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Ann
02/03/2022 10:53:05
this is what i would have done
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core
02/03/2022 10:53:28
ahhh ok
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core
02/03/2022 10:53:31
im crying
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core
02/03/2022 10:53:44
i thought i knew this 😭😭
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Ann
02/03/2022 10:54:58
are you literally in tears over this?
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Ann
02/03/2022 10:55:13
if so, i would advise you to do your best to calm down.
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Ann
02/03/2022 10:55:41
emotional distress is a much more significant issue than one otherwise inconsequential math problem.
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core
02/03/2022 10:56:40
ur right. im just unsure as to how i should learn this tbh
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core
02/03/2022 10:56:56
like solving simultaneous equations with 3 variables?
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Ann
02/03/2022 10:57:16
no
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Ann
02/03/2022 10:57:24
what you have here is not a system of equations in three variables
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Ann
02/03/2022 10:57:33
at least, not presented as such by the problem
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Ann
02/03/2022 10:58:11
rather it is a family of systems of equations in two variables (x,y) where each system within the family is identified by a number (m) called the parameter
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core
02/03/2022 11:01:23
lowk not gonna lie i dont know what a parameter is
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core
02/03/2022 11:01:30
family of systems of equations?
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Ann
02/03/2022 11:02:18
a collection of many systems of equations
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Ann
02/03/2022 11:02:33
...have you used desmos before in any capacity?
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core
02/03/2022 11:03:24
tep
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core
02/03/2022 11:03:25
yep
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core
02/03/2022 11:03:29
to graph equations
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Ann
02/03/2022 11:03:59
you can think of m as a slider
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Ann
02/03/2022 11:04:18
and each of these equations as a line that is graphed
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Ann
02/03/2022 11:04:46
and your task is to find the position(s) of the slider at which certain things happen
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Ann
02/03/2022 11:04:54
such as the system having infinitely many solutions, as in your problem
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core
02/03/2022 11:09:04
ohh ok!!
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core
02/03/2022 11:09:25
can you recommend a video that would teach me all this?
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core
02/03/2022 11:09:37
i tried looking for one but cant find a suitable one
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Ann
02/03/2022 11:24:02
i don't have any videos on hand sorry
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Skull
02/03/2022 12:15:32
https://cdn.discordapp.c…6462/unknown.png
unknown.png
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MattDog_222
02/03/2022 12:19:33
Do u know log laws
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John Kipmann
02/03/2022 12:19:35
.
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Skull
02/03/2022 12:20:18
yes
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John Kipmann
02/03/2022 12:20:31
use log laws
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John Kipmann
02/03/2022 12:21:29
do you know what e^ln(x) is?
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Skull
02/03/2022 12:21:59
ah its the 7th one
https://cdn.discordapp.c…8358/unknown.png
unknown.png
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Skull
02/03/2022 12:22:04
i only learned it till 5
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MattDog_222
02/03/2022 12:22:11
use this
https://cdn.discordapp.c…1520/unknown.png
unknown.png
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John Kipmann
02/03/2022 12:22:23
yes
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Skull
02/03/2022 12:22:34
thank u both
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MattDog_222
02/03/2022 12:22:40
do you know the base of ln?
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Skull
02/03/2022 12:22:44
ye e
1
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MattDog_222
02/03/2022 12:22:50
yup
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MattDog_222
02/03/2022 12:23:07
so $e^{\operatorname{log}_e(x)} = x$
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TeXit
02/03/2022 12:23:09
**MattDog\_222**
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Skull
02/03/2022 12:30:55
how would u do this tho
https://cdn.discordapp.c…0824/unknown.png
unknown.png
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MattDog_222
02/03/2022 12:31:24
ok so
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02/03/2022 12:31:56
sec
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MattDog_222
02/03/2022 12:36:28
idk an easy solution to it. According to symbolab u should get $\operatorname{ln}^2(x) = \operatorname{ln}^3(x)$
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TeXit
02/03/2022 12:36:33
**MattDog\_222**
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MattDog_222
02/03/2022 12:36:53
thus x = 1 or x = e, but i dont kkknow how they got to that equality
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zedzilla
02/03/2022 12:39:43
Take ln of both sides
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zedzilla
02/03/2022 12:40:16
And use logarith properties to simplify/bring stuff out of exponents
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zedzilla
02/03/2022 12:41:42
Take ln of the left side you get ln (x^ln(x)) You can bring that exponent out as multiplication: ln(x) * ln(x) = ln^2(x)
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zedzilla
02/03/2022 12:42:36
Take ln of the right ln(e^ln^3(x))) Ln cancels exponentiation with base e So you get ln^3(x)
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MattDog_222
02/03/2022 12:44:39
\begin{align} x^{\operatorname{ln}\,x} &= e^{(\operatorname{ln}\,x)^3} \notag\\ \operatorname{ln}(x^{\operatorname{ln}\,(x)}) &= \operatorname{ln}(e^{\operatorname{ln}^3 x}) \notag\\ \operatorname{ln}\,x \cdot \operatorname{ln}(x^1) &= (e^{(\operatorname{ln}^3 x)})\notag \\ \operatorname{ln}^2\,x &= (e^{(\operatorname{ln}^3 x)})\notag \\ \end{align} wip
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TeXit
02/03/2022 12:47:11
**MattDog\_222** Compile Error! Click the :errors: reaction for more information. (You may edit your message to recompile.)
