so double that is the individual letters
#help-26
glacial kite
but like ya I get what you mean, and we are most likely supposed to write a code to help us solve it
once I determine the common patterns though?
like I'm not quite sure how I would go about determining what exactly they should be in plain text
shrewd horizon
well then guess that the common letter pairs are probably also the common letter pairs in english
like "th"
and if you start getting nonsense when you do that you probably got something wrong and need to go back and change it
shrewd horizon
...thinking about it, you probably don't actually have to go very far with the guessing because once you have a couple of guesses you could probably backsolve for which 2x2 matrix would work for both of them
like, if "th" encrypts to "fl" and "he" encrypts to "zs" then surely there aren't that many keys that will do that
glacial kite
so if I go through each pair and tally the total times it appears, I then need to guess common letter pairs?
shrewd horizon
yeah that's what i'm suggesting
glacial kite
Is there like a code I could use to do that though? by hand there is so many rip
shrewd horizon
well you could probably just do something like py import collections text = "..." pairs = [''.join(pair) for pair in zip(text[::2], text[1::2])] print(collections.Counter(pairs))
glacial kite
Hmm
I'm not good with coding so I'll go to google to see I guess
thanks for the help
.close
glacial kite
yeah that's what i'm suggesting
one more quick question, what if I did individual letters and used the frequency they appear in? and compare it to frequency of a large chunk of text
topaz sinewBOT
one more quick question, what if I did individual letters and used the frequency...
shrewd horizon
you would probably end up with nonsense
the text was encrypted in pairs, the letters within those pairs are going to be pretty scrambled
glacial kite
ohh hmm
but like if I say look at the encrypted letter d, would every d not be the same letter in the plain text?
like if "d" (encrypted) was "a" (unencrypted), it would always be that or am I thinking wrong
pseudo bear
@glacial kite It's modulo 27, so you have 27⁴ decryption key matrixes to try for the first ciphertext. See which of those decryption matrixes produces plaintext with English letter frequencies.
27⁹ for the second one.
glacial kite
I'm kinda confused what you're saying, there is 27^4 possible decryption matrixes?
shrewd horizon
but like if I say look at the encrypted letter d, would every d not be the same ...
no. it's encrypted in pairs, within the pairs they get messed up
pseudo bear
Yes, you're going modulo 27 on everything.
So, you have a matrix with entries that can be 0 through 26.
When n = 2, the matrix is 2×2, so 4 entries.
That's 27⁴ possible matrixes.
That can be done by a computer pretty quickly.
27⁹ is quite a bit harder, since it's like 8 trillion.
glacial kite
no. it's encrypted in pairs, within the pairs they get messed up
oh man, so then once I get the frequency of the pairs how do I start though
shrewd horizon
compare those frequencies with the frequencies of pairs in english text
glacial kite
That can be done by a computer pretty quickly.
what do you mean by this, how would I do that?
ohh
pseudo bear
Well, you fill in a matrix with all possibilities, one by one.
You do the decryption for each one of those matrixes.
You see if the letter frequencies resemble English.
Like start with [0, 0; 0, 0] all the way to [26, 26; 26, 26].
glacial kite
compare those frequencies with the frequencies of pairs in english text
but why won't doing individual letters work is my question, yet the pairs work? like if I have (ab) as a pair and (ac) as a pair, if somewhere else (bc) appears would it just be the same b and c from letters from before or possibly different
shrewd horizon
but why won't doing individual letters work is my question, yet the pairs work? ...
would it just be the same b and c from letters from before or possibly different
it might be different
pseudo bear
@glacial kite Multiplying a vector with a matrix mixes up the original letters.
shrewd horizon
look at how it's encrypted: split the text into pairs, and mess with each pair
glacial kite
Well, you fill in a matrix with all possibilities, one by one.
so I how would I code this though?, cause like the only way to determine if its the right matrix would be the plain text makes sense right?
pseudo bear
Like you might have 25x + 3y and 6x + 2y as the ciphertext from a plaintext of x and y.
Well, what kind of matrix multiplication library are you using?
glacial kite
okay so I should analyze the pairs together only, because they stay together in the plaint text right
I don't know I havent tried coding it cause I'm not good at coding
pseudo bear
OK, then you can use Wolfram Alpha.
thorny flameBOT
Chai T. Rex
pseudo bear
So, you'll do something like:
for k0 from 0 to 27:
for k1 from 0 to 27:
for k2 from 0 to 27:
for k3 from 0 to 27:
for each two bytes of the file, a and b:
c = a * k0 + b * k2
d = a * k1 + b * k3
@glacial kite
glacial kite
(a b) being a pair of encrypted text?
glacial kite
Yes
pseudo bear
OK, now there's a speedup.
If you take the even positioned letters, they also resemble English's frequencies.
Like HELLO.
The E and L and so on will have English frequencies for the letters.
HELLOHOWAREYOU
The whole Hello, how are you thing will have English letter frequencies.
So will the highlighted letters alone.
