kheerii
#help-41
grizzled pagodaBOT
proven vapor
you can multiply and divide by 6 in your case and then use this result directly
tough mica
okay
proven vapor
although this is fine too
tough mica
lets do the taylor expansion of ln(1 + x) and multiply by 6 in numerator and denominator
tough mica
although this is fine too
limit should be 6, its approaching 6
I mean -6
because it was -ln(1 + 6x)
so we know the function is continous at $x_0 = 0$
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
proven vapor
indeed
tough mica
I can do the taylor expansion centered at 0 if you want for the log, no problem
proven vapor
now find the derivative (if it exists)
tough mica
im not in a hurry
tough mica
now find the derivative (if it exists)
first principles I assume
,, \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = \lim_{h \to 0} \frac{\frac{-\ln(1+6x)}{x} +6}{h}
proven vapor
not quite
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
tough mica
we know the left term in the numerator is approaching -6
we have a 0/0 undeterminate form
we may need to apply lh
vast spade
,, \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = \lim_{h \to 0} \frac{\frac{-\ln(1+6x...
\frac{-\ln(1+6(x+h))}{x+h}
tough mica
,,\frac{-\ln(1+6(x+h))}{x+h}
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
tough mica
oh you are right
im so stupid
,, \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = \lim_{h \to 0} \frac{\frac{-\ln(1+6(x+h))}{x+h} +6}{h}
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
proven vapor
x is equal to 0 in your case
tough mica
but x = 0
tough mica
x is equal to 0 in your case
exactly
,align &\lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \ &\implies \lim_{h \to 0} \frac{\frac{-\ln(1+6(x+h))}{x+h} +6}{h} \ &\implies \lim_{h \to 0} \frac{\frac{-\ln(1+6(h))}{h} +6}{h} \ &\implies \lim_{h \to 0} \frac{\frac{-\ln(1+6h)}{h} +6}{h} \ &\implies \lim_{h \to 0} \frac{6h-\ln(1+6h)}{h^2}
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
tough mica
this is surely a lhopital
proven vapor
yeah sure
tough mica
I skipped like one arithmetic simplification but I didnt wanted to make the latex too long, hopefully I didnt do any mistakes
anyways we have 0/0 undeterminate form, lets differentiate with respect to h, shall we
proven vapor
just for your information, Taylor Series expansions and L'hopital's rule are basically the exact same method, since both of them involve finding the derivatives of our function
so you don't need to worry too much about which one you're using
whichever you find easier you can use that
tough mica
okay thank u, I guess depending on context one is easier than the other
,align &\frac{d}{dh} \left(6h - \ln(1+6h)\right) = 6 - \frac{1}{1+6h} \times 6 \ &\implies = 6 - \frac{6}{1+6h}
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
split sail
I’m sure this is not a real analysis course, but the assumptions needed in order to use LHopital rule and Taylor expansion are totally different.
proven vapor
I’m sure this is not a real analysis course, but the assumptions needed in order...
yeah I just meant that it doesn't matter for what they're doing currently
tough mica
with taylor expansion you guys mean maclaurin series for a function of degree 2? in other words, a taylor polynomial of degree 2 centered at 0 ?
I dont really know what I am talking about so I might just close my mouth tbh I am having trouble with basic calculus
,, \lim_{h \to 0} \frac{6 - \frac{6}{1+6h}}{2h}
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
tough mica
,, \lim_{h \to 0} \frac{\frac{6 + 36h - 6}{1+6h}}{2h} = \lim_{h \to 0} \frac{\frac{36h}{1+6h}}{2h}
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
tough mica
,, = \lim_{h \to 0} \frac{36h}{2h+12h^2} = \lim_{h \to 0} \frac{36}{2+12h} = 18
grizzled pagodaBOT
938c2cc0dcc05f2b68c4287040cfcf71
tough mica
is this correct?
split sail
spot on
tough mica
I’m sure this is not a real analysis course, but the assumptions needed in order...
yeah this is just pre-calc, its not proof based like anal, anyways, have a good one
amber waspBOT
amber waspBOT
Available help channel!
low remnant
How do do you graph piecewise functions?
amber waspBOT
How do do you graph piecewise functions?
split sail
you sketch the individual pieces
amber waspBOT
@low remnant Has your question been resolved?
low remnant
No
amber waspBOT
@low remnant Has your question been resolved?
chrome yoke
In the popular icebreaker 'The Boat is Sinking' were 𝑛 > 2 participants playing in a finite number of rounds, with all the participants being in the first round of the game.
In each round the game master, purposefully selects a unique integer 𝑖 ∈ A = {2, 3, 5} to be announced to the participants such that when they are asked to form groups of 𝑖 members each, (𝑖−1) people will be eliminated.
