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redeye
02/06/2022 19:17:40
okay because first we find out how many ways we can arrange the distinct letters which is n! and when we incorporate S into these strings we have k places to plug in S.. which is n+1 C k Since they are related and happens together , we've got n! (n+1) C k
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Chai T. Rex
02/06/2022 19:18:09
Yes, also you can see it another way. First, we place the distinct letters:``` xAxBxCx xAxCxBx xBxAxCx xBxCxAx xCxAxBx xCxBxAx ```
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help-10
75b1bffbb1124175815afc02aa6e7131
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Chai T. Rex
02/06/2022 19:18:13
Let's say k = 2.
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help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:18:40
So, there will be 4C2 = 6 variations for each row there.
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help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:19:20
``` xAxBxCx SASBxCx SAxBSCx SAxBxCS xASBSCx xASBxCS xAxBSCS ```
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help-10
75b1bffbb1124175815afc02aa6e7131
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Chai T. Rex
02/06/2022 19:19:30
That row turned into 6 final rows.
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help-10
75b1bffbb1124175815afc02aa6e7131
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Chai T. Rex
02/06/2022 19:19:39
And so do all the other 3! - 1 rows.
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help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:20:24
And so, since we have 3! things that turn into 4C2 final rows each, that's 3! × 4C2.
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help-10
75b1bffbb1124175815afc02aa6e7131
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redeye
02/06/2022 19:25:36
I'm not sure i understand this. but i understood the previous way
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help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:25:51
Well, you know that you get an arrangement of the ABC, right?
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help-10
75b1bffbb1124175815afc02aa6e7131
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redeye
02/06/2022 19:26:03
yes
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help-10
75b1bffbb1124175815afc02aa6e7131
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Chai T. Rex
02/06/2022 19:26:04
And then you place the 2 Ss.
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help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:26:50
There are 4C2 ways of placing the 2 Ss, so if your arrangement is ACB, you get SASBC, SABSC, SABCS, ASBSC, ASBCS, ABSCS.
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1
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532
help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:27:09
So, your 1 ACB arrangement becomes 6 arrangements with the Ss filled in.
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help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:27:12
Does that make sense?
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help-10
75b1bffbb1124175815afc02aa6e7131
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redeye
02/06/2022 19:27:58
yes.. so i just have to multiply with other arrangement of ACB and get final result
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532
help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:28:05
Yes.
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help-10
75b1bffbb1124175815afc02aa6e7131
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Chai T. Rex
02/06/2022 19:29:01
3! arrangements before Ss are added in, and each one turns into 4C2 final ones after the Ss are filled in, so 3! × 4C2.
0
1
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help-10
75b1bffbb1124175815afc02aa6e7131
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Chai T. Rex
02/06/2022 19:29:11
It's basically the idea of why you multiply.
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help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:29:34
Each of the 3! is worth 4C2 final arrangements.
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help-10
75b1bffbb1124175815afc02aa6e7131
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redeye
02/06/2022 19:29:39
yeah. thank you so much! it makes sense now
1
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help-10
75b1bffbb1124175815afc02aa6e7131
537,482,727,557,955,600
Chai T. Rex
02/06/2022 19:29:45
No problem.
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help-10
75b1bffbb1124175815afc02aa6e7131
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redeye
02/06/2022 19:32:05
.close
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help-10
6ea5c7314df84b5193c3a297bcf1234d
434,889,445,792,022,600
skoptec
02/06/2022 20:48:52
https://cdn.discordapp.c…810/IMG_4232.jpg
IMG_4232.jpg
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help-10
6ea5c7314df84b5193c3a297bcf1234d
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skoptec
02/06/2022 20:49:11
Can someone help me
1
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skoptec
02/06/2022 21:07:26
:thonk:
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help-10
ade39c480961464bad2f15a312987657
478,518,656,523,960,300
scroll忍
11/06/2021 09:45:02
how do we solve for question 1 b?
