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Ansh_
01/22/2022 12:54:44
$3x + 1 - a < 0$
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TeXit
01/22/2022 12:54:46
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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Ansh_
01/22/2022 12:55:34
so $x\geq \frac{1}{3}$ and $a > 3x+1 \geq 3\cdot \frac{1}{3} + 1 =2$
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TeXit
01/22/2022 12:55:36
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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7e866702f9414552bd66fd2437414f97
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Ansh_
01/22/2022 12:56:12
So, since both the inequalities are satisfied, you get $x\geq \frac{1}{3}$ is acceptible
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TeXit
01/22/2022 12:56:15
**Ansh**
https://cdn.discordapp.c…233012371577.png
706934233012371577.png
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7e866702f9414552bd66fd2437414f97
421,006,765,572,882,500
LoLer
01/22/2022 12:56:22
Yep
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7e866702f9414552bd66fd2437414f97
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LoLer
01/22/2022 12:56:37
Ah okay so you substitute and do it
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LoLer
01/22/2022 12:57:59
Hmm so this is acceptible
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7e866702f9414552bd66fd2437414f97
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LoLer
01/22/2022 12:58:02
In the other case
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7e866702f9414552bd66fd2437414f97
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LoLer
01/22/2022 12:58:29
We get (a-1)/3< x<=1/3
1
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7e866702f9414552bd66fd2437414f97
421,006,765,572,882,500
LoLer
01/22/2022 12:58:44
So here we get x<=1/3
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7e866702f9414552bd66fd2437414f97
421,006,765,572,882,500
LoLer
01/22/2022 12:58:52
So when we combine x belongs to r?
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7e866702f9414552bd66fd2437414f97
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LoLer
01/22/2022 13:00:46
Right @Ansh_ ?
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7e866702f9414552bd66fd2437414f97
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LoLer
01/22/2022 13:00:50
Sorry for the ping
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Ansh_
01/22/2022 13:04:56
Umm
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Ansh_
01/22/2022 13:06:44
Actually.. you need to mention that the range of values *acceptable for "x" is dependent on the range of values "a" is picked up from
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7e866702f9414552bd66fd2437414f97
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LoLer
01/22/2022 13:08:22
So like I need to mention if a>2 then x can take thi value and a<2 can take that
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7e866702f9414552bd66fd2437414f97
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Ansh_
01/22/2022 13:08:39
Yeah
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LoLer
01/22/2022 13:13:30
Thanks
1
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7e866702f9414552bd66fd2437414f97
421,006,765,572,882,500
LoLer
01/22/2022 13:13:33
.close
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Mr Carrot Man
01/22/2022 13:17:00
please can someone help explain what I'm meant to be doing here?
https://cdn.discordapp.c…7550/unknown.png
unknown.png
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4284051489d44287861c781a4593e5e6
551,269,104,800,104,450
EndTimes
01/22/2022 13:37:55
Multiply the factors together
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551,269,104,800,104,450
EndTimes
01/22/2022 13:37:58
Lol
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Jason_Bjorn
01/22/2022 13:54:25
if `A` is 4x3 matrix and `det(A) = 8` then how do I find `det(7A)`? is it `7^rows` or `7^cols` ?
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Jason_Bjorn
01/22/2022 13:55:00
Or does that trick only work on square matrices?
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Deus_Vult
01/22/2022 13:58:33
How exactly is the determinant of non square matrices defined.. ?
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kirby your mom
01/22/2022 13:59:26
The determinant can only be found for a square matrix right?
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Jason_Bjorn
01/22/2022 14:02:00
huh
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321,074,029,291,372,540
Jason_Bjorn
01/22/2022 14:02:03
good to know
1
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Jason_Bjorn
01/22/2022 14:02:52
thank you
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2438a0ffb348411d86544380ac34ead1
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Deus_Vult
01/22/2022 14:02:52
is this an exercise?
