would i plug in 2 for the f(x) then
#help-17
shrewd moth
then you just have f(2+h) = 3 + 3h + h^2
plug that into the equation
then solve for f(2)
hushed ether
you cancel out all non-h variables
covert forum
hold on
shrewd moth
f(2) = 4 - 2 + 1
hushed ether
no
shrewd moth
f(2) = 3
shrewd moth
(3+3h+h^2) - 3
hushed ether
if yyoure right
hushed ether
oh
shrewd moth
final answer
shrewd moth
look you have the equation:
(f(2+h) - f(2))/h
you are also given f(x) as x^2 - x + 1
covert forum
so now im at
shrewd moth
so literally all you have to do is find f(2+h) and f(2) then plug those in an solve
covert forum
(5h + h^2 + 1 + 3)/h
covert forum
5h + h^2 + 1
shrewd moth
yep
shrewd moth
should turn out to be 4+ 4h + h^2 - (2+h) + 1
covert forum
4 + 4h + h^2 - 2+h + 1
shrewd moth
you forgot the parenthesis
covert forum
do i need to?
shrewd moth
it would be (x - h)^2 + (x - h) + 1
just use the number given lol
shrewd moth
do i need to?
yes because in this case you would have -2 +h instead of -2 -h
covert forum
okay i understand
shrewd moth
which is the next step from 4+ 4h + h^2 - (2+h) + 1
that turns into: 4 + 4h + h^2 - 2 - h + 1
covert forum
itd be
4 + 4h + h^2 - 2 - h + 1
3 + 2h + h^2..?
shrewd moth
collect the like terms, you get 4 + 1 -2, then 4h - h, and a h^2
shrewd moth
itd be
4 + 4h + h^2 - 2 - h + 1
3 + 2h + h^2..?
incorrect
covert forum
i
covert forum
okay
shrewd moth
then solve for f(2)
covert forum
thats 3
covert forum
i did that
shrewd moth
alright then solve
shrewd moth
yep now just divide everthing by h
covert forum
would it be h + 3?
shrewd moth
correct
shrewd moth
np
covert forum
im going to try another one
vocal sleetBOT
@covert forum Has your question been resolved?
covert forum
yes
tame root
Hi, I’m in having a lot of issues, this looks easy but I feel it isn’t. Basically I need to add parenthesis so that the operation gives 24 and 32 as a result. Changing signs isn’t allowed and changing the position of the numbers isn’t allowed either, Only add or remove parentheses. I already solved the ones below so they work as an example, but please help me it’s so hard
vocal sleetBOT
Hi, I’m in having a lot of issues, this looks easy but I feel it isn’t. Basicall...
@tame root Has your question been resolved?
tame root
pls help
tame root
add parentheses to represent multiplication
yeah but where? exactly in what number?
solar crane
yeah but where? exactly in what number?
(16-12-8)(-24/4)=24
tame root
(16-12-8)(-24/4)=24
thank you very much, and do you maybe have the one which gives +32? i dont find it either
solar crane
thank you very much, and do you maybe have the one which gives +32? i dont find ...
let me think, i may be able to. ill give it a solid 15min bc i have my own hw to do as well :)
tame root
let me think, i may be able to. ill give it a solid 15min bc i have my own hw to...
oh ok, its fine, take your time
solar crane
dang i got -32 😭
tame root
dang i got -32 😭
yeah, that is one of the answers and i already got it as well
idk how to make it positive
it looks so easy but actually its not 😭
solar crane
yeah it confusing
tame root
yeah it confusing
i even tried to ask AI and it couldnt solve it either
solar crane
oh wow
tame root
yeah i keep trying that
but i cant
maybe im trying to see if i can put any parentheses in the -12 -8 -24 so it become 8 and then divide that 8 by 4 to get 2 and then multiply the 16 by that 2
Bruh not even AI can solve it omg its so hard
ill keep trying that
IM GETTING SO STRESSED
BRUH
IM STARTING TO FEEL THIS IS IMPOSSIBLE
😭
first i tried to put it like this: -12-((8-24)/4))
i also tried -12-8-(24/4)
none of those are correct
-(12-8-24/4)
OMG YES
THAT GIVES 2
and now
i multiple that by the 16
of the outside
so it would be 16(-(12-8-24/4))
thanks
ill close the ticket now
.close
vocal sleetBOT
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Available help channel!
dim quail
vocal sleetBOT
dim quail
I don't know where to start
distant eagle
I don't know where to start
Choose a point (x,y) in the plane R^2. Consider the plane that passes through the points (1,13,1), (x,0,0) and (0,y,0) and find the volume of the tetrahedron it generates. Define f(x,y) as the volume of this tetrahedron
Every plane can be obtained in this way
So now you just have to minimise the function f(x,y) over R^2
Also I think $(x,y)$ should be chosen in some restricted subset, like maybe $(1,+\infty)\times(13,+\infty)$
twin meteorBOT
d
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quartz wadi
Hello
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Available help channel!
hoary apex
Question: in a 2-digit number, digit in units place is twice the digit in tens place. If 27 is added to it, digits are reversed, find the number.
vocal sleetBOT
Question: in a 2-digit number, digit in units place is twice the digit in tens p...
hoary apex
.open
Question: in a 2-digit number, digit in units place is twice the digit in tens place. If 27 is added to it, digits are reversed, find the number.
