jackpot: This guy, e be like say u snuff a little alcohol, bah? Why are u quoting people and replying nonsense? I drafted a solution that will convince even non-mathematicians on how the answer is gotten. I am not a stereotyped mathematician.

A mere 5 seconds look at the question, I pictured the answer. Integral powers of 3 ends with the cycle of digits {3, 9, 7, 1}.



1998Mod4=2

and 3 raised to power of the residue class of 2 yields 9.

and 9Mod5=4.

Maybe thats how you want the solution to look like?

SMH.

Laplacian:
@Humphry, i suggest u & Benbuks should always provide d incorrect steps in any wrong solutions like jackpot alwaz does and myselt too, not 2 simply dismis it & leave d solver in doubt&confusion...even if my solution does not cover d general case, it has @ least settled d case pointed out by jackpot abov....and dat should worth some apprreciation...
u 'r modest lady jackpot & i like ur styl of criticism....i 've not really wrked on provin d general case though, but i 'll giv it a second thought now that u hav underlined it...but i know it will hav 2 incoperate d NORM and follow a similar chain of reasonin as abov....by d way, wat's preventin u from supplying a proof? Or 're u just watchin 4rm d sidelines just 2 handpick my errors?....
@ALL, am not here 2 enter into competition wit anybdy, 4 those dat copy questions (witout havin wit them) from textbooks & paste here.....i'll only attempt questions only by individuals who hav difficulties wit them & are genuinely desperate 4 their solution...

Laplacian:
@Humphry, i suggest u & Benbuks should always provide d incorrect steps in any wrong solutions like jackpot alwaz does and myselt too, not 2 simply dismis it & leave d solver in doubt&confusion...even if my solution does not cover d general case, it has @ least settled d case pointed out by jackpot abov....and dat should worth some apprreciation...
u 'r modest lady jackpot & i like ur styl of criticism....i 've not really wrked on provin d general case though, but i 'll giv it a second thought now that u hav underlined it...but i know it will hav 2 incoperate d NORM and follow a similar chain of reasonin as abov....by d , wat's preventin u from supplying a proof? Or 're u just watchin 4rm d sidelines just 2 handpick my ?....
@ALL, am not here 2 enter into competition with a anybdy, 4 those dat copy questions (witout havin wit them) from textbooks & paste here.....i'll only attempt questions only by individuals who hav difficulties wit them & are genuinely desperate 4 their solution...

Laplacian:
@Humphry, i suggest u & Benbuks should always provide d incorrect steps in any wrong solutions like jackpot alwaz does and myselt too, not 2 simply dismis it & leave d solver in doubt&confusion...even if my solution does not cover d general case, it has @ least settled d case pointed out by jackpot abov....and dat should worth some apprreciation...
u 'r modest lady jackpot & i like ur styl of criticism....i 've not really wrked on provin d general case though, but i 'll giv it a second thought now that u hav underlined it...but i know it will hav 2 incoperate d NORM and follow a similar chain of reasonin as abov....by d way, wat's preventin u from supplying a proof? Or 're u just watchin 4rm d sidelines just 2 handpick my errors?....
@ALL, am not here 2 enter into competition wit anybdy, 4 those dat copy questions (witout havin challenges wit them) from textbooks & paste here.....i'll only attempt questions only by individuals who hav difficulties wit them & are genuinely desperate 4 their solution...

jackpot: I will provide a lazy solution to the problem sha.

A set is open if none of its points are boundary points.

Now, let P and Q be open sets. Then boundary(P) lies outside P and boundary(Q) lies outside Q.

Now, P n Q is a subset of P. P n Q is also a subset of Q. This means that boundary(P) and boundary(Q) lies outside P n Q.

BOUNDARY(P n Q) IS A SUBSET OF [BOUNDARY(P) u BOUNDARY(Q)]. Infact if x € boundary(P n Q), then either x € P or x € Q (BUT NOT BOTH AT THE SAME TIME) since P and Q are open sets.
Thus, boundary(PnQ) lies outside PnQ.

Hence, PnQ is open.


Feel free to critize this solution, folks.

Humphrey77: my love @(*jackpot) please joke with this;:prove that a conical tent of a given capacity will require the least amount of canvas when the height is square root of 2 times the radius of the base. (:hint: let the tent be a cone of semi-vertical angle )

Laplacian:
?

benbuks: I'v seen sine rule and cosine rule...but what about tangent rule..? Does it exist?..if yes am curious to see the proof please....if no why.?....am here with 1 am nt sure if its tangent rule...my generals ..am waitin

smurfy:

Haha! Tan rule? It exists nah.

tan rule = sine rule/cosine rule

jackpot: @Laplacian and Humphrey,

I said criticize, not to type question mark and to reply "GOOD".

Well, if you can draw pictorially two open sets(remember to use dotted lines for the edges), then you will understand this proof.

Fetus: Halo peeps..kindly solve dis showin d workins....(1) find the equation of the tangent and Normal @ any point on the parabola x=6t, y=3t^2.....(2)

Humphrey77: if 3+5 qual 8 prove that 1+1 equal 2

Humphrey77: sin2x+sinx is equal to 1 we know that sin2x is equal to 2sinxcosx. clearly; we have 2sinxcosx +sinx equal to 1 . so let sinx equal to y; by subtitution into

sin2x + sinx equal to 1 we obtain the equation: 4y"4-3y"2-2y+1 equal to zero ; by solving for y we obtain y equal to 1; clearly recall that sinx is equal to y so we have x eq
ual to arcsin(1) we have x equal to 90 so x is equal to 90

Laplacian:
?

BOUNDARY(P n Q) IS A SUBSET OF [BOUNDARY(P) u BOUNDARY(Q)]z....u didnt back up d above assertion in ur proof and its a vital part of d proof...a more logical consequence of ur explanation should b;
BOUNDARY(P n Q) IS A SUBSET OF [(P) u (Q)]...bcuz since boundary(P) and boundary(Q) lies outside P n Q, it follows directly dat boundary PnQ lies in P u Q

again; (BUT NOT BOTH AT THE SAME TIME)...OBVIOUSLY does not follow from d fact dat P & Q are open: as an illustration, supposin Q lies wholly in P, then x€ boundary of both P and Q....which contradicts ur assertion...

benbuks: Am working as a computer operator in a company,my manager general, jackpot ask me to creat a 5-digit password for one our agents, such that
1. the square root of the first is the second
2. The second is 5 more than the third
3.the third and the forth are consecutive even and their sum is 10
4. The sum of the whole digits is 30

if i dont creat the right password i might lose my job, u kw my madam, na no nonsense woman o abeg help me create this password...

smurfy:

Ha! This is crazy!

My advice? Resign honourably. She'd still sack you anyway.