Ignoring the nonhighlighted letters.
glacial kite
what do you mean english frequencies, like I can see how frequent they appear
pseudo bear
Well, E is the most frequent letter in English.
It's like ETAOINRSH or something like that.
E most common, then T, then A, then O, etc.
Does that make sense?
glacial kite
ye
pseudo bear
So, if your supposed plaintext has E the most common and then T and a few more, it's probably English.
pseudo bear
Well, if the most frequent letters, in order of frequency, are ETAOIN, then it's probably English.
Since English letter frequencies have E as the most frequent, then T, then A, then O, etc.
Like you're not going to expect a lot of Zs in your plaintext because Z isn't used very much.
glacial kite
ya
pseudo bear
But you're going to expect a lot of Es.
They get used all the time.
So, you can use that on your plaintext.
But you can also use it on every second or third letter in your plaintext.
Does that make sense?
glacial kite
But you can also use it on every second or third letter in your plaintext.
bit confused on this, is this an assumption we're making since it will appear a lot on my plaintext
pseudo bear
Since what will appear a lot?
glacial kite
e
pseudo bear
No, I mean the letter frequencies, not a letter.
Like ETAOINRSH.
The most frequent letter should be E, the second most T, etc.
glacial kite
right
pseudo bear
Do you see how that can be used to identify English text from gibberish?
glacial kite
yes
pseudo bear
OK, so if it's roughly ETAOINRSH from your supposed plaintext, that's one to set aside as maybe being English.
So save that key.
Find all the keys where it produces English like text according to the letter frequencies, then you can go back in and read the plaintext for each key to choose the key that gives real English text.
Does that procedure make sense?
glacial kite
OK, so if it's roughly ETAOINRSH from your supposed plaintext, that's one to set...
What do you mean by this?
pseudo bear
Well, you find the letter frequencies in the supposed plaintext.
glacial kite
like I get those letters are the most frequent
pseudo bear
Let's say X is the most frequent in the plaintext.
XHRYZ or something.
That's probably not English text.
But if it's ETAOINRSH or maybe TAEOZRNS, it might be English, because that's pretty close.
Does that make sense?
pseudo bear
No, by English I mean something is written in the English language.
Like we need to find the key that gives us plaintext written in the English language.
glacial kite
ya
pseudo bear
One way to try to filter out non-English text is to throw away the keys that don't get roughly ETAOINRSH on the letter frequencies.
glacial kite
I'm kinda confused as to what we are trying to establish with that fact
pseudo bear
Well, let's say the key the computer is trying gets the letter frequencies XRSHQ.
Where X is the most common letter, then R, then S, then H, then Q, and so on.
That text probably won't be English, so we can throw out that key.
Does that make sense?
glacial kite
right
so are we using the key test to try to get the most frequent letters in the english language
pseudo bear
- We try each possible decryption key.
- We use that key to get the plaintext.
- We get the letter frequencies of the plaintext.
- We see if they're roughly ETAOINRSH.
- If so, we save the key for later. Otherwise, we throw away the key.
Then at the end, we have a few keys that give English-like text.
glacial kite
okay that makes sense
pseudo bear
Now, there's a speedup.
If you take all the letters and get their frequencies, that method works.
If you take every other letter and get their frequencies, that method also works.
Like HELLOHOWAREYOU is in English (Hello, how are you).
So, HELLOHOWAREYOU has letter frequencies.
But let's take every other letter instead.
HELLOHOWAREYOU
Keep only those letters.
HLOOAEO
Does it make sense how I took every other letter?
glacial kite
yes
pseudo bear
Sorry, back.
OK, now every other letter will also have English-like frequencies.
@glacial kite
So, you can check half of them and see.
Does that make sense?
glacial kite
sort of yes
pseudo bear
Are you stuck on anything?
glacial kite
No, I'm just not sure as to where you're going with it so I may need to see more to understand
pseudo bear
Oh, OK.
Well, here's the trick.
The decryption key is a 3×3 matrix for the second ciphertext.
That's a matrix with 9 entries.
Each of the entries can have 27 different numbers.
Which means you have 27⁹ possible keys.
,w 27^9
thorny flameBOT
pseudo bear
That 7.6 trillion keys.
That's going to take your computer a VERY long time to go through all of them.
Does that make sense so far?
glacial kite
yes
pseudo bear
OK, so here's the trick.
Let's go back to your first ciphertext with a 2×2 matrix for a key.
Notice how the key has two columns.
The k₀ and k₂ column and the k₁ and k₃ column.
Do you see those?
glacial kite
yes
pseudo bear
OK, now notice the resulting plaintext on the right side of the equal sign.
The first plaintext character only needs the first column's numbers.
It only has k₀ and k₂.
So, it only needs half of the key to get the first character of each pair.
Does that make sense?
glacial kite
yes
pseudo bear
Similarly, the second plaintext character only needs the second column of the key.
So, you can do each column separately.
You try all possibilities for the first column, you check whether the first characters of the plaintext pairs are in English.
Then you try all possibilities for the second column.
And you see if the second characters of the plaintext are in English.
