Write Your Heart Out ツ discussion

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Fit, tea, I, try, jk, to, IO, out, kat, and jr.

10 words guys! I feel so accomplished.

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Pug 1 word!

Jewel
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Typing your name with your foot isn't that hard.

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No words :(

It's hard when you use your tablet :P

Yup!!

Julia *Stormfeather* {We're all stories, in the end} wrote: "Eocnwobfwphfspuvdpu fpugadofbaogrqxpwpjdobtyvdakvaogxwkvfwphcqkcfpqkvqphdceofihcvjvapjfv

Pug 1 word!"

You also had of same line as pug, three letters after it even.

☯ Mimaimi {Raggedy Man, Goodnight} {Call me Mai} ☯ wrote: "AJKFIEKJEFNBEFKIJAQFGKJQNIKWEK.FAEDKEIJIGWJKBGINKFANKFVIHLWIFEIJNNKFEQO8HIGFTNEWTOUIGTNBIOEWBKNWIOTGBINEOHWAEK.F4EILTIHLWIREIERWIEFWKFDJNRIQ9IODFUJLBEUIBTW4E9OWENLEFHBJKRENQBOIFBEWLFNKFLWEFKNFILFJB..."

There's jig, wife, and new too.

Lol well in on my IPod so it's hard bashing your keyboard with out a real keyboard :)


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Fry, pad, am, how, concave, 5 words!

Eh, I looking to see if I actually put words or if it is a just gibberish.

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Really complex math problem :P

I never liked math. Now I really don't like it.

TOO MANY VARIABLES!!!

What!?!?!???!??!?!?!?!?!? (sarcastically)
I LOVE!!!!! Math!!!!

