LaTeX\LaTeX Storage Note

To store LaTeX\LaTeX codes that might be useful later

Strictly not for chatting and trying LaTeX\LaTeX codes :)

Note by Percy Jackson
2 months, 4 weeks ago

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  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

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so i have uncovered your tactic! now to give you a tste of ur own medicine :)

NSCS 747 - 1 month, 3 weeks ago

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NSCS 747 - 1 month, 3 weeks ago

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NSCS 747 - 1 month, 3 weeks ago

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percy it seems like i have uncovered your method of creating the abyss thanks to the empty comment that pall mortom has made in my testing note i have concluded that that is the most probable way you made that abyss and i am going to test it here and develop ways of doing it without lag on old devices so just ignore any empty souls i put here

NSCS 747 - 1 month, 3 weeks ago

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LOL, you're so naive. YOur method is wrong, and don't dirty my storage note, do it in Latex Club if you like @Nathan Soliman

Percy Jackson - 1 month, 3 weeks ago

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well its just as good as urs

NSCS 747 - 1 month, 2 weeks ago

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@Nscs 747 no, mine is better

Percy Jackson - 1 month, 2 weeks ago

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@Percy Jackson how its nothing :)

NSCS 747 - 1 month, 2 weeks ago

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to test latex go here https://brilliant.org/discussions/thread/testing-19/

NSCS 747 - 1 month, 4 weeks ago

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\colorbox{white}{\large\color{white}\text{your text}} this is more for me to remember

NSCS 747 - 2 months, 3 weeks ago

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Problem 1Problem 2Problem 3Problem 4Problem 5Problem 6Problem 7Problem 8Problem 9Problem 10Problem 11Problem 12Problem 13Problem 14Problem 15Problem 16Problem 17Problem 18Problem 19Problem 20Problem 21\begin{array}{|l|l|l|l|l|l|l|} \hline\\[-7px]\hspace{15px}\href{#}{\textsf{Problem 1}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 2}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 3}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 4}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 5}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 6}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 7}}\hspace{15px}\\[3px]\hline\\[-7px] \hspace{15px}\href{#}{\textsf{Problem 8}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 9}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 10}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 11}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 12}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 13}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 14}}\hspace{15px}\\[7px] \hspace{15px}\href{#}{\textsf{Problem 15}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 16}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 17}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 18}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 19}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 20}}\hspace{15px} &\hspace{15px}\href{#}{\textsf{Problem 21}}\hspace{15px}\\\hline \end{array}

Tables! (courtesy of Páll Márton)

Percy Jackson - 2 months, 3 weeks ago

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=def\overset{def}{=} - \overset{def}{=} - \overset command is useful to make def on your = signs :)

Percy Jackson - 2 months, 4 weeks ago

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Rules -\text{Rules -}

1. Please don’t use this note for chatting\text{1. Please don't use this note for chatting}

2. This note is only to store your LaTeXcodes that you might need later, but take lot of space.\text{2. This note is only to store your \LaTeX codes that you might need later, but take lot of space.}

3. More rules will come later, but please follow the rules\text{3. More rules will come later, but please follow the rules} :)

Percy Jackson - 2 months, 4 weeks ago

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@Percy Jackson, I forgot how to the equal sign with def over it. Can you help me?

Yajat Shamji - 2 months, 4 weeks ago

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I posted in the Latex Club, please check there @Yajat Shamji.

Percy Jackson - 2 months, 4 weeks ago

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Important facts\text{Important facts}

1. The rpm of a gear is inversely proportional to its number of teeth2. The gears connected at the top of one another move with same speed.\text{1. The rpm of a gear is inversely proportional to its number of teeth} \\ \text{2. The gears connected at the top of one another move with same speed.}

Visual explanation\text{Visual explanation}

<Picture Latex code here>

It is clear from the picture, that there is a/no problem in direction.Hence, the system will/will not work.\text{It is clear from the picture, that there is a/no problem in direction.} \\ \text{Hence, the system will/will not work.}