https://cdn.discordapp.c…4558/unknown.png
unknown.png
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help-10
ade39c480961464bad2f15a312987657
478,518,656,523,960,300
scroll忍
11/06/2021 09:55:31
isnt the answer supposed to be 7.85m/s?
https://cdn.discordapp.c…5295/unknown.png
unknown.png
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help-10
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ShatteredSunlight
11/06/2021 10:02:11
This question does not make sense at all. It implies Jumbo phases through Penggy since $v_J > v_P$ after the collision, which either means further pushing or Jumbo passes through Penggy.
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help-10
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TeXit
11/06/2021 10:02:14
**ShatteredSunlight**
https://cdn.discordapp.c…388507758592.png
178897388507758592.png
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help-10
ade39c480961464bad2f15a312987657
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scroll忍
11/06/2021 10:03:21
did it say phases through penggy?
1
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help-10
ade39c480961464bad2f15a312987657
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scroll忍
11/06/2021 10:11:50
nevermind isok i will try to figure it out
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scroll忍
11/06/2021 10:12:02
.close
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Phascolarctos
02/06/2022 22:14:52
Hi! I'm trying to disprove the following by contradiction. $$c\sqrt{n} \leq log_2^3(n), \forall n \geq n_0$$
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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TeXit
02/06/2022 22:14:55
**Phascolarctos**
https://cdn.discordapp.c…672433045504.png
308736672433045504.png
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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Phascolarctos
02/06/2022 22:16:33
My professor has told me that I cannot use limits or derivatives, but is this even possible? I've been trying to wrack my brain around this for several hours 😭
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help-10
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Phascolarctos
02/06/2022 22:18:37
I've tried using properties such as $$log(n)<log^2(n)<log^3(n)$$
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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TeXit
02/06/2022 22:18:40
**Phascolarctos**
https://cdn.discordapp.c…672433045504.png
308736672433045504.png
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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Phascolarctos
02/06/2022 22:18:52
$$log(n)<n$$
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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TeXit
02/06/2022 22:18:55
**Phascolarctos**
https://cdn.discordapp.c…672433045504.png
308736672433045504.png
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scroll忍
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Kaynex
02/06/2022 22:20:20
Well, the contradiction would be to assume that c√n ≤ log2(n)³ Is true for all n ≥ n0, and prove something obviously false.
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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Phascolarctos
02/06/2022 22:21:25
I've been doing that, but I can't quite seem to get it to line up properly.
1
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help-10
eb1c7c71db7c44b08b5cf388754e219f
308,736,672,433,045,500
Phascolarctos
02/06/2022 22:21:53
The log and that pesky cube are especially hard to manipulate
1
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536
help-10
eb1c7c71db7c44b08b5cf388754e219f
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Kaynex
02/06/2022 22:24:16
You can manipulate this into 2^(³√[c√n]) ≤ n But this doesn't seem to provide anything obvious
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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Kaynex
02/06/2022 22:25:05
What class is this? What theorems are you working with?
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help-10
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Phascolarctos
02/06/2022 22:28:24
I hadn't actually thought of doing that! I guess I just thought that cube-root would be difficult to manipulate, but maybe I'll try playing around with this. But off the bat, I would agree with you 😛 It is for a Data Structures & Algorithms course, in regards to proving whether a function f(n) is is O(g(n)), Omega(g(n...
1
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help-10
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Phascolarctos
02/06/2022 22:28:52
We don't really have many theorems to play with unfortunately. Just algebraic manipulation and proof techniques.
1
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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Phascolarctos
02/06/2022 22:36:27
the bummer is that if you just write it as $$\frac{log_2^3(n)}{\sqrt{n}}$$ and take the limit as n goes to infinity, you get $c<0$, but the conditions of the problem state that $c>0$, so boom! Contradiction.
