LogoDWhiz: 39468

Laplacian:
hey, wat symbol is between f(x)f(y) and f(xy)?
Wats d symbol between f(x + y) and f(x) + f(y)?
Write this in words f : Q>0 ! R

Laplacian:
?

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:
@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 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: 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.

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 look like?

SMH.

Laplacian:
guy am stil an amatur ooo, (not yet a topologist)..
Let a<m<A and b<n<B denot d two open sets...
suppos, on d contrary, dat their intersection, p, is a closed set...
Then we can find x and y such dat
x<=p<=y, where a, b<x and y<A, B
now suppose, without loss of generality, dat A<B.... we can always find d numbers z such dat
y<z<A, since z<A<B, z should b in their , but y<z a contradiction, showing dat z is not in their intersection...hence our supposition dat p is a set is untenable....and d result follows

jackpot: If you're not cleared as to how the answer above is gotten, note that for any natural number n,

3⁴ⁿ=(3⁴)ⁿ = 81ⁿ = 10M+1, for some integer M.

Similarly,
3⁴ⁿ⁺¹=3(3⁴ⁿ)=30M+3
3⁴ⁿ⁺²=3²(3⁴ⁿ)=90M+9
3⁴ⁿ⁺³=3³(3⁴ⁿ)=270M+27.

Observe that 3¹⁹⁹⁸ can be written as 3⁴ⁿ⁺², where n=499.

Now, for some integer M,

3¹⁹⁹⁸=3⁴ⁿ⁺²=90M+9=18(5)M+(5+4)=5(18M+1)+4.

From, the last equation, it is obvious why 3 raised to power 1998 leaves a remainder of 4 when divided by 5.

Gracias.

jackpot: Hi Sir Laplacian

how can a set be less than or equal to a point x?

Laplacian:
solvin d differential eqn u cannot get y=1,
suppose y=1, indeed y'=0, y"=0,
substitute into ur differential eqn,
4y"4-3y"2-2y+1=0 to obtain

0-0-2+1=0
or
-1=0

hw did u solve ur differential eqn?

Humphrey77: if ,m and n are open set than show that the intersection is also open
































@ laplacian