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+---- Thread: Vote for Us! (June) (/showthread.php?tid=6189)
RE: Vote for Us! (June) - Summer - 06-23-2017
Vote 20!
RE: Vote for Us! (June) - Gildarts - 06-23-2017
22
RE: Vote for Us! (June) - Omni - 06-23-2017
#18
RE: Vote for Us! (June) - Dane Regan - 06-23-2017
Vote number (α³ + β³ + γ³) where...
The equation z³ - 5z² + 4z + 14 = 0 has the roots α, β, and γ.[spoiler]23
(α + β + γ)³ = α³ + 3α²β + 3α²γ + β³ + 3β²α + 3β²γ + γ³ + 3γ²α + 3γ²β + 6αβγ = α³ + β³ + γ³ + 3(α + β + γ)(αβ + βγ + γα) - 3αβγ
α³ + β³ + γ³ = (α + β + γ)³ - 3(α + β + γ)(αβ + βγ + γα) + 3αβγ
As z³ - 5z² + 4z + 14 = 0 = (z - α)(z - β)(z - γ)
By comparing coefficients of different powers of z:
α + β + γ = 5
αβ + βγ + γα = 4
αβγ = -14
So α³ + β³ + γ³ = 5³ - 3*5*4 + 3*(-14) = 23[/spoiler]
RE: Vote for Us! (June) - Jaixe Furiael - 06-23-2017
Voted 5
RE: Vote for Us! (June) - Arle Nadja - 06-23-2017
Vote 16
RE: Vote for Us! (June) - Tamsin Suzaku - 06-23-2017
Voted: 20 (381/323/2001/601)
RE: Vote for Us! (June) - Cell - 06-24-2017
23
RE: Vote for Us! (June) - Alex Mercer - 06-24-2017
Voted 17
RE: Vote for Us! (June) - Summer - 06-24-2017
Vote 21!
RE: Vote for Us! (June) - Amaterasu - 06-24-2017
Vote 21 (385/327/2004/605)
RE: Vote for Us! (June) - Dane Regan - 06-24-2017
Voted
The area under the curve y = 60sin^2(x)/(e^x) from 0 to t as t tends to infinity.
[spoiler]24
General method outline:
Use double angle identites to write y in terms of e^x and cos(2x).
Integrate it by parts.
Do fancy maths.
Get an answer for the indefinite integral.
Plug in limits and stuff.
Should get 24.[/spoiler]
RE: Vote for Us! (June) - Gildarts - 06-24-2017
23
RE: Vote for Us! (June) - Arle Nadja - 06-24-2017
Vote 17
RE: Vote for Us! (June) - Guu - 06-24-2017
Voted: 23
RE: Vote for Us! (June) - Tamsin Suzaku - 06-24-2017
Voted: 21 (392/331/2010/610)
RE: Vote for Us! (June) - Jaixe Furiael - 06-24-2017
Voted 6
RE: Vote for Us! (June) - Alex Mercer - 06-24-2017
Voted 18
RE: Vote for Us! (June) - Todd Ingram - 06-24-2017
20
RE: Vote for Us! (June) - Zack Fair - 06-24-2017
Voted: 16 (395/334/2013/613)