Find all positive integers 𝑛 such that the game will eventually end with two people to be declared as winners.
chrome yoke
I wonder where do you start from here?
chrome yoke
Hmmmm then
lusty pine
actually i have no fucking clue
wait for someoje else to do it, sorry
my best idea would be to create a tree of sort
like, for example 3 participants when formed to be a group of 2 would make 2 people
hm actually 3=n i=2 is the only one that leads to 2 people winning in the first round
chrome yoke
Hmmmmm
lusty pine
we find groups of n and i which leads to 3 people left
2 wont work, 3=i works if 5=n, 5=i doesent work
im pretty sure you can find a pattern here
wait a minute
indigo cloud
its not quite clear whether the game master wants 2 people to win in the end or not. what will they call when they are allowed to call several numbers
lusty pine
nvm
lusty pine
its not quite clear whether the game master wants 2 people to win in the end or ...
im guessing we want to find all the possible n
chrome yoke
im guessing we want to find all the possible n
Yup
indigo cloud
that doesnt answer my question
lusty pine
uh
indigo cloud
if there are n=5 people, the game master could call out i=2 or i=3. one would lead to 2 people winning, the other wouldnt
lusty pine
basically whatver possible is made out of picking i
lusty pine
if there are n=5 people, the game master could call out i=2 or i=3. one would le...
but like, since its technichally possible to get 2 people to win, n=5 works right?
lusty pine
idk its my personal take on it
lusty pine
maybe the game master doesnt like the people
lmao
indigo cloud
I mean he will sometimes purposefully call out numbers that will throw out more people compared to calling out another number
chrome yoke
It said that I has to be unique so for each round. There is only one 1 and it always end with 2
indigo cloud
!original
amber waspBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
chrome yoke
2 people
"Find the number of participants in the first round so that after some rounds,
you can successfully end up with 2, given that i is the same for every round and i is part of (2,3,5)
indigo cloud
wait what. i is the same every round?
chrome yoke
Yup
indigo cloud
that changes things quite a bit
chrome yoke
Say 13, i ≠ 2 because it becomes 12 and it just stucks there
indigo cloud
yes
play around a bit more
it will also help to write the numbers in base 2, 3 or 5
wait no
that still doesnt make sense
indigo cloud
after your initial round you will never be able to call that number again
you cant call 3 for 13
because that will lead to 12
chrome yoke
If we set i = 3 then it go to 11 right?
Then it becomes 9
Then it stuck because its divisible
Oh wait huh
chrome yoke
because that will lead to 12
Oh yeh
indigo cloud
do you have a picture of the problem
chrome yoke
lusty pine
thinking about it abit more, each round the i would be diffrent
indigo cloud
yeah it needs to be
indigo cloud
if there are n=5 people, the game master could call out i=2 or i=3. one would le...
but this is still unclear
chrome yoke
Okay so the answer is just 3 according to the problem maker
indigo cloud
who made up the problem
chrome yoke
Reasoning :
5 is not possible because
in forming groups of 2, you can eliminate 1
in forming groups of 3, you eliminate 2
so i = 2, 3 which is a contradiction since you only want exactly one value i
so 2->3 -> 5 ->9 -> doesnt yield any chain
Other odd numbers somehow either just got stucked or has a lot of i
lusty pine
what
indigo cloud
ok so just bad problem writing
the problem should have asked "find all positive n such that in each round it will be possible for the game master to uniquely select such a number i and that after some number of rounds 2 people survive"
or something like that
chrome yoke
And 3 only works
lusty pine
And 3 only works
wdym
lusty pine
what
indigo cloud
n=5 is an impossible gamestate because its not possible for the game master to select a unique i
so its excluded
thats what the problem writer wanted to do. they just failed to write it down properly
indigo cloud
yes
amber waspBOT
amber waspBOT
Available help channel!
chrome yoke
Suppose in its first move, the knight can choose which among the colors of squares (red or blue) it will move on. Then, in the succeeding moves, he can only choose to walk on the squares using his chosen color as the bases.
For example, if the knight begins in d4 (this illustration)
If his first move is f5,
Then in the next move, his only choices are h6, e7, d4, and g3
and suppose his next move is e7,
he can only choose from g8, c6, and f5
How many ways can such a knight go from b1 to h8?
chrome yoke
I can't seem to generalize it properly
lusty pine
hm
so basically the knight if assuming picks blue can only move to squares where if its red it cant pick right?
chrome yoke
Yup
lusty pine
even if its multiple moves before?
like for example, the knight goes to c3 d5 e3 from b1, can it go to d1 or no?
chrome yoke
Yes it can
Though one path is considered as one regardless of arrangements and going back etc
wise willow
Suppose in its first move, the knight can choose which among the colors of squar...
yooo chesss
amber waspBOT
@chrome yoke Has your question been resolved?
wise willow
Suppose in its first move, the knight can choose which among the colors of squar...
you need permutations combinations and deep analysis on this
fresh ocean
Only blue path lets you visit h8 from b1 by my calculations
And once you choose the color, you may visit only 16 squares on the board
chrome yoke
Why is red not possible?
fresh ocean
And if you consider loops, there are infinite ways, but if we restrict ourselves to visit the squares only once, we still need brute forcing imo
fresh ocean
Why is red not possible?
coz in that case, h8 is not one of the 16 squares
I wrote a quick python script to brute force this, change in hue is progressive move in the shortest path
ignore the names, its a matplotlib thing
The red moves on the other hand give this
chrome yoke
I wrote a quick python script to brute force this, change in hue is progressive ...
This doesn't look 16 squares to me
fresh ocean
sry its 12 most of the time
my bad
it keeps changing between 12 and 13
I plotted for all squares lol
chrome yoke
How does one briteforce it?
fresh ocean
take a starting square, and note all possible squares it can move to
repeat till no new square is found
change starting square and do the same again
chrome yoke
C3 is obv the only starting square
fresh ocean
yes
but from c3 you can move to 3 more new squares
and from those more and more and so on
chrome yoke
I wrote a quick python script to brute force this, change in hue is progressive ...