Casework\text{Casework}

Without loss of generality, let the leftmost gear in some color rotate at 2 rpm.\text{Without loss of generality, let the leftmost gear in some color rotate at 2 rpm.}

Up Setup\text{Up Setup}

Speed of Silver gear=50×220=5rpm\colorbox{silver}{\color{#333333}\text{Speed of Silver gear}} =\dfrac{50\times 2}{20}=5 \text{rpm}

Speed of brown gear=20×510=10 rpm\colorbox{#624F41}{\color{#FFFFFF}\text{Speed of brown gear}}=\dfrac{20\times 5}{10}=10 \text{ rpm}

Speed of Silver gear=50×220=5 rpm\colorbox{silver}{\color{#333333}\text{Speed of Silver gear}} =\dfrac{50\times 2}{20}=5 \text{ rpm}

Speed of brown gear=20×510=10 rpm\colorbox{#624F41}{\color{#FFFFFF}\text{Speed of brown gear}}=\dfrac{20\times 5}{10}=10 \text{ rpm}

Speed of gold gear=20×550=2 rpm\colorbox{gold}{\color{#333333}\text{Speed of gold gear}} = \dfrac{20\times 5}{50}= 2\text{ rpm}

Speed of Bronze gear=50×225=4 rpm\colorbox{#815331}{\color{#FFFFFF}\text{Speed of Bronze gear}}=\dfrac{50\times 2}{25}=4 \text{ rpm}

Speed of inner brown gear=20×525=4 rpm\colorbox{#624F41}{\color{#FFFFFF}\text{Speed of inner brown gear}}=\dfrac{20\times 5}{25}=4 \text{ rpm}

Speed of brown gear=20×525=4 rpm\colorbox{#624F41}{\color{#FFFFFF}\text{Speed of brown gear}}=\dfrac{20\times 5}{25}=4 \text{ rpm}

Speed of Purple gear(A)=10×420=2 rpm\colorbox{#69047e}{\color{#FFFFFF}\text{Speed of Purple gear(A)}} =\dfrac{10\times 4}{20}=2\text{ rpm}

Down Setup\text{Down Setup}

Speed of brown gear=50×210=10 rpm\colorbox{#624F41}{\color{#FFFFFF}\text{Speed of brown gear}}=\dfrac{50\times 2}{10}=10 \text{ rpm}

Speed of silver gear=10×1020=5 rpm\colorbox{silver}{\color{#333333}\text{Speed of silver gear}} = \dfrac{10\times 10}{20}= 5\text{ rpm}

Speed of gold gear=20×550=2 rpm\colorbox{gold}{\color{#333333}\text{Speed of gold gear}} = \dfrac{20\times 5}{50}= 2\text{ rpm}

Speed of inner brown gear = Speed of gold gear=2 rpm\colorbox{#624F41}{\color{#FFFFFF}\text{Speed of inner brown gear}} \ \color{#333333}{=} \ \colorbox{gold}{\color{#333333}\text{Speed of gold gear}} = 2\text{ rpm}

Speed of gold gear=2 rpm\colorbox{gold}{\color{#333333}\text{Speed of gold gear}} =2\text{ rpm}

Speed of silver gear=20×220=2 rpm\colorbox{silver}{\color{#333333}\text{Speed of silver gear}} = \dfrac{20\times 2}{20}= 2\text{ rpm}

Speed of brown gear=20×210=4 rpm\colorbox{#624F41}{\color{#FFFFFF}\text{Speed of brown gear}}=\dfrac{20\times 2}{10}=4 \text{ rpm}

Speed of blue gear(B)=10×420=2 rpm\colorbox{#3d99f6}{\color{#FFFFFF}\text{Speed of blue gear(B)}}=\dfrac{10\times 4}{20}=2 \text{ rpm}

Answer\text{Answer}

Speed of Purple gear(A)=Speed of Blue gear(B)=2 rpm\large{\color{#69047e}\text{Speed of Purple gear(A)} = \color{#3d99f6}\text{Speed of Blue gear(B)}=\color{#333333}2\text{ rpm}}

Latex code for Gear Problems :)

Percy Jackson - 2 months, 4 weeks ago

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