The OFFICIAL Homework Help Topic (UPDATE. READ.) - Page 2 - VGF

Swordmaster Link · 02-14-2005, 05:34 PM

As a mod, shouldn't you...prevent death in your forum or something? [img]tongue.gif[/img]

***Ace Mercury*** · 02-14-2005, 05:37 PM

Not if it provokes intelligent, on-topic discussion.

Swordmaster Link · 02-14-2005, 05:38 PM

Last time I checked, you can't discuss anything when you're dead. [img]graemlins/lol.gif[/img]

***CaptHayfever*** · 02-14-2005, 07:35 PM

^Try telling that to Macduff's son.

And remember, "They've kill'd me, mother."

The Missing Link · 02-14-2005, 08:36 PM

Quote:

Originally posted by Swordmaster Link:
Last time I checked, you can't discuss anything when you're dead. [img]graemlins/lol.gif[/img]

That's because you're not 1337.

Any more math brilliance we want rebuffed tonight?

"There are some who call me... Link?"

"Carpe Gaium Domesticum!" (Seize the Cucco!)
Zelda: The Grand Adventures | Triforce MUCK
ザ行方不明リンク
悪いユウモアの賢人

Swordmaster Link · 02-14-2005, 09:46 PM

Quote:

Originally posted by The Minish Link:
</font><blockquote>quote:</font><hr />Originally posted by Swordmaster Link:
Last time I checked, you can't discuss anything when you're dead. [img]graemlins/lol.gif[/img]

That's because you're not 1337.</font>[/quote]On second thought, battle to the death it is!

The Missing Link · 02-15-2005, 01:04 AM

^

"There are some who call me... Link?"

"Carpe Gaium Domesticum!" (Seize the Cucco!)
Zelda: The Grand Adventures | Triforce MUCK
ザ行方不明リンク
悪いユウモアの賢人

ocarinagirl · 02-18-2005, 11:00 PM

....Yes. ANYWAY. Homework help. You can either ask for it, give advice, or try to solve that math problem. Don't listen to Andre. [img]tongue.gif[/img]

The Missing Link · 02-19-2005, 02:06 AM

Quote:

Originally posted by Down With The King:
Find the other roots of this equation

x^3+2x^2+6x+3

Let this expression be equal to ax³ + bx² + cx + d. (Thus a = 1, b = 2, c = 6, and d = 3.)

First we must find the "depressed cubic" within the cubic by applying the substitution x = y - b / 3a.

This arrives at
ay³ + (c - b² / 3a)y + (d + 2b³/27a² - bc / 3a) =
y³ + (6 - 4/3)y + (3 + 16/27 - 4) =
y³ + 14y/3 - 11/27 = 0.

This gives an equation of the form y³ + Ay = B (A = 14/3, B = 11/27).

Now we must find numbers s and t such that 3st = A and s³ - t³ = B. Solving the first equation for s, s = A / 3t, we see that (A / 3t)³ - t³ = B, so t^6 + Bt³ - A³/27 = 0. If we substitue u = t³, this becomes u² + Bu - A³/27 = 0, which is quadratic and has solution
u = -B ± sqrt(B² + 4A³/27) / 2 =
(-11/27 ± sqrt(121/729 + 10976/729)) / 2 =
(-11/27 ± sqrt(121 + 10976)/27) / 2 =
(-11 ± sqrt(121 + 10976)) / 54 =
(-11 ± sqrt(11097)) / 54 =
(-11 ± 9 sqrt(137)) / 54.

We'll take the positive root, so u = (-11 + 9 sqrt(137)) / 54 = 1.74707....

Thus, as u = t³, t = cubrt(u) = cubrt((-11 + 9 sqrt(137)) / 54) = 1.20440....

We then know that s = A/(3t), so s = 14/9t = 1.29156....

It has been shown that s - t is a root of the "depressed cubic", so s - t = 0.087159... is a root of y³ + 14y/3 - 11/27 = 0.

Thus, x = y - b / (3a) = 0.087159... - 2/3 = -0.57950... is a root of the equation.

Dividing this solution via synthetic division from the initial expression, the other two roots can be found from the equation x^2 + (1.42049...)x + (5.17681...) = 0.

Using the quadratic formula, we can solve for x with x =
((-1.42049...) ± sqrt((-1.42049...)² - 4(5.17681...))) / 2 =
((-1.42049...) ± sqrt(-18.68945...)) / 2 =
-0.71024... ± i * sqrt(18.68945...) / 2 =
(-0.71024...) ± i(2.16157...).