B4 is missing here hmmm
fresh ocean
How do you get to b4 if you start from b1?
fresh ocean
but thats a red move not blue
chrome yoke
That third maneuver is a blue move
fresh ocean
no its not? you move one down and two left. thats red
chrome yoke
That third manuever corresponds to that b5 square in the illustration?
Oh nvm
I'm tunnel blind
One way for a4
4 paths for b6
Meaning c8 also 4?
fresh ocean
I wrote a quick python script to brute force this, change in hue is progressive ...
there is more than 4 paths to b6 which have no repeats
thats why I said you need to calculate this by hand and combinatorial approach doesnt work since you can have any number of steps till you reach the end
amber waspBOT
@chrome yoke Has your question been resolved?
low remnant
How do I solve quadratics by completing the square?
amber waspBOT
How do I solve quadratics by completing the square?
low remnant
$2x^2 +3x -6=0$
grizzled pagodaBOT
me.dusk
simple blade
what do you mean by completing squares?
low remnant
I wanna learn the completing the square method
low remnant
what do you mean by completing squares?
Idk man its the name of the method
little dagger
do you mean this?
low remnant
**me.dusk**
How do I solve this completing the square?
low remnant
do you mean this?
I guess
simple blade
write the equating in form of (x-a)^2=b
low remnant
How do i get rid of C?
simple blade
take the 6 to other side
grizzled pagodaBOT
me.dusk
simple blade
divide by two
low remnant
Ok
simple blade
both side
low remnant
$frac{(2x^2)(2)}$
grizzled pagodaBOT
me.dusk
simple blade
write it clearly
in normal way write it
how are you creating that screen then i will also do
wicked girder
first let x^2 be by itself (to do this divide everything by 2)
now ur left with x^2 + (3/2)x -3=0
to complete the squares,
**always divide the co efficient of x then square it
in this case it’s ((3/2)/2)^2 = (3/4)^2
now u both add and minus that number in the equation to get **
x^2 + (3/2)x (3/4)^2 -(3/4)^2 -3=0
now u can factorise the first 3 terms due to perfect squares and u get
(x + 3/4)^2 -9/16 -3 =0
(x + 3/4)^2 -57/160
the idea of completing the squares is the bolded bit
simple blade
you disturbed my flow
simple blade
**me.dusk**
$x^2-3x/2=-3$
grizzled pagodaBOT
CAPTAIN DARK KNIGHT
simple blade
$(x/2)^2=(-3/4)$
grizzled pagodaBOT
CAPTAIN DARK KNIGHT
simple blade
$x^2-3x/2+(x/2)^2=-3+(-3/4)$
grizzled pagodaBOT
CAPTAIN DARK KNIGHT
simple blade
$x^2-3x/2+9/16=-39/16$
grizzled pagodaBOT
CAPTAIN DARK KNIGHT
simple blade
$(x-3/4)^2=-39/16$
grizzled pagodaBOT
CAPTAIN DARK KNIGHT
simple blade
$x=3/4+-i39^1/2/4$
grizzled pagodaBOT
CAPTAIN DARK KNIGHT
amber waspBOT
@low remnant Has your question been resolved?
ebon bobcat
im struggling on this so bad
amber waspBOT
im struggling on this so bad
tawdry torrent
mb
ebon bobcat
its good
so i did SinA/18 = Sin67/b = Sin44/c
but i was taufght that you need at least both values of at least one of those fraction things
to solve
but it doesnt give me
and idk how
nvm
.close
stark sky
How do I do this excersise using the annihilator method?
amber waspBOT
How do I do this excersise using the annihilator method?
stark sky
Is it even possible to do it with that method?
i did y' = p and i calculated the y(homogenous)
i think the annihilator for this excersise is D(D^2 + 4)
amber waspBOT
@stark sky Has your question been resolved?
stark sky
<@&286206848099549185>
frigid sierra
How do I do this excersise using the annihilator method?
This is DE 2nd how do you say (stage?)
I) y(homogenous)
y = e^(lambda*x)
y’=…
y’’=….
If lamda 1 is not same as lambda 2
y1 is = e^(lambda1*x)
y2 same but with lambda 2
If lambda 1 = lambda 2
y1= e^(lambdax)
y2 = xe^(lambdax)
You can have lambda 1 and lambda 2 not equal R
Then y is a lil different
stark sky
I don't think we are that far yet cuz idk what lambda is
frigid sierra
Once you do that….
Y(homogenous) = C1y1 + C2y2
C1 and C2 you can get with variation of constant or with …
Thats it
frigid sierra
I don't think we are that far yet cuz idk what lambda is
Basically greek letter lambda
stark sky
damn bro
frigid sierra
I mean its up to you, you can mark it as anyrging
Anything*
i can link you to a very good course on DE but it is in slovene, you might be able to learn from visual only
stark sky
nah its alright, i guess i'll just ask my professor about it this week
frigid sierra
stark sky
thanks for trying to help me tho
frigid sierra
This is part 1, you have part 2,3,4,5
stark sky
.close
amber waspBOT
modest junco
How do I do this excersise using the annihilator method?
