$$\begin{equation}z_1=r_1e^{i\theta},,z_2=r_2e^{i\theta}, z_1z_2=r_1e^{i\theta}\times r_2e^{i\theta}=r_1r_2e^{i(\theta_1+\theta_2)}:and:\frac{z_1}{z_2}=\frac{r_1e^{i\theta_1}}{r_2e^{i\theta_2}}=\frac{r_1}{r_2}e^{i(\theta_1-\theta_2)}\end{equation}$$
#latex
hushed iris
solid orioleBOT
Parallax Error
$$\begin{equation}z_1=r_1e^{i\theta},\,z_2=r_2e^{i\theta}, z_1z_2=r_1e^{i\theta}\times r_2e^{i\theta}=r_1r_2e^{i(\theta_1+\theta_2)}\:and\:\frac{z_1}{z_2}=\frac{r_1e^{i\theta_1}}{r_2e^{i\theta_2}}=\frac{r_1}{r_2}e^{i(\theta_1-\theta_2)}\end{equation}$$
```Compilation error:```! LaTeX Error: Bad math environment delimiter.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.57 $$\begin{equation}
z_1=r_1e^{i\theta},\,z_2=r_2e^{i\theta}, z_1z_2=r_1e^...
Your command was ignored.
Type I <command> <return> to replace it with another command,```
hushed iris
huh
$$|z_1z_2|=r_1r_2=|z_1||z_2|:\textnormal{and}:arg(z_1z_2)=\theta_1+\theta_2=\argz_1+\argz_2$$
solid orioleBOT
Parallax Error
$$|z_1z_2|=r_1r_2=|z_1||z_2|\:\textnormal{and}\:arg(z_1z_2)=\theta_1+\theta_2=\argz_1+\argz_2$$
```Compilation error:```! Undefined control sequence.
l.57 ...{and}\:arg(z_1z_2)=\theta_1+\theta_2=\argz
_1+\argz_2$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```
hushed iris
$$|z_1z_2|=r_1r_2=|z_1||z_2|:\textnormal{and}:\arg(z_1z_2)=\theta_1+\theta_2=\arg z_1+\arg z_2$$
solid orioleBOT
Parallax Error
peak tangle
e=mc2
$$e-mc2
$$|z_1z_2|=r_1r_2=|z_1||z_2|:\textnormal{and}:\arg(z_1z_2)=\theta_1+\theta_2=\arg z_1+\arg z_2$$
solid orioleBOT
Sornio
peak tangle
$$e=mc2$$
solid orioleBOT
Sornio
peak tangle
$$e=1010000002$$
solid orioleBOT
Sornio
$$e=10*1000000*2$$
solid orioleBOT
Parallax Error
distant forum
$y=mx+c$
solid orioleBOT
Legend
obsidian light
solid orioleBOT
fading bronze
$y = mx + c$
solid orioleBOT
Sheikh NotPixel Ibn sululu
upbeat locust
$10^5$
solid orioleBOT
pcb
opal tree
upbeat locust
$$
solid orioleBOT
pcb
solid orioleBOT
Sheikh Aboola Al Thani
$$
Sheikh Aboola Al Thani
Sheikh Aboola Al Thani
$$|z_1z_2|=r_1r_2=|z_1||z_2|:\textnormal{and}:arg(z_1z_2)=\theta_1+\theta_2=\argz_1+\argz_2$$
```Compilation error:```! Undefined control sequence.
l.57 ...l{and}:arg(z_1z_2)=\theta_1+\theta_2=\argz
_1+\argz_2$$
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.```
coarse quail
$$\begin{equation}z_1=r_1e^{i\theta},,z_2=r_2e^{i\theta}, z_1z_2=r_1e^{i\theta}\times r_2e^{i\theta}=r_1r_2e^{i(\theta_1+\theta_2)}:and:\frac{z_1}{z_2}=\frac{r_1e^{i\theta_1}}{r_2e^{i\theta_2}}=\frac{r_1}{r_2}e^{i(\theta_1-\theta_2)}\end{equation}$$
solid orioleBOT
Sheikh Aboola Al Thani
$$\begin{equation}z_1=r_1e^{i\theta},,z_2=r_2e^{i\theta}, z_1z_2=r_1e^{i\theta}\times r_2e^{i\theta}=r_1r_2e^{i(\theta_1+\theta_2)}:and:\frac{z_1}{z_2}=\frac{r_1e^{i\theta_1}}{r_2e^{i\theta_2}}=\frac{r_1}{r_2}e^{i(\theta_1-\theta_2)}\end{equation}$$
```Compilation error:```! LaTeX Error: Bad math environment delimiter.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.57 $$\begin{equation}
z_1=r_1e^{i\theta},,z_2=r_2e^{i\theta}, z_1z_2=r_1e^{...
Your command was ignored.
Type I <command> <return> to replace it with another command,```
frosty venture
wait do u want me to display the question too?
opal tree
wait do u want me to display the question too?
Display the expression
frosty venture
Display the expression
k
opal tree
And “problem C” at the top
frosty venture
Problem C
\
$log_3(\tfrac{\sin(2\pi)}{\tan(\pi/3)} + \sum_{n=0}^{10}(\frac{1+\sqrt{1+\sqrt{1}}}{1+(1^{-1} + 1^{1-1} \cdot \cos{(\pi/4)}} - \tfrac{2^{4}-2^{3}}{(1+\sqrt{1})^2)^n)$
damn
solid orioleBOT
nasi
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
opal tree
😭
frosty venture
ill do the working
$\log_3{(\tfrac{0}{\sqrt{3}} + \sum_{n=0}^{\infty}(\frac{1+\sqrt{2}}{1+\sqrt{2}} - \frac{8}{4})^{n})$
solid orioleBOT
nasi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
opal tree
I need a whole working
opal tree
It’s okay
zinc glade
$\log_3{(\frac{0}{\sqrt{3}} + \sum_{n=0}^{\infty}(\frac{1+\sqrt{2}}{1+\sqrt{2}} - \frac{8}{4})^{n})}$
solid orioleBOT
skySLAYER
zinc glade
@frosty venture there were 2 issues
1st fraction u had used \tfrac it should be \frac
U forgot to close the 1st curly brackets after the log
Also I reccomend using \left and \right
It's much better
Ull get something like this
$\log_3\left(\tfrac{0}{\sqrt{3}} + \sum_{n=0}^{\infty}(\frac{1+\sqrt{2}}{1+\sqrt{2}} - \frac{8}{4})^{n}\right)$
solid orioleBOT
skySLAYER
zinc glade
$\log_3\left(\tfrac{0}{\sqrt{3}} + \sum_{n=0}^{\infty}(\frac{1+\sqrt{2}}{1+\sqrt...
@frosty venture
frosty venture
Also I reccomend using \left and \right
ohhh thanks 🙏
golden zenithBOT
Gave +1 rep to skyslayer_1#0
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
upbeat locust
$a$
solid orioleBOT
pcb
upbeat locust
$sum{i=0}^{\infty}(9*10^-i)$
solid orioleBOT
pcb
solid orioleBOT
pcb
upbeat locust
$\sum_{i=0}^{\infty}(9*10^-i)$
solid orioleBOT
pcb
rich depot
,list
solid orioleBOT
rich depot
,time
solid orioleBOT
You haven't set your timezone! Set it using the interactive timezone picker with ,ti --set.
rich depot
,calc(1+2)
solid orioleBOT
Result:
3
sturdy sable
Please delete @lofty raven
golden zenithBOT
lofty raven
Please delete <@664510916104028181>
thanks for letting me know
golden zenithBOT
Gave +1 rep to oriole1906#0
sturdy sable
thanks for letting me know
Yw
polar python
$(\frac{5+6}{2}\ ,\ \frac{-1-7}{2})$
solid orioleBOT
Itachi Uchiha
frank drum
,help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
frank drum
,list
strong mesaBOT
No messages deleted, make sure the messages aren't over two weeks old.
golden zenithBOT
finite basaltBOT
@tranquil drum Your messages have been blocked for spam!
prime rampart
$\frac{\sin x}{n} = six$
solid orioleBOT
Stampybest333
prime rampart
$six=6$
solid orioleBOT
Stampybest333
prime rampart
$\therefore \frac{\sin x}{n} = 6$
solid orioleBOT
Stampybest333
prime rampart
I hope this changes your life
solid orioleBOT
barty
solid orioleBOT
epicdude99
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
epicdude99
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
ripe niche
[ \frac{8}{x} = 2x+1 ]
So,
[\frac{8}{x} = \frac{2x+1}{1} ]
[ 8=2x^2+x ]
[ 0=2x^2+x-8 ]
solid orioleBOT
epicdude99
ionic knot
[ 8/x = 2x+1 ]
damn,
[ 8/x = \frac{2x+1}{1} ]
[ 8=2x^2+x ]
[ 0=2x^2+x-8 ]
solid orioleBOT
Ames AKA Max
ripe niche
\begin{tikzpicture}
\draw
(0, 0) coordinate (A) node[left] {$A$} % a node A at (0,0) with a label
-- (4,0) coordinate (C) node[right] {$C$} % a node C at (4,0) with a label
node[midway, below]{$?$} % a label betwenn A and C
-- (4,2) coordinate (B) node[above right] {$B$} % a node B at (4,2) with a label
node[midway, right]{$4$} % a label between C and B
-- cycle % close the path
node[midway, above, sloped]{10}% a label between B and A
\end{tikzpicture}
solid orioleBOT
epicdude99
\begin{tikzpicture}
\draw
(0, 0) coordinate (A) node[left] {$A$} % a node A at (0,0) with a label
-- (4,0) coordinate (C) node[right] {$C$} % a node C at (4,0) with a label
node[midway, below]{$?$} % a label betwenn A and C
-- (4,2) coordinate (B) node[above right] {$B$} % a node B at (4,2) with a label
node[midway, right]{$4$} % a label between C and B
-- cycle % close the path
node[midway, above, sloped]{10}% a label between B and A
\end{tikzpicture}
```Compilation error:```! Package tikz Error: Giving up on this path. Did you forget a semicolon?.
See the tikz package documentation for explanation.
Type H <return> for immediate help.
...
l.59 \end{tikzpicture}
This error message was generated by an \errmessage
command, so I can't give any explicit help.
Pretend that you're Hercule Poirot: Examine all clues,```
ripe niche
[ \frac{8}{x} = 2x+1 ]
So,
[\frac{8}{x} = \frac{2x+1}{1} ]
[ 8=2x^2+x ]
[ 0=2x^2+x-8 ]
solid orioleBOT
epicdude99
urban flint
[ \frac{6}{2x} = \frac{56+2x^2}{5} ]
[ \frac{6}{2x} = \frac{56+2x^2}{5} ]
how do you work
urban flint
$$ sinx= 2 $$
solid orioleBOT
Shadooo
solid orioleBOT
Shadooo
urban flint
$$ \frac{\sinfuljoyacts}{sin}= x$$
solid orioleBOT
Shadooo
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
fluid trail
yooo this is such a cool ass feature
ripe niche
Ikr
But it's frustrating tho 😖
If u like coding and stuff then this shi is definitely for ya
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
worn arch
,tex |z| >= |z - 10|
solid orioleBOT
zx7ly
worn arch
,tex |x + yi| >= |x + yi - 10|
solid orioleBOT
zx7ly
worn arch
,tex x^2 + y^2 >= x^2 + y^2 + 100
solid orioleBOT
zx7ly
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
worn arch
,tex 0 >= 100
solid orioleBOT
zx7ly
obsidian knoll
,tex ( k^2 - 45/360 * pi * (K/2)^2 ) / (k^2)
solid orioleBOT
chmclez
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
lofty raven
,tex
solid orioleBOT
lofty raven
$$ 10/10 $$
solid orioleBOT
helpun
lofty raven
,tex help
solid orioleBOT
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
lofty raven
,calc 7/10
solid orioleBOT
Result:
0.7
ahh
uneven haven
@ionic gull also this
open lion
Im not sure what I expected from a channel named 'latex,' but it definitely wasn't maths
ionic gull
Im not sure what I expected from a channel named 'latex,' but it definitely wasn...
