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205,506
help-1
fdbb99176760413ca3cd08e085ec6579
872,024,354,572,103,700
<><><>
01/19/2022 03:05:05
Try to find inverse function for f(x)
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help-1
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872,024,354,572,103,700
<><><>
01/19/2022 03:06:02
look
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help-1
fdbb99176760413ca3cd08e085ec6579
872,024,354,572,103,700
<><><>
01/19/2022 03:07:59
let $y = -\sqrt{1+\sqrt{1+x}}$ we want to solve for $x$. $y^2 = 1+\sqrt{1+x} \iff y^2-1=\sqrt{1+x} \iff 1+x = (y^2-1)^2 \iff x = y^4-2y^2 \iff f^{-1}(x) = x^4-2x^2$
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help-1
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TeXit
01/19/2022 03:08:13
**azeem321**
https://cdn.discordapp.c…354572103731.png
872024354572103731.png
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help-1
fdbb99176760413ca3cd08e085ec6579
872,024,354,572,103,700
<><><>
01/19/2022 03:10:03
sorry, i need to start reading questions
0
1
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help-1
fdbb99176760413ca3cd08e085ec6579
872,024,354,572,103,700
<><><>
01/19/2022 03:10:17
I thought the graph in sketch was f(x)
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1
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help-1
fdbb99176760413ca3cd08e085ec6579
872,024,354,572,103,700
<><><>
01/19/2022 03:12:13
if a root doesn't exist, it's most likely because it's undefined when you put it under the radical
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help-1
fdbb99176760413ca3cd08e085ec6579
706,934,233,012,371,600
Ansh_
01/19/2022 03:20:20
This one is rather simple :o
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help-1
fdbb99176760413ca3cd08e085ec6579
706,934,233,012,371,600
Ansh_
01/19/2022 03:20:36
^ right?
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help-1
fdbb99176760413ca3cd08e085ec6579
706,934,233,012,371,600
Ansh_
01/19/2022 03:22:09
Note that the graph for y = -root(1 + root(1+x)) is decreasing starts at x = -1, corresponding to y = -1 and continues decreasing forever while y = x^4 - 2x^2 is always above y = -1
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help-1
fdbb99176760413ca3cd08e085ec6579
706,934,233,012,371,600
Ansh_
01/19/2022 03:22:19
So only one intersection point, (-1, -1)
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1
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help-1
fdbb99176760413ca3cd08e085ec6579
706,934,233,012,371,600
Ansh_
01/19/2022 03:26:17
As for this one, you just need to know that _Inverse of a function only exists if the function is 1-1 on-to in that interval_ :o
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help-1
fdbb99176760413ca3cd08e085ec6579
706,934,233,012,371,600
Ansh_
01/19/2022 03:28:45
So ask yourself... since it's a cubic equation, what is it's peculiar behaviour? where does the graph go as x tends to + ∞ and - ∞, look out for the turning points on the graph, and note that after turning, the graph doesn't remain 1-1, is why you need to separate the graph into 3 intervals according to the turning poi...
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help-1
fdbb99176760413ca3cd08e085ec6579
706,934,233,012,371,600
Ansh_
01/19/2022 03:28:54
one of them... might satisfy your options
0
1
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help-1
fdbb99176760413ca3cd08e085ec6579
869,532,694,688,706,600
EpsilonNought
01/19/2022 04:02:07
@Brightness u still there
1
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help-1
73a467e950a14624bbee23883baca47e
456,226,577,798,135,800
Deleted User
01/19/2022 04:14:59
https://cdn.discordapp.c…20119_101435.jpg
IMG_20220119_101435.jpg
1
0
321,445,119,171,756,000
Shuri2060
9525
a μ-er
false
205,507
help-1
73a467e950a14624bbee23883baca47e
456,226,577,798,135,800
Deleted User
01/19/2022 04:15:11
Is exercise 1 solvable using the sum of integers formula
1
0
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205,507
help-1
73a467e950a14624bbee23883baca47e
456,226,577,798,135,800
Deleted User
01/19/2022 04:15:27
1/2 * n (n+1)
1
0
null
null
null
null
null
205,507
help-1
73a467e950a14624bbee23883baca47e
456,226,577,798,135,800
Deleted User
01/19/2022 04:15:34
Or do we have to do it manually
1
0
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205,507
help-1
73a467e950a14624bbee23883baca47e
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:18:02
Yes you can use that here
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1
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:46:33
How sir
1
0
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help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:46:51
I'm not sure how
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:47:06
Just break up the sum
0
1
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:47:16
Can you show me
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:47:33
sum of 9 - 2i is the same as sum of 9 plus sum of -2i
0
1
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:49:06
$\sum_{i = 1}^4(9 - 2i) = \sum_{i = 1}^4{9} - 2\sum_{i = 1}^4{i}$
0
1
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null
null
205,508
help-1
a1e51649b5544272a7c43eaf23145680
510,789,298,321,096,700
TeXit
01/19/2022 04:49:08
**Beans**
https://cdn.discordapp.c…743388381195.png
348696743388381195.png
0
1
782,087,086,416,461,800
LittleMouse
2603
LittleMouse
false
205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:51:00
Ok ty
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:51:07
But that's additivity
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:51:25
Not the sum of integers formula
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:51:27
1/2 * n (n+1)
1
0
782,087,086,416,461,800
LittleMouse
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:51:33
We don't use that one so we
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:52:22
Look at the $\sum_{i = 1}^4{i}$
0
1
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
510,789,298,321,096,700
TeXit
01/19/2022 04:52:24
**Beans**
https://cdn.discordapp.c…743388381195.png
348696743388381195.png
0
1
null
null
null
null
null
205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:52:30
Yeah ok
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:52:33
If n was big
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:52:37
You could use it
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:52:43
Right?