I think it's the annihilator, tell me if not:
Substitute u=y'
u'+tan(x)u=cos²(x)-2sin(x)cos(x)
Then-
μ:=e^{∫tan(x)dx}=e^-ln(cos(x))=1/(cos(x))
Abd the previous equation amounts to-
(u/cos(x))'=cos(x)-2sin(x)
Integrate both sides with respect to x-
u/cos(x)=sin(x)+2cos(x)+C
u=sin(x)cos(x)+2cos²(x)+Ccos(x)
=sin(2x)/2+1+cos(2x)+Ccos(x)
=y'
Hence:
y=-cos(2x)/4+x+sin(2x)/2+Csin(x)+K
For C,K in R
Ask if you didn't understand
Oh maybe irrelevant
amber waspBOT
Available help channel!
stark sky
I think it's the annihilator, tell me if not:
Substitute u=y'
u'+tan(x)u=cos²(x...
i'm ngl bro idk what you did in the middle of all that
modest junco
Bernoulli is with y² or yⁿ, what I showed you is with an integrating factor, might be called annihilator somewhere else
modest junco
its bernoulli
You don't solve what you sent with Bernoulli
stark sky
ah integrating factor
modest junco
Do you know that?
stark sky
You don't solve what you sent with Bernoulli
we learned a different bernoulli method where we subtitute y = uv
here we can substitute y' = p and then p = uv
stark sky
Do you know that?
we briefly went over it but no not really
i should really study that in
I'm gonna study the integrating factor and then try to do the excersise with the method
i saved your solution
thanks for your help bro
.close
cold heron
Independent Trials and the Binomial Probabilities
is p here a function take k?. I don't understand
sterile nymph
p(k) is a function that returns the likelihood of k heads coming up in an n-toss sequence
Assuming a fair coin, p(k) = nCk/2^n
cold heron
like this?
cold heron
I feel confusion between binomial coefficients and binomial probabilities
sterile nymph
the binomial coefficient is just nCk
a binomial probability distribution is a distribution that uses the binomial coefficient
lusty spade
i dont know how to solve
amber waspBOT
i dont know how to solve
lusty spade
seems like no one knows
mint wraith
i dont know how to solve
trying to find value of x?
lusty spade
yes
indigo cloud
apply log on both sides
lusty spade
what
amber waspBOT
@lusty spade Has your question been resolved?
viscid locust
i dont know how to solve
notice 15^(2x+1) = 15(15^2x)
and 4^(2x-7) = (4^2x)/4^7
fyi, x is approximately -4.965311478
stark sky
I have a question regarding this pic
amber waspBOT
I have a question regarding this pic
stark sky
is the tangential acceleration of P relative to A equal to the teangential acceleration of P relative to B?
and if that's true, then why?
amber waspBOT
@stark sky Has your question been resolved?
stark sky
<@&286206848099549185>
amber waspBOT
@stark sky Has your question been resolved?
stark sky
.close
amber waspBOT
amber waspBOT
Available help channel!
hard canopy
amber waspBOT
hard canopy
,rotate
grizzled pagodaBOT
hard canopy
I’m doing question 1f)
Here is my diagram
Ik not all points are labeled
The top left diagram is with m and n
I need to use mass points for this
amber waspBOT
@hard canopy Has your question been resolved?
hard canopy
@sudden flare
amber waspBOT
@hard canopy Has your question been resolved?
hard canopy
<@&286206848099549185>
amber waspBOT
@hard canopy Has your question been resolved?
hard canopy
,rotate
grizzled pagodaBOT
hard canopy
,rotate
grizzled pagodaBOT
grizzled pagodaBOT
amber waspBOT
@hard canopy Has your question been resolved?
amber waspBOT
amber waspBOT
Available help channel!
ebon bobcat
yo im confused on this a lil bit
amber waspBOT
yo im confused on this a lil bit
ebon bobcat
lemme post pics
idk if the selected choice is correct, ill show my work
thats my work for parentheses
and the bottom equation is what i have before isolating a^2
im just wondering what it can be since all of the options dont factor in the addition of c^2 from the other side
anybody have any feedback on where i might be goign wrong
rapid peak
that -c in the last equation should be -c^2
rapid peak
yes
ebon bobcat
ok thanks
always helpful to have someone look over with a different view
thanks again
.close
hushed hedge
Hello! I had a question pertaining to probability
amber waspBOT
Hello! I had a question pertaining to probability
hushed hedge
The question was: How many ways are there to pick AMOR from the word AZAMORRA MORADA. I have some ideas, but couldn't come up with a proper solution that I could replicate. Thanks for your help!
amber waspBOT
Show your work, and if possible, explain where you are stuck.
hushed hedge
I thought to maybe start by finding the amount of cases I can find AMOR(54), but struggled to see how to find the total amount of probable ways without overcounting
rapid peak
how are you picking?
uncut karma
||is this calc? Or did I just forget this from geometry||
cobalt grove
you choose just 4 random letters from the whole word you just count the amount of letters and choose 4 random letters meaning just a combination thing
hushed hedge
So would using combinations work
hushed hedge
Because wouldn't there be repeats due to the extra letters
hushed hedge
Ok
cobalt grove
total means you wanna know how many 4 letter words you can construct using all of these letters
cobalt grove
np
unsure if u get 151 there
oh you just
I think i know what u did
feel free to .close
amber waspBOT
amber waspBOT
Available help channel!
split sail
amber waspBOT
split sail
Its a multiple answer type question
I am okay with C & D..
but I cant understand how to do A & B
I tried but it seems all answers are correct here
signal furnace
!show
amber waspBOT
Show your work, and if possible, explain where you are stuck.
signal furnace
I tried but it seems all answers are correct here
I agree that A is right, I can’t say the same for B
split sail
can you tell how u got it?
solar gust
can you tell how u got it?