Thus, it is solved. The roots are (-0.57950...) and (-0.71024...) ± (2.16157...)i.

"There are some who call me... Link?"

"Carpe Gaium Domesticum!" (Seize the Cucco!)
Zelda: The Grand Adventures | Triforce MUCK
ザ行方不明リンク
悪いユウモアの賢人

[ February 19, 2005, 04:12 PM: Message edited by: The Minish Link ]

ocarinagirl · 02-24-2005, 05:42 PM

Yaaaaaay, good job! *cookie*

I'm going to lock this topic, but only because I want to make seperate topics for different subjects. I was going to do that earlier, but lately I've been having to read Shakespeare until my eyes bled.

More will be explained in the other topics.... [img]tongue.gif[/img]

[ February 24, 2005, 04:44 PM: Message edited by: Bad Andi ]

02-14-2005, 05:34 PM	#21
Swordmaster Link Super Bodyguard & King of the Arcade Join Date: Apr 2000 Location: Wherever you want me to be Gender: Posts: 29,999 Thanks: 215 Thanked 538 Times in 376 Posts Points: 1,092.85 Bank: 1,182,106.00 Total Points: 1,183,198.85 Donate	As a mod, shouldn't you...prevent death in your forum or something? [img]tongue.gif[/img]

02-14-2005, 05:37 PM	#22
*Ace Mercury* Marshmallow Knight ☆ Supermod Join Date: Jun 2000 Location: Southern Ontario Gender: Posts: 18,943 Thanks: 360 Thanked 1,493 Times in 783 Posts Blog Entries: 1 Points: 97,978.84 Bank: 12,202,050.71 Total Points: 12,300,029.55 Donate	Not if it provokes intelligent, on-topic discussion.

02-14-2005, 05:38 PM	#23
Swordmaster Link Super Bodyguard & King of the Arcade Join Date: Apr 2000 Location: Wherever you want me to be Gender: Posts: 29,999 Thanks: 215 Thanked 538 Times in 376 Posts Points: 1,092.85 Bank: 1,182,106.00 Total Points: 1,183,198.85 Donate	Last time I checked, you can't discuss anything when you're dead. [img]graemlins/lol.gif[/img]

02-14-2005, 07:35 PM	#24
*CaptHayfever* Smash Supermod Join Date: Jul 2002 Location: (n) - the place where I am Gender: Posts: 19,273 Thanks: 160 Thanked 733 Times in 474 Posts Points: 105,386.73 Bank: 923.79 Total Points: 106,310.52 Donate	^Try telling that to Macduff's son. And remember, "They've kill'd me, mother."

02-15-2005, 01:04 AM	#27
The Missing Link Professional Lurker Join Date: Dec 2000 Location: New Hyrule, Washington, US Gender: Posts: 15,575 Thanks: 80 Thanked 183 Times in 110 Posts Points: 6,760.45 Bank: 55,328.64 Total Points: 62,089.09 Donate	^ "There are some who call me... Link?" "Carpe Gaium Domesticum!" (Seize the Cucco!) Zelda: The Grand Adventures \| Triforce MUCK ザ行方不明リンク悪いユウモアの賢人

02-18-2005, 11:00 PM	#28
ocarinagirl Senior Member Join Date: Jan 2001 Location: Ehhh? What? Where am I?! Gender: Posts: 3,010 Thanks: 0 Thanked 0 Times in 0 Posts Points: 7,919.83 Bank: 500.00 Total Points: 8,419.83 Donate	....Yes. ANYWAY. Homework help. You can either ask for it, give advice, or try to solve that math problem. Don't listen to Andre. [img]tongue.gif[/img]

02-24-2005, 05:42 PM	#30
ocarinagirl Senior Member Join Date: Jan 2001 Location: Ehhh? What? Where am I?! Gender: Posts: 3,010 Thanks: 0 Thanked 0 Times in 0 Posts Points: 7,919.83 Bank: 500.00 Total Points: 8,419.83 Donate	Yaaaaaay, good job! cookie I'm going to lock this topic, but only because I want to make seperate topics for different subjects. I was going to do that earlier, but lately I've been having to read Shakespeare until my eyes bled. More will be explained in the other topics.... [img]tongue.gif[/img] [ February 24, 2005, 04:44 PM: Message edited by: Bad Andi ]