Does that process of doing one column of the key at a time make sense?
glacial kite
yes
pseudo bear
OK, now for the 3×3 matrix one, you do each of the 3 columns separately.
So, each column has 3 numbers that can be 0 through 26.
That 27³, and there are 3 columns, so 3 · 27³ total key parts to check.
,w 3 27^3
thorny flameBOT
glacial kite
yea we're just doing a lot less of them
pseudo bear
So, we do the key column by column.
We keep the columns that give English-like text.
So, we'll have a list of column-1 keys, a list of column-2 keys, and for the second ciphertext, a list of column-3 keys.
Do you know about Cartesian products?
pseudo bear
Let's say you have three sets.
{A, B} × {C, D} × {E, F, G}
The cartesian product tries all combinations of three items, one from each set.
(A, C, E)
(A, C, F)
(A, C, G)
(A, D, E)
(A, D, F)
(A, D, G)
(B, C, E)
(B, C, F)
(B, C, G)
(B, D, E)
(B, D, F)
(B, D, G)
Every single possible combination of those three sets.
Does the idea make sense?
glacial kite
ye
pseudo bear
OK, so we'll have a list of column-1 keys that our computer found out make English-like letter frequencies.
And we'll have the same thing for column 2 and 3.
And then we'll take the cartesian product of all the possible key columns.
Which will give us a bunch of completed keys that have all three of their columns.
Does that make sense?
Like a column-1 key that gives English-like text, combined with a column-2 key that gives English-like text, combined with a column-3 key that gives English-like text.
glacial kite
right
pseudo bear
That will give you an entire key.
Then you can have the computer display that text to you.
Along with the key.
If the text really is in English, you've found the right key and you can read the plaintext.
Otherwise, you go on to the next full key in the Cartesian product.
There won't be many keys in the Cartesian product because we've thrown away the non-English key columns.
And that'll be most of them.
pseudo bear
Yes, if you're new to coding, it will be difficult. Let's go over it.
Let's do the second ciphertext, since it has more columns.
So, the columns each have three entries.
0 through 26.
glacial kite
right
pseudo bear
So, that's a Cartesian product.
{0, ⋯, 26} × {0, ⋯, 26} × {0, ⋯, 26}
One item from each set.
All the possible combinations.
To do that in a programming language, here's how.
for row1 from 0 to 26:
for row2 from 0 to 26:
for row3 from 0 to 26:
Here, we have the three rows of this part of the Cartesian product.
Does that make sense or is it complicated looking?
glacial kite
that makes sense
pseudo bear
So, inside those nested for loops, we need to get the plaintext.
for row1 from 0 to 26:
for row2 from 0 to 26:
for row3 from 0 to 26:
let plaintext = getPlaintext(row1, row2, row3, ciphertext)
Then, still inside the nested for loop, you need to check whether each triple's (pair but with three items) first character gives the right English letter frequencies. Then, do the same with the second character of each triple. Then, the third character of each triple.
Then, you add [row1, row2, row3] to a first column list if the first character in each triple has English frequencies.
And so on for the other columns.
Hmm, here's how you could do it.
fn checkIfColumnIsEnglish(ciphertext, row1, row2, row3, columnNumber)
You make that function.
Or method or whatever.
Then, in your main function,
for row1 from 0 to 26:
for row2 from 0 to 26:
for row3 from 0 to 26:
for columnNumber from 1 to 3:
if checkIfColumnIsEnglish(ciphertext, row1, row2, row3, columnNumber):
possibleKeyColumns[columnNumber].add([row1, row2, row3])
Then you have to fill in the function's code.
Then, in main, after you have all that, you can do:
for column1 in possibleKeyColumns[1]:
for column2 in possibleKeyColumns[2]:
for column3 in possibleKeyColumns[3]:
let plaintext = decrypt(ciphertext, column1, column2, column3)
print(plaintext)
waitForEnterKey()
@glacial kite If you have any questions, let me know.
glacial kite
I dont really have much coding experience only a bit in python so trying to understand
pseudo bear
It's sort of Pythonish.
glacial kite
I honestly dont think I'd be able to code that LOL,
like don't I have to analyze the decrypted text in each run of the code or?
pseudo bear
Yes, that will be in the checkIfColumnIsEnglish function.
We're leaving that until later, but if we pretend that function works, the main part should make sense.
glacial kite
yea it does
my thing though is like you're explaining it all but I don't think im gonna be able to code it all, like I understand the process pretty well but implementing it myself is another story
pseudo bear
Yeah, it can be hard if you're new to programming.
What you want to do is break it into parts that you can write separately, so that each part is easy to do.
Like we did the Cartesian products in the main part.
And if we pretend the other functions work, then we can understand how that part works.
All we need is two Cartesian products.
One to find the possible key columns.
One to combine them into full keys.
Those are the two nested for loops.
One for each Cartesian product.
Then, the decrypt method uses something like this:
You do the vector times the matrix.
Then you notice which column and which row each part of the answer comes from.
So, the first character is a times column 1, row 1 plus b times column 1, row 2.