Modulus of sum = sum of modulus
grizzled pagodaBOT
Civil Service Pigeon
signal furnace
Should I say what I was gonna say or are you gonna explain it
solar gust
I let u civil
signal furnace
can you tell how u got it?
Without loss of generality, we can let $z_1=2i$
grizzled pagodaBOT
Civil Service Pigeon
signal furnace
b/c all the configurations depending on where you pick z1 are just rotations of each other
signal furnace
**Civil Service Pigeon**
So this means you need to consider the tangents from (0,2) to x^2+y^2=1
Except I’m lazy so we’re not finding them directly
,w graph x^2+y^2=1
grizzled pagodaBOT
signal furnace
Note that you can make two 30-60-90 triangles
From these, the coordinates of the points of contact (and thus z2 and z3 follow directly)
You should get they’re $\left(\pm \frac{\sqrt 3}{2}, \frac{1}{2} \right)$
grizzled pagodaBOT
Civil Service Pigeon
signal furnace
Now, we can be a bit more lazy instead of brute forcing A and B
For A, note it’s just saying the centroid of the triangle is a distance of 1 from the origin (note the triangle is equilateral)
And for B, since $|z_2|=|z_3|=1$, $\frac{1}{z_2}=\overline{z_2}$ and similar for $z_3$
grizzled pagodaBOT
Civil Service Pigeon
signal furnace
(The proof is trivial by De Moivre’s)
Note that the example we chose for doesn’t yield a value of 9 for the expression in B, so we can automatically disregard it as false
—————
k I’m done
@solar gust do you have anything you want to add
split sail
hmm
btw maan, is there any way to do this for when it can't be obtained this way..?
Like for this case we got it because of knowing centroid..
signal furnace
<@560122149126275093> Thanks maan💖
solar gust
<@432085903196815361> do you have anything you want to add
Nothing to add, except that i apologize to the triangular inequality
signal furnace
Nothing to add, except that i apologize to the triangular inequality
Triangle inequality will forgive you if you solve this
(The solution uses the triangle inequality and it’s a pretty nice question)
split sail
Triangle inequality will forgive you if you solve this <:catthumbsup:61454018874...
that could blast my head ngl🥲
Are you all in universities?
signal furnace
I’d be cooked if I was
It’s the middle of the night here and I’m up because my ceiling was leaking 💀
solar gust
Bro ceiling leaking, like water going through it, sounds not good
signal furnace
Bro ceiling leaking, like water going through it, sounds not good
Eh it’s not leaking
It can wait til the morning
split sail
I am going.. I have more pending topics to complete :(. thanks for helping guyss. btw I will leave closing the channel to you guys
signal furnace
.close
amber waspBOT
solar gust
Eh it’s not **leaking**
Oh ok
signal furnace
Modulus of sum = sum of modulus
The math gods are very angry at you for saying this 
amber waspBOT
Available help channel!
placid yarrow
amber waspBOT
placid yarrow
pigeon hole principle question
why is it not 6
this is what I drew:
B W G
B W G
oh wait i sorta see whats wrong with my diagram
mortal dawn
One can draw BBBBBG and end up with only 2 pairs.
placid yarrow
how would we work this out since we dont know how many socks there are in total
like assuming it may have an infinite amount of socks isnt it possiblke that you keep drawing blue socks
mortal dawn
Ignore the random drawing and intentionally pick socks such that you try not to get a pair each time you draw one.
lament valley
One can draw BBBBBG and end up with only 2 pairs.
wouldn't that be 4 pairs?
mortal dawn
(BB) (BB) [BG] 2 pairs and one mismatch
placid yarrow
Ignore the random drawing and intentionally pick socks such that you try not to ...
which drawing are you referring to
mortal dawn
which drawing are you referring to
When you pull a sock from the drawer, that's drawing one sock from the drawer.
lament valley
(BB) (BB) [BG] 2 pairs and one mismatch
so there is another b and g inside that we didn't choose?
or
can there be an odd number of socks of a color
mortal dawn
Pretend it's not a drawer but a sock factory that makes socks faster than you can pick them up. 😆
There are infinite socks.
placid yarrow
is this quesion solvable? im finding it a little hard to think of a way to answer it 💀
coral wigeon
it is solvable
placid yarrow
but there couild be infinite socks but you could be drawing teh same sock everytime no?
mortal dawn
is this quesion solvable? im finding it a little hard to think of a way to answe...
Yes. Let's make this a game. I choose a sock and you choose a sock. Each time, we add it to the same pile, and each time you cause a matching pair to be made, the other person gets a point.