1
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help-10
eb1c7c71db7c44b08b5cf388754e219f
510,789,298,321,096,700
TeXit
02/06/2022 22:36:30
**Phascolarctos**
https://cdn.discordapp.c…672433045504.png
308736672433045504.png
0
1
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null
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536
help-10
eb1c7c71db7c44b08b5cf388754e219f
308,736,672,433,045,500
Phascolarctos
02/06/2022 22:37:06
but apparently we can't do that 😦
1
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help-10
eb1c7c71db7c44b08b5cf388754e219f
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Phascolarctos
02/06/2022 22:42:42
Anyways, thanks for your help @Kaynex !
1
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help-10
eb1c7c71db7c44b08b5cf388754e219f
308,736,672,433,045,500
Phascolarctos
02/06/2022 22:42:44
.close
1
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help-10
010495be9a2146149d440cd55421332e
355,287,686,959,071,200
Trenton
02/06/2022 22:46:23
https://cdn.discordapp.c…711/IMG_1303.png
IMG_1303.png
1
0
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help-10
010495be9a2146149d440cd55421332e
355,287,686,959,071,200
Trenton
02/06/2022 22:46:43
I would like to ask part b plz
1
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help-10
010495be9a2146149d440cd55421332e
355,287,686,959,071,200
Trenton
02/06/2022 22:46:57
The p=k+1 of the induction
1
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help-10
010495be9a2146149d440cd55421332e
355,287,686,959,071,200
Trenton
02/06/2022 22:47:18
https://cdn.discordapp.c…636/IMG_1322.jpg
IMG_1322.jpg
1
0
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help-10
010495be9a2146149d440cd55421332e
355,287,686,959,071,200
Trenton
02/06/2022 22:47:44
I used the assumption already
1
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help-10
010495be9a2146149d440cd55421332e
355,287,686,959,071,200
Trenton
02/06/2022 22:48:27
Now I want to conclude the rightmost term is less than or equals to RHS, with a proper reason
1
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help-10
010495be9a2146149d440cd55421332e
355,287,686,959,071,200
Trenton
02/06/2022 22:49:48
I wonder if n$\sum_{i=1}^n x_i^{k+1}$ $\sum_{i=1}^n x_i^{k+2} $ is less than or equal to $n^2$$(\sum_{i=1}^n x_i^{k+2} )^2$
1
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help-10
010495be9a2146149d440cd55421332e
510,789,298,321,096,700
TeXit
02/06/2022 22:50:26
**Trenton**
https://cdn.discordapp.c…686959071242.png
355287686959071242.png
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010495be9a2146149d440cd55421332e
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Trenton
02/06/2022 22:50:37
@Helpers
1
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help-10
010495be9a2146149d440cd55421332e
355,287,686,959,071,200
Trenton
02/06/2022 22:55:11
.close
1
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Kaynex
7520
Kaynex
false
538
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LBK
02/06/2022 23:24:22
Take a pack of playing cards and discard the picture cards, that is the jack, queen and king, of each suit. Shuffle the cards and deal out 10 of them. Calculate the mean score by adding together the 10 face values and dividing by 10. Put the 10 cards back in the pack and shuffle again. Deal out a further 10 cards and c...
1
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help-10
3811b9b970ad445ebee9ebdbff97a7b7
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LBK
02/06/2022 23:46:35
@Helpers
1
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help-10
3811b9b970ad445ebee9ebdbff97a7b7
118,536,946,527,109,120
Migillope
02/06/2022 23:48:57
so... it actually wants you to run the experiment huh
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Migillope
02/06/2022 23:49:01
did you do it?
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prnv
02/07/2022 00:52:02
https://cdn.discordapp.c…198/unknown.jpeg
unknown.jpeg
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b7e44726b5644a61a86f102dd97aec53
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prnv
02/07/2022 00:54:10
.close
1
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Luczow
02/07/2022 01:07:50
Would any one be able to help me out on question 5 please
1
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Luczow
02/07/2022 01:18:21
It is a question about polynomials
1
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Luczow
02/07/2022 01:24:19
@Helpers
1
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help-10
4dd2077d5af74797a31e98fda5f0cca4
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Migillope
02/07/2022 01:26:31
Are you deleting the ping and reporting it every few minutes?