Finally
dim pumice
do you not understand the question itself or how to solve it?
hoary apex
(My discord is sending doubles messagez apparently)
hoary apex
do you not understand the question itself or how to solve it?
I dont understand it
dim pumice
take a number like 47, whats the units place digit and whats the tens place digit?
hoary apex
take a number like 47, whats the units place digit and whats the tens place dig...
Unit digit is 7 and tens digit is 40
:shrug:
dim pumice
ok the idea is right, but we only consider single digits like 0, 1, ..., 9
so tens digit would just be 4 in that case
hoary apex
Alright
dim pumice
now is 47 with digits 4 and 7 allowed?
hoary apex
Yeah
dim pumice
well it says the units digit has to be twice the tens digit
hoary apex
Hmmm
hoary apex
well it says the units digit has to be twice the tens digit
Tens digit= x
Units digit= 2x
dim pumice
yeah
hoary apex
can you just name any allowed number?
27?
dim pumice
2 and 7, but 2×2 ≠ 7
hoary apex
I dont really know what is an "allowed number"
dim pumice
like, a 2 digit number with the units digit being twice the tens digit
hoary apex
Oh
hoary apex
like, a 2 digit number with the units digit being twice the tens digit
Then 24
hoary apex
now if you add 27
You there man?
dim pumice
yeah, so 24 does not work
you would just have to try out all the other possible combinations
hoary apex
you would just have to try out all the other possible combinations
I think i cant do that way, i must do in the way of generalised form
dim pumice
why not? There are only 4 possible ways
hoary apex
why not? There are only 4 possible ways
I cant say that to my teacher after she cut my marks into -5 for doing that
dim pumice
then that's your teacher doing you wrong
hoary apex
then that's your teacher doing you wrong
Well there is nothing i can do about that
dim pumice
but ok, let's think about how to solve it using x
hoary apex
Alrighr
dim pumice
Then
x+2x+27
= generalised form = 10x + 2x + 27 = reversed
problem here is that x+2x does not sum up to the number as you would expect
if we take x=2 as the tens digits, we would just get 2 + 2×2 = 6
hoary apex
Hmmm
dim pumice
maybe think about why it's called the tens digits
hoary apex
maybe think about why it's called the tens digits
Unit digit = x
Tens digit = 2x
10(2x) + x + 27= 10x + 2x(reversed)
21x + 27 = 12x
21x - 12x = 27
9x = 27
x = 27/9 = 3
X = 3
2x = 6
Original digit 36 on reverse
= 63
dim pumice
10x + 2x + 27 = 10(2x) + x
hoary apex
My brain isnt braining
dim pumice
10x is ten times the tens digit and then 2x is twice the tens digit
hoary apex
it's still not 10(2x) + x + 27
10(2x) + x + 27 on reversed is 10x + 2x
dim pumice
yeah, but like, lets take x=2 again, then 10(2x) + x would be 42
but now the tens digit is twice the units digits, not the other way around like it should
crude anvil
10x +2x +27 = 10(2x) +x
12x+27=20x +x
12x+27=21x
12x-21x= -27
-9x= -27
x=-9/-27
x=3
@crude anvil
dim pumice
yeah just give out the solution
hoary apex
yeah, but like, lets take x=2 again, then 10(2x) + x would be 42
How?
10(2x) + x =
10(2x3) + 3 =
60 + 3 = 63 Reversed number
Original = 36
crude anvil
how
dim pumice
you dont want to add 27 to the reversed number though
hoary apex
No
Since as per the question the smaller number or the original number was less by 27 so 27 was added to left hand side so that both sides become equal.
hoary apex
you dont want to add 27 to the reversed number though
You there?
dim pumice
Unit digit = x
Tens digit = 2x
10(2x) + x + 27= 10x + 2x(reversed)
21x + 27 = 1...
ok so you say 10(2x) + x + 27 = 10x + 2x, but now if x=3, we get
63 + 27 = 36
hoary apex
ok so you say 10(2x) + x + 27 = 10x + 2x, but now if x=3, we get
63 + 27 = 36
Yep
Original number is reversed so it became 63
crude anvil
I don't understand yet
hoary apex
No no original number is 36 and
When 36 is reversed its became 63
dim pumice
so how would you fix the equation?
crude anvil
ok
vocal sleetBOT
vocal sleetBOT
Available help channel!
loud spade
vocal sleetBOT
loud spade
I believe this to be the way to work out this question, but the solutions to the question shows a similar but different thing
I have no idea why the variables are switched in the way that they are - if someone could explain this to me i'd be forever grateful
vocal sleetBOT
@loud spade Has your question been resolved?
bitter pilot
I have no idea why the variables are switched in the way that they are - if some...