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Deus_Vult
01/22/2022 14:03:01
or your own question
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Jason_Bjorn
01/22/2022 14:03:12
both-ish
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2438a0ffb348411d86544380ac34ead1
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Deus_Vult
01/22/2022 14:03:13
because it's weird unless they were trying to trick you
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2438a0ffb348411d86544380ac34ead1
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Deus_Vult
01/22/2022 14:03:22
what is the exercise
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Jason_Bjorn
01/22/2022 14:03:40
I was wondering why we were only finding the determinant of square matrices
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Jason_Bjorn
01/22/2022 14:04:01
b/c that trick never said to use row or cols
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Jason_Bjorn
01/22/2022 14:04:10
but I get it now
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Jason_Bjorn
01/22/2022 14:05:38
why is `x` sometimes bolded?
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Jason_Bjorn
01/22/2022 14:05:46
to say is a vector?
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Jason_Bjorn
01/22/2022 14:05:50
and not cross product?
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Deus_Vult
01/22/2022 14:06:06
It's because the determinant is a recursive function _defined_ for square matrices
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2438a0ffb348411d86544380ac34ead1
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Deus_Vult
01/22/2022 14:06:43
which x ? in what operation?
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2438a0ffb348411d86544380ac34ead1
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Jason_Bjorn
01/22/2022 14:06:54
like `Ax = b`
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2438a0ffb348411d86544380ac34ead1
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Jason_Bjorn
01/22/2022 14:07:06
x would be bold
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2438a0ffb348411d86544380ac34ead1
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Deus_Vult
01/22/2022 14:09:44
oh maybe to denote that it's indeed a vector
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Deus_Vult
01/22/2022 14:10:06
Ax=b is simply a linear map.
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Jason_Bjorn
01/22/2022 14:10:19
not sure what you are saying but ok
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2438a0ffb348411d86544380ac34ead1
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Jason_Bjorn
01/22/2022 14:10:29
haven't heard `linear map` yet
1
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2438a0ffb348411d86544380ac34ead1
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Deus_Vult
01/22/2022 14:16:09
its a system of equation
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Deus_Vult
01/22/2022 14:16:26
but essentialy yea x is a vector and Ax is a multiplication of matrix A and vector x.
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Jason_Bjorn
01/22/2022 14:19:18
thank you @Deus_Vult
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Deus_Vult
01/22/2022 14:20:16
Np :PES_Happy:
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Jason_Bjorn
01/22/2022 14:20:24
.close
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e8b2a340dd154da2b01023791512ca06
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thehackpod
01/22/2022 15:14:41
Hi guys, I have this function and the exercise asks to determine the incremental ratio of it in [0, e - 1]
1
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thehackpod
01/22/2022 15:14:47
https://cdn.discordapp.c…1332_Gallery.jpg
Screenshot_20220122-211332_Gallery.jpg
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e8b2a340dd154da2b01023791512ca06
295,163,226,134,675,460
thehackpod
01/22/2022 15:15:27
What do I have to do exactly? I'm used to exercise that ask for example to calculate the incremental ratio on a certain value, for example 1. What does this interval mean?
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e8b2a340dd154da2b01023791512ca06
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thehackpod
01/22/2022 15:16:03
I don't know what to subsitutite in (f(x0+h) - f(x0))/h
1
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e8b2a340dd154da2b01023791512ca06
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thehackpod
01/22/2022 15:16:22
For h that tends to 0
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e8b2a340dd154da2b01023791512ca06
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thehackpod
01/22/2022 15:27:51
Guys please, I think the exercise is pretty easy itself, it's just that I don't know where to start from. I know the formula for h that tends to 0 of the increemntal ratio. I also know the one for x that tends to the value x0
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e8b2a340dd154da2b01023791512ca06
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thehackpod
01/22/2022 15:28:07
But I've never done it with intervals...
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e8b2a340dd154da2b01023791512ca06
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thehackpod
01/22/2022 15:39:40
.close
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879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:10:59
Find solution to the following equations with unknown variables $w, x, y, z$ and constants $c_{i}$.
