SUPER-FUN-HAPPY-MATHS-TIME

[zzdfa]

=  (because as . becomes 1 because x^2 -> 0 alot faster than 3x->0)


=        (because x^2->0 alot faster than x->0)                    

remember doing derivatives by first principles? let .



but we also know that , so .  

[taiga]

Idk for 0.9 recurring  = 1

I would have just said

1/3 + 1/3 + 1/3 = 1

therefore
0.3333 + 0.3333 + 0.3333 = 1

[Martoman]

hey guys

I know its been answered before but not my way.

Q7)



Let

So that

Now subbing in:



We know from u that

Meaning =

Cracking out the partial fractions in terms of u tells us that in the form =

Changing terminals and combining all our info:

Crunching out to

[golden]

Maths:

13.) Show that .
(Source: Damo17)

0.9999.... = 0.9 reoccurring (9).
0.9 reoccurring (9) = 0.9 + 0.09 + 0.009 ...
0.9 x 1/10 = 0.09
0.09 x 1/10 = 0.009 (etc.)
Therefore r = 1/10.

S = a(1-r^n)/(1-r)
As n approaches infinity, r^n approaches 0.
S = a(1)/(1-r)
S = a/(1-r)
a = 'first number', i.e. 0.9
r = 1/10

S = 0.9/(1-1/10)
S = 0.9/0.9
S = 1

As required.

[golden]

May I ask to what equivalence (in terms of what year in VCE or perhaps beyond) are the questions?

[onur369]

May I ask to what equivalence (in terms of what year in VCE or perhaps beyond) are the questions?

it looks like further maths to me, number sequences

[golden]

15.) Neobeo is walking around in Luna Park, and notices an alleyway called 'Infinite Ice Cream'.  Neobeo notes that the 'Infinite Ice-Cream' appears to possess an infinitely large number of people selling ice-cream.  Upon walking outside any particular shop, Neobeo feels a huge compulsion to purchase an ice-cream.  For every shop that Neobeo visits, he is 37\% less likely to purchase an ice-cream then at the previous shop.  After purchasing an ice-cream, Neobeo leaves Luna Park.  What is the probability of Neobeo purchasing an ice-cream at the second shop in 'Infinite Ice Cream'?

I'm not too sure about this question. I got 23.31%.
Pr(2nd) = 0.63y
Pr(added totals) = 100y/37
0.63y/(100y/37)
0.2331

[golden]

I get the feeling that some of the other questions aren't Further Mathematics equivalent.

[onur369]

I get the feeling that some of the other questions aren't Further Mathematics equivalent.

I did general maths(standard) in year 11 and the difficulty is the same lol.

[golden]

With regards to these questions? http://vce.atarnotes.com/forum/index.php/topic,12907.0.html

[dcc]

15.) Neobeo is walking around in Luna Park, and notices an alleyway called 'Infinite Ice Cream'.  Neobeo notes that the 'Infinite Ice-Cream' appears to possess an infinitely large number of people selling ice-cream.  Upon walking outside any particular shop, Neobeo feels a huge compulsion to purchase an ice-cream.  For every shop that Neobeo visits, he is 37\% less likely to purchase an ice-cream then at the previous shop.  After purchasing an ice-cream, Neobeo leaves Luna Park.  What is the probability of Neobeo purchasing an ice-cream at the second shop in 'Infinite Ice Cream'?

I'm not too sure about this question. I got 23.31%.
Pr(2nd) = 0.63y
Pr(added totals) = 100y/37
0.63y/(100y/37)
0.2331

I'm not entirely sure what you've done here, but the answer is correct.

[brightsky]

15.) Neobeo is walking around in Luna Park, and notices an alleyway called 'Infinite Ice Cream'.  Neobeo notes that the 'Infinite Ice-Cream' appears to possess an infinitely large number of people selling ice-cream.  Upon walking outside any particular shop, Neobeo feels a huge compulsion to purchase an ice-cream.  For every shop that Neobeo visits, he is 37\% less likely to purchase an ice-cream then at the previous shop.  After purchasing an ice-cream, Neobeo leaves Luna Park.  What is the probability of Neobeo purchasing an ice-cream at the second shop in 'Infinite Ice Cream'?

I'm not too sure about this question. I got 23.31%.
Pr(2nd) = 0.63y
Pr(added totals) = 100y/37
0.63y/(100y/37)
0.2331

I'm not entirely sure what you've done here, but the answer is correct.

dcc, would you be able to post some new questions?

[dcc]

How about trying 17 or 18?

[dcc]

17.) Find

[kamil9876]

Consider a network of (finitely many) cities such that between every city there exists a road, and each road is strictly one way (you can travel in one direction ONLY). Show that there exists a path that visits each city exactly once. (A directed Hamiltonian path)