1
0
569,167,697,925,898,240
Camilleone
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false
205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:52:47
That's all.
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:53:00
You can use it for any number replaced with 4 there
0
1
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:53:13
Of course
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:53:19
Ty
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:53:47
https://cdn.discordapp.c…20119_105330.jpg
IMG_20220119_105330.jpg
1
0
null
null
null
null
null
205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:53:47
What about this
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:53:48
Im stuck here
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:54:54
@A Lonely Bean
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:55:44
Is that $\sum_{i = 1}^n\sum_{j = 1}^m(2i + 3j)$ ?
0
1
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:55:58
I think you can use additivity here too
0
1
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null
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
510,789,298,321,096,700
TeXit
01/19/2022 04:56:06
**Beans**
https://cdn.discordapp.c…743388381195.png
348696743388381195.png
0
1
null
null
null
null
null
205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:56:15
Yes
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:56:25
But how to solve
1
0
null
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:56:31
From the step im at
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 04:57:48
Can't really see what's in the end there
0
1
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:59:38
https://cdn.discordapp.c…2640/unknown.png
unknown.png
1
0
null
null
null
null
null
205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 04:59:39
like this
1
0
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205,508
help-1
a1e51649b5544272a7c43eaf23145680
348,696,743,388,381,200
A Lonely Bean
01/19/2022 05:01:52
Ye it's correct, the sum is 90, which is the same as 6(1 + 2 + 3) + 3*18
0
1
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null
205,508
help-1
a1e51649b5544272a7c43eaf23145680
456,226,577,798,135,800
Deleted User
01/19/2022 05:11:06
Super ty
1
0
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:14:43
https://cdn.discordapp.c…1444/unknown.png
1
0
null
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null
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:15:27
Am I missing something here, when x = 1/n, xn^2=n which goes to infinity when the limit is taken
1
0
null
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null
null
null
205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:15:31
so how does it converge pointwise?
1
0
null
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null
null
null
205,509
help-1
3267e02ba532491fbac6371cf5e011fd
484,702,191,156,985,860
themateo713
12/21/2021 08:25:57
wrong perspective. You look at f(x), so x stays fixed. As n goes to infinity, in what category does x fall ?
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Camilleone
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3267e02ba532491fbac6371cf5e011fd
684,674,576,998,858,800
kloser
12/21/2021 08:26:40
(not helping) wait are you the same guy who posted a question about 3 cats + 4 cats?
0
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:26:55
:happy:
1
0
null
null
null
null
null
205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:27:14
so isn't just x 0 if n->infty
1
0
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null
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:27:34
0<=x<=1/infty
1
0
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
484,702,191,156,985,860
themateo713
12/21/2021 08:28:38
if x = 0, f(x) = 0. Otherwise there is always a n big enough (like 2*floor(1/x + 1)) such that 2/n < x, and then f(x) = 0
0
1
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help-1
3267e02ba532491fbac6371cf5e011fd
484,702,191,156,985,860
themateo713
12/21/2021 08:30:01
see how to do the integral ?
0
1
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:30:38
is it related to rearranging the limits?
1
0
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
484,702,191,156,985,860
themateo713
12/21/2021 08:31:16
it is about breaking up the integral into integrals where the bounds correspond to f's definition
0
1
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:32:11
something like this?