Yeah same when for the first time I saw it 😭
visual glacier
$$ hi $$
solid orioleBOT
theannoyingpoliticsguy
solid orioleBOT
Zingsuu
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
feral raven
I was expecting gloves and thigh highs
obsidian knoll
$$ YOYOYOYOYOYOYOYOY $$
solid orioleBOT
hi
obsidian knoll
,W HIHI
solid orioleBOT
twilit saffron
$$ Fart $$
solid orioleBOT
Quin
lofty raven
peak efficiency
solid orioleBOT
Zingsuu
jaunty fossil
,help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
jaunty fossil
$a^x$
solid orioleBOT
CoolGuy
jaunty fossil
$a = -w^2 x$
solid orioleBOT
CoolGuy
jaunty fossil
Why does it always react with delete symbol when I message? Is there something wrong that I am doing?
solid orioleBOT
helpun
unique dust
$baddies$
solid orioleBOT
constipated
solid orioleBOT
Sir Gator III
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
hard meteor
$$$\begin{align}
y &= ax^n\cdot bx^p \
f = ax^n &\qquad g'= bx^p \qquad\qquad \overbrace{\int f\cdot g' = f\cdot g' -\int f'\cdot g}^{\text{Integration by parts}}\
f' = anx^{n-1} &\qquad g= \int bx^p dx = \frac{b}{p+1}x^{p+1}\
\int (ax^n\cdot bx^p)dx &= ax^n \cdot bx^p - \int anx^{n-1}\cdot \frac{b}{p+1}x^{p+1}\
\int (ax^n\cdot bx^p)dx &= bax^{p+n} - \frac{anb}{(p+1)(n+p+1)}x^{n+p+1} + c
\end{align}$$$
solid orioleBOT
Sir Gator III
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
hard meteor
**epicdude99**
```latex
\begin{tikzpicture}
\draw
(0, 0) coordin...
wait what tikz works?
\begin{tikzpicture}[scale=1]
\begin{axis}
\addplot[name path=A,color=blue, very thick, smooth, domain=0:11] {3*x^0.5};
\addplot[name path=B,color={rgb:red,107;green,142;blue,35}, very thick, smooth, domain=0:11] {10-x};
\path[name path=C] (\pgfkeysvalueof{/pgfplots/xmin},0) -- (\pgfkeysvalueof{/pgfplots/xmax},0);
\path[name path=D] (\pgfkeysvalueof{/pgfplots/xmin},0) -- (\pgfkeysvalueof{/pgfplots/xmax},0);
\addplot [blue!30] fill between [
of=A and C,soft clip={domain=0:4},
];
\addplot [blue!30] fill between [
of=B and D,soft clip={domain=4:10},
];
\end{axis}
\end{tikzpicture}
Sir Gator III
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
hard meteor
dang ig axis drawings don't work
hard meteor
\begin{tikzpicture}
\draw
(0,0) -- (1,0);
\draw[x={(2cm,0.5cm)},color=red] (0,0) -- (1,0);
\end{tikzpicture}
solid orioleBOT
Sir Gator III
keen pollen
$fuck_chemistry$
solid orioleBOT
Tamas
urban flint
$fuck{chemistry}$
solid orioleBOT
shadoo
mild nexus
$\text{why f chem? I like chem....}$
solid orioleBOT
Adam
potent lotus
$no$
solid orioleBOT
Sheikh Maxina Bin Him
polar python
$$$\begin{align}
y &= ax^n\cdot bx^p
f = ax^n &\qquad g'= bx^p \qquad\qquad \overbrace{\int f\cdot g' = f\cdot g' -\int f'\cdot g}^{\text{Integration by parts}}
f' = anx^{n-1} &\qquad g= \int bx^p dx = \frac{b}{p+1}x^{p+1}
\int (ax^n\cdot bx^p)dx &= ax^n \cdot bx^p - \int anx^{n-1}\cdot \frac{b}{p+1}x^{p+1}
\int (ax^n\cdot bx^p)dx &= bax^{p+n} - \frac{anb}{(p+1)(n+p+1)}x^{n+p+1} + c
\end{align}$$$
.help
urban flint
$$\begin{align}
y &= ax^n\cdot bx^p
f = ax^n &\qquad g'= bx^p \qquad\qquad \overbrace{\int f\cdot g' = f\cdot g' -\int f'\cdot g}^{\text{Integration by parts}}
f' = anx^{n-1} &\qquad g= \int bx^p dx = \frac{b}{p+1}x^{p+1}
\int (ax^n\cdot bx^p)dx &= ax^n \cdot bx^p - \int anx^{n-1}\cdot \frac{b}{p+1}x^{p+1}
\int (ax^n\cdot bx^p)dx &= bax^{p+n} - \frac{anb}{(p+1)(n+p+1)}x^{n+p+1} + c
\end{align}$$
solid orioleBOT
shadoo
$$\begin{align}
y &= ax^n\cdot bx^p \
f = ax^n &\qquad g'= bx^p \qquad\qquad \overbrace{\int f\cdot g' = f\cdot g' -\int f'\cdot g}^{\text{Integration by parts}}\
f' = anx^{n-1} &\qquad g= \int bx^p dx = \frac{b}{p+1}x^{p+1}\
\int (ax^n\cdot bx^p)dx &= ax^n \cdot bx^p - \int anx^{n-1}\cdot \frac{b}{p+1}x^{p+1}\
\int (ax^n\cdot bx^p)dx &= bax^{p+n} - \frac{anb}{(p+1)(n+p+1)}x^{n+p+1} + c
\end{align}$$
```Compilation error:```! Package amsmath Error: Erroneous nesting of equation structures;
(amsmath) trying to recover with `aligned'.
See the amsmath package documentation for explanation.
Type H <return> for immediate help.
...
l.55 \end{align}
$$
Try typing <return> to proceed.
If that doesn't work, type X <return> to quit.```
hard meteor
didn't I send that 💀
lusty raft
,help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
lusty raft
,list
solid orioleBOT
lusty raft
$(P + \frac{a}{V^2} (V-b) = nRT$
solid orioleBOT
mush
lusty raft
$E_{Cell} = E^o_{cell} - \frac{RT}{nF} ln (\frac{[Zn^{2+}]{[Cu^{2+}^2]}$
solid orioleBOT
mush
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
lusty raft
$\frac{RT}{nF} ln \frac{[Zn^{2+}]} {[Cu^{2+}]^2}$
solid orioleBOT
mush
mossy granite
how does this thing even work?
sand mango
how does this thing even work?
Real
mossy granite
I sbluld go read
yes so sbluld i
sand mango
$\delta$\
solid orioleBOT
Little mishal
solid orioleBOT
Little mishal
solid orioleBOT
Oni
urban flint
$alpha+beta=\frac{-b}{a}$
solid orioleBOT
shadoo
torn frigate
$alpha+beta=\frac{-b}{a}$
$\alpha+\beta=\frac{-b}{a}$
solid orioleBOT
Saif
urban flint
Precede special characters with a backslash
alr ty
golden zenithBOT
Gave +1 rep to saifurrahman!
sand mango
$\Omega$
solid orioleBOT
Little mishal
sand mango
$\text{R}=\frac{V}{I}$
solid orioleBOT
Little mishal
sand mango
Fire
sand mango
why are you so rude
ok buddy
lusty raft
$C_2H_4$
solid orioleBOT
mush
fringe scarab
Can anyone tell me how to learn like this things
@torn frigate, can you please tell me
torn frigate
@solid oriole help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
torn frigate
,list
solid orioleBOT
torn frigate
,help tex
solid orioleBOT
torn frigate
@fringe scarab You may go through these resources
torn frigate
$$ \mathbb{Z} $$
solid orioleBOT
Saif
lusty raft
$$ \mathbb{ZNOTES}$$
solid orioleBOT
mushancholic
digital knoll
urban flint
$$\sqrt[3]{27} = 3$$
solid orioleBOT
Melancholic shadoo
fringe scarab
@lusty raft, nice to meet you I am from bd. I need help with learning latex
@urban flint, do you know where to learn LaTex
@torn frigate, any resources to learning latex and use it to solve a problem from start to end in softpaper
urban flint
<@642013179106295870>, do you know where to learn LaTex
no
lusty raft
<@1178579448031891519>, nice to meet you I am from bd. I need help with learning...
As-salamu alaykum Ayman, Tomar jonno taza guideline:
-
Install a Distribution
- TeX Live (cross-platform)
- MiKTeX (Windows)
- MacTeX (Mac)
-
Choose an Editor:
- Overleaf (online)
- TeXShop (Mac)
- TeXworks (Windows)
-
Learn the Basics
- Start with a simple document:
\documentclass{article} \begin{document} Hello, World! \end{document} - Learn to compile to PDF
- Start with a simple document:
-
Key Concepts
- Document Structure: Sections, formatting, lists
- Math Typesetting: Use
\( ... \)for inline,\[ ... \]for display. - References: Use
\label{}and\ref{}for citations
-
Resources
- YouTube: Find tutorial videos
-
Practice
- Create simple documents, then add figures, tables, and more
-
Experiment
- Explore packages (e.g.,
amsmath,graphicx) for advanced features
- Explore packages (e.g.,
solid orioleBOT
kurfu
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
fringe scarab
As-salamu alaykum Ayman, Tomar jonno taza guideline:
1. **Install a Distributio...
Walikum Salam, thank you @lusty raft, ami shesta korbo. Ar tumi ki kon classe. Ar tumi to onaek bhalo extracurriculars paiso. Tumi ke middle easte. Ar tomaki ami privaletly message de
golden zenithBOT
Gave +1 rep to spyderbillu!
fringe scarab
Watch yt videos
Thank you @ripe niche
golden zenithBOT
Gave +1 rep to dingus_0_0!
urban flint
How the f you learned then
magic
lusty raft
Walikum Salam, thank you <@1178579448031891519>, ami shesta korbo. Ar tumi ki ko...
how do u know about my extracurriculars? no im from Dhaka, sure u can dm me
fringe scarab
@lusty raft you there
urban flint
$$ 1) Sin^2x + Cos^2x = 1$$
$$ Sin^2x - 1 = Cos^2x$$
$$ Cos^2x - 1 = Sin^2x$$
$$ 2) 1 - Sec^2x = Tan^2x$$
$$ 1 + Tan^2x = Sec^2x$$
$$ Sec^2x - Tan^2x = 1$$
$$ 3) Cosec^2x - Cot^2x = 1$$
$$ 1 + Cot^2x = Cosec^2x$$
$$ 1 - Cosec^2x = Cot^2x$$
$$ 4) Sin(A \pm B) = SinACosB \pm CosASinB$$
$$ 5) Sin(2A) = 2SinACosA$$
$$ 6) Cos(A \pm B) = CosACosB \pm SinASinB$$
$$ 7) Cos(2A) = (CosA)^2 - (SinA)^2$$
$$ 8) Tan(A+B) = \frac{TanA \pm TanB}{ 1 \mp TanATanB}$$
$$ 9) Tan(2A) = \frac{2TanA}{1-Tan^2A}$$
$$ 10) Cot(A+B) = \frac{CotACotB-1}{CotB+CotA}$$
$$ 11) Cot(2A) = \frac{Cot^2A+1}{2CotA}$$
$$ 12) Sin(A+B)Sin(A-B) = Sin^2A - Sin^2B (or) Cos^2B - Cos^2A$$
$$ 13) Cos(A+B)Cos(A-B) = Cos^2A - Sin^2B (or) Cos^2B - Sin^2A $$
solid orioleBOT
Melancholic shadoo
lusty raft
$Cl_2 + 2Br^- -> 2Cl^- + Br_2$
solid orioleBOT
mush
urban flint
$Cl_2 + 2Br^- \to 2Cl^- + Br_2$
solid orioleBOT
BETRAAAYAAAAAL g..
urban flint
$$ y = 2x+1 -x^2 $$
$$ y = x^2-4x+1 $$
$$ y = 2x^2-8x + 1 $$
$$ x^2 - 4x+1 = 2x+1 -x^2 $$
$$ 2x^2-6x=0 $$
$$ 2x(x-3)=0 $$
$$ x = 0\ or\ 3 $$
$$ 2x^2-8x+1 = x^2-4x+1 $$
$$ x^2-4x =0 $$
$$ x(x-4)=0 $$
$$x=0\ or\ x= 4 $$
solid orioleBOT
BETRAAAYAAAAAL g..
solid orioleBOT
done.
still hollow
$$ Sin(2) $$
still hollow
$$ Sin(2) $$
solid orioleBOT
done.
golden zenithBOT
round solar
$$i^2$$
solid orioleBOT
doublerone
round solar
$$sig(1/((n^2)(b-1)^2)$$
solid orioleBOT
doublerone
solid orioleBOT
doublerone
urban flint
$$ sin^2x + cos^2x = 1 $$
$$ cos^2x = 1-sin^2x $$
$$ sin^2x = 1-cos^2x $$
$$ tanx = \frac{sinx}{cosx} $$
$$ cotx = \frac{cosx}{sinx} $$
$$ secx = \frac{1}{cosx} (note: sec\ means\ secant\ and\ cosec\ means\ cosecant) $$
$$ cosecx = \frac{1}{sinx} $$
$$ cotx = \frac{1}{tanx} $$
$$ cot^2x = 1+cosec^2x $$
$$ tan^2x = 1+sec^2x $$
solid orioleBOT
shadoo g..
sand mango
$$ sin^2x + cos^2x = 1 $$
$$ cos^2x = 1-sin^2x $$
$$ sin^2x = 1-cos^2x $$
$$ tan...
shadoo g..
urban flint
shadoo g..