I choose blue first.
coral wigeon
but there couild be infinite socks but you could be drawing teh same sock everyt...
then you'd have 3 pairs after you pick 6 socks
lament valley
bb bb bw g so 8?
vast scaffold
bbb ggg w
placid yarrow
then you'd have 3 pairs after you pick 6 socks
doesnt a pair have to be the same colour though
so blue blue is a pair, but blue green is not a pair
lament valley
you get 2 pairs, then one of each color
vast scaffold
if you draw 4 blue socks
you have 2 pairs
so if you draw inf blue socks
you have inf pairs
mortal dawn
You can also approach this by initially just picking 2 pairs explicitly, then picking more socks until you would be forced to make another pair.
amber waspBOT
@placid yarrow Has your question been resolved?
frigid kindle
if i have 410 people
i have 58.3% girl
41.7%
how many people for girl?
runic kraken
what have you done until now
frigid kindle
none
runic kraken
okay
so you have a total amount of people of 410
so thats 100%
you have 58.3% that are girls
now whats left is to find what that percentage is in people
jovial field
Ok
See it means that out of 410 people 58.3 percent are girls
Now how do u find percentage of something
frigid kindle
idk
in percentage male is 41.7%
gentle cedar
Make the percentage into fraction and multiply it with the total people
frigid kindle
is this 41.7%/100% * 410
gentle cedar
Remove the percentage signs
mystic shoal
explain $\textbf{2. Prove that the projection of A on B is equal to A·b,where}$
b is a unit vector in the direction of B.
Through the initial and terminal points of A pass planes perpendicular to B at $G$ and $H$ respectively as in the adjacent figure; then
Projection of A on $\mathbf{B}=\overline{GH}=\overline{EF}=A\cos\theta=\mathbf{A}\cdot\mathbf{b}$
gentle cedar
(4.17/100)*410
grizzled pagodaBOT
↠Devine
mystic shoal
<@&286206848099549185>
frigid kindle
how is this 4.17/100?
gentle cedar
41.7/100 sorry
lusty pine
explain $\textbf{2. Prove that the projection of A on B is equal to A·b,where}$
...
!occupied
amber waspBOT
explain $\textbf{2. Prove that the projection of A on B is equal to A·b,where}$
...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
gentle cedar
how is this 4.17/100?
Mistake
gentle cedar
Anyways 41.7 shift the decimal we have 417. At denominator the 100 becomes 1000
Now multiply 417 and 410
Whatever answer you get it will be divided by 1000
Shift the decimal back to the left side again to get ur answer
frigid kindle
Anyways 41.7 shift the decimal we have 417. At denominator the 100 becomes 1000
...
41.7/100
2 zero = 41.7
1 zero = 4.17
0 zero = 0, 417?
gentle cedar
Well yeah... You can multiply that with 410
gentle cedar
0.417
Why you put a comma?
frigid kindle
there is no dot on my calculator so i had to use coma
gentle cedar
So 170.97 is the answer
You can round it off to 171
I'm sorry... I just wanted to help, maybe i could see the question?
frigid kindle
i dont think this is 171
but 172
jovial field
No
gentle cedar
No... 170.97 round off is 171
gentle cedar
if i have 410 people
i have 58.3% girl
41.7%
how many people for girl?
If this is question, then
53.3% girl means
(53.3/100)*410
frigid kindle
according to mr robot with giga brain
410-238 = 172
gentle cedar
according to mr robot with giga brain
410-238 = 172
I was looking at 41.7% that's boys sorry
gentle cedar
Yes it was mistake
Sorry
Anyways that is correct answer
jovial field
Oof
gentle cedar
Yes sir
frigid kindle
172 boys i gues
gentle cedar
Yes
frigid kindle
but how come the formula we counted is 171 ? not 172
grizzled pagodaBOT
gentle cedar
Well i don't have a calculator... Bruh making wrong multiplication
gentle cedar
according to mr robot with giga brain
410-238 = 172
Well what ya know, chatgpt sure is stoopid
frigid kindle
chatgpt is rigged
old lake
its just not made to do math
frigid kindle
so the answer is 171 boys 238 girls
gentle cedar
239 girls
jovial field
No mod to close these eh?
It gets closed automatically but it takes time
When one gets a timeout
spare belfry
I have lost a role for this
I wonder, how did you lose it?
jovial field
See
gentle cedar
It gets closed automatically but it takes time
Aight... Hope to see you more ma dude... I'm also interested in learning and helping
jovial field
I used to ping people when I used to write something related to their question when they were off or when they left the channel unclosed
But at some point mods felt it was too much and I got timed out
old lake
rip
old lake
🇼
old lake
lmao
spare belfry
Not to get roles 👑
I don't think your perm is permantely revoked, is it?
you can still get it back by helping
old lake
But yea srsly I need a nitro
jovial field
No but once u get timed out
old lake
what role did you have?
lusty pine
I don't think your perm is permantely revoked, is it?
what perm
jovial field
U cannot be assigned a role automatically
jovial field
Helpful role
old lake
what does it do
spare belfry
lusty pine
oppailol you had the helpful role??
gentle cedar
Idc about roles
jovial field
Allows to access helper lounge
gentle cedar
Close the darn helpbox 
lusty pine
first tine i saw you you were blue
restive harness
.close
amber waspBOT
spare belfry
<@982507190566932510> .close
I don't have the permission to do that
gentle cedar
right i forgot
Type .close plz
jovial field
Fr
jovial field
No helpers have that perms
jovial field
I am top helpful
I was tooo
restive harness
@jovial field ping me whenever you need something from top helpful
spare belfry
No helpers have that perms
I mean I usually get consent from helpees before closing
restive harness
But my role was taken away
nooo why
jovial field
Told the reason above
jovial field
I used to ping people when I used to write something related to their question w...