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879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:11:15
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
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879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:11:17
$c_{1} = x^{w}$ \\ $c_{2} = x^{z}$ \\ $c_{3} = y^{w}$ \\ $c_{4} = y^{z}$
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879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:11:20
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
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879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:11:48
I have been working on this, and have had some help from this discord, but I am a bit stuck and would appreciate some guidance, I will post some steps I have taken
1
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879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:11:59
Using the rules of logarithmson the RHS, the exponents $r$ on each log $m$ is equivilant to $r$ multiplied by log $m$. We then divide both sides by $r$.
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879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:12:02
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
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879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:12:20
1. $$\frac{\ln(c_{1})}{w} = \ln(x)$$ \\ 2. $$\frac{\ln(c_{2})}{z} = \ln(x)$$ \\ 3. $$\frac{\ln(c_{3})}{w} = \ln(y)$$ \\ 4. $$\frac{\ln(c_{4})}{w} = \ln(y)$$
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879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:12:25
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
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879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:12:34
LHS of equations 1 and 2 can be equated to each other, due to their RHS being equal. The same for equations 3 and 4.
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879ef6f67d6a40a98174b7e1e8eae50c
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Jaw-Ahm
12/21/2021 17:12:43
5. $$\frac{\ln(c_{1})}{w} = \frac{\ln(c_{2})}{z}$$ \\ 6. $$\frac{\ln(c_{3})}{w} = \frac{\ln(c_{4})}{z}$$
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879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:12:46
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
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205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:12:59
As $c_{i}$ are constants, we can make the substitutions, where $a, b, c,$ and $d$ are constants:
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0
null
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null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:13:01
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
0
1
null
null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:13:03
$\ln(c_{1}) = a$ \\ $\ln(c_{2}) = b$ \\ $\ln(c_{3}) = c$ \\ $\ln(c_{4}) = d$
1
0
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null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:13:24
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
0
1
null
null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:14:15
Which results in our equations looking like:
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0
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null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:14:25
5. $$\frac{a}{w} = \frac{b}{z}$$ \\ 6. $$\frac{c}{w} = \frac{d}{z}$$
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0
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205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:14:28
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
0
1
null
null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:14:47
Now here is where I am stuck, I am just not sure how I can express the original variables, in terms of the constants
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0
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null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:26:19
We can now express these as two linear equations:
1
0
469,185,954,658,123,800
Mugiwara No Ligma
1540
Mugiwara No Ligma
false
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:26:29
7. $$z = \frac{b}{w}w$$ \\ 8. $$z = \frac{d}{c}w$$
1
0
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null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:27:44
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
0
1
null
null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:27:56
This provides us with infinite solutions, so we can set a constraint such that:
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0
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null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:29:11
$$\frac{b}{a} \neq \frac{d}{c}$$
1
0
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null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:29:14
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
0
1
null
null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:30:07
This allows us to arive at a unique solution where
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0
null
null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:30:12
$z = w = 0$
1
0
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null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:30:15
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
0
1
null
null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 17:31:20
Plugging in these to the original equations we get that the solution to $y$ and $x$ are part of an infinite set.
1
0
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null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 17:31:22
**Jaw-Ahm**
https://cdn.discordapp.c…623905058817.png
308021623905058817.png
0
1
null
null
null
null
null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 18:33:25
Right now it would be good if someone could look this over, and judge correctness and perhaps share alternate routes to arrive to a better sollution
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0
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205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
691,679,326,164,222,100
Euclid31415
12/21/2021 19:02:08
Won't taking z=w=0 assume that the constants c_{i} are all =1. I thought you were supposed to solve for x,y,z,w in terms of c_{i}
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1
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205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 19:02:37
Yes this is what I am thinking too. I just wanted to show the best I have come up with
1
0
null
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null
205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
308,021,623,905,058,800
Jaw-Ahm
12/21/2021 19:02:57
I can't find a way to express w, x, y and z in terms of c_i
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0
null
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205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
485,820,733,537,386,500
Brun。
12/21/2021 19:08:47
if you skip this step you get that $c_4=c_3^{log_{c_2}c_1}$
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1
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205,587
help-1
879ef6f67d6a40a98174b7e1e8eae50c
510,789,298,321,096,700
TeXit
12/21/2021 19:08:50
**Brun。**
https://cdn.discordapp.c…733537386526.png
485820733537386526.png
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