?
still hollow
I can type black listed words using this bot?
stable sapphire
$$[ \text{Price Elasticity of Demand (PED)} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} ]$$
solid orioleBOT
Ved Karjagi
stable sapphire
\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\section*{Price Elasticity of Demand (PED)}
\textbf{Price elasticity of demand (PED)} is defined as:
[
\text{PED} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}
]
If we abbreviate change in by the Greek letter $\Delta$, this formula can be rewritten as:
[
\text{PED} = \frac{%\Delta Q}{%\Delta P}
]
Simplifying, the above formula can be rewritten as:
[
\text{PED} = \frac{\frac{\Delta Q}{Q} \times 100}{\frac{\Delta P}{P} \times 100} = \frac{\frac{\Delta Q}{Q}}{\frac{\Delta P}{P}}
]
where:
\begin{itemize}
\item $\Delta Q = Q_{\text{final value}} - Q_{\text{initial value}}$
\item $Q = Q_{\text{initial value}}$
\item $\Delta P = P_{\text{final value}} - P_{\text{initial value}}$
\item $P = P_{\text{initial value}}$
\end{itemize}
\end{document}
solid orioleBOT
Ved Karjagi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
ripe niche
$BRUZZ$
solid orioleBOT
epicdude99
round solar
$$i^2 = 2 🙀 $$
solid orioleBOT
doublerone
round solar
lol we can enter emojis?
$$🇺🇳🇦🇫🇦🇽🇦🇱🇩🇿🇦🇸🇦🇩🇦🇴🇦🇮🇦🇶🇦🇬🇧🇩🇦🇷🇦🇲🇦🇼🇦🇺🇦🇹🇦🇿🇧🇸🇧🇭🇧🇧🇧🇾🇧🇪🇧🇿🇧🇯🇧🇲🇧🇹🇧🇴🇧🇦🇧🇼🇧🇷🇮🇴🇻🇬🇧🇳🇧🇬🇧🇫🇧🇮🇰🇭🇨🇲🇨🇦🇨🇻🇧🇶🇰🇾🇨🇫🇹🇩🇨🇱🇨🇳🇨🇽🇨🇨🇨🇴🇰🇲🇨🇬🇨🇩🇨🇰🇨🇷🇨🇮🇭🇷🇨🇺🇨🇼🇨🇿🇨🇾🇩🇰🇩🇯🇩🇲🇩🇴🇪🇨🇪🇬🇬🇶🇸🇻🇪🇷🇪🇪🇪🇹🇪🇺🇫🇰🇫🇴🇫🇯🇫🇮🇫🇷🇬🇫🇵🇫🇹🇫🇬🇦🇬🇲🇬🇪🇩🇪🇬🇭🇬🇮🇬🇷🇬🇱🇬🇩🇬🇵🇬🇺🇬🇹🇬🇬🇬🇳🇬🇼🇬🇾🇭🇹🇭🇳🇭🇰🇭🇺🇮🇸🇮🇳🇮🇩🇮🇷🇮🇶🇮🇪🇮🇲🇮🇹🇯🇲🇯🇵🇯🇪🇯🇴🇰🇿🇰🇪🇰🇮🇽🇰🇰🇼 🇰🇬🇱🇦🇱🇻🇱🇧🇱🇸🇱🇷🇱🇾🇱🇮🇱🇹🇲🇴🇲🇰🇲🇬🇲🇼🇲🇾🇲🇻🇲🇱🇲🇹🇲🇭🇲🇷🇲🇶🇲🇺🇾🇹🇲🇽🇫🇲🇲🇩🇲🇨🇲🇳🇲🇪🇲🇸🇲🇦🇲🇿🇲🇲🇳🇦🇳🇷🇳🇵🇳🇱🇳🇨🇳🇿🇳🇮🇳🇪🇳🇬🇳🇺🇳🇫🇰🇵🇲🇵🇳🇴🇴🇲🇵🇰🇵🇼🇵🇸🇵🇦🇵🇬🇵🇾🇵🇪🇵🇭🇵🇳🇵🇱🇵🇹🇵🇷🇶🇦🇷🇪🇷🇴🇷🇼🇷🇺🇼🇸🇸🇹🇸🇲🇸🇦🇸🇳🇷🇸🇸🇨🇸🇱🇸🇬🇸🇰🇸🇽🇸🇮🇬🇸🇸🇧🇸🇴🇿🇦🇰🇷$$
$$The world$$
solid orioleBOT
doublerone
round solar
bruhh
round solar
omg
$$🇦🇫🇦🇽🇦🇱🇩🇿🇦🇸🇦🇩🇦🇴🇦🇮🇦🇶🇦🇬🇧🇩🇦🇷🇦🇲$$
$$🇦🇺🇦🇹🇦🇿🇧🇸🇧🇭🇧🇧🇧🇾🇧🇪🇧🇿🇧🇯🇧🇲🇧🇹🇧🇴$$
$$🇧🇦🇧🇼🇧🇷🇮🇴🇻🇬🇧🇳🇧🇬🇧🇫🇧🇮🇰🇭🇨🇲🇨🇦🇨🇻$$
$$🇧🇶🇰🇾🇨🇫🇹🇩🇨🇱🇨🇳🇨🇽🇨🇨🇨🇴🇰🇲🇨🇬🇨🇩🇨🇰$$
$$🇨🇷🇨🇮🇭🇷🇨🇺🇨🇼🇨🇿🇨🇾🇩🇰🇩🇯🇩🇲🇩🇴🇪🇨🇪🇬$$
$$🇬🇶🇸🇻🇪🇷🇪🇪🇪🇹🇪🇺🇫🇰🇫🇴🇫🇯🇫🇮🇫🇷🇬🇫🇵🇫$$
$$🇹🇫🇬🇦🇬🇲🇬🇪🇩🇪🇬🇭🇬🇮🇬🇷🇬🇱🇬🇩🇬🇵🇬🇺🇬🇹$$
$$🇬🇬🇬🇳🇬🇼🇬🇾🇭🇹🇭🇳🇭🇰🇭🇺🇮🇸🇮🇳🇮🇩🇮🇷🇮🇶$$
$$🇮🇪🇮🇲🇮🇹🇯🇲🇯🇵🇯🇪🇯🇴🇰🇿🇰🇪🇰🇮🇽🇰🇰🇼🇰🇬$$
$$🇱🇦🇱🇻🇱🇧🇱🇸🇱🇷🇱🇾🇱🇮🇱🇹🇲🇴🇲🇰🇲🇬🇲🇼🇲🇾$$
$$🇲🇻🇲🇱🇲🇹🇲🇭🇲🇷🇲🇶🇲🇺🇾🇹🇲🇽🇫🇲🇲🇩🇲🇨🇲🇳$$
$$🇲🇪🇲🇸🇲🇦🇲🇿🇲🇲🇳🇦🇳🇷🇳🇵🇳🇱🇳🇨🇳🇿🇳🇮🇳🇪$$
$$🇳🇬🇳🇺🇳🇫🇰🇵🇲🇵🇳🇴🇴🇲🇵🇰🇵🇼🇵🇸🇵🇦🇵🇬🇵🇾$$
$$🇵🇪🇵🇭🇵🇳🇵🇱🇵🇹🇵🇷🇶🇦🇷🇪🇷🇴🇷🇼🇷🇺🇼🇸🇸🇹$$
$$🇸🇲🇸🇦🇸🇳🇷🇸🇸🇨🇸🇱🇸🇬🇸🇰🇸🇽🇸🇮🇬🇸🇸🇧🇸🇴$$
$$🇦🇼🇿🇦🇰🇷$$
$$ 🇺🇳 the world $$🇦🇫🇦🇽🇦🇱🇩🇿🇦🇸🇦🇩🇦🇴🇦🇮🇦🇶🇦🇬🇧🇩🇦🇷🇦🇲$$
$$🇦🇺🇦🇹🇦🇿🇧🇸🇧🇭🇧🇧🇧🇾🇧🇪🇧🇿🇧🇯🇧🇲🇧🇹🇧🇴$$
$$🇧🇦🇧🇼🇧🇷🇮🇴🇻🇬🇧🇳🇧🇬🇧🇫🇧🇮🇰🇭🇨🇲🇨🇦🇨🇻$$
$$🇧🇶🇰🇾🇨🇫🇹🇩🇨🇱🇨🇳🇨🇽🇨🇨🇨🇴🇰🇲🇨🇬🇨🇩🇨🇰$$
$$🇨🇷🇨🇮🇭🇷🇨🇺🇨🇼🇨🇿🇨🇾🇩🇰🇩🇯🇩🇲🇩🇴🇪🇨🇪🇬$$
$$🇬🇶🇸🇻🇪🇷🇪🇪🇪🇹🇪🇺🇫🇰🇫🇴🇫🇯🇫🇮🇫🇷🇬🇫🇵🇫$$
$$🇹🇫🇬🇦🇬🇲🇬🇪🇩🇪🇬🇭🇬🇮🇬🇷🇬🇱🇬🇩🇬🇵🇬🇺🇬🇹$$
$$🇬🇬🇬🇳🇬🇼🇬🇾🇭🇹🇭🇳🇭🇰🇭🇺🇮🇸🇮🇳🇮🇩🇮🇷🇮🇶$$
$$🇮🇪🇮🇲🇮🇹🇯🇲🇯🇵🇯🇪🇯🇴🇰🇿🇰🇪🇰🇮🇽🇰🇰🇼🇰🇬$$
$$🇱🇦🇱🇻🇱🇧🇱🇸🇱🇷🇱🇾🇱🇮🇱🇹🇲🇴🇲🇰🇲🇬🇲🇼🇲🇾$$
$$🇲🇻🇲🇱🇲🇹🇲🇭🇲🇷🇲🇶🇲🇺🇾🇹🇲🇽🇫🇲🇲🇩🇲🇨🇲🇳$$
$$🇲🇪🇲🇸🇲🇦🇲🇿🇲🇲🇳🇦🇳🇷🇳🇵🇳🇱🇳🇨🇳🇿🇳🇮🇳🇪$$
$$🇳🇬🇳🇺🇳🇫🇰🇵🇲🇵🇳🇴🇴🇲🇵🇰🇵🇼🇵🇸🇵🇦🇵🇬🇵🇾$$
$$🇵🇪🇵🇭🇵🇳🇵🇱🇵🇹🇵🇷🇶🇦🇷🇪🇷🇴🇷🇼🇷🇺🇼🇸🇸🇹$$
$$🇸🇲🇸🇦🇸🇳🇷🇸🇸🇨🇸🇱🇸🇬🇸🇰🇸🇽🇸🇮🇬🇸🇸🇧🇸🇴$$
$$🇦🇼🇿🇦🇰🇷$$
$$ 🇺🇳 the world 🇺🇳 $$
solid orioleBOT
doublerone
$$🇦🇫🇦🇽🇦🇱🇩🇿🇦🇸🇦🇩🇦🇴🇦🇮🇦🇶🇦🇬🇧🇩🇦🇷🇦🇲$$
$$🇦🇺🇦🇹🇦🇿🇧🇸🇧🇭🇧🇧🇧🇾🇧🇪🇧🇿🇧🇯🇧🇲🇧🇹🇧🇴$$
$$🇧🇦🇧🇼🇧🇷🇮🇴🇻🇬🇧🇳🇧🇬🇧🇫🇧🇮🇰🇭🇨🇲🇨🇦🇨🇻$$
$$🇧🇶🇰🇾🇨🇫🇹🇩🇨🇱🇨🇳🇨🇽🇨🇨🇨🇴🇰🇲🇨🇬🇨🇩🇨🇰$$
$$🇨🇷🇨🇮🇭🇷🇨🇺🇨🇼🇨🇿🇨🇾🇩🇰🇩🇯🇩🇲🇩🇴🇪🇨🇪🇬$$
$$🇬🇶🇸🇻🇪🇷🇪🇪🇪🇹🇪🇺🇫🇰🇫🇴🇫🇯🇫🇮🇫🇷🇬🇫🇵🇫$$
$$🇹🇫🇬🇦🇬🇲🇬🇪🇩🇪🇬🇭🇬🇮🇬🇷🇬🇱🇬🇩🇬🇵🇬🇺🇬🇹$$
$$🇬🇬🇬🇳🇬🇼🇬🇾🇭🇹🇭🇳🇭🇰🇭🇺🇮🇸🇮🇳🇮🇩🇮🇷🇮🇶$$
$$🇮🇪🇮🇲🇮🇹🇯🇲🇯🇵🇯🇪🇯🇴🇰🇿🇰🇪🇰🇮🇽🇰🇰🇼🇰🇬$$
$$🇱🇦🇱🇻🇱🇧🇱🇸🇱🇷🇱🇾🇱🇮🇱🇹🇲🇴🇲🇰🇲🇬🇲🇼🇲🇾$$
$$🇲🇻🇲🇱🇲🇹🇲🇭🇲🇷🇲🇶🇲🇺🇾🇹🇲🇽🇫🇲🇲🇩🇲🇨🇲🇳$$
$$🇲🇪🇲🇸🇲🇦🇲🇿🇲🇲🇳🇦🇳🇷🇳🇵🇳🇱🇳🇨🇳🇿🇳🇮🇳🇪$$
$$🇳🇬🇳🇺🇳🇫🇰🇵🇲🇵🇳🇴🇴🇲🇵🇰🇵🇼🇵🇸🇵🇦🇵🇬🇵🇾$$
$$🇵🇪🇵🇭🇵🇳🇵🇱🇵🇹🇵🇷🇶🇦🇷🇪🇷🇴🇷🇼🇷🇺🇼🇸🇸🇹$$
$$🇸🇲🇸🇦🇸🇳🇷🇸🇸🇨🇸🇱🇸🇬🇸🇰🇸🇽🇸🇮🇬🇸🇸🇧🇸🇴$$
$$🇦🇼🇿🇦🇰🇷$$
$$ 🇺🇳 the world $$🇦🇫🇦🇽🇦🇱🇩🇿🇦🇸🇦🇩🇦🇴🇦🇮🇦🇶🇦🇬🇧🇩🇦🇷🇦🇲$$
$$🇦🇺🇦🇹🇦🇿🇧🇸🇧🇭🇧🇧🇧🇾🇧🇪🇧🇿🇧🇯🇧🇲🇧🇹🇧🇴$$
$$🇧🇦🇧🇼🇧🇷🇮🇴🇻🇬🇧🇳🇧🇬🇧🇫🇧🇮🇰🇭🇨🇲🇨🇦🇨🇻$$
$$🇧🇶🇰🇾🇨🇫🇹🇩🇨🇱🇨🇳🇨🇽🇨🇨🇨🇴🇰🇲🇨🇬🇨🇩🇨🇰$$
$$🇨🇷🇨🇮🇭🇷🇨🇺🇨🇼🇨🇿🇨🇾🇩🇰🇩🇯🇩🇲🇩🇴🇪🇨🇪🇬$$
$$🇬🇶🇸🇻🇪🇷🇪🇪🇪🇹🇪🇺🇫🇰🇫🇴🇫🇯🇫🇮🇫🇷🇬🇫🇵🇫$$
$$🇹🇫🇬🇦🇬🇲🇬🇪🇩🇪🇬🇭🇬🇮🇬🇷🇬🇱🇬🇩🇬🇵🇬🇺🇬🇹$$
$$🇬🇬🇬🇳🇬🇼🇬🇾🇭🇹🇭🇳🇭🇰🇭🇺🇮🇸🇮🇳🇮🇩🇮🇷🇮🇶$$
$$🇮🇪🇮🇲🇮🇹🇯🇲🇯🇵🇯🇪🇯🇴🇰🇿🇰🇪🇰🇮🇽🇰🇰🇼🇰🇬$$
$$🇱🇦🇱🇻🇱🇧🇱🇸🇱🇷🇱🇾🇱🇮🇱🇹🇲🇴🇲🇰🇲🇬🇲🇼🇲🇾$$
$$🇲🇻🇲🇱🇲🇹🇲🇭🇲🇷🇲🇶🇲🇺🇾🇹🇲🇽🇫🇲🇲🇩🇲🇨🇲🇳$$
$$🇲🇪🇲🇸🇲🇦🇲🇿🇲🇲🇳🇦🇳🇷🇳🇵🇳🇱🇳🇨🇳🇿🇳🇮🇳🇪$$
$$🇳🇬🇳🇺🇳🇫🇰🇵🇲🇵🇳🇴🇴🇲🇵🇰🇵🇼🇵🇸🇵🇦🇵🇬🇵🇾$$
$$🇵🇪🇵🇭🇵🇳🇵🇱🇵🇹🇵🇷🇶🇦🇷🇪🇷🇴🇷🇼🇷🇺🇼🇸🇸🇹$$
$$🇸🇲🇸🇦🇸🇳🇷🇸🇸🇨🇸🇱🇸🇬🇸🇰🇸🇽🇸🇮🇬🇸🇸🇧🇸🇴$$
$$🇦🇼🇿🇦🇰🇷$$
$$ 🇺🇳 the world 🇺🇳 $$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.82
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
round solar
rip
$$🇦🇫🇦🇽🇦🇱🇩🇿🇦🇸🇦🇩🇦🇴🇦🇮🇦🇶🇦🇬🇧🇩🇦🇷🇦🇲$$
$$🇦🇺🇦🇹🇦🇿🇧🇸🇧🇭🇧🇧🇧🇾🇧🇪🇧🇿🇧🇯🇧🇲🇧🇹🇧🇴$$
$$🇧🇦🇧🇼🇧🇷🇮🇴🇻🇬🇧🇳🇧🇬🇧🇫🇧🇮🇰🇭🇨🇲🇨🇦🇨🇻$$
$$🇧🇶🇰🇾🇨🇫🇹🇩🇨🇱🇨🇳🇨🇽🇨🇨🇨🇴🇰🇲🇨🇬🇨🇩🇨🇰$$
$$🇨🇷🇨🇮🇭🇷🇨🇺🇨🇼🇨🇿🇨🇾🇩🇰🇩🇯🇩🇲🇩🇴🇪🇨🇪🇬$$
$$🇬🇶🇸🇻🇪🇷🇪🇪🇪🇹🇪🇺🇫🇰🇫🇴🇫🇯🇫🇮🇫🇷🇬🇫🇵🇫$$
$$🇹🇫🇬🇦🇬🇲🇬🇪🇩🇪🇬🇭🇬🇮🇬🇷🇬🇱🇬🇩🇬🇵🇬🇺🇬🇹$$
$$🇬🇬🇬🇳🇬🇼🇬🇾🇭🇹🇭🇳🇭🇰🇭🇺🇮🇸🇮🇳🇮🇩🇮🇷🇮🇶$$
