Maths- Gym for Brainiacs

Ganso wrote:what are we supposed to do on that question?

kiranr wrote:Well, i did not do it using a circle. I just got two formations of moves that keep repeating when the triangle is moving along the side of the square and three formations that keep repeating when the triangle is moving from one side to the adjacent line. I got the numbers of each moves. Along the side, the two sets of moves are 6.6 and 2.5 and from side to side, the three sets of moves are 2.33, 2 and 0.76. Then i just added it up for all the three rounds.

In the first round it moves 29.3 +7.09. In the third round, 29.3 + 5.52 and the second round 18.2 + 7.42. The number before the plus for the movement along the sides and the number after the plus for movement from side to side.

The total comes out to 96.5.

Immortal Babun wrote:You both solved the question, kiranr and spanky

Next question

Disappearing Squares!

topic: goemetry
difficulty: medium
requirements: last year of high school




I'm lazy to explain, see the picture above. A square area is divided into 9 smaller square units. All of the small squares possess identical area. Now, I remove the one in the middle( see the white part in the pic above). Afterwards, I divide the small squares into 9 smaller squares again and remove the middle part again. Repeat...( see the pic ).

Questions:

1. How much area of the initial square will remain ( black area) if we repeat the process 10 times?
2. How much area of the initial square will remain ( black area) if we repeat the process infinite numbers of times?
3. How long are the boders of the removed areas for each step ( white area)? Calculate the version for infinite numbers of removals as well.


This whole question is an appetizer to the real one which I'll post after

kiranr wrote:For Babun's question...

Assume the side is 1.

1) First round => Black Area = 8/9. Second round => 7*8/81

Tenth round => (7 * 8^9)/(3^20) is the remaining black area.

2) Should be approximately 0?

3) For the nth round the side will be 1/(3^n) where n = 1,2,3,..,infinity.

spanky489 wrote:

kiranr wrote:For Babun's question...

Assume the side is 1.

1) First round => Black Area = 8/9. Second round => 7*8/81

Tenth round => (7 * 8^9)/(3^20) is the remaining black area.

2) Should be approximately 0?

3) For the nth round the side will be 1/(3^n) where n = 1,2,3,..,infinity.

and i assumed the first round was when the whole area is black

kiranr wrote:
He is asking for the borders of each white square after every step right?

Ganso wrote:y u no ask just the area of the white squares? Im too lazy for that.I want to post this question i was answering yesterday before i leave,see if you guys can pull it off

topic: sets(i think thats how its called in english)
difficulty: easy/medium
requirements: high school(not American high school.legit high schools)


16 – About the sets
A = {x ∈ N/| 5x – 1|> 8} and

B = {x ∈ Z/x²+x-6≤0}
which options are correct
01) A ∩ B = A
02) –1 ∈ (B – A)
04) {0, 1, 2} ⊂ A
08) A ∩ B is a unitary set(only one element on the set in case thats not how its called in english)
16) {–2, –1, 0} ⊂ B

kiranr wrote:Spanky, I am not a good programmer. I just know the stuff.

area(i+1)=area(i)-8.^(i-1)*a(i+1).^2

Aren't you calculating the white area in this as 8^(i-1) * a(i+1)^2 is the black area right?

kiranr wrote:

Ganso wrote:y u no ask just the area of the white squares? Im too lazy for that.I want to post this question i was answering yesterday before i leave,see if you guys can pull it off

topic: sets(i think thats how its called in english)
difficulty: easy/medium
requirements: high school(not American high school.legit high schools)


16 – About the sets
A = {x ∈ N/| 5x – 1|> 8} and

B = {x ∈ Z/x²+x-6≤0}
which options are correct
01) A ∩ B = A
02) –1 ∈ (B – A)
04) {0, 1, 2} ⊂ A
08) A ∩ B is a unitary set(only one element on the set in case thats not how its called in english)
16) {–2, –1, 0} ⊂ B

Well, i forgot the terms.. What is Z?

and what is the C symbol?

Ganso wrote:
Z are integers, ...-1,0,1.....N are naturals 0,1,2,3....

here is a useful page if you dont remember

http://www.rapidtables.com/math/symbols/Set_Symbols.htm

Ill give you set A,it is made up of every x>2

spanky489 wrote:ok in that case i get 30.79% for the first one. 2nd stays unchanged. waiting for babun until i start the 3rd.

kiranr wrote:For Babun's question...

Assume the side is 1.

1) First round => Black Area = 7/9. Second round => 7*8/81

Tenth round => (7 * 8^9)/(3^20) is the remaining black area.

2) Should be approximately 0?

3) For the nth round the side will be 1/(3^n) where n = 1,2,3,..,infinity.

Ganso wrote:y u no ask just the area of the white squares? Im too lazy for that.I want to post this question i was answering yesterday before i leave,see if you guys can pull it off

topic: sets(i think thats how its called in english)
difficulty: easy/medium
requirements: high school(not American high school.legit high schools)


16 – About the sets
A = {x ∈ N/| 5x – 1|> 8} and

B = {x ∈ Z/x²+x-6≤0}
which options are correct
01) A ∩ B = A
02) –1 ∈ (B – A)
04) {0, 1, 2} ⊂ A
08) A ∩ B is a unitary set(only one element on the set in case thats not how its called in english)
16) {–2, –1, 0} ⊂ B

Now to the questions:

01) A ∩ B={ } or nothingness as element , the only element they've got in common(unitary set). Obviously A is infinitly greater than 3 ( all x>2) so this option is wrong.

02) B-A= {-3, -2, -1, 0, 1, 2} . As you see –1 ∈ (B – A) -> correct.

04) A={ 3, 4, 5, ....., n} with n element from N. {0, 1, 2} don't belong to A.

08) Correct, see my solution in 01).

16) {–2, –1, 0} ⊂ {-3, -2, -1, 0, 1, 2}=B which is correct.

Ganso wrote:

Are you guys majoring in engineering or something related to math? its not easy to solve that while not being in high school

Immortal Babun wrote:

Ganso wrote:

Are you guys majoring in engineering or something related to math? its not easy to solve that while not being in high school

me-> majouring in maths
spanky-> chemistry+engineering combo
kiranr-> seems like ecomonical mathetmatician

I hate it how kids learn maths in school from the very start. Elementary teachers are dumb ( most of them) so they dumb down kids until they reach high school and then they learn everything anew with crippled knowledge
For example, maths without sets don't make sense at all. You see questions like these in textbooks:

6= x-2 , find x.

The question is unsolvable until x is defined. Does x bleong to natural, real or integers? For example, if x is element of A={9, 10} then the question is unsolvable
Sets should be taught as the first subject in any school :lol!:

kiranr wrote:

Immortal Babun wrote:

Ganso wrote:

Are you guys majoring in engineering or something related to math? its not easy to solve that while not being in high school

me-> majouring in maths
spanky-> chemistry+engineering combo
kiranr-> seems like ecomonical mathetmatician

I hate it how kids learn maths in school from the very start. Elementary teachers are dumb ( most of them) so they dumb down kids until they reach high school and then they learn everything anew with crippled knowledge
For example, maths without sets don't make sense at all. You see questions like these in textbooks:

6= x-2 , find x.

The question is unsolvable until x is defined. Does x bleong to natural, real or integers? For example, if x is element of A={9, 10} then the question is unsolvable
Sets should be taught as the first subject in any school :lol!:

I am a Mechanical engineer, now working in finance. I am 27 and forgotten most of my math concepts except the ones i use, like probability and statistics.