And do the same with the second character.
glacial kite
the k part is the decryption key
pseudo bear
I guess you could rename it kInverse or something like decryptionKey.
glacial kite
so the encryption key can be different
pseudo bear
Yes, unless it's the identity matrix, I think it'll have a different inverse than itself.
glacial kite
well they just said they use k to encrypt it and inverse of k multiplied by the encrypted message gives the decrypted message
okay
pseudo bear
But that's the way to handle overwhelm.
You break the problem into parts.
If the part seems easy enough, you make it.
If not, you break that part into parts.
Then you try the same with the subparts.
Some things, you'll need help with, like figuring out if the letter frequencies are "close enough" to ETAOINRSH.
But other things won't be so difficult.
Like you could probably do the decrypt function in the second nested for loops.
It gives you an entire key.
And the ciphertext.
And then you return the plaintext.
If that's too hard, break it into parts.
Each part gets its own function.
pseudo bear
You mean not solving each column separately?
Oh, I thought of a way to throw away more keys.
When you get each full key, get the plaintext and do a frequency analysis on it, and only print it if it passes the test.
glacial kite
actually I may not the 3 letter text has like 65000 entries 😭
pseudo bear
Yeah, you have to separate it into columns to have any hope of getting the answer in a reasonable time.
You can't try 7.6 trillion keys without waiting probably thousands of years.
glacial kite
I think ima leave this project for a bit and ask my prof, seems to hard for me rn
pseudo bear
OK.
glacial kite
thanks for all the help
I may ping you sometime if I end up trying it again if thats ok
pseudo bear
You're welcome. Sure, that's fine.
glacial kite
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
shadow ridge
Hello, I have a question. When i try to expand this https://www.desmos.com/calculator/hgdplpjvd7?lang=fr with r=0.01 so half the probability I still get almost the same curve
topaz sinewBOT
Hello, I have a question. When i try to expand this https://www.desmos.com/calcu...
shadow ridge
I would expect it to converge to 1 if n=200 but not so fast. Am I interpreting this wrongly ?
It's based on pulling characters with a pity system.
I you wind the counter increasing the liekliheood rate of +2% every pull gets reset
topaz sinewBOT
@shadow ridge Has your question been resolved?
topaz sinewBOT
@shadow ridge Has your question been resolved?
hearty spoke
Not sure what you are expecting on 100 trials with the probability increasing every failure. You have a linear part and an exponential part. Going from failure 75 to 85 alone is far less likely than losing 10 consecutive coin flips.
topaz sinewBOT
@shadow ridge Has your question been resolved?
shadow ridge
I'm sorry I think the framing of my problem is wrong.
Let me start over. This is a gacha game simulator I'm trying to crack, to understand how probabilities evolve as people are pulling.
To get a successfull 6 star pull you get 2% cance till the 50th pull and after that the increase your chance by 2% till you're guaranteed to get it.
@hearty spoke as you identified that is what we're seeing in the graph. However at every pull even if you get a 6 star, you're usually interested in the rate up, which is 50% or 35%. Thus if you get the guaranteed and then you fou fall in the 65% you would still need to continue pulling.
What I'm trying to identify is how to model that part. Also the probability falls to 2%. and need to be built up.
hearty spoke
There are too many grammatical and contextual issues with your phrasing to make that understandable
shadow ridge
Uhm could you tell me which parts are confusing you so that I can clarify them ?
hearty spoke
Literally all of it.
What is a rate up, what is 50% or 35%
"If you get the guaranteed and the you fou fall in the 65%"
What guaranteed, 65% of what?
shadow ridge
Ok. 🙂 I'll explain it with a proxy problem. If you knew the game it would have been obvious, but from outside view I understand.
I'll delete the previous statements not to confuse people, once I rewrote the problem.
hearty spoke
You also did not ask anything about modeling, you asked why it converged so fast. People are not mind readers.
shadow ridge
You also did not ask anything about modeling, you asked why it converged so fast...
@hearty spoke I appreciate you taking time to to write as well as giving constructive feeback, however I feel the last part is not needed. If you feel like you need to be patronizing could you take it elsewhere ? Obviously I didn't identify that the model is incomplete and was surprised by the result/
I'll probably close this topic and reframe the problem in a more palatable way. I think I might have a solution.
.close
crisp yacht
topaz sinewBOT
iron frigate
$a^2 +2a^2 = 3 a^2$
thorny flameBOT
Deep.
iron frigate
That leaves us with $\frac {9a^3 -15a} {3a^2}$
thorny flameBOT
Deep.
iron frigate
I believe you can do it from here
crisp yacht
I believe you can do it from here
oh thanks but what do i do next i forgot it
crisp yacht
is this the answer
iron frigate
is this the answer
No
iron frigate
Do you know what $\frac x {x^2}$ is?
thorny flameBOT
Deep.
crisp yacht
Do you know what $\frac x {x^2}$ is?
thats the fraction what is i t
crisp yacht
ohh sorry
crisp yacht
Well simplify it for me please
are you still there
iron frigate
Do you know how to deal with fractions?