https://cdn.discordapp.c…3748/unknown.png
unknown.png
1
0
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null
null
205,509
help-1
3267e02ba532491fbac6371cf5e011fd
484,702,191,156,985,860
themateo713
12/21/2021 08:33:14
for the integral, n appears to be held constant, so there are no limits
0
1
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205,509
help-1
3267e02ba532491fbac6371cf5e011fd
714,074,341,809,061,900
Mushfiqur
12/21/2021 08:35:57
Can anyone help me with this problem:- What's the average distance between two random dots in a square that has a length of 1 unit
0
1
null
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null
205,509
help-1
3267e02ba532491fbac6371cf5e011fd
225,110,750,161,666,050
Neko
12/21/2021 08:36:39
.close
1
0
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help-1
369a3087601a4dc0b2a5675805b78a94
175,328,346,291,306,500
Swivel
01/19/2022 07:41:36
Can someone help me get started with this? 🙂
https://cdn.discordapp.c…9776/unknown.png
unknown.png
1
0
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205,510
help-1
369a3087601a4dc0b2a5675805b78a94
706,934,233,012,371,600
Ansh_
01/19/2022 07:43:25
c_1 and c_2 are scalars... just put u and v in terms of i and j and equate with a = j + i
0
1
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null
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null
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205,510
help-1
369a3087601a4dc0b2a5675805b78a94
175,328,346,291,306,500
Swivel
01/19/2022 07:45:46
in terms of?
1
0
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205,510
help-1
369a3087601a4dc0b2a5675805b78a94
706,934,233,012,371,600
Ansh_
01/19/2022 07:48:48
u = 3i + 6j and v = 8i + 19j
0
1
321,445,119,171,756,000
Shuri2060
9525
a μ-er
false
205,510
help-1
369a3087601a4dc0b2a5675805b78a94
706,934,233,012,371,600
Ansh_
01/19/2022 07:48:49
...
0
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null
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369a3087601a4dc0b2a5675805b78a94
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Swivel
01/19/2022 07:57:02
hmm could you elaborate?
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f56fb1f924da4248b464d3ec646eabc9
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Swivel
01/19/2022 08:12:20
.reopen
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782,087,086,416,461,800
LittleMouse
2603
LittleMouse
false
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f56fb1f924da4248b464d3ec646eabc9
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Herels
01/19/2022 08:17:17
a = i + j = c1\*u + c2*v
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Peppermint Demon
3120
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false
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f56fb1f924da4248b464d3ec646eabc9
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Swivel
01/19/2022 08:17:36
yes
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help-1
f56fb1f924da4248b464d3ec646eabc9
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Herels
01/19/2022 08:17:37
you have u and v
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help-1
f56fb1f924da4248b464d3ec646eabc9
411,882,877,933,060,100
Herels
01/19/2022 08:17:57
just write c1\*u + c2*v in terms of i and j
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null
null
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help-1
f56fb1f924da4248b464d3ec646eabc9
411,882,877,933,060,100
Herels
01/19/2022 08:18:12
and solve for c1 and c2
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help-1
f56fb1f924da4248b464d3ec646eabc9
411,882,877,933,060,100
Herels
01/19/2022 08:24:03
,w inverse {{3,8},{6,19}}
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help-1
f56fb1f924da4248b464d3ec646eabc9
510,789,298,321,096,700
TeXit
01/19/2022 08:24:06
Results provided by WolframAlpha
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f56fb1f924da4248b464d3ec646eabc9
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Herels
01/19/2022 08:25:07
,w {{19/9, -8/9},{-6/9, 3/9}} \times {{1},{1}}
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help-1
f56fb1f924da4248b464d3ec646eabc9
706,934,233,012,371,600
Ansh_
01/19/2022 08:26:28
~~so lazy~~ XD
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help-1
f56fb1f924da4248b464d3ec646eabc9
411,882,877,933,060,100
Herels
01/19/2022 08:26:47
~~i have better things to do lol~~
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help-1
f56fb1f924da4248b464d3ec646eabc9
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Ansh_
01/19/2022 08:27:20
then just add 'em and get it done with >_< you just have to add the row entries anyways
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help-1
f56fb1f924da4248b464d3ec646eabc9
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Herels
01/19/2022 08:28:03
yea lol
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Swivel
01/19/2022 08:33:36
Thanks 🙂
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Gaping Hole
01/19/2022 08:36:59
Hey fellow discorders. I am in Precalculus on the start of my semester and I have been trying to grasp my type of learning into my class. I was given polynomials and 6 different ways on how to do it such as square root, difference of squares, and Etc… I get the types done. But I can’t understand this in the applicatio...
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help-1
9c51a3d4165f492d94483eca2a52e413
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Gaping Hole
01/19/2022 08:38:11
It’s more of a conceptual question.
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help-1
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A Lonely Bean
01/19/2022 08:39:52
So you're curious about applications of zeros of polynomials?
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help-1
9c51a3d4165f492d94483eca2a52e413
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Gaping Hole
01/19/2022 08:40:37
I’m curious on how all my learning of factoring polynomials and square roots incorporates to real life
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help-1
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A Lonely Bean
01/19/2022 08:42:20
Well for example you can represent height of an object in free fall as a polynomial function
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help-1
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A Lonely Bean
01/19/2022 08:42:47
Or taylor polynomials are used to approximate values of sin and cos for not-so-nice angles
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help-1
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Door 'GG' VB
01/19/2022 08:43:34
Also solving linear differential equations often involves solving polynomials
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