This
amber waspBOT
Available help channel!
ancient oar
Why is this true?
amber waspBOT
Why is this true?
proper umbra
They multiplied it by $\frac{\sqrt{n^3+1} + \sqrt{n^3}}{\sqrt{n^3+1} + \sqrt{n^3}}$
grizzled pagodaBOT
Calc III Victim
amber waspBOT
amber waspBOT
Available help channel!
modern marsh
Is f(x,y) continuous at the origin
amber waspBOT
amber waspBOT
Available help channel!
open rampart
need help with finding the distance between two points / plotting. the coordinates are (2,-6) (-Sqr root of 3, -3). The main thing that is tripping me up is the square root, once i get that sorted I will know how to proceed. BEcause to find the distance I am using the d = sqr root of (x2-x1)^2 + (y2-y1)^2 formula
celest cove
sure, what is the scary root doing to you
open rampart
ok so i realized that i shouldve just searched up how to subtract a square root because that is my issue i apologize if i am wasting your time but what i mean to ask is how do i subtract a square root from a whole number
old lake
you can't
open rampart
ah
celest cove
you cant unless it it simplifies to one, like sqrt(4)
tepid verge
do you really mean to say subtract?
little dagger
you can but it might give approx value
old lake
I mean you can but the answer will be an irrational number as well
old lake
root 3 is an irrational number
tepid verge
2 - sqrt(3) is a perfectly good number
old lake
you might wanna keep it as it is
open rampart
ah ok because this is just a review section from this trig book i am studying on the topic of the coordinate system
old lake
cite your sources
isnt 2-root3 irrational too?
tulip tapir
yes it is...
old lake
if he wants to actually subtract it
tulip tapir
but just because it's an irrational doesn't mean it's a bad number
old lake
which is what he is saying
old lake
but just because it's an irrational doesn't mean it's a *bad* number
ayo im not racist
open rampart
hold up so the next step after subtracting would be to square it so I am assuming my next step would be to square (- sqr root of 3 -2) and that would eliminate the sqr root?
tulip tapir
@open rampart i'm assuming what you mean is you want a decimal representation?
old lake
hold up so the next step after subtracting would be to square it so I am assumin...
it wont
tulip tapir
of 2 - sqrt 3
open rampart
no
old lake
^
tulip tapir
there's no way to get an exact representation, it has an infinite nonrepeating decimal sequence
so you can't just subtract it
open rampart
i want to find the distance between two points, and so in (x2-x1)^2 the x2 is - sqr root of 3 and the x1 is -3
so i guess what im asking is what would i do in this scenario
old lake
you dont need to solve the root
tulip tapir
hang on
open rampart
would i have to do something to the -sqr root of 3 itsef?
tulip tapir
what do you mean
old lake
just put the answer in terms of root 3
tepid verge
need help with finding the distance between two points / plotting. the coordinat...
in that case, x2 - x1 = 2 - (-sqrt(3)) = 2 + sqrt(3)
old lake
unless they want a decimal answer from you
open rampart
in that case, x2 - x1 = 2 - (-sqrt(3)) = 2 + sqrt(3)
hold on sorry the x1 is positive 2
and the x2 is negative root 3
tulip tapir
simplify $(x_2 - x_1)^2 = (-\sqrt 3 + 2)^2 \to (-\sqrt 3)^2 + 2^2 + 2(-2 \sqrt 3)$
old lake
hold on sorry the x1 is positive 2
its the same..
tepid verge
and the x2 is negative root 3
true, so the above is actually x1 - x2
grizzled pagodaBOT
ren
little dagger
wait no
open rampart
is *this* what you want to do
yes except its - root 3 -2 squared
little dagger
of square roots
open rampart
i dont think i need an approximation
fossil path
who can to help me with this sum
tulip tapir
what exactly do you need
amber waspBOT
who can to help me with this sum
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
open rampart
what exactly do you need
i think you guys have helped i will try to figure it out i think i got confused on what im confused about
open rampart
thank yu for ur help tho
tulip tapir
np
amber waspBOT
If you are done with this channel, please mark your problem as solved by typing .close
open rampart
.close
amber waspBOT
little dagger
i have a formula for approx (idk how it was derived)
it is
(x + y)/2√y
x = number you're finding for
y = closest square root to it
so for √3
it would be
(3 + 4)/2√4 = 1.75
open rampart
wait hold on
little dagger
(.reopen)
open rampart
.reopen
amber waspBOT
✅
open rampart
so i have (-root 3 -2) squared, and im confused about what happens when i sqr this. Would it become root 9 + 2 root 3 +2 root 3 +4 and then 3+ 4 root 3 +4 and then 7 +4 root 3?
hold on let me send an image of what i have worked out
little dagger
,rotate
grizzled pagodaBOT
little dagger
it's on phone
open rampart
ok so it would just be 7 + 4 root 3?
little dagger
correct
little dagger
,rotate
grizzled pagodaBOT
little dagger
what's the question?
open rampart
what would i do with the root 3
open rampart
so it would just become 4 +2 root 3?
