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205,788
help-1
b6502d37dc67407db5152902f63ce8c4
510,789,298,321,096,700
TeXit
01/30/2022 22:32:46
**Camilleone**
https://cdn.discordapp.c…697925898261.png
569167697925898261.png
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1
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205,788
help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:33:28
Oh, right. So then P(n+1) is If $b_1 + \dots + b_m \leq (n+1)$, then $b_1!\dots b_m! \leq (n+1)!$?
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205,788
help-1
b6502d37dc67407db5152902f63ce8c4
510,789,298,321,096,700
TeXit
01/30/2022 22:33:30
**beeswax**
https://cdn.discordapp.c…727098101810.png
709959727098101810.png
0
1
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null
205,788
help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:33:42
yes
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:34:55
Wait, so then my inductive hypothesis is only $$b_1 + \dots + b_m \leq (n+1)!$$
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help-1
b6502d37dc67407db5152902f63ce8c4
510,789,298,321,096,700
TeXit
01/30/2022 22:34:57
**beeswax**
https://cdn.discordapp.c…727098101810.png
709959727098101810.png
0
1
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205,788
help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:37:02
your inductive hypothesis is P(n)
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:37:15
that is: If $b_1 + ... + b_m \leq n$, then $b_1! \cdots b_m! \leq n!$
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help-1
b6502d37dc67407db5152902f63ce8c4
510,789,298,321,096,700
TeXit
01/30/2022 22:37:18
**Camilleone**
https://cdn.discordapp.c…697925898261.png
569167697925898261.png
0
1
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:37:28
this is your inductive hypothesis
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:38:04
now you need to prove: if $b_1 + \dots + b_m \leq (n+1)$, then $b_1! \dots b_m! \leq (n+1)!$
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help-1
b6502d37dc67407db5152902f63ce8c4
510,789,298,321,096,700
TeXit
01/30/2022 22:38:06
**Camilleone**
https://cdn.discordapp.c…697925898261.png
569167697925898261.png
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1
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205,788
help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:39:07
Oh, so this is good so far then
https://cdn.discordapp.c…041877/image.png
image.png
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:39:29
i would find some issue with the first line's second half tbh
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:39:47
first green line i mean
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:40:21
and i have no idea where you learned the phrasing of the last two lines, but that is _not_ how you write induction
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:40:30
Oh yeah, I'll delete that right hand side of the "and"
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:40:46
isn't that what you want to show? why are you assuming it?
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:41:54
I thought that was our inductive hypothesis?
0
1
331,558,346,333,224,960
jan Niku
2119
jan Niku
false
205,788
help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:42:24
We use P(n) to prove P(n+1)?
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:43:19
do you want to read those lines again
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:43:28
this is what we want to do
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:43:39
the inductive hypothesis is only P(n)
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:43:59
which means the only assumption is P(n) _for some n_, and we want to use this to show P(n+1) is true
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:44:08
we cannot just assume P(n) is true for all n
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:45:10
So, it was just an issue with the "for all" part?
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:47:24
yes
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:47:34
for all and for some are two very different things
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:51:12
Oh, okay. So, are we pretty much just using $n \leq (n+1)$ and $n! \leq (n+1)!$ here?
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help-1
b6502d37dc67407db5152902f63ce8c4
510,789,298,321,096,700
TeXit
01/30/2022 22:51:15
**beeswax**
https://cdn.discordapp.c…727098101810.png
709959727098101810.png
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205,788
help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 22:51:20
In the inductive case I mean
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1
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:51:40
maybe you should try the induction first
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 22:51:42
see what happens
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 23:03:49
Mkay, so I did this and I'm not quite sure what I have at my disposal to get that what I have implies that factorial product inequality for (n+1)!
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 23:03:54
https://cdn.discordapp.c…058290/image.png
image.png
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/30/2022 23:13:03
There's no time limit for these help channels, right? I'm just going to get some food real quick
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 23:20:25
Well, there's a sort of time limit that's dependent on when the bot asks you if the question is resolved
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 23:20:31
Otherwise no
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 23:21:06
About the latest picture: you don't need to say m is fixed again
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 23:21:16
Cause you fixed it at the start
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 23:22:12
You should begin by letting b_1,...,b_m be positive integers such that b_1 + ... + b_m \leq n+1
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help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 23:22:37
And then now consider the product of the factorials
0
1
214,305,946,090,995,700
Dzoni
0850
Dzoni
false
205,788
help-1
b6502d37dc67407db5152902f63ce8c4
569,167,697,925,898,240
Camilleone
01/30/2022 23:22:43
^ continue from there
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help-1
b6502d37dc67407db5152902f63ce8c4
709,959,727,098,101,800
beeswax
01/31/2022 00:13:07
Ah, I think I might see where it’s going.