Lol. solve this

Evaluate ∫(1/(1+x^5))dx.
Note that –1 = –1(cos0°+i sin0°)
∴the roots of the equation x^5+1 = 0 are
(–1)^(1/5) (cos((0°+360k°)/5)+i sin((0°+360k°)/5)) , where k = 0, 1, 2, 3, 4
= –1(cos0°+i sin0°) , –1(cos72°+i sin72°) , –1(cos144°+i sin144°) , –1(cos216°+i sin216°) , –1(cos288°+i sin288°)
= –1 , –cos72°–i sin72° , cos36°–i sin36° , cos36°+i sin36° , –cos72°+i sin72°
∴x^5+1
= (x+1)(x+cos72°+i sin72°)(x–cos 36°+i sin36°)(x–cos 36°–i sin36°)(x+cos 72°–i sin72°)
= (x+1)((x–cos36°)²+sin²36°)((x+cos72°)²+sin²72°)
= (x+1)(x²–2x cos36°+cos²36°+sin²36°)(x²+2x cos72°+cos²72°+sin²72°)
= (x+1)(x²–2x sin54°+1)(x²+2x sin18°+1)
For finding the EXACT value of sin18° and sin54°,
Consider 3×18° = 90°–2×18°
sin(3×18°) = sin(90°–2×18°)
sin(3×18°) = cos(2×18°)
3sin18°–4 sin³18° = 1–2 sin²18°
4sin³18°–2sin²18°–3sin18°+1 = 0
(sin18°–1)(4sin²18°+2sin18°–1) = 0
sin18° = 1(rej.) or 4sin²18°+2sin18°–1 = 0
sin18° = (–2±√(2²–4(4)(–1)))/(2×4)
= (–2±√20)/8
= (√5–1)/4 or (–√5–1)/4(rej.)
∴sin54°
= sin(3×18°)
= 3sin18°–4sin³18°
= (3(√5–1))/4–4((√5–1)/4)³
= (3(√5–1))/4–(4(5√5–15+3√5–1))/64
= (12√5–12–5√5+15–3√5+1)/16
= (√5+1)/4
∴(x+1)(x²–2x sin54°+1)(x²+2x sin18°+1)
= (x+1)(x²–((√5+1)x)/2+1)(x²+((√5–1)x)/2+1)
∴Let 1/(1+x^5) ≡ A/(x+1)+(Bx+C)/(x²–((√5+1)x)/2+1)+(Dx+E)(x²+((√5–1)x)/2+1)
1 ≡ A(x²–((√5+1)x)/2+1)(x²+((√5–1)x)/2+1)+(Bx+C)(x+1)(x²+((√5–1)x)/2+1)+(Dx+E)(x+1)(x²–((√5+1)x)/2+1)
1 ≡ A(x^4–x³+x²–x+1)+(Bx+C)(x+1)(x²+((√5–1)x)/2+1)+(Dx+E)(x+1)(x²–((√5+1)x)/2+1)
Put x = –1,
1 = 5A
A = 1/5
∴1 ≡ (x^4–x³+x²–x+1)/5+(Bx+C)(x+1)(x²+((√5–1)x)/2+1)+(Dx+E)(x+1)(x²–((√5+1)x)/2+1
1 ≡ (x^4–x³+x²–x+1)/5+(Bx+C)(x³+((√5+1)x²)/2+((√5+1)x)/2+1)+(Dx+E)(x³–((√5–1)x²)/2–((√5–1)x)/2+1)
1 ≡ (1/5+B+D)x^4+((–2/5+(√5+1)B+2C–(√5–1)D+2E)x³)/2+(2/5+(√5+1)B+(√5+1)C–(√5–1)D–(√5–1)E)x²)/2+((–2/5+2B+(√5+1)C+2D–(√5–1)E)x)/2+1/5+C+E
　　╭
　　│1/5+B+D = 0…………………………………………...(1)
　　│(–2/5+(√5+1)B+2C–(√5–1)D+2E)/2 = 0……………....(2)
∴─┤(2/5+(√5+1)B+(√5+1)C–(√5–1)D–(√5–1)E)/2 = 0……(3)
　　│(–2/5+2B+(√5+1)C+2D–(√5–1)E = 0…………………(4)
　　│1/5+C+E = 1…………………………………………...(5)
　　╰
(3)×2–(2)×2:4/5+(√5–1)C–(√5+1)E = 0……(6)
(3)×2–(4)×2:4/5+(√5–1)B–(√5+1)D = 0……(7)
(7)–(1)×4√5–5)B–(√5+5)D = 0……(8)
From (1), B+D = –1/5……(9)
(9)×(√5–5)–(8):2√5D = –(√5–5)/5
D = (5–√5)/(10√5)
= (√5–1)/10
(8)+(9)×(√5+5):2√5B = –(√5+5)/5
B = –(√5+5)/(10√5)
= –(√5+1)/10
(6)–(5)×4√5–5)C–(√5+5)E = –4……(10)
From (5), C+E = 4/5……(11)
(11)×(√5–5)–(10):2√5E = –4(√5–5)/5+4 = (40–4√5)/5
E = (40–4√5)/(10√5)
= (4√5–2)/5
(10)+(11)×(√5+5):2√5C = –4–4(√5+5)/5 = –(4√5+40)/5
C = –(4√5+40)/(10√5)
= –(4√5+2)/5
∴∫(1/(1+x^5))dx
= ∫[(1/5)/(x+1)+((–(√5+1)x)/10–(4√5+2)/5)/(x²–((√5+1)x)/2+1)+(((√5–1)x)/10+(4√5–2)/5)/(x²+((√5–1)x)/2+1)]dx
= (ln│x+1│)/5–((√5+1)/10)∫[(x+(8√5+4)/(√5+1))/(x²–((√5+1)x)/2+1)]dx+((√5–1)/10)∫[(x+(8√5–4)/(√5–1))/(x²+((√5–1)x)/2+1)]dx+C_1
= (ln│x+1│)/5+((√5–1)/20)∫[(2x+2√5+18)/(x²+((√5–1)x)/2+1)]dx–((√5+1)/20)∫[(2x–2√5+18)/(x²–((√5+1)x)/2+1)]dx+C_1
= (ln│x+1│)/5+((√5–1)/20)∫[(2x+√5–1)/(x²+((√5–1)x)/2+1)]dx+(((√5–1)(√5+19))/20)∫[dx/(x²+((√5–1)x)/2+1)]–((√5+1)/20)∫[(2x–(√5+1))/(x²–((√5+1)x)/2+1)]dx+(((√5+1)(√5–19))/20)∫[dx/(x²–((√5+1)x)/2+1)]+C_1
= (ln│x+1│)/5+((√5–1)/20)ln│x²+((√5–1)x)/2+1│–((√5+1)/20)ln│x²–((√5+1)x)/2+1│+((9√5–7)/10)∫[dx/((x+(√5–1)/4)²+1–(√5–1)²/16)]–((9√5+7)/10)∫[dx/((x–(√5+1)/4)²+1–(√5+1)²/16))]+C_2
= (ln│x+1│)/5+((√5–1)/20)ln│2x²+(√5–1)x+2│–((√5+1)/20)ln│2x²–(√5+1)x+2│+((9√5–7)/10)∫[dx/((x+(√5–1)/4)²+(2√5+10)/16)]–((9√5+7)/10)∫[dx/((x–(√5+1)/4)²+(10–2√5)/16)]+C_3
= (ln│x+1│)/5+((√5–1)/20)ln│2x²+(√5–1)x+2│–((√5+1)/20)ln│2x²–(√5+1)x+2│+[(9√5–7)/(10√(2√5+10)/4)]tan^(–1) [(x+(√5–1)/4)/(√(2√5+10)/4)]–[(9√5+7)/(10√(10–2√5)/4)]tan^(–1) [(x–(√5+1)/4)/(√(10–2√5)/4)]+C
= (ln│x+1│)/5+((√5–1)/20)ln│2x²+(√5–1)x+2│–((√5+1)/20)ln│2x²–(√5+1)x+2│+[(18√5–14)/(5√(2√5+10))]tan^(–1) [(4x+√5–1)/√(2√5+10)]–[(18√5+14)/(5√(10–2√5))]tan^(–1) [(4x–√5–1)/√(10–2√5)]+C