$$🇮🇪🇮🇲🇮🇹🇯🇲🇯🇵🇯🇪🇯🇴🇰🇿🇰🇪🇰🇮🇽🇰🇰🇼🇰🇬$$
$$🇱🇦🇱🇻🇱🇧🇱🇸🇱🇷🇱🇾🇱🇮🇱🇹🇲🇴🇲🇰🇲🇬🇲🇼🇲🇾$$
$$🇲🇻🇲🇱🇲🇹🇲🇭🇲🇷🇲🇶🇲🇺🇾🇹🇲🇽🇫🇲🇲🇩🇲🇨🇲🇳$$
$$🇲🇪🇲🇸🇲🇦🇲🇿🇲🇲🇳🇦🇳🇷🇳🇵🇳🇱🇳🇨🇳🇿🇳🇮🇳🇪$$
$$🇳🇬🇳🇺🇳🇫🇰🇵🇲🇵🇳🇴🇴🇲🇵🇰🇵🇼🇵🇸🇵🇦🇵🇬🇵🇾$$
$$🇵🇪🇵🇭🇵🇳🇵🇱🇵🇹🇵🇷🇶🇦🇷🇪🇷🇴🇷🇼🇷🇺🇼🇸🇸🇹$$
$$🇸🇲🇸🇦🇸🇳🇷🇸🇸🇨🇸🇱🇸🇬🇸🇰🇸🇽🇸🇮🇬🇸🇸🇧🇸🇴$$
$$🇦🇼🇿🇦🇰🇷$$
$$ 🇺🇳 the world 🇺🇳 $$
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doublerone
still hollow
$$🇳🇬$$
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v̵̋̎o̴̾͝ǐ̸̌d̸̙͘.̴̓͋
still hollow
Racist.
round solar
$$ \frac{3^x }{3^4y} = (3^3) * (3^0.5) $$
$$ 3^(x) * 3^(-4y) = 3^3.5 $$
$$ 3^(x-4y) = 3^3.5 $$
$$ x-4y = 3.5 $$
$$ x - 3.5 = 4y $$
$$ \frac{x}{4} - \frac{7}{8} = y $$
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duoblereno
round solar
breh
$$ \frac{3^x }{3^4y} = (3^3) * 3^(0.5) $$
$$ 3^(x) * 3^(-4y) = 3^(3.5) $$
$$ 3^(x-4y) = 3^(3.5) $$
$$ x-4y = 3.5 $$
$$ x - 3.5 = 4y $$
$$ \frac{x}{4} - \frac{7}{8} = y $$
solid orioleBOT
duoblereno
round solar
-_-
$$ \frac{3^x }{3^4y} = (3^3) * 3(^0.5) $$
$$ 3^(x) * 3^(-4y) = 3^(3.5) $$
$$ 3^(x-4y) = 3^(3.5) $$
$$ x-4y = 3.5 $$
$$ x - 3.5 = 4y $$
$$ \frac{x}{4} - \frac{7}{8} = y $$
solid orioleBOT
duoblereno
round solar
$$ \frac{3^x }{3^4y} = (3^3) * 3^0.5 $$
$$ 3^(x) * 3^(-4y) = 3^(3.5) $$
$$ 3^(x-4y) = 3^(3.5) $$
$$ x-4y = 3.5 $$
$$ x - 3.5 = 4y $$
$$ \frac{x}{4} - \frac{7}{8} = y $$
solid orioleBOT
duoblereno
round solar
omg
$$ \frac{3^x }{3^{4y}} = (3^3) * 3^{0.5} $$
$$ 3^x * 3^{-4y} = 3^{3.5} $$
$$ 3^{x-4y} = 3^{3.5} $$
$$ x-4y = 3.5 $$
$$ x - 3.5 = 4y $$
$$ \frac{x}{4} - \frac{7}{8} = y $$
solid orioleBOT
duoblereno
drifting herald
tf
solid orioleBOT
Alt
still hollow
how to make under root using this bot?
urban flint
how to make under root using this bot?
\sqrt
slender pecan
golden zenithBOT
Gave +1 rep to .shadoooo!
still hollow
$\sqrt(4)$
solid orioleBOT
Alt
slender wadi
who here got the allergy
unkempt horizon
$$ \int \frac{t}{2e} dt = \int \frac{1}{2e} t dt = \frac{1}{2e} \frac{t^2}{2} $$
solid orioleBOT
Geagle
round solar
$$ \frac{a+b}{1} $$
solid orioleBOT
dumbledore (apparently)
round solar
$$ \frac{\not{a+b}}{1} $$
solid orioleBOT
dumbledore (apparently)
round solar
$$ \frac{\not{a} + \not{b}}{1} $$
solid orioleBOT
dumbledore (apparently)
round solar
$$ \frac{\not{a} + \not{b}}{\not{a} + \not{b}} $$
solid orioleBOT
dumbledore (apparently)
round solar
$$ \frac{\not{a} + \not{b}}{\not{abcdef}} $$
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dumbledore (apparently)
round solar
$$ \frac{\not{a} + \not{b}}{\not{a}\not{b}\not{c}} $$
solid orioleBOT
dumbledore (apparently)
round solar
$$ \frac{\frac{\not{a}}{\not{b}\not{c}d\not{e}}}{ \frac{\not{f}}{\not{g}\not{h}\not{i}}} $$
solid orioleBOT
dumbledore (apparently)
round solar
lg
urban flint
$$ f'(g(x))\cdot g'(x) $$
solid orioleBOT
shingsuu (mimi hate club vp)
solid orioleBOT
dumbledore (apparently)
round solar
:/
urban flint
$$ [ (1+x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \cdots ]
For ((u+2)^{1/2}), we can rewrite it as:
[ (u+2)^{1/2} = 2^{1/2} \left(1 + \frac{u}{2}\right)^{1/2} ]
Using the binomial expansion for (\left(1 + \frac{u}{2}\right)^{1/2}):
[ \left(1 + \frac{u}{2}\right)^{1/2} = 1 + \frac{1}{2} \cdot \frac{u}{2} + \frac{\frac{1}{2} \left(\frac{1}{2} - 1\right)}{2!} \left(\frac{u}{2}\right)^2 + \frac{\frac{1}{2} \left(\frac{1}{2} - 1\right) \left(\frac{1}{2} - 2\right)}{3!} \left(\frac{u}{2}\right)^3 + \cdots ]
Simplifying the terms:
[ \left(1 + \frac{u}{2}\right)^{1/2} = 1 + \frac{u}{4} - \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{u^2}{8} + \frac{1 \cdot (-1) \cdot (-3)}{6} \cdot \frac{u^3}{48} + \cdots ]
[ = 1 + \frac{u}{4} - \frac{u^2}{32} + \frac{u^3}{128} + \cdots ]
Multiplying by (2^{1/2}):
[ (u+2)^{1/2} = \sqrt{2} \left(1 + \frac{u}{4} - \frac{u^2}{32} + \frac{u^3}{128} + \cdots\right) ]
Thus, the expansion of ((u+2)^{1/2}) is:
[ (u+2)^{1/2} = \sqrt{2} + \frac{\sqrt{2}u}{4} - \frac{\sqrt{2}u^2}{32} + \frac{\sqrt{2}u^3}{128} + \cdots ] $$
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silver
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slender wadi
$$ [ (1+x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + \cdot...