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help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:17:14
https://cdn.discordapp.c…5280/unknown.png
unknown.png
1
0
null
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null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:17:56
u sub
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:18:04
yeah im just stuck rn
1
0
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null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:18:10
let me know if this is right so far
1
0
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null
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null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:18:47
https://cdn.discordapp.c…0746/unknown.png
unknown.png
1
0
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:19:01
good so far
0
1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:19:18
now i dont know what to multiply to get 1/2radicalx
1
0
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:21:14
idk what you mean
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1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:21:24
just multiply both sides by 2
0
1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:21:35
to get 2du = 1/sqrt(x)
0
1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:22:54
im still confused
1
0
null
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:23:18
what’s confusing you
0
1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:23:50
what would 2du help me with
1
0
null
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null
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null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:24:42
it would tell you what 1/sqrt(x) is equal to
0
1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:24:48
so you can sub it back into the integral
0
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:24:53
this is how u sub works
0
1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:25:03
https://cdn.discordapp.c…5570/unknown.png
unknown.png
1
0
null
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null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:25:27
yes but would i not need to get something on the outside like this problem?
1
0
null
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null
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:25:31
the 1/3
1
0
null
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null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:25:42
that works too
0
1
null
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null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:26:09
would you mind running me through it and then explaining it?
1
0
null
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null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:27:26
sure
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:27:34
so you already have the u sub
0
1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:27:53
du = 1/(2sqrt(x)) dx
0
1
null
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null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:28:06
2du = 1/sqrt(x) dx
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:28:11
u = sqrt(x)
0
1
null
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null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:28:25
so we can just sub this back into the original integral to get
0
1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:28:36
2sin(u) du
0
1
null
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null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:29:16
and then i just derive from there right?
1
0
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null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:29:59
integrate but yes
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1
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205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:30:23
https://cdn.discordapp.c…0007/unknown.png
unknown.png
1
0
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:30:36
thats it right
1
0
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null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:30:37
yeah
0
1
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null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:31:06
,w d/dx (-2cos(sqrt(x)))
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
510,789,298,321,096,700
TeXit
01/31/2022 01:31:11
Results provided by WolframAlpha
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:31:12
just to check
0
1
214,305,946,090,995,700
Dzoni
0850
Dzoni
false
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:32:22
can i run you by some more problems?
1
0
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:32:47
sure
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:33:49
https://cdn.discordapp.c…3294/unknown.png
unknown.png
1
0
183,668,144,404,037,630
Ann
0413
Ann
false
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:33:55
i know i prolly already messed up
1
0
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:34:19
is u sqrt(1-x)
1
0
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:34:30
you didn’t exactly mess up
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:34:38
but you should solve for x in terms of u
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:35:00
so you can avoid integration by parts
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
652,336,711,325,712,400
quantum
01/31/2022 01:35:07
even though it’s not that bad anyways
0
1
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:37:00
does this look right?
1
0
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 01:38:54
i already think i forgot something but i dont know how i would go about doing it
1
0
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 02:03:23
@Helpers
1
0
null
null
null
null
null
205,789
help-1
7304d3cd2f1445b6b37ef449fa4b886c
456,226,577,798,135,800
Deleted User
01/31/2022 02:14:31
.close
1
0
null
null
null
null
null
205,790
help-1
09b779efeeae4d199c34c9253aa917f4
898,441,976,142,237,800
Hyperlix
01/31/2022 02:19:09
how do you graph x + y = 7?
1
0
null
null
null
null
null
205,790
help-1
09b779efeeae4d199c34c9253aa917f4
353,366,222,450,065,400
TheWhiteShadow
01/31/2022 02:23:12
it's an equation with a y-int of 7 and a gradient of -1
0
1
null
null
null
null
null
205,790
help-1
09b779efeeae4d199c34c9253aa917f4
898,441,976,142,237,800
Hyperlix
01/31/2022 02:23:47
how did you get the gradient?
1
0
null
null
null
null
null
205,790
help-1
09b779efeeae4d199c34c9253aa917f4
929,724,109,011,681,300
RDT
01/31/2022 02:24:13
take x=0 , u get y=7 take y=0 , u get x=7 so line passes through 0,7 and 7,0 connect the points u get a line
0
1
null
null
null
null
null
205,790
help-1
09b779efeeae4d199c34c9253aa917f4
898,441,976,142,237,800
Hyperlix
01/31/2022 02:24:52
ahhh
1
0
null
null
null
null
null
205,790
help-1
09b779efeeae4d199c34c9253aa917f4
898,441,976,142,237,800
Hyperlix
01/31/2022 02:24:57
ok
1
0
null
null
null
null
null
205,790
help-1
09b779efeeae4d199c34c9253aa917f4
353,366,222,450,065,400
TheWhiteShadow
01/31/2022 02:25:18
cuz x is multiplied by -1
0
1
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null