https://cdn.discordapp.c…587749494784.png
205143587749494784.png
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MattDog_222
02/03/2022 12:56:35
\begin{align} x^{\operatorname{ln}\,x} &= e^{(\operatorname{ln}\,x)^3} \notag\\ \operatorname{ln}(x^{\operatorname{ln}\,(x)}) &= \operatorname{ln}(e^{\operatorname{ln}^3 x}) \notag\\ \operatorname{ln}\,x \cdot \operatorname{ln}(x^1) &= \operatorname{ln}^3 x \cdot ln(e^1) \notag \\ \operatorname{ln}^2\,x &= \operatorname{ln}^3 x \cdot 1 \notag \end{align} wip
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MattDog_222
02/03/2022 12:57:44
can u correct this @zedzilla
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zedzilla
02/03/2022 12:58:45
Third line should be this on the right: ln^3(x) * ln(e) = ln^3(x)
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zedzilla
02/03/2022 12:59:16
Ln was dropped on the right between line 2 and 3
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TeXit
02/03/2022 12:59:27
**MattDog\_222**
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zedzilla
02/03/2022 12:59:42
Yea that looks ok
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MattDog_222
02/03/2022 12:59:46
sec
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MattDog_222
02/03/2022 13:00:34
i myself dont understand from line 2 to 3 RHS
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zedzilla
02/03/2022 13:00:44
Ok you have
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zedzilla
02/03/2022 13:00:50
e^a
0
1
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zedzilla
02/03/2022 13:00:55
Take ln of that
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zedzilla
02/03/2022 13:01:01
ln(e^a)
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zedzilla
02/03/2022 13:01:22
Log property lets me bring that exponent inside the log outside as multiplication
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zedzilla
02/03/2022 13:01:39
So ln(e^a) = a*ln(e)
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MattDog_222
02/03/2022 13:01:39
omg yes
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zedzilla
02/03/2022 13:01:50
Yep good stuff
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MattDog_222
02/03/2022 13:01:56
logs are the worst algebra ever
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MattDog_222
02/03/2022 13:02:10
i'd take trig substitution integration over it (sometimes)
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zedzilla
02/03/2022 13:02:11
It doesn't matter what kind of weird exponent you have the property still works the same
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help-1
0dc25adf24cb40d2b847dfdbd9a8750d
279,869,739,415,633,920
zedzilla
02/03/2022 13:02:19
Hahaha i love logs xD
0
1
null
null
null
null
null
205,868
help-1
0dc25adf24cb40d2b847dfdbd9a8750d
279,869,739,415,633,920
zedzilla
02/03/2022 13:02:48
Well let me not say that who knows what kinda weird shit they have you do with them in some theory courses
0
1
null
null
null
null
null
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
714,074,341,809,061,900
Mushfiqur
02/03/2022 13:07:41
P(x) = x^3+bx^2+cx+d is a polynomial in x. You are given that P(1) < 0, P(4) > 0, P(6) < 0 and P(10) > 0. If all of the roots of P(x) are integers, what is the maximum possible value of |d|?