$$what the fuck how to you figure this out$$
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Velpun
urban flint
$$what the fuck how to you figure this out$$
magic
golden zenithBOT
Attention required <@&572709257036955649>
Reason provided:
scam link still remaining
mossy granite
thanks whoever it was (im too lazy to go check)
sturdy sable
thanks whoever it was (im too lazy to go check)
Twas me lol
mossy granite
Twas me lol
thank you :>
golden zenithBOT
Gave +1 rep to oriole1906!
manic turtle
$$ \frac{x(x+4)}{x^2+4} \not= \frac{x}{x^2+4} + \frac{x+4}{x^2+4} $$
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Huang
feral raven
uwu
prime rampart
$$\frac{x(x+4)}{x^2+4}=\frac{Ax+B}{x^2+4}+\frac{C}{x^2+4}$$
solid orioleBOT
aaaaaaaaa
prime rampart
$$\frac{x(x+4)}{x^2+4}=\frac{x^2}{x^2+4}+\frac{4x}{x^2+4}$$
solid orioleBOT
aaaaaaaaa
manic turtle
$$ \int \frac{1}{y} dy = \int dx $$
solid orioleBOT
Huang
torn frigate
Given that $x - \frac{1}{x} = \sqrt{5}$, find the value of $\frac{x^{10} + x^6 + x^4 + 1}{1 + x^2 + x^8 + x^{10}}$
solid orioleBOT
Saif
torn frigate
$$ \left(x - x^{-1} \right)^2 = x^2 - 2 + x^{-2} = \left(\sqrt{5} \right)^2 $$
$$ \fbox{$\therefore x^2 + x^{-2} = 7$} $$
$$ \left(x + x^{-1} \right)^2 = x^2 + 2 + x^{-2} = 7 + 2 = 9 $$
$$ \fbox{$\therefore x + x^{-1} = 3$} $$
$$ \left(x + x^{-1} \right)^3 = x^3 + 3x + 3x^{-1} + x^{-3} = 3^3 $$
$$ x^3 + x^{-3} + 3 \left( x + x^{-1} \right) = 27 \rightarrow x^3 + x^{-3} = 27 - 3(3) $$
$$ \fbox{$\therefore x^3 + x^{-3} = 18$} $$
$$ \left(x + x^{-1} \right)^4 = x^4 + 4x^2 + 6 + 4x^{-2} + x^{-4} = 3^4 $$
$$ x^4 + x^{-4} + 6 + 4 \left( x^2 + x^{-2} \right) = 81 \rightarrow x^4 + x^{-4} = 81 - 6 - 4(7) $$
$$ \fbox{$\therefore x^4 + x^{-4} = 47$} $$
$$ \left(x + x^{-1} \right)^5 = x^5 + 5x^3 + 10x + 10x^{-1} + 5x^{-3} + x^{-5} = 3^5 $$
$$ x^5 + x^{-5} + 5 \left( x^3 + x^{-3} \right) + 10 \left( x + x^{-1} \right) = 243 \rightarrow x^5 + x^{-5} = 243 - 5(18) - 10(3) $$
$$ \fbox{$\therefore x^5+ x^{-5} = 123$} $$
solid orioleBOT
Saif
torn frigate
$$ \left(x - x^{-1} \right)^2 = x^2 - 2 + x^{-2} = \left(\sqrt{5} \right)^2 $$
$$ \fbox{$\therefore x^2 + x^{-2} = 7$} $$
$$ \left(x + x^{-1} \right)^2 = x^2 + 2 + x^{-2} = 7 + 2 = 9 $$
$$ \fbox{$\therefore x + x^{-1} = 3$} $$
$$ \left(x + x^{-1} \right)^3 = x^3 + 3x + 3x^{-1} + x^{-3} = 3^3 $$
$$ x^3 + x^{-3} + 3 \left( x + x^{-1} \right) = 27 \rightarrow x^3 + x^{-3} = 27 - 3(3) $$
$$ \fbox{$\therefore x^3 + x^{-3} = 18$} $$
$$ \left(x + x^{-1} \right)^4 = x^4 + 4x^2 + 6 + 4x^{-2} + x^{-4} = 3^4 $$
$$ x^4 + x^{-4} + 6 + 4 \left( x^2 + x^{-2} \right) = 81 \rightarrow x^4 + x^{-4} = 81 - 6 - 4(7) $$
$$ \fbox{$\therefore x^4 + x^{-4} = 47$} $$
$$ \left(x + x^{-1} \right)^5 = x^5 + 5x^3 + 10x + 10x^{-1} + 5x^{-3} + x^{-5} = 3^5 $$
$$ x^5 + x^{-5} + 5 \left( x^3 + x^{-3} \right) + 10 \left( x + x^{-1} \right) = 243 \rightarrow x^5 + x^{-5} = 243 - 5(18) - 10(3) $$
$$ \fbox{$\therefore x^5+ x^{-5} = 123$} $$
$$ \frac{x^{10} + x^6 + x^4 + 1}{1 + x^2 + x^8 + x^{10}} \rightarrow \frac{\not{x^5} \left( x^5 + x + x^{-1} + x^{-5} \right)}{\not{x^5} \left( x^{-5} + x^{-3} + x^3 + x^5 \right)} $$
$$ \frac{x^5 + x + x^{-1} + x^{-5}}{x^{-5} + x^{-3} + x^3 + x^5} \rightarrow \frac{x^5 + x^{-5} + x + x^{-1}}{x^{-5} + x^5 + x^{-3} + x^3} \rightarrow \frac{123 + 3}{123 + 18} $$
$$ \frac{x^{10} + x^6 + x^4 + 1}{1 + x^2 + x^8 + x^{10}} = \frac{126}{141} = \frac{42}{47} = \frac{m}{n} $$
$$ \fbox{$\therefore m + n = 89$} $$
solid orioleBOT
Saif
torn frigate
$$ \left(x - x^{-1} \right)^2 = x^2 - 2 + x^{-2} = \left(\sqrt{5} \right)^2 $$
$$ \fbox{$\therefore x^2 + x^{-2} = 7$} $$
$$ \left(x + x^{-1} \right)^2 = x^2 + 2 + x^{-2} = 7 + 2 = 9 $$
$$ \fbox{$\therefore x + x^{-1} = 3$} $$
$$ \left(x + x^{-1} \right)^3 = x^3 + 3x + 3x^{-1} + x^{-3} = 3^3 $$
$$ x^3 + x^{-3} + 3 \left( x + x^{-1} \right) = 27 \rightarrow x^3 + x^{-3} = 27 - 3(3) $$
$$ \fbox{$\therefore x^3 + x^{-3} = 18$} $$
$$ \left(x + x^{-1} \right)^5 = x^5 + 5x^3 + 10x + 10x^{-1} + 5x^{-3} + x^{-5} = 3^5 $$
$$ x^5 + x^{-5} + 5 \left( x^3 + x^{-3} \right) + 10 \left( x + x^{-1} \right) = 243 \rightarrow x^5 + x^{-5} = 243 - 5(18) - 10(3) $$
$$ \fbox{$\therefore x^5+ x^{-5} = 123$} $$
$$ \frac{x^{10} + x^6 + x^4 + 1}{1 + x^2 + x^8 + x^{10}} \rightarrow \frac{\not{x^5} \left( x^5 + x + x^{-1} + x^{-5} \right)}{\not{x^5} \left( x^{-5} + x^{-3} + x^3 + x^5 \right)} $$
$$ \frac{x^5 + x + x^{-1} + x^{-5}}{x^{-5} + x^{-3} + x^3 + x^5} \rightarrow \frac{\left(x^5 + x^{-5}\right) + \left(x + x^{-1}\right)}{\left(x^{-5} + x^5\right) + \left(x^{-3} + x^3\right)} \rightarrow \frac{123 + 3}{123 + 18} $$
$$ \frac{x^{10} + x^6 + x^4 + 1}{1 + x^2 + x^8 + x^{10}} = \frac{126}{141} = \frac{42}{47} = \frac{m}{n} $$
$$ \fbox{$\therefore m + n = 89$} $$
solid orioleBOT
Saif
torn frigate
Given that $x - \frac{1}{x} = \sqrt{5}$, where $x$ is a positive rational number, find the value of $\frac{x^{10} + x^6 + x^4 + 1}{1 + x^2 + x^8 + x^{10}}$. Express your answer in the form $\frac{m}{n}$ where $(m, n) = 1$, and therefore find the value of $m + n$
solid orioleBOT
Saif
torn frigate
@valid ice Do you think there could be a simpler solution to this?
Or is this the optimal way?
valid ice
Or is this the optimal way?
Nice solution. That’s probably the best approach.
torn frigate
Nice solution. That’s probably the best approach.
I have a couple other qs I need your help with, lemme send
$(6m+7)(6n+7) - (5m+4)(5n+4) = 2024$ where $m, n$ are integers. Find $m + n$
solid orioleBOT
Saif
torn frigate
,rotate
solid orioleBOT
torn frigate
Q19
A and B take turns tossing a standard 6-sided dice. The first person who accumulates 6 or more dots wins. A starts first. If the probability for B to win by tossing the dice twice is $\frac{m}{n}$, and $(m, n) = 1$, find $m+n$
solid orioleBOT
Saif
torn frigate
If there is only one element in set $A = { x \in \mathbb{Z} | x^2 - (a+2)x + 2 - a < 0 }$, and the range of a positive real number $a$ is $(m, n]$, find $m+n$.
solid orioleBOT
Saif
torn frigate
Would be great if you could help with these at your convenience, no rush!
torn frigate
What I did for this was:
Irrespective of whether m, n are odd, the first term would always be odd. Therefore the second term needs to be odd too. For the second term to be odd, both m and n need to be odd. Therefore m and n are odd.
If m and n are odd, 5m and 5n would always end in 5, therefore 5m + 4 and 5n + 4 would always end in 9. Two numbers ending in 9, when multiplied, give a product that ends in 1. Therefore term two has last digit 1.
Since term two has last digit 1, term one must have last digit 5, so that they subtract to give 4. For the last digit of term one to be 5, at least one of 6m and 6n need to end in 8. The only last digit that fits both criteria is 3. Therefore at least one of m and n ends in 3.
Those have been my deductions so far.
manic turtle
$\sin(2x)=\frac{2tan(x)}{1+tan^2(x)}$\
$\cos(2x)=\frac{1-tan^2(x)}{1+tan^2(x)}$\
solid orioleBOT
Huang
torn frigate
$$ (6m + 7)(6n + 7) = 2024 $$
$$ 36mn + 42(m + n) + 49 - 25mn - 20(m + n) - 16 = 2024 $$
$$ 11mn + 22(m + n) + 33 = 2024 $$
$$ mn + 2m + 2n + 3 = 184 $$
$$ mn + 2m + 2n + 4 = 185 $$
$$ m(n + 2) + 2(n + 2) = 185 $$
$$ (m + 2)(n + 2) = 185 $$
$$ 185 = 5 \cdot 37 \rightarrow 185 = (3 + 2)(35 + 2) $$
$$ \fbox{$\therefore m + n = 38$} $$
solid orioleBOT
Saif
manic turtle
$$f^-1(x) = \frac{1}{f'(f^-1(x))}$$
solid orioleBOT
Huang
torn frigate
$$f^-1(x) = \frac{1}{f'(f^-1(x))}$$
$$f^{-1}(x) = \frac{1}{f'(f^{-1}(x))}$$
solid orioleBOT
Saif
manic turtle
$$f^{-1}(x) = \frac{1}{f'(f^{-1}(x))}$$
thanks lol
golden zenithBOT
Gave +1 rep to saifurrahman!
valid ice
Q19
For Q19 above, let g(x) = f(x) - 2024x, => g(1)=g(2)=g(3)=g(4)=0 => (x-1)(x-2)(x-3)(x-4) | g(x).
will take look at the others if i have time
mossy granite
$$ \left(x - x^{-1} \right)^2 = x^2 - 2 + x^{-2} = \left(\sqrt{5} \right)^2 $$
$...
wall text
broken vapor
,help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
vagrant pier
,help
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A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
manic turtle
$$log_3(x^2+4x)>0$$
where $$x^2+4x>0$$
solid orioleBOT
Huang
round solar
h
$$ h $$
solid orioleBOT
doublerone
round solar
$heh$
solid orioleBOT
doublerone
solid orioleBOT
doublerone
round solar
x^2
$$test$$
solid orioleBOT
doublerone
Compile Error! Click the reaction for more information.
