Math Community Quiz

[thepenguin77]

I just solved this so it is possible. I couldn't do the final collision step by hand because it had both an X in a power as well as an X, so I just did an intersect. But good luck to all.

Remember: 1 + x^1 + x^2 ... x^n == (1-x^(n+1))/(1-x)

[nemo]

i am way too lazy to solve it.. sorry

[ruler501]

I should have it by morning I couldn't work on it today had UIL
I'll just edit the answer into the post if noone else has answered it by then
Its number 1 on this comic right:

[thepenguin77]

That's the one.

[aeTIos]

haha nice comic

[ruler501]

I'm not going to have time to work on this... sorry I'd love to solve just have lots of homework and have to go to clubs

EDIT: The problem does not give us enough information there are multiple ways you could solve this. Ask another question Its been nearly 4 days

[thepenguin77]

Sorry, forgot about this. I'm out of questions. I'm in Colorado, so I accidentally left my work at home. But the answer was like 6.9 something.

First one to ask a question gets it.

[ruler501]

what is the fifth decimal place of 10 when converted to base phi^2
If I don't figure it out before you just show me proof and I'll have to believe it

I will be solving this tomorrow so please give me proof if you post before then

[Builderboy]

seems a bit like the last one?  Either way I can't solve this one either

[nemo]

phi^2 == 2.61803399
10 in binary is 1010 so it should be close to that. anyway.
phi^2 ^ -5 = 0.00813061876
phi^2 ^ -4 = 0.0212862363
phi^2 ^ -3 = 0.05572809
phi^2 ^ -2 = 0.145898034
phi^2 ^ -1 = 0.381966011
phi^2 ^ 0 = 1
phi^2 ^ 1 = 2.61803399
phi^2 ^ 2 = 6.85410197
phi^2 ^ 3 = 17.9442719
10 / 6.85410197 = 1.45898034, mod = 3.14589803 (that is eerily similar to pi..) 1
3.14589803 / 2.61803399 = 1.20162612, mod = .527864045                             1
.52786404 / 1 = .52786404, mod = .527864045                                               0.
.527864045 / .381966011 = 1.38196601, mod = .145898034                             1
.145898034 / .145898034 = 1, mod = 0                                                          1
0 /.... ok etc.
110.11 is 10 in the phi^2 base. there really isn't a 5th digit after the decimal place, it's assumed to be a 0.

gosh all those decimals look really bad and then i come up with the answer 110.11 which looks harmless..

[ruler501]

That looks good so you can have it. Technically it would have one since it is an irrational number but I'll except just 2 digits because it might take alot of digits to make it to 5 digits

[nemo]

i'm pretty sure it's 110.11, a terminating decimal.

i'll have a new question soon.. just gotta think of one

[Xeda112358]

Wait, not finished...
EDIT:NEVER MIND
TO convert a base from base 10 to some other base, do log(x)/log(a) where a is the base you want to convert to.
So log(10) is 1
1/log((sqrt(5)+1)^2/4) is your answer
2.3924859833

[ruler501]

That only works to convert between different log bases we're talking about number bases.

[Xeda112358]

Yep, sorry, just caught that. Sorry, lack of sleep
I get:
(sqrt(5)+3)/2=phi^2→D
10/D^2=1.458980338...
First digit=1
.458980338*D=1.201626124
Second digit=1
Decimal=.201626124....*D=.527864045
10 % phi^2=
11.527864045
phi^4+ph^2+.527864045...=10
So the 5th digit after the decimal is 6

EDIT: I forgot the /2 part of the (sqrt(5)+3)/2
EDIT: There is a mistake if anybody can catch it...