY THE RULE THAT GOVERNS THE SEQUENCE) :HAPPY

WHAT ARE ALGEBRAIC NUMBERS? :*@HAPPY

WHAT ARE HAPPY AND SAD NUMBERS?

SLAMI

@ ,* MADAM JACKPOT I WAITED FOR YOUR SOLUTION TO THE PROBLEM 5,__ 1205,__ 271205.
WELL ALL IS WELL EVEN IN THE WELL . ( :hint multiply 15 to the previous +5 to get the next term) ! HAPPY DAY TO MY QUEEN SALMI!

lufemos: Wat r d criteria needed in statin d properties of a differential equation, ie how do I identify d order, degree, linearity and homogenity of a DE

hmmm.
for the order of differential eqn: is d order of d highest differential coefficient (derivative) contained in d eqn. e.g. d^2(y)/dx^2+2dy/dx+ydx=sinx is an example of 2nd order.

for the degree of differential eqn: is d power to which the highest order differential coefficient is raised when d eqn is rationalised i.e fractional power is removed. e.g (dy/dx)^3+y^2=x.
remaining soln loading by A.K.A SERIES.

Humphrey77: .NICE , (:THE SEQUENCE IS A MULTIPLE OF 3 WE HAVE THE SEQUENCE AS 6,39,204,1024,5154,25779. ( RULE MULTIPLY 5 TO THE PREVIOUS TERM AND ADD 9 , TO GET THE NEXT TERM @ ,MADAM JACKPOT YOUR FORMULA DID NOT SATISFY THE RULE THAT GOVERNS THE SEQUENCE) :HAPPY

Story!!!

Remember when I told you earlier that there are many answers to this question?

What rule-satisfication are you talking about?

I hope you are not referring to the discombobulated crap of a hint you supposedly gave?

To the original question, my answer is on point.

Are you treasuring your answer? Oh well, I treasure my answer too as better.

Humphrey77: GREAT! WHAT ARE MONIC EQUATION?

Do u mean harmonic equation?

jackpot: Story!!!

Remember when I told you earlier that there are many answers to this question?

What rule-satisfication are you talking about?

I hope you are not referring to the discombobulated crap of a hint you supposedly gave?

To the original question, my answer is on point.

Are you treasuring your answer? Oh well, I treasure my answer too as better.

jackpot: Story!!!

Remember when I told you earlier that there are many answers to this question?

What rule-satisfication are you talking about?

I hope you are not referring to the discombobulated crap of a hint you supposedly ga

To the original question, my answer is on point.

Are you treasuring your answer? Oh well, I treasure my answer too as better.

we know by defination a sequence must have a common term (*chain) .and to the question what kind of sequence do you produce. Alright give me the rules that governs yr results

rhydex 247:

Do u mean harmonic equation?

MONIC EQUATION (*ABSTRACT ALGEBRA)

Humphrey77: we know by defination a sequence must have a common term (*chain) .and to the question what kind of sequence do you produce. Alright give me the rules that governs yr results

Before Jackpot gives that, can you also provide the steps u used in getting your results?

echibuzor:
Before Jackpot gives that, can you also provide the steps u used in getting your results?

i support u sir

A MONIC EQUATION IS TYPE OF EQUATION THAT EXIST WHEN THE leading coefficient of a polynomial is one. example x raise to power 4 + (xy)raise to power 3 + x raise to power 2 equal to zero.

what are HAPPY AND SAD NUMBERS

Humphrey77: what are HAPPY AND SAD NUMBERS

A happy number is defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers).
Culled From Wikipedia

For example, 19 is happy, as the associated sequence is:

12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1.
The 143 happy numbers up to 1,000 are:

1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338, 356, 362, 365, 367, 368, 376, 379, 383, 386, 391, 392, 397, 404, 409, 440, 446, 464, 469, 478, 487, 490, 496, 536, 556, 563, 565, 566, 608, 617, 622, 623, 632, 635, 637, 638, 644, 649, 653, 655, 656, 665, 671, 673, 680, 683, 694, 700, 709, 716, 736, 739, 748, 761, 763, 784, 790, 793, 802, 806, 818, 820, 833, 836, 847, 860, 863, 874, 881, 888, 899, 901, 904, 907, 910, 912, 913, 921, 923, 931, 932, 937, 940, 946, 964, 970, 973, 989, 998, 1000
Culled From Wikipedia