crisp yacht
Do you know how to deal with fractions?
yeah i do a bit
thorny flameBOT
Deep.
crisp yacht
**Deep.**
yeah i see it and i simplify i t
down
how do i like do it where do i start
crisp yacht
yeah im starting to remember that
sorry havent did that in like ages thats why but i remember
that one
iron frigate
Hence you’ll be left with $\frac {(3a^2 -5)} {a}$
thorny flameBOT
Deep.
crisp yacht
oh alright so i will be left with that one
crisp yacht
Hence you’ll be left with $\frac {(3a^2 -5)} {a}$
deep am i finished
crisp yacht
Hence you’ll be left with $\frac {(3a^2 -5)} {a}$
are you there
iron frigate
Yea?
iron frigate
Ya sure np
crisp yacht
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
steady geyser
Given $X \sim \mathcal{N}(45, 5^2)$, $Y \sim \mathcal{N}(50, 6^2)$, and $\rho_{XY} = -0.5$, where (X, Y) is joint bivariate normal distribution.
does it mean that
$X = 5Z_1 + 45$ and $Y = 3Z_2 - 3Z_1 + 50$, where $Z_1 \sim Z_2 \sim \mathcal{N}(0, 1)$ and independent
topaz sinewBOT
Given $X \sim \mathcal{N}(45, 5^2)$, $Y \sim \mathcal{N}(50, 6^2)$, and $\rho_{X...
thorny flameBOT
Everule
topaz sinewBOT
@steady geyser Has your question been resolved?
topaz sinewBOT
@steady geyser Has your question been resolved?
steady geyser
<@&286206848099549185>
wheat laurel
Given $X \sim \mathcal{N}(45, 5^2)$, $Y \sim \mathcal{N}(50, 6^2)$, and $\rho_{X...
maybe you can send this in #probability-statistics
topaz sinewBOT
@steady geyser Has your question been resolved?
simple prawn
topaz sinewBOT
simple prawn
I don’t understand how to solve number 2
topaz sinewBOT
@simple prawn Has your question been resolved?
vernal vale
I don’t understand how to solve number 2
have you tried just solving $f=g$?
thorny flameBOT
jan Niku (Shuri for Honorable)
last turtle
Draw their graph
The intersection points of f and g shall be the solution
Oh nvm find the intersection points too
topaz sinewBOT
@simple prawn Has your question been resolved?
slow bluff
topaz sinewBOT
slow bluff
Can anyone review my work and let me know if it looks correct? I have no way to verify the answer as this is not due for an assignment.
<@&286206848099549185>
alpine mist
at t=0, the functions of x and y have a particular answer as well
topaz sinewBOT
@slow bluff Has your question been resolved?
slow bluff
The question is asking for dw/dt and I plugged t=0 in on my second to last line of work so I should be covered right?
topaz sinewBOT
@slow bluff Has your question been resolved?
mortal path
The question is asking for dw/dt and I plugged t=0 in on my second to last line ...
You also have to put in the values of x and y, you'll get these by following what Zybikron said
slow bluff
slow bluff
You also have to put in the values of x and y, you'll get these by following wha...
Like this?
And would I need to plug those inside the parentheses as well?
mortal path
Yeah, now just put t=0
slow bluff
Yeah, now just put t=0
mortal path
You can use the equations of x and y to find their values
The ones given in the question
slow bluff
Inside cos()?
mortal path
No, equations for x and y
x=e^t
y=ln(t+1)
slow bluff
at t=0 x=1 and y=0
Ahh so you’re saying I can plug those values into every x and y in this expression?
and if I do that I end up with cos(pi) = -1
topaz sinewBOT
@slow bluff Has your question been resolved?
slow bluff
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
neon iron
I need help
topaz sinewBOT
I need help
neon iron
Hello!
tidal bloom
For the first question you only need to know that the total of the four angles needs to be 360degrees
neon iron
And we see there are 2 right angles = 90
we add them both
We get 180
For E and D
How do we get them ?
Cause there is also a little circle
tidal bloom
Yes so e and d need to be 180 together. The task says e is twice the angle of d. So: 2d+d=180.
neon iron
I’m sorry I don’t understand this we didn’t take it in grade 7 😭
So 3d = 69
*60
Because we divide 180 by 3 ?
tidal bloom
Yes
neon iron
But it is shown as only one D ?
tidal bloom
You need to imagine that e=2d and e+d need to be 180 so you get this equation: 3d=180. And then dividing by 3 you get d=60
neon iron
so E= 120
D = 60
And then we add them we get 180
And we have two right angles
Which = to 180
So we add 180 +180 = 360
tidal bloom
Yes
tidal bloom
In this question you need to know that above the straight line the summ of the angles is 180degrees. So d+100=180
And Inside of this 5 cornered objekt you have 360 degrees again.
neon iron
Wait wait I don’t understand sorry😭
tidal bloom
If you have a circle this circle has 360 degrees. But in this question the angle with 100 degrees and d form only half of a circle. So they need to be 180 together.
neon iron
How did u know d forms ?
tidal bloom
If you add the circle of d and the one from the 100degrees angle you get exactly half a circle.