Actual math problem.

This is what i am learning

See, I LIKR Jimmey Buffet's shg "'''''''math Sucks'" so yeah.

I did that all with my nose. A boo-ya!

No thank you!!!!!!!!!!!!!!!!!

Lol. i know right?

Travis{Be the change you want to see in the world} Muhammad Gandhi wrote: "Lol. solve this

Evaluate ∫(1/(1+x^5))dx.
Note that –1 = –1(cos0°+i sin0°)
∴the roots of the equation x^5+1 = 0 are
(–1)^(1/5) (cos((0°+360k°)/5)+i sin((0°+360k°)/5)) , where k = 0, 1, 2, 3, 4
= –1..."

WHAT?!?!?!?!?!?!?!?!?!

And I thought Geometry was hard.





Wait, are you serious. Like, for real serious?

haha

Yeah, and geometry is easy.

Not what I am learning. It's all about dilations and stuff and my teacher stinks. Even my dad didn't get it and he got an A on everything when he took Geometry.

Wow, my teacher rocked! He was awesome and yeah

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Travis{Be the change you want to see in the world} Muhammad Gandhi wrote: "Wow, my teacher rocked! He was awesome and yeah"

Yeah, apparently I got stuck with the really bad Math teacher and my sister got stuck with the really bad History teacher. Don't let me get started on that teacher.


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I spelled so. Out of everything that was on there, so was the word I spelled.

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talk,

☯ Mimaimi {Raggedy Man, Goodnight} {Call me Mai} ☯ wrote: "You got "ref" as in reference... XD"

You're right, or it could be ref as in referee.

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I got cal, soy, hag,

CAL!

Oh yah! Now I see those words!

Dont get ne started on my Geography teacher

I remember when my sister had Geography and Geometry the same year. She kept confusing the two names and said Geog when she meant Geom and Geom when she meant Geog.

lol they r kinda confusing :)

Lol. thats funny

I know. She just told me, "Oh my gosh. That was such a confusing year." And I'm just like...kksksldodickr,fikcdjjkxcmswl8dej3m,k3jms xkijnmede3 mx 4nejesw nmx

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(when you bash your phone keyboard lol)

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Yup I know the feeling

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Now real keyboard!


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...It autocorrected things as I went...

...

:P

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