Vote for Us! (June)

[Summer]

Vote 20!

[Gildarts]

22

[Omni]

#18

[Dane Regan]

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]

[Jaixe Furiael]

Voted 5

[Arle Nadja]

Vote 16

[Tamsin Suzaku]

Voted: 20 (381/323/2001/601)

[Cell]

23

[Alex Mercer]

Voted 17

[Summer]

Vote 21!

[Amaterasu]

Vote 21 (385/327/2004/605)

[Dane Regan]

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]

[Gildarts]

23

[Arle Nadja]

Vote 17

[Guu]

Voted: 23

[Tamsin Suzaku]

Voted: 21 (392/331/2010/610)

[Jaixe Furiael]

Voted 6

[Alex Mercer]

Voted 18

[Todd Ingram]

20

[Zack Fair]

Voted: 16 (395/334/2013/613)