1
0
null
null
null
null
null
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
872,024,354,572,103,700
<><><>
02/03/2022 13:11:30
oh this isn't so bad
0
1
898,441,976,142,237,800
Hyperlix
0041
Hyperlix
false
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
872,024,354,572,103,700
<><><>
02/03/2022 13:11:34
think about it
0
1
null
null
null
null
null
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
872,024,354,572,103,700
<><><>
02/03/2022 13:11:50
The roots are integers
0
1
null
null
null
null
null
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
872,024,354,572,103,700
<><><>
02/03/2022 13:12:07
If P(1) <0 and
0
1
null
null
null
null
null
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
872,024,354,572,103,700
<><><>
02/03/2022 13:12:12
P(4) > 0
0
1
805,217,272,087,838,700
Mathematics Bot
0196
Bot
true
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
872,024,354,572,103,700
<><><>
02/03/2022 13:12:19
What can you say happened between (1,4)
0
1
null
null
null
null
null
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
872,024,354,572,103,700
<><><>
02/03/2022 13:12:22
?
0
1
null
null
null
null
null
205,869
help-1
07e4a3e4223f4dc4a2318e46105e3641
706,934,233,012,371,600
Ansh_
02/03/2022 13:13:34
~~that sounds so haunted in so many ways~~
0
1
null
null
null
null
null
205,871
help-1
2a3aff6718e54cd2a226b34e380abe79
589,246,519,295,737,900
arfelious
02/03/2022 13:39:51
If i have 1000 images and i randomly view 50 of them every day, after how many days would i view every images in theory? Is it like coupon collector's problem?
1
0
null
null
null
null
null
205,871
help-1
2a3aff6718e54cd2a226b34e380abe79
205,143,587,749,494,800
MattDog_222
02/03/2022 13:53:01
I think they're asking for the mean of the distribution
0
1
null
null
null
null
null
205,871
help-1
2a3aff6718e54cd2a226b34e380abe79
205,143,587,749,494,800
MattDog_222
02/03/2022 13:53:50
idk which distribution it would be though, if its a common one
0
1
null
null
null
null
null
205,871
help-1
2a3aff6718e54cd2a226b34e380abe79
261,933,205,387,477,000
riemann
02/03/2022 14:10:04
yes it's exactly the coupon collector's problem
0
1
null
null
null
null
null
205,871
help-1
2a3aff6718e54cd2a226b34e380abe79
589,246,519,295,737,900
arfelious
02/03/2022 14:19:49
Thanks
1
0
null
null
null
null
null
205,871
help-1
2a3aff6718e54cd2a226b34e380abe79
589,246,519,295,737,900
arfelious
02/03/2022 14:19:50
.close
1
0
null
null
null
null
null
205,872
help-1
dde2ece08f3c442cbc8e27ea116709cb
326,803,048,041,283,600
nhat
02/03/2022 14:22:55
i am not sure how to find the probability of these.
https://cdn.discordapp.c…9642/unknown.png
unknown.png
1
0
null
null
null
null
null
205,872
help-1
dde2ece08f3c442cbc8e27ea116709cb
326,803,048,041,283,600
nhat
02/03/2022 14:23:30
im supposed to use the z table and this equation
1
0
null
null
null
null
null
205,872
help-1
dde2ece08f3c442cbc8e27ea116709cb
326,803,048,041,283,600
nhat
02/03/2022 14:23:31
https://cdn.discordapp.c…6746/unknown.png
unknown.png
1
0
null
null
null
null
null
205,872
help-1
dde2ece08f3c442cbc8e27ea116709cb
261,933,205,387,477,000
riemann
02/03/2022 14:32:25
do you know what $P(X=a)$ means?
0
1
null
null
null
null
null
205,872
help-1
dde2ece08f3c442cbc8e27ea116709cb
510,789,298,321,096,700
TeXit
02/03/2022 14:32:28
**riemann**
https://cdn.discordapp.c…205387477002.png
261933205387477002.png
0
1
null
null
null
null
null
205,872
help-1
dde2ece08f3c442cbc8e27ea116709cb
326,803,048,041,283,600
nhat
02/03/2022 14:33:26
it means the probability of x=something
1
0
null
null
null
null
null
205,872
help-1
dde2ece08f3c442cbc8e27ea116709cb
261,933,205,387,477,000
riemann
02/03/2022 14:33:37
and do you know what the formula $f(a)$ means?
0
1
null
null
null
null
null
205,872
help-1
dde2ece08f3c442cbc8e27ea116709cb
510,789,298,321,096,700
TeXit
02/03/2022 14:33:40
**riemann**
https://cdn.discordapp.c…205387477002.png
261933205387477002.png
0
1
null
null
null
null
null