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round solar
hmm $x^2$
$$test$$
solid orioleBOT
doublerone
round solar
oo
round solar
Finding X intercepts,
For equation 1, $y = 16 - 2x$
Let y = 0
$$0 = 16 - 2x$$
$$x = \frac{-16}{-2}$$
$$x = 8$$
Hence ;
$$(x-8)(R) = x^3 - 15x^2 + 66x - 80$$
Finding First term of R
$$xR - 8R = x^3 -15x^2 + 66x - 80$$
Here only xR can lead to $x^3$, so it is assumed the first term of R is equal to $x^2$
Finding Second term of R
$$xR - 8R = -15x^2$$
Since the first term of R is $x^2$,
$$xR - 8x^2 = -15x^2$$
$$xR = 8x^2 - 15x^2$$
$$xR = -7x^2$$
$$R = \frac{-7x^2}{x}$$
$$R = -7x$$
$$(x-8)(x^2 - 7x + c) = x^3 - 15x^2 + 66x -80$$
Expanding the first equation to find c
$$x(x^2 - 7x + c) - 8(x^2 - 7x + c) = x^3 - 15x^2 + 66x -80$$
$$x^3 - 7x^2 + cx - 8x^2 + 56x -8c = x^3 - 15x^2 + 66x - 80$$
$$Simplify$$
$$(c+56)x - 8c = 66x - 80$$
$$c+56 = 66$$
$$c = 10$$
$$R = x^2 - 7x + 10$$
Simplifying R:
$$R = x^2 - 2x - 5x + 10$$
$$R = x(x-2) - 5(x-2)$$
$$R = (x-5)(x-2)$$
equation:
$$y = (x-8)(x-5)(x-2)$$
X intercepts: (8,0) (5,0) (2,0)
solid orioleBOT
doublerone
round solar
Finding Intercepts between line and curve:
$$x^3 - 15x^2 + 66x - 80 = 16 - 2x$$
$$x^3 - 15x^2 + 68x - 96 = 0$$
Since both graphs intersect at (8,0)
$$(x-8)(R) = x^3 - 15x^2 + 68x - 96$$
We know that the first and second term of R are $(x^2 - 7x)$
So $-8R = -96$
$$R = \frac{-96}{-8}$$
$$R = 12$$
$$(x - 8)(x^2 - 7x + 12)$$
simplifying R:
$$R = x^2 - 7x + 12$$
$$R = x^2 -3x -4x + 12$$
$$R = x(x-3) - 4(x-3)$$
$$R = (x-4)(x-3)$$
$$y = (x-8)(x-4)(x-3)$$
$$y = 16-2x$$
$$y = 16 - 2(4)$$
$$y = 8$$
$$y = 16-2(3)$$
$$y = 10$$
Graph intercepts: (8,0 (4,8) (3,10)
solid orioleBOT
doublerone
round solar
finding area under graph by Integrating $x^3 - 15x^2 + 66x - 80$
$$\int x^3 - 15x^2 + 66x - 80 dx$$
$$ = \frac{x^4}{4} -5x^3 + 33x^2 - 80x$$
area from x = 3 to x = 4
$$\left(\frac{4^4}{4} -5(4)^3 + 33(4)^2 - 80(4)\right) - \left(\frac{3^4}{4} -5(3)^3 + 33(3)^2 - 80(3)\right)$$
$$ = 9.75$$
area from x = 4 to x = 5
$$\left(\frac{5^4}{4} -5(5)^3 + 33(5)^2 - 80(5)\right) - \left(\frac{4^4}{4} -5(4)^3 + 33(4)^2 - 80(4)\right)$$
$$ = 4.25$$
Area from x = 4 to x = 8
$$= \frac{1}{2}(4)(8) - 4.25$$
$$= 11.75$$
Area from x = 3 to x = 4
$$= 9.75 - \frac{1}{2} (8+10)$$
$$= 0.75$$
Shaded area $= 11.75 + 0.75 = 12.5$ Ans.
solid orioleBOT
doublerone
prime rampart
,help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
prime rampart
,list
solid orioleBOT
prime rampart
,help cmd
solid orioleBOT
You really shouldn't take it literally :upside_down:. Please type ,help ping, for example!
The full command list may be found using ,list.
round solar
$$ X_x$$
solid orioleBOT
doublerone
wide haven
,list
solid orioleBOT
round solar
$$[x]^{31291381}_{342852}$$
solid orioleBOT
doublerone
sturdy vortex
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
brave oasis
,help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
serene vale
,help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
jolly kraken
znc grow
golden zenithBOT
This command can only be used in bot-stuff channels.
jolly kraken
omg
manic turtle
$\int_{a}^{b} f(t) dt=\int_{a}^{b} f(a+b-t) dt$
solid orioleBOT
Huang
solid orioleBOT
doublerone
manic turtle
If the set of vectors $v_1,v_2,v_3$ are not linearly independent, $\forall c_1,c_2,c_3\quad c_1\textbf{v}_1 + c_2\textbf{v}_2 + c_3 = 0$
solid orioleBOT
Huang
manic turtle
If the set of vectors $v_1,v_2,v_3$ are not linearly independent, $\forall c_1,c_2,c_3\quad c_1\textbf{v}_1 + c_2\textbf{v}_2 + c_3\textbf{v}_3 = 0$
solid orioleBOT
Huang
polar python
$ \\To print NREC \
\document class [ac, paper] {article}
\begin {document}
NREC
\end {document} $
polar python
$
\begin{aligned}
\frac{\partial(r,\theta)}{\partial(x,y)}
&=
\begin{matrix}
{\frac{x}{r} }& {\frac{y}{r} }
-\frac{y}{x^{2}+y^{2}} & \frac{x}{x^{2}+y^{2}}
\end{matrix}
\frac{x^{2}+y^{2}}{r(x^{2}+y^{2})}
= \frac{1}{r}.
\end{aligned}
$
solid orioleBOT
Kurosaki Ichigo
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
frail sluice
$f(x) = 3^{x+2}$
$y = 3^{x+2}$
$x = 3^{y+2}$
$\log_3 (x) = y-2$
$y = \log_3 (x) + 2$
$f^{-1} (x) = \log_3 (x) + 2$
solid orioleBOT
Muhammad Hasan
frail sluice
$\alpha = 38.68 \text{ (taking it positive)}$
$\text{ Since sinx was negative, we'll look at quadrants where sin is negative in CAST diagram and it'll be third and fourth quad}$
$x = 180 + 38.68, 360 - 38.68$
solid orioleBOT
Muhammad Hasan
frail sluice
$2c+30 = \frac{9c}{5} + 32$
$2c - 2 = \frac{9c}{5}$
$10c-10 = 9c$
$\boxed{c = 10}$
solid orioleBOT
Muhammad Hasan
silent oasis
\begin{tikzpicture}
\draw (0,1) to[bend left=10] (0,6);
\draw (0,1) to[bend right=5] (0,0);
\draw (0,0) to[bend right=10] (2,0);
\draw (2,0) to[bend right=5] (2.25,2);
\draw (2.25,2) to[bend right=10] (3,2);
\draw (1.75,2.125) to[bend right=8] (2.25,2);
\draw (3,2) to[bend right=5] (3,-0.25);
\draw (3,-0.25) to[bend right=10] (5,-0.25);
\draw (5,-0.25) to[bend right=5] (5.25,7.25);
\draw (5.25,7.25) to[bend right=30] (3,10);
\draw (3,10) to[bend right=15] (2,10);
\draw (2,10) to[bend right=30] (0.5,8.28);
\draw (5.25,7.25) to[bend left=5] (6.25,7.15);
\draw (6.25,7.15) to[bend left=5] (6.25,2.5);
\draw (6.25,2.5) to[bend left=20] (5.25,2.25);
\draw (-1,7.08) to[bend right=90] (3.25,7.08);
\draw (-1,7.08) to[bend left=90] (3.25,7.08);
\end{tikzpicture}
\begin{tikzpicture}
\draw (0,1) to[bend left=10] (0,6);
\draw (0,1) to[bend right=5] (0,0);
\draw (0,0) to[bend right=10] (2,0);
\draw (2,0) to[bend right=5] (2.25,2);
\draw (2.25,2) to[bend right=10] (3,2);
\draw (1.75,2.125) to[bend right=8] (2.25,2);
\draw (3,2) to[bend right=5] (3,-0.25);
\draw (3,-0.25) to[bend right=10] (5,-0.25);
\draw (5,-0.25) to[bend right=5] (5.25,7.25);
\draw (5.25,7.25) to[bend right=30] (3,10);
\draw (3,10) to[bend right=15] (2,10);
\draw (2,10) to[bend right=30] (0.5,8.28);
\draw (5.25,7.25) to[bend left=5] (6.25,7.15);
\draw (6.25,7.15) to[bend left=5] (6.25,2.5);
\draw (6.25,2.5) to[bend left=20] (5.25,2.25);
\draw (-1,7.08) to[bend right=90] (3.25,7.08);
\draw (-1,7.08) to[bend left=90] (3.25,7.08);
\end{tikzpicture}'
solid orioleBOT
kayla
silent oasis
ohhh
lyric token
What's this
silent oasis
latex
lyric token
Nuh uh
silent oasis
yah
lyric token
Nah
wide haven
..
$\begin{pmatrix}\alpha_{11} & \cdots & \alpha_{1m} \\vdots & \ddots & \vdots \\alpha_{m1} & \cdots & \alpha_{mm}\end{pmatrix};\otimes;\begin{pmatrix}\beta_{11} & \cdots & \beta_{1k} \\vdots & \ddots & \vdots \\beta_{k1} & \cdots & \beta_{kk}\end{pmatrix}=\begin{pmatrix}\alpha_{11}\beta_{11} & \cdots & \alpha_{11}\beta_{1k} & \cdots & \alpha_{1m}\beta_{11} & \cdots & \alpha_{1m}\beta_{1k} \\vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\alpha_{11}\beta_{k1} & \cdots & \alpha_{11}\beta_{kk} & \cdots & \alpha_{1m}\beta_{k1} & \cdots & \alpha_{1m}\beta_{kk} \\vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\alpha_{m1}\beta_{11} & \cdots & \alpha_{m1}\beta_{1k} & \cdots & \alpha_{mm}\beta_{11} & \cdots & \alpha_{mm}\beta_{1k} \\vdots & \ddots & \vdots & \ddots & \vdots & \ddots & \vdots \\alpha_{m1}\beta_{k1} & \cdots & \alpha_{m1}\beta_{kk} & \cdots & \alpha_{mm}\beta_{k1} & \cdots & \alpha_{mm}\beta_{kk}\end{pmatrix} $\end{document}
solid orioleBOT
attacker2007 🎀
wide haven
finally
$\mathcal{U} =\begin{pmatrix}\frac{1}{2} & \frac{1}{2} & \frac{1}{2} & 0 & 0 & \frac{1}{2} \\frac{1}{2} & \frac{i}{2} & -\frac{1}{2} & 0 & 0 & -\frac{i}{2} \\frac{1}{2} & -\frac{1}{2} & \frac{1}{2} & 0 & 0 & -\frac{1}{2} \0 & 0 & 0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0 \\frac{1}{2} & -\frac{i}{2} & -\frac{1}{2} & 0 & 0 & \frac{i}{2} \0 & 0 & 0 & -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} &0\end{pmatrix}$\end{document}
$H \otimes \mathcal{I} = \begin{pmatrix} \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}} \end{pmatrix} \otimes \begin{pmatrix} 1 & 0 \0 & 1 \end{pmatrix}=\begin{pmatrix} \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} & 0 \0 & \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \\frac{1}{\sqrt{2}} & 0 & -\frac{1}{\sqrt{2} & 0 \0 & \frac{1}{\sqrt{2}} & 0 & -\frac{1}\sqrt{2} \end{pmatrix} \end{document}
solid orioleBOT
attacker2007 🎀
wide haven
$H \otimes 1 = \begin{pmatrix} \frac{1}{\sqrt&{2}} & \frac{1}{\sqrt&{2}} \\frac{1}{\sqrt&{2}} & -\frac{1}{\sqrt&{2}} \end{pmatrix} \otimes \begin{pmatrix} 1 & 0 \0 & 1 \end{pmatrix}=\begin{pmatrix} \frac{1}{\sqrt&{2}} & 0 & \frac{1}{\sqrt&{2}} & 0 \0 & \frac{1}{\sqrt&{2}} & 0 & \frac{1}{\sqrt&{2}} \\frac{1}{\sqrt&{2}} & 0 & -\frac{1}{\sqrt&{2}} & 0 \0 & \frac{1}{\sqrt&{2}} & 0 & -\frac{1}{\sqrt&{2}} \end{pmatrix} \end{document}
solid orioleBOT
attacker2007 🎀
$H \otimes 1 = \begin{pmatrix} \frac{1}{\sqrt&{2}} & \frac{1}{\sqrt&{2}} \\\frac{1}{\sqrt&{2}} & -\frac{1}{\sqrt&{2}} \end{pmatrix} \otimes \begin{pmatrix} 1 & 0 \\0 & 1 \end{pmatrix}=\begin{pmatrix} \frac{1}{\sqrt&{2}} & 0 & \frac{1}{\sqrt&{2}} & 0 \\0 & \frac{1}{\sqrt&{2}} & 0 & \frac{1}{\sqrt&{2}} \\\frac{1}{\sqrt&{2}} & 0 & -\frac{1}{\sqrt&{2}} & 0 \\0 & \frac{1}{\sqrt&{2}} & 0 & -\frac{1}{\sqrt&{2}} \end{pmatrix} \end{document}
```Compilation error:```! Missing { inserted.