Because they fill all the room above the straight line.
tidal bloom
No, we know d. Because we know that d+100=180=>d=80
tidal bloom
And then we can find out e because we know that all angles together need to be 360
neon iron
So e is 70?
tidal bloom
Yes
neon iron
Wow math sometimes could be really complicated hahaha
Okay let me try to do
Q14
Okay so we have 50
And 2 unknown E
And D inside a circle
There is 80 inside circle too but outside
tidal bloom
This circle outside is helpful because it is the same as d. You can see this because it is between the same to lines, just in the other direction.
neon iron
Yes but how do I know it’s really not understanding for me 😭😭
tidal bloom
I mean if two lines cross each other and do not make a turn, it is kind of obvious that the angle does not change.
tidal bloom
It is 80 and you know it is the same as d.
neon iron
OH WAIT
tidal bloom
So d is also 80.
tidal bloom
Yes
neon iron
OHHH
okay okay so D = 80 because the 80 inside a circle
Okay
So
We add them both
We get
160
And we have 50
We add them we get
210
we have two E
So we divide by 2
We get 105
So En =105
tidal bloom
Not really, because the circle outside is not of interest. It just shows you that d is 80.
tidal bloom
Yes and 130+2e=360 again
neon iron
so to get E we have to subtract from 360 - 130 = 230
We divide 230 by 2
We get 115
So 2e = 115
neon iron
If you divide by 2 you always divide on both sides.
Explain plsss
tidal bloom
You have 2e=230
Now you divide by 2.
But not just the 230, you also divide 2e by 2
neon iron
So which answe is correct?
tidal bloom
Because you want to know what the angle e is
If 2e=230 that means that 1e is only 115
This is why we divide.
We want to know what one e is. Not 2 what we already know before.
neon iron
But it says “ fund each of the equal angle e”
tidal bloom
So 2e = 115
So this is correct, but you have to cancle out the 2
Yes and each angle is 115 degrees.
neon iron
Ohhh okayyy
tidal bloom
But if you write 2e=115 that means that both angles together are 115
tidal bloom
Yes
neon iron
Q15 I’m trying this time
😭
D and E are supplementary
We have 130 outside so D = 130
E = 50
Same For the other Angle D = 130
And the other E = 50
tidal bloom
Ok you got me wrong there. The angle is only the same as outside if the setup is just like in task 14. You see these angles are the same just pointing in the other direction. In this task you need to think back to task 13
tidal bloom
D and the 130 are only have a circle again. You see they only fill the room above the straight line not beneath it.
You see the partial circles drawn around the numbers? If they add up to a whole circle they are together 360degrees but if they only add up to half a circle they are together 180 degrees.
neon iron
How can we know it add up a whole circle
tidal bloom
You will agree that this is half a circle?
neon iron
Yea cause it doesn’t look complete
tidal bloom
and you can actually tell that it is exact half a circle because they fill exactly the room above the line but none under it.
neon iron
OH YES
tidal bloom
And you can just take it as a rule that all the angles inside a objekt with four corners are together 360 degrees.
if you have only 3 corners they add up to 180 degrees
neon iron
Okay so
Now we have 130 inside a circle
And D beside it
Does this mean it’s half and it’s 180
So we take it as 180?
neon iron
So D = 50
tidal bloom
exactly
tidal bloom
yes that is what the same name is supposed to say
neon iron
So we have 50 and 50
Which is 100
Now we subtract from 360
We get 260
So E = 130
tidal bloom
Yes
neon iron
Thank you so much
u just saved me
Ur amazing thank you so much
😭😭😭
U had a lot of patience
tidal bloom
😇
lyric crow
hi im so confused
topaz sinewBOT
hi im so confused
lyric crow
if f(-x)=(2,-1) what is f^-1(x)?
would it be the same as you would do f(x)? just inverse the points?
topaz sinewBOT
@lyric crow Has your question been resolved?
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@lyric crow Has your question been resolved?
lofty hamlet
Hello
mellow venture
lofty hamlet
Pls sir
mellow venture
read the message above your message Hello
lofty hamlet
15 min should i wait
lofty hamlet
Then you tell the answer?
mellow venture
no
mellow venture
yw
we do not give the answer straight away, we lead you to it through helping you
you need to tell us where ur stuck at and what work you have has been done
noble gulch
For example, have you consider factorizing the differential operator on the left hand side?
topaz sinewBOT
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topaz sinewBOT
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bitter crater
a) The equation ln(4 - 2x) + ln(9 - 3x) = 2ln(x + 1) is defined for A < x < B Enter A B
Hint: You can't log a negative number so fid the range of values of x that make 4-3x, 9-3x and x+1>0
i cant figure out how to work this out
topaz sinewBOT
a) The equation ln(4 - 2x) + ln(9 - 3x) = 2ln(x + 1) is defined for A < x < B En...
bitter crater
i am pretty slow haha
wooden matrix
yeah, you need x values st 4-2x>0, 9-3x>0 and x+1>0 simultaneously
bitter crater
oh i see
i keep overthinking questions like this and just solved for x haha
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final turtle
Course: Abstract Algebra
topaz sinewBOT
Course: Abstract Algebra
final turtle
I already constructed the adjacency matrix by finding the other 7 rows for (a). Can you clarify what is (b) asking?