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Migillope
02/07/2022 01:26:37
Don't do that, just be patient
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Luczow
02/07/2022 01:27:12
Sorry
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Brightness
02/07/2022 01:49:50
https://cdn.discordapp.c…994/IMG_0510.png
IMG_0510.png
1
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3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 01:50:20
Shouldn’t it be 4 instead of the 2
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help-10
3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 01:50:35
This is my third time asking, please help, I have an examination tomorrow.
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help-10
3fc8100e8dc34bc5af32342fe2688908
510,789,298,321,096,700
TeXit
02/07/2022 02:01:58
**Ansh** ```latex For (ii), $\alpha = 2e^{i \frac{2\pi}{3}}$ I suppose ```
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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706,934,233,012,371,600
Ansh_
02/07/2022 02:02:47
where do you it should be 4?
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help-10
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Ansh_
02/07/2022 02:04:38
$\implies (\alpha + \alpha^2)(\alpha - \alpha^2) =\alpha^2 - 8\alpha$
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help-10
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TeXit
02/07/2022 02:05:16
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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help-10
3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 02:05:54
@Ansh_ this is from finding the cube roots from part (a)
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help-10
3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 02:06:07
Which has a mod 2 for each of the cube roots
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help-10
3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 02:06:27
But then it squared itself so I believe it should be 4e^i(2pi/3)
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help-10
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Ansh_
02/07/2022 02:06:36
huh?
https://cdn.discordapp.c…3966/unknown.png
unknown.png
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help-10
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Ansh_
02/07/2022 02:07:19
$\alpha= 2e^{i \frac{2\pi}{3}} \implies \alpha^2 = 4e^{i \frac{4\pi}{3}}$ no?
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help-10
3fc8100e8dc34bc5af32342fe2688908
510,789,298,321,096,700
TeXit
02/07/2022 02:07:21
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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help-10
3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 02:12:15
Yeah
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help-10
3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 02:12:34
So this is wrong right?
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help-10
3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 02:19:37
@Ansh_
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Ansh_
02/07/2022 02:20:07
Sorry, yep it's wrong
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Ansh_
02/07/2022 02:21:34
actually
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Ansh_
02/07/2022 02:21:57
maybe the arg(alpha) in (0, pi/2) has sth to do here and maybe the alpha you got isn't correct?
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Ansh_
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Ansh_
02/07/2022 02:24:32
Aaah got what's going on here lmao
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help-10
3fc8100e8dc34bc5af32342fe2688908
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Ansh_
02/07/2022 02:24:53
$\alpha = 2e^{-\frac{2\pi i}{3}}$ here
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help-10
3fc8100e8dc34bc5af32342fe2688908
510,789,298,321,096,700
TeXit
02/07/2022 02:25:13
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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help-10
3fc8100e8dc34bc5af32342fe2688908
706,934,233,012,371,600
Ansh_
02/07/2022 02:28:48
@Brightness
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help-10
3fc8100e8dc34bc5af32342fe2688908
706,934,233,012,371,600
Ansh_
02/07/2022 02:29:32
SO your equation would be: \\ $x^2 - (4e^{-\frac{2\pi i}{3}}) + ( 4e^{-\frac{4\pi i}{3}} - e^{-\frac{2\pi i}{3}}) = 0$
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help-10
3fc8100e8dc34bc5af32342fe2688908
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TeXit
02/07/2022 02:29:56
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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help-10
3fc8100e8dc34bc5af32342fe2688908
475,966,350,322,303,000
Brightness
02/07/2022 02:30:47
Okay thanks and there is another quite challenging problem
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