<to be read again>
&
l.49 ...es 1 = \begin{pmatrix} \frac{1}{\sqrt&{2}}
& \frac{1}{\sqrt&{2}} \\\...
A left brace was mandatory here, so I've put one in.
You might want to delete and/or insert some corrections
so that I will find a matching right brace soon.
(If you're confused by all this, try typing `I}' now.)```
wide haven
...
the root twos broke >.<
[
H \otimes \mathbb{I}
\begin{pmatrix}
\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} \
\frac{1}{\sqrt{2}} & -\frac{1}{\sqrt{2}}
\end{pmatrix}
\otimes
\begin{pmatrix}
1 & 0 \
0 & 1
\end{pmatrix}
\begin{pmatrix}
\frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} & 0 \
0 & \frac{1}{\sqrt{2}} & 0 & \frac{1}{\sqrt{2}} \
\frac{1}{\sqrt{2}} & 0 & -\frac{1}{\sqrt{2}} & 0 \
0 & \frac{1}{\sqrt{2}} & 0 & -\frac{1}{\sqrt{2}}
\end{pmatrix}
]
solid orioleBOT
attacker2007 🎀
stable sapphire
\[
H \otimes \mathbb{I}
=
\begin{pmatrix}
\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}...
that is crazy
wide haven
It's not that bad
It's basically applying a hadamard gate on a qubit and doing nothing on the other qubit
So you can get the tensor product between them if you wanted to
main sentinel
stable sapphire
$x^2$
solid orioleBOT
Ved Karjagi
solid orioleBOT
Ved Karjagi
stable sapphire
$$ x^2 $$
solid orioleBOT
Ved Karjagi
stable sapphire
$$
\center{x^2}
$$
solid orioleBOT
Ved Karjagi
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
wide haven
$$
\text{Fick's First Law of Diffusion states that: }
\mathbb{J} = -\mathbb{D}\frac{d\phi}{dx}
$$
solid orioleBOT
attacker2007 🎀
wide haven
$$
\text{Consequently, Fick's Second Law of Diffusion states that: }
\frac{\delta\phi}{\delta t} = \mathbb{D}\frac{\delta^2\phi}{\delta x^2}
$$
solid orioleBOT
attacker2007 🎀
wide haven
$$
\text{If we wish to compute in 2 or more dimensions, the Laplacian(}
\Delta = \nabla^2
\text{)}
\text{ must be used, which results in: }
\frac{\delta\phi}{\delta t} = \mathbb{D}\delta_{\phi}
$$
$$
\frac{\delta\phi}{\delta t} = \mathbb{D}\delta_{\phi}
$$
solid orioleBOT
attacker2007 🎀
attacker2007 🎀
$$
\text{If we wish to compute in 2 or more dimensions, the Laplacian(}
\Delta = \nabla^2
\text{)}
\text{ must be used, which results in: }
\frac{\delta\phi}{\delta t} = \mathbb{D}\delta_{\phi}
$$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.53
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
foggy garnet
$1+1$
solid orioleBOT
hersheys
lofty raven
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
$$x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$
```Compilation error:```! Display math should end with $$.
<to be read again>
l.49 $$x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}$
The `$' that I just saw supposedly matches a previous `$$'.
So I shall assume that you typed `$$' both times.
Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l
ocal/texlive/2023/texmf-dist/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/local/texli```
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$
$\text {if $ b^2 - 4ac < 0 $, quadratic has no real roots}$
how does text work huh
uh
i see
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
ooo
$\text meow $ a-b $$
k
$$ ax^2 + bx + c = 0,
\text if $ b^2 - 4ac > 0, x \in \mathbb{R} $$
$R=mgcos{\theta}$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$ T_A = \frac{9mg}{4} - mgcos{\theta} $$
$$ \newline T_B = 4T_A = 9mg - 4mgcos{\theta} $$
$$ 9mg - 4mgcos{\theta} = 4mg + \frac{9}{2}mg $$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$ T_A = \frac{9mg}{4} - mgcos{\theta} \
T_B = 4T_A = 9mg - 4mgcos{\theta}
9mg - 4mgcos{\theta} = 4mgcos{\theta} + \frac{9}{2}mg
8mgcos{\theta} = \frac{9}{2}mg
cos{\theta} = \frac{9}{2*8} $$
ok
$$help
erm
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
,help
solid orioleBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
lofty raven
,list
solid orioleBOT
solid orioleBOT
Failed to load your guild. Please try again in a few minutes.
lofty raven
,whohas community moderator
solid orioleBOT
Failed to load your guild. Please try again in a few minutes.
lofty raven
@unkempt horizon any clue why it fails every time? havent been able to get members of a role in forever
,config
solid orioleBOT
solid orioleBOT
lofty raven
$$ T_A = \frac{9mg}{4} - mgcos{\theta}
T_B = 4T_A = 9mg - 4mgcos{\theta}
9mg - 4mgcos{\theta} = 4mgcos{\theta} + \frac{9}{2}mg
8mgcos{\theta} = \frac{9}{2}mg
cos{\theta} = \frac{9}{2*8} $$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
$$ T_A = \frac{9mg}{4} - mgcos{\theta}
T_B = 4T_A = 9mg - 4mgcos{\theta}
9mg - 4mgcos{\theta} = 4mgcos{\theta} + \frac{9}{2}mg
8mgcos{\theta} = \frac{9}{2}mg
cos{\theta} = \frac{9}{2*8} $$
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.50
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.```
lofty raven
$$ T_A = \frac{9mg}{4} - mgcos{\theta} $$
$$ T_B = 4T_A = 9mg - 4mgcos{\theta} $$
$$ 9mg - 4mgcos{\theta} = 4mgcos{\theta} + \frac{9}{2}mg $$
$$ 8mgcos{\theta} = \frac{9}{2}mg $$
$$ cos{\theta} = \frac{9}{2*8} $$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$\int\frac{1}{x} dx = \ln{x} + C$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\int\frac{1}{x}dx$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
\hi\
$ \text{The mass-energy equivalence is described by the famous equation}
[E=mc^2]
\text{discovered in 1905 by Albert Einstein.
In natural units ($c$ = 1), the formula expresses the identity}
[E=m]
$
lofty raven
$\int u\frac{dv}{dx}dx = uv - \int v\frac{du}{dx}dx$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$\int f'(x) dx = f(x) + c$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$\lambda\begin{pmatrix} 1\ 2\ 3 \end{pmatrix}$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$cos{\theta} = \frac{\begin{pmatrix} a_1\ a_2\ a_3 \end{pmatrix} \cdot \begin{pmatrix} b_1\ b_2\ b_3 \end{pmatrix}}{\sqrt{a_1^2 + a_2^2 + a_3^2}\sqrt{b_1^2 + b_2^2 + b_3^3}}$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
unkempt horizon
<@779240673429028875> any clue why it fails every time? havent been able to get ...
no clue fr
lofty raven
$$\int\frac{4}{x}dx = 4\int\frac{1}{x}dx = 4\ln{x} + C$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\beginpmatrix 5 \ 4 \ 3 \endpmatrix$$
foggy garnet
$(a+b)^{n} = \sum_{k=0}^{n} a^{n-k} b^{k}$
solid orioleBOT
hersheys
lofty raven
$$tan{r+1} = \frac{tan{r}+tan{1}}{1-tan{r}{tan{1}}$$
$$=\frac{sin{r}cos{1}+cos{r}sin{1}}{1-\frac{sin{r}sin{1}}{cos{r}cos{1}}}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$cos(r+1)=cos(r)cos(1)-sin(r)sin(1)$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\frac{sin(r+1)}{cos(r+1)} = \frac{sin(r)cos(1)+cos(r)sin(1)}{cos(r+1)}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\frac{sin(r)cos(1)+cos(r)sin(1)}{cos(r+1)} - \frac{sin(r)}{cos(r)}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\frac{sin(r)cos(1)cos(r)+cos^2(r)sin(1)}{cos(r+1)cos(r)}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\frac{\frac{sin(2r)}{2}cos(1)+cos^2(r)sin(1)}{cos(r+1)cos(r)}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\frac{cos(r)[sin(r)cos(1)+cos(r)sin(1)]}{cos(r+1)cos(r)}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\frac{sin(r)cos(1)+cos(r)sin(1)}{cos(r+1)}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\frac{sin(r)cos(1)cos(r)+cos^2(r)sin(1) - sin(r)[cos(r)cos(1)-sin(r)sin(1)]}{cos(r+1)cos(r)}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$cos^2(r)sin(1)+sin^2(r)sin(1)$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$= sin(1)[cos^2(r)+sin^2(r)]$$
$$cos^2(r) + sin^2(r) = 1 \therefore sin(1)[cos^2(r)+sin^2(r)] = sin(1)$$
YES
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
lofty raven
$$\frac{sin(r+1)}{cos(r+1)} = \frac{sin(r)cos(1)+cos(r)sin(1)}{cos(r+1)}$$
$$\frac{sin(r)cos(1)+cos(r)sin(1)}{cos(r+1)} - \frac{sin(r)}{cos(r)}$$
$$\frac{sin(r)cos(1)cos(r)+cos^2(r)sin(1) - sin(r)[cos(r)cos(1)-sin(r)sin(1)]}{cos(r+1)cos(r)}$$
$$\frac{cos^2(r)sin(1) + sin(r)cos(r)cos(1)- sin(r)cos(r)cos(1)-sin^2(r)sin(1)}{cos(r+1)cos(r)}$$
$$=\frac{sin(1)[cos^2(r)+sin^2(r)]}{cos(r+1)cos(r)}$$
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
solid orioleBOT
helpy/femdevil/takenbydemonlord😝
stable sapphire
Write the equations in a standard form, and align the variables
$\qquad 2x + 3y = 21$
$\qquad x - y = -2$
Multiply one or both equations to make the coefficients of one of the variables the same with opposite signs
$\qquad 2x + 3y = 21$
$\qquad(x - y = -2) \times 3$
$\qquad3x - 3y = -6$
Cancel out one of the variables and solve for the other one
$\qquad \quad \phantom{3}\ 2x + \cancel{3y} = 21$
$\qquad +\quad 3x - \cancel{3y} = -6$
$\qquad \rule{3.5cm}{0.4pt}$
$\qquad \qquad 5x \phantom{+ \cancel{3y}}= 15$
$\qquad x = 3$
Solve for the variable that we cancelled out earlier
$\qquad x - y = -2$
$\qquad y = x + 2$
$\qquad y = (3) + 2 = 5$
solid orioleBOT
Ved Karjagi
stable sapphire
Yum
civic quiver
Write the equations in a standard form, and align the variables
$\qquad 2x + 3y = 21$
$\qquad x - y = -2$
Multiply one or both equations to make the coefficients of one of the variables the same with opposite signs
$\qquad 2x + 3y = 21$
$\qquad(x - y = -2) \times 3$
$\qquad3x - 3y = -6$
Cancel out one of the variables and solve for the other one
$\qquad \quad \phantom{3}\ 2x + \cancel{3y} = 21$
$\qquad +\quad 3x - \cancel{3y} = -6$
$\qquad \rule{3.5cm}{0.4pt}$
$\qquad \qquad 5x \phantom{+ \cancel{3y}}= 15$
$\qquad x = 3$
Solve for the variable that we cancelled out earlier
$\qquad x - y = -2$
$\qquad y = x + 2$
$\qquad y = (3) + 2 = 5$
solid orioleBOT
t0ken
lofty raven
copy
fallow nexus
whats 9 + 10
hazy jacinth
21
lofty raven
how does this shit work
gotta put $ before and after
olive imp
gotta put $ before and after
$2+2$
solid orioleBOT
Ayesha
olive imp
cute
lofty raven
!!
half minnow
$=5$
solid orioleBOT
himalayancat
half minnow
$○ ○$
$ ^ $
solid orioleBOT
himalayancat
$○ ○$
$ ^ $
```Compilation error:```! LaTeX Error: Unicode character ○ (U+25CB)
not set up for use with LaTeX.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.49 $○
○$
You may provide a definition with
\DeclareUnicodeCharacter```
half minnow
$' '$
$ - $
solid orioleBOT
himalayancat
$' '$
$ - $
```Compilation error:```! Double superscript.