I think I figured it out
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topaz sinewBOT
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graceful jetty
equationsystem
topaz sinewBOT
equationsystem
topaz sinewBOT
@graceful jetty Has your question been resolved?
graceful jetty
<@&286206848099549185>
wooden matrix
<@&286206848099549185>
what have you tried?
graceful jetty
uhm
so i multiplied the second one with 2 on every number
so 2 lg x + 2 lg y = 10
wooden matrix
Ok
wooden matrix
Ok
graceful jetty
3 lg x = 15 - 3 * lg y
wooden matrix
sure
wooden matrix
right
graceful jetty
so then i added lg y^-2 to the other side
wooden matrix
yeah, it's equivalent to solving 3X+2Y=13 and X+Y=5
wooden matrix
X=log(x)
Y=log(y)
wooden matrix
No
graceful jetty
10 doesnt = lg 10
graceful jetty
what is X
wooden matrix
log(x)
wooden matrix
X=log(x)
Y=log(y)
You mean you didn't read*
graceful jetty
I just never knew X = lg x
wooden matrix
I defined them to be...
wooden matrix
to make the system of linear equations more obvious
wooden matrix
then just find x and y once you found X and Y
wooden matrix
X=3, Y=2
graceful jetty
yea
wooden matrix
you had them backwards.
graceful jetty
Im sorry for being difficult, I just don't understand
ohh
yea
i do understand
lol
how do i cancel out the log?
lg
From Log x = 2
wooden matrix
log(x)=3
graceful jetty
yea
wooden matrix
$\log_a(b)=c\iff b=a^c$
thorny flameBOT
Mosh
wooden matrix
definition of logs
graceful jetty
yea, but what is a?
wooden matrix
a is the base of the log
graceful jetty
Okay, thank you so much
i got it
x = 1000
and y = 100
you made logs so much simpler
thank you again and sorry for being difficult
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pastel basin
I'm not sure where to begin so far, I've gotten X^2 = 4 and X=2 I'm not sure what to do now that I've solved for X.
topaz sinewBOT
I'm not sure where to begin so far, I've gotten X^2 = 4 and X=2 I'm not sure wha...
static void
do you remember how to find the area between two curves using an integral?
pastel basin
do you remember how to find the area between two curves using an integral?
Isn't that just finding the difference between f(x) and g(x)?
static void
yeah
pastel basin
yeah I can do that!
static void
integrating the distance between both curves
pastel basin
Would a certain equation be involved?
topaz sinewBOT
@pastel basin Has your question been resolved?
pastel basin
@static void 1/3x^3 + 9x - 4/3x^3 +3x and i plugged in the x-intercepts which are 1.5 and -1.5 and i got 0, but it could be 29. 25
<@&286206848099549185>
topaz sinewBOT
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neon iron
im confused how do i find this ive tried to just
topaz sinewBOT
im confused how do i find this ive tried to just
junior widget
When two points are on the same vertical line they have the same x value
Same can be said with horizontal and y values
neon iron
so x is 2 and y is 4?
junior widget
Yes!
junior widget
4 > 2
junior widget
No problem
neon iron
5 star rating
junior widget
Haha
neon iron
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neon iron
hello this is a physics question but does anyone know
topaz sinewBOT
hello this is a physics question but does anyone know
neon iron
what is the energy of the photons by a laser pointer having a 650 nm wavelength
wooden matrix
$E=\frac{hc}{\lambda}$
thorny flameBOT
Mosh
wooden matrix
@neon iron
topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
pls help
fading cypress
find the area of the whole grey region, then minus the white region
fading cypress
yep
neon iron
= 106
fading cypress
exactly!
fading cypress
sure
fading cypress
do you know how to find the perimeter?
neon iron
by multplying breadth and length?
neon iron
oh
fading cypress
so youve got 2 lengths and 2 widths which when summed give the perimeter
neon iron
by what is the width it isnt written
fading cypress
oh its not for the rectangle you gave before
neon iron
L x W
neon iron
A - L ?
fading cypress
not quite, so youre multiplying L and W
fading cypress
yep!
fading cypress
yep
white flicker
Its easier to understand why you divide when you write down L x W = A, then rearrange them to find W
neon iron
ohhhh
fading cypress
do you know how to find the perimeter from there?
fading cypress
thats area
neon iron
so 20 x 2
fading cypress
yep!
fading cypress
hahah
white flicker
To find perimeter of a rectangle or square remember this equation: P = (2 x W) + (2 x L)
fading cypress
no worries!
neon iron
To find perimeter of a rectangle or square remember this equation: P = (2 x W) +...
ahaaa
thanks both i now undersatnd !!