little dagger
2√(4+√3)
open rampart
how did the 2 get outside the root
open rampart
wait why would it multiply if its the root of 16 + 4 root 3?
little dagger
wait what
is
3+6
open rampart
9
open rampart
9
open rampart
wait so are you saying that the 16 inside the root turns to 4 and then it turns to 2 and then it goes outside the root?
little dagger
nope
i am saying
we can write
√(16+4√3)
as
√(4*4)+4√3)
then we can take 4 common
√(4 x [4+4√3])
open rampart
thanks for being patient with me
little dagger
uhm lemme think think think
little dagger
by the 4 common
i rewrote the expression
for simplification
i made it such that we can apply
√(ab) = √a*√b
open rampart
ok so im looking at the solution for this question and it states that the distance is 4.79 between the two points
little dagger
what is ques?
open rampart
Number 19
little dagger
,rotate
grizzled pagodaBOT
open rampart
right
grizzled pagodaBOT
little dagger
ans. is coming to 9.74 as you can see
little dagger
i think it's incorrect
little dagger
I mean i have applied it correctly
little dagger
same thing as it's in square
open rampart
Then it would be 2+ root 3
Dang wtf
Should I keep using this book if it’s incorrect
I got it from half priced books lol it’s from the 90s
little dagger
if you look actual answer closely, it's
9.74 and in book it's 4.79
they have reversed it by mistake
little dagger
sure
and one more thing: never be sorry for the things you don't understand
ask it again
amber waspBOT
fathom bramble
,w sqrt((2+sqrt3)^2 + (6+3)^2)
It's 6-3
little dagger
how?
fathom bramble
how?
The distance between two points is the modulus of the vector that goes from one point to the other
amber waspBOT
Available help channel!
fathom bramble
To get the vector it's Ending point-starting point
amber waspBOT
To get the vector it's Ending point-starting point
fathom bramble
Thus sqrt ((2+sqrt(3))^2+(-6-(-3))^2
-6-(-3)=-3, squaring it gives 9
Thus the distance between the points is the modulus of the vector(2+✓3,3)
little dagger
The distance between two points is the modulus of the vector that goes from one ...
y2 is -3 and y1 is -6
fathom bramble
y2 is -3 and y1 is -6
-3-(-6)=3
little dagger
oh wait yes
fathom bramble
The squares are the same, they both yield 9
little dagger
my bad
fathom bramble
little dagger
,w sqrt((2+sqrt3)^2 + (6-3)^2)
grizzled pagodaBOT
little dagger
true
fathom bramble
Also, should probably close this since the channel marked it as me posting a problem
.close
amber waspBOT
little dagger
thanks to prim
amber waspBOT
Available help channel!
knotty lance
How to do 6 choose 2?
amber waspBOT
How to do 6 choose 2?
covert dock
So my question is about allied angles in trig
covert dock
OK thanks
knotty lance
So my question is about allied angles in trig
Deja vu @tropic wadi
covert dock
?
sterile nymph
n choose k is n!/((n-k)! k!)
amber waspBOT
knotty lance
Stop evading a ban. If you want to appeal your ban, then DM <@833145701701124116...
Bro im not
Someone banned me twice
I can show video evidence
sterile nymph
???
mystic lotus
Yes the people who banned you were in fact the server staff
sterile nymph
If you were banned twice, but you're still here, you're obviously evading a ban.
mystic lotus
DM @dense tiger if you want to appeal your ban
amber waspBOT
Available help channel!
woven crown
amber waspBOT
potent cradle
Use: Symbolab it will be able to help you. (And with any future equations)
potent cradle
you just put the equation in...
woven crown
yea but its a multiple choice bro
its asking which of the following is true
how is symbolab gonna help
also how tf do i type that in
pseudo crescent
Think about what each of the integral means
forget about symbolab btw
What do the integrals mean in terms of area under graph of f(x)?
pseudo crescent
correct
pseudo crescent
you got it?
woven crown
so from -2 to 3 it would be -6
pseudo crescent
right
pseudo crescent
correct
woven crown
i appreciate ur help tyvm
pseudo crescent
np
potent cradle
also Mae I do have a quick question before u go
are you like familiar with derivatives?
pseudo crescent
yeah, i guess so
pseudo crescent
ill have to go for few mins, ill be back soon
potent cradle
alr
woven crown
show me
also that question before i dont think u can use symbolab
dont go around telling ppl to use symbolab if u js dk
pseudo crescent
I am stuck on this stupid question for like 15min
you can send it in my DMs or here, if machewi wants to see it as well. Or you can open your own channel
woven crown
amber waspBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@woven crown Has your question been resolved?
woven crown
how do i get the slope of the tangent
split sail
sincerest apologies but i need some advising regarding how to proceed from the last line
split sail
or if i screw up anything in the eqns
signal furnace
sincerest apologies but i need some advising regarding how to proceed from the l...
amber waspBOT
amber waspBOT
Available help channel!
ionic zodiac
how do i do part a
amber waspBOT
how do i do part a
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
signal furnace
Ok I don’t rlly like this question, but I know what they’re trying to do
They’re trying to get you to remember that about 99.7% of the data is within 3 standard deviations of the mean
Meaning [39,57] is the interval of all days within 3 standard deviations of the mean
(This is false since you could just shift)
And this the mean is (39+57)/2 = (idk)
ionic zodiac
oh yeah