<recently read> ^
l.49 $' '
$
I treat `x^1^2' essentially like `x^1{}^2'.
Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l
ocal/texlive/2023/texmf-dist/fonts/enc/dvips/lm/lm-mathsy.enc}]
(./705488212965064777.aux)```
himalayancat
$1234
56789$
unborn bloom
**himalayancat**
radiohead ref
lofty raven
close enuf
lofty raven
$$\ln\left(\frac{p}{q}\right) = a, \ln\left(q^2p\right) = b$$
$$\frac{p}{q} = e^a, q^2p=e^b$$
solid orioleBOT
helpy/femdevil/takenbydemonlord
rapid nymph
$$hi$$
solid orioleBOT
Raiyan
rapid nymph
$$ln(5/3)$$
solid orioleBOT
Raiyan
rapid nymph
$$6x + 2y =7$$
$$2x + 4y = 8 $$
$$solve for x and y$$
solid orioleBOT
Raiyan
rapid nymph
/sum
rapid nymph
$$/frac{0.17}{2.67} x 100$$
solid orioleBOT
Raiyan
solid orioleBOT
Raiyan
solid orioleBOT
Raiyan
rapid nymph
$$\frac{0.17}{2.67}$$
solid orioleBOT
Raiyan
rapid nymph
$$D = \frac{1}{no. of lines per mllimeter x 10^{3}}$$
solid orioleBOT
Raiyan
rapid nymph
$$D = \frac{1}{no.\ of\ lines\ per\ mllimeter\ x\ 10^{3}}$$
solid orioleBOT
Raiyan
rapid nymph
$$D = \frac{1}{no.\ of\ lines\ per\ millimeter\ x\ 10^{3}}$$
solid orioleBOT
Raiyan
rapid nymph
$$D = \frac{1}{no.\ of\ lines\ per\ millimeter\ \times\ 10^{3}}$$
solid orioleBOT
Raiyan
rapid nymph
$$+$$
solid orioleBOT
Raiyan
rapid nymph
$$_$$
solid orioleBOT
Raiyan
rapid nymph
$$_$$
solid orioleBOT
Raiyan
rapid nymph
$$hi\ ben$$
solid orioleBOT
Raiyan
radiant island
$\mathcal{L}$
solid orioleBOT
Pugs
radiant island
$\mathcal{LMAO}$
solid orioleBOT
Pugs
rare raft
$\mathcal{GAY}$
solid orioleBOT
hayzy 月下獣
radiant island
Sexy
sturdy sable
$\mathcal{Sexy}$
solid orioleBOT
EminemSomething
sturdy sable
$\mathcal{SEXY}$
solid orioleBOT
EminemSomething
rare raft
**EminemSomething**
Is this how they propose in roman?
radiant island
$\mathfrak{NO}$
solid orioleBOT
Pugs
solid orioleBOT
AlexV
olive leaf
$\mathfrak{NOU}$
valid ice
$\mathfrak{UVW}$
solid orioleBOT
Boeing-747
valid ice
$\mathcal{UVW}$
scenic orchid
$\mathcal{GAY}$
solid orioleBOT
Broski 6w9
valid ice
$\mathcal{abcdeABCDE}$
solid orioleBOT
AlexV
solid orioleBOT
AlexV
valid ice
$\textgoth{ABCDE}$
solid orioleBOT
AlexV
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
radiant island
$\textgoth{ABCDE}$
LOL
valid ice
Apparently with the right package it can display blackletter font
radiant island
$\textbf{PUGSISGAY}$
solid orioleBOT
Pugs
rare raft
Ohh
prime rampart
Yea
rare raft
Ohh
prime rampart
$amazing$
solid orioleBOT
ripilicious
prime rampart
Amazing
rare raft
$/textit{WHO WAS IN PARIS}$
solid orioleBOT
hayzy 月下獣
radiant island
Wait lemme try sth
rare raft
Well
radiant island
$/textit{WHO WAS IN PARIS}$
Forward slash my lad
rare raft
Fuck
radiant island
Let's test it's limit
$$F^{'}{\mu \nu} = \partial{\mu}(A_{\nu} + \partial_{\nu}f) - \partial_{\nu}(A_{\mu} + \partial_{\mu}f)$$
$$F^{'}{\mu \nu} = \partial{\mu}A_{\nu} + \partial_{\mu}\partial_{\nu}f - \partial_{\nu}A_{\mu} - \partial_{\nu}\partial_{\mu}f$$
solid orioleBOT
Pugs
void hawkBOT
rare raft
$\textit{who was in paris}
cyan ridge
u need to end it w a $
rare raft
$\textit{who was in paris}$
solid orioleBOT
hayzy 月下獣
rare raft
IK I FORGOT
radiant island
$who was in paris$
solid orioleBOT
Pugs
radiant island
Ah the spacing
valid ice
Try a continued fraction
radiant island
$F^{'}{\mu \nu} = \partial{\mu}(A{\nu} + \partial{\nu}f) - \partial{\nu}(A{\mu} + \partial{\mu}f) \rightarrow F^{'}{\mu \nu} = \partial{\mu}A{\nu} + \partial{\mu}\partial{\nu}f - \partial{\nu}A{\mu} - \partial{\nu}\partial{\mu}f$
cyan ridge
rip
solid orioleBOT
Pugs
radiant island
Ah right
radiant island
Ye
rare raft
Hmm
cyan ridge
$\textit{yall need to} \mathbf{CALM DOWN}$
solid orioleBOT
TicTac
cyan ridge
no space TT
rare raft
Put a space
valid ice
$\frac 1 {1+\frac 1{1+\frac 1 {1+\frac 1{1+\cdots}}}}$
radiant island
$\textit{yall need to} \mathbf{CALM DOWN}$
$\mathfrak{NAH}$
solid orioleBOT
Pugs
rare raft
Wtf
radiant island
What'd you try?
solid orioleBOT
AlexV
cyan ridge
nais
rare raft
$\underline{white girls be like}$
solid orioleBOT
hayzy 月下獣
radiant island
Bruh
valid ice
$1+\frac 1 {1+\frac 1{1+\frac 1 {1+\frac 1{1+\cdots}}}}=\varphi$
solid orioleBOT
AlexV
valid ice
$\aquarius$
solid orioleBOT
AlexV
valid ice
Nice
cyan ridge
wha??
valid ice
$\aries \taurus \gemini$
cyan ridge
i was just about to do that xd
solid orioleBOT
AlexV
cyan ridge
XD
valid ice
$\Re (z) + i\Im (z)$
solid orioleBOT
AlexV
valid ice
$\Re$
solid orioleBOT
AlexV
solid orioleBOT
AlexV
valid ice
$\tilde \approx \aquarius$
solid orioleBOT
AlexV
outer sky
Nice
scenic orchid
$\amongus
valid ice
For small $x, (1+x)^n \aquarius 1+ nx$.
sturdy sable
$\amogus
solid orioleBOT
AlexV
scenic orchid
For small $x, (1+x)^n \aquarius 1+ nx$
solid orioleBOT
Broski 6w9
scenic orchid
For small $ok
sturdy sable
Wait what
lyric rapids
Wat
prime rampart
$visibleconfusion$
solid orioleBOT
ripilicious
lapis rock
,tex $$
\begin{tikzpicture}
\draw (0,1) to[bend left=10] (0,6);
\draw (0,1) to[bend right=5] (0,0);
\draw (0,0) to[bend right=10] (2,0);
\draw (2,0) to[bend right=5] (2.25,2);
\draw (2.25,2) to[bend right=10] (3,2);
\draw (1.75,2.125) to[bend right=8] (2.25,2);
\draw (3,2) to[bend right=5] (3,-0.25);
\draw (3,-0.25) to[bend right=10] (5,-0.25);
\draw (5,-0.25) to[bend right=5] (5.25,7.25);
\draw (5.25,7.25) to[bend right=30] (3,10);
\draw (3,10) to[bend right=15] (2,10);
\draw (2,10) to[bend right=30] (0.5,8.28);
\draw (5.25,7.25) to[bend left=5] (6.25,7.15);
\draw (6.25,7.15) to[bend left=5] (6.25,2.5);
\draw (6.25,2.5) to[bend left=20] (5.25,2.25);
\draw (-1,7.08) to[bend right=90] (3.25,7.08);
\draw (-1,7.08) to[bend left=90] (3.25,7.08);
\end{tikzpicture}
$$
void hawkBOT
solid orioleBOT
alex or cal [she/they]
lapis rock
Thanks lads
lapis rock
Yes Pierrot?
final parcel
sus
final parcel
$\int \taurus^2 d \taurus$
solid orioleBOT
The πerrot [inactive/NieR]
final parcel
yes
a taurus integral
amazing
$\int \taurus^2 d \taurus = \frac{\taurus^3}{3}+\aries$
solid orioleBOT
The πerrot [inactive/NieR]
final parcel
where aries is a constant of integration
lapis rock
a taurus integral
What the fuck
lapis rock
where aries is a constant of integration
What the fuck
river scroll
,calc 9+10
solid orioleBOT
Result:
19
Result:
1.2247448713916
wow, just wow
lapis rock
:D
prime rampart
$:D$
solid orioleBOT
ripilicious
prime rampart
$0_0$
solid orioleBOT
ripilicious
$0_0$
final parcel
$0_{0_{0_{0}^{0}}^{0_{0}^{0}}}^{0_{0_{0}^{0}}^{0_{0}^{0}}}$
solid orioleBOT
The πerrot [inactive/NieR]
$0_{0_{0_{0}^{0}}^{0_{0}^{0}}}^{0_{0_{0}^{0}}^{0_{0}^{0}}}$
valid ice
$\large\smile$
solid orioleBOT
AlexV
calm wing
$\large\smile$
solid orioleBOT
Kamala Harris
topaz zodiac
why is there a channel called latex
who has a latex fetish
...oh its for a bot.
solid orioleBOT
isomorphic to pi_1(D^2,0)
radiant island
who has a latex fetish
I do
static warren
$\LaTeX$
solid orioleBOT
turtius - رمضان كريم
static warren
$\YoUr MoM$
solid orioleBOT
turtius - رمضان كريم
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
solid orioleBOT
turtius - رمضان كريم
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
static warren
bruh calm
final parcel
everyone b goin wild with the bot fr
and this is the day where the ZNotes community learned how to use LaTeX
radiant island
Lol
solid orioleBOT
AlexV
radiant island
Bruh-
valid ice
😊
static warren
bad apple latex edition?
valid ice
Thought other people would be experimenting with different colours :)
valid ice
$\color{red}{\sum_{n=1}^{\infty}\frac 1{n^2}= \frac {\pi ^2}6}$
solid orioleBOT
AlexV
valid ice
So one weakness about the bot us that you can’t delete what has been typeset after some time.
final parcel
$\Sigma \text{balls}$
solid orioleBOT
The πerrot [inactive/NieR]
valid ice
$\color{orange}{\mathfrak{Hello Everybody!}}$
solid orioleBOT
AlexV
solid orioleBOT
AlexV
valid ice
$\color{red}{\int} \color{orange}{\int} \color{yellow}{\int} \color{green}{\int} \color{blue}{\int} \color{purple}{\int}$
solid orioleBOT
AlexV
final parcel
$\color{red}{G} \color{yellow}{a} \color{green}{y}$
solid orioleBOT
The πerrot [inactive/NieR]
teal gust
$\color{orange}{\mathfrak{i failed my gcse maths}}$
solid orioleBOT
astro
teal gust
oh shit
valid ice
but you get an A for typesetting in LateX :)
half ermine
$\color{purple}{\mathfrak{hello?}}$
solid orioleBOT
mauve
valid ice
$\color{green}{\mathfrak{1234567890}}$
solid orioleBOT
AlexV
lapis rock
$\color{pink}{\mathfrak{swag}}$
solid orioleBOT
alex or cal [she/they]
solid orioleBOT
satan [in/jail]
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
topaz zodiac
it ried
solid orioleBOT
isomorphic to pi_1(D^2,0)
static warren
$\color{orange}{\mathfrak{greetings comrade}$
solid orioleBOT
turtius - رمضان كريم
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