,clsose
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neon iron
Hi, I think this is a pretty dumb question but I would be very grateful if you can help me. In my math class my teacher told me my answer to this Inequation is wrong. But didn't explain why so can someone explain to me why is wrong?
topaz sinewBOT
Hi, I think this is a pretty dumb question but I would be very grateful if you c...
neon iron
This is the supposed right answer
mild hearth
neon iron
Hope it's enough steps
but it doesn't make any sense for the < to stay like that
because it would make X less than -17/2
when it was clearly bigger
1 step before
what am i doing wrong
grim jacinth
Line 1 to Line 2 is wrong
You multiplied by a negative number, so you need to switch the sign
Switch the inequality:
< to >
topaz sinewBOT
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Available help channel!
obsidian hearth
Can anyone solve this pattern?
topaz sinewBOT
Can anyone solve this pattern?
topaz sinewBOT
@obsidian hearth Has your question been resolved?
obsidian hearth
So basically how do I tell which one is next to the other?
<@&286206848099549185>
topaz sinewBOT
@obsidian hearth Has your question been resolved?
obsidian hearth
I don't know if this helps or not but this one shows the main and minor roads in each order they are in
So it looks like except for 0 on the main roads to get the next one I simply add 2.
And for the minor roads except for the next to last I just add 1 to get the next one.
obsidian hearth
Looking at this bigger sample it's not that simple
topaz sinewBOT
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next scaffold
Can somebody please explain to me plane symmetry, axis symmetry, and why which things are which?
topaz sinewBOT
Can somebody please explain to me plane symmetry, axis symmetry, and why which t...
topaz sinewBOT
@next scaffold Has your question been resolved?
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@next scaffold Has your question been resolved?
long stirrup
axis is rotational i guess
but then it would be both, both, plane
not both plane both
you can rotate the N by 180° and it doesn't change, and you can rotate the triangle thing by 60°
and the heart can't do that
oh wait it can?
so they are all both?
i think i was wrong from the beginning
edgy comet
topaz sinewBOT
empty sail
<@&286206848099549185>
You have to wait at least 15 minutes before pinging helpers
edgy comet
Sorry
topaz sinewBOT
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edgy comet
<@&286206848099549185>
edgy comet
<@&286206848099549185>
topaz sinewBOT
@edgy comet Has your question been resolved?
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@edgy comet Has your question been resolved?
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rough seal
edgy comet
Any idea where I would go from here <@&286206848099549185>
tender snow
t is just the value of that expression
Your solution looks more complicated that necessary I think
tender snow
It represents sqrt(k+1) - sqrt (k) dude
t is just a symbol I'm using to denote that difference
For convenience
You can denote it by anything
edgy comet
is my proof correct? or would urs be more correct
tender snow
I think mine is more rigorous
Actually one small mistake in mine, instead of writing k>=3 it should be k>=2
Because I'm considering k+1
Rest everything is same and correct
sage lagoon
Let
𝐴={𝑥:𝑥 is a course offered by TUA}
𝐵={𝑥:𝑥 is a college in TUA}
-
Define a relation that will relate the elements of set 𝐴 to elements of set 𝐵.
-
Is the relation in # 1 a relation or not? Justify your answer.
-
Define a relation that will relate the elements of set 𝐵 to elements of set 𝐴.
-
Is the relation in # 1 a relation or not? Justify your answer.
sage lagoon
Am i correct in number 1?
or is there any other way to define the relation from A to B?
topaz sinewBOT
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topaz sinewBOT
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mossy nest
Suppose we have 28 football players, 14 boys and 14 girls.
In the locker room we have football jerseys numbered from 1 to 99. How many ways can the jerseys be distributed to the players, if Alex must have a jersey with a number 1 larger than Emily?
topaz sinewBOT
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topaz lynx
my issue is
MARK SCHEME
so after the collision
A is going LEFT
and B is going RIGHT
they WILL NOT collide again at this point
until B hits the wall and rebounds
IF the velocity of B AFTER HITTING THE WALL is greater than the velocity OF A
THEN they will collide again, right?
BUT, heres my issue.
Surely then, if the collision between the wall is perfectly elastic
this will only be a good thing? As energy wont be lost so the velocity of B is likely to be higher?
if its not elastic, kinetic energy will be lost so the velocity of B will be lower
i think theres a flaw in my understanding of the question somewhere
where have i went wrong?
topaz sinewBOT
@topaz lynx Has your question been resolved?
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@topaz lynx Has your question been resolved?
topaz sinewBOT
@topaz lynx Has your question been resolved?
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@topaz lynx Has your question been resolved?
viscid thistle
I’m back
This is what I got
I had to do part A to do part B sorry
@topaz lynx
and feel free to dm any other mechanics questions
viscid thistle
this will only be a good thing? As energy wont be lost so the velocity of B is l...
bro, if e=1, then B won’t move
viscid thistle
where have i went wrong?
that’s where you missed out,
if e = 1, then no kinetic energy is transferred to B
ergo it doesn’t move
viscid thistle
no worries my guy
and as I said earlier, feel free dm any mech question straight to me
sweet shard
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