I actually think either way works out because the bounds are linear
loud spade
oh shit i got a different answer but maybe i made some algebra error
one sec
oh yeah i did
it gives the same answer
huh that makes absolutely no sense to me though
cuz essentially they switched y and x but then the function is e^(x-y) and that didnt swtich so how tf does it work
bitter pilot
I just checked, both give the same
I made an awful sketch
But essentially you are having the exact region in both planes
Which makes sense because of (1,2) and (2,1) symmetry wise
loud spade
i see its the exact same section of the plane regardless
so yeah i guess if its symmetrical over y=x then that can always be the case
bitter pilot
Most of the time this works with linear stuff I think there was a theorem of Fubini
vocal sleetBOT
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Available help channel!
short kraken
vocal sleetBOT
potent gorge
uhhh it’s not
potent gorge
lol it happens
short kraken
its cause i was doing (x+4)(x-4) so i thought i could just do difference of squares
i didnt apply it right
which is why i was wrong
potent gorge
yeah
short kraken
.close
vocal sleetBOT
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Available help channel!
random rock
Why do you need to put the answer in absolute value when simplifying radicals with variables to an even nth root
vocal sleetBOT
Why do you need to put the answer in absolute value when simplifying radicals wi...
hard atlas
for example $\sqrt{(-5)^2}=5=\abs{-5}$
twin meteorBOT
Denascite
vocal sleetBOT
@random rock Has your question been resolved?
oblique garden
Can someone help me with betweeness of points, section formula, midpoint formula my geometry teacher blows through them so fast and I barely understand its to a point I have to go to discord for help😭🙏
vocal sleetBOT
Can someone help me with betweeness of points, section formula, midpoint formula...
tranquil trellis
just post the question don't ask to ask
oblique garden
just post the question don't ask to ask
Oh I didn’t know but like its multiple things Im having issues with
true grail
ask the question & we'll tell u what u need to know
proven knot
Learning on the job so to speak
true grail
ok these r both straightforward enoguh
true grail
My teacher makes it so hard to understand and she teaches insanely fast
have u tried asking her to slow down a little? she might listrn, eho knows
oblique garden
Tried😔
oblique garden
kk
true grail
bc i dont have my laptop and that makes it hard to type
anyway
so has the definition of a midpoint been explained to you?
oblique garden
Well, not really but Im guessing by the name its just the point that lies in the middle between values Im not rlly sure
She barely teaches and goes super fast so I can barely grasp on anything😭
true grail
Well, not really but Im guessing by the name its just the point that lies in the...
ye that's it
oblique garden
Ohhh so maybe I do know a few lol
true grail
anyway u know that if the midpoint is halfway between two other points that must be true of the x & y coords, no?
oblique garden
anyway u know that if the midpoint is halfway between two other points that must...
What do you mean true?
Like the same distance for both cords
true grail
as in, if the midpoint is halfway between two other points (which it is by definition) then the midpoint's x coord must be halfway between the first point's x-coord and the second point's x coord
and likewise for the y coords
oblique garden
Im confused
Wait
Wait Im confused
I don’t get it
Is there any way you can show an image or visualize it
Oh waitt
So the midpoint x and y cord must be halfway of the 2 other points/values x and y cords
true grail
So the midpoint x and y cord must be halfway of the 2 other points/values x and ...
yes
true grail
same for z if we're 3d
true grail
but we can ignore that rn
oblique garden
Ohhh
oblique garden
but we can ignore that rn
alrr
true grail
that axis points straight up away from x and y
true grail
the point is, the midpoint here has an x-coord that's the average of -5 and 2
which is to say, -1.5
oblique garden
Wait Im confused, what do you mean by average and how did you get to -1.5?
So the -5 is the x cord of one coordinate and -1 being the other x value of the other cord.
true grail
Wait Im confused, what do you mean by average and how did you get to -1.5?
add -5 and 2, then divide by 2
true grail
So the -5 is the x cord of one coordinate and -1 being the other x value of the ...
1 is the y-value of the first coord
oblique garden
1 is the y-value of the first coord
Wait I meant that, my bad my brain got confused for a second
oblique garden
add -5 and 2, then divide by 2
Is that part of the method to get the answer?
true grail
Is that part of the method to get the answer?
that'e just what it means to find the average of two numbers: add them and divide by 2
oblique garden
that'e just what it means to find the average of two numbers: add them and divid...
Oh I seeee
true grail
which gives u the halfway point
oblique garden
So thats it? then I do the same for the other coordinate
true grail
the y coord, yes
oblique garden
6+1 divided by 2 is 3.5
So -1.5 in the first box and 3.5 in the other and thats the answer?
true grail
yup
oblique garden
Does that method apply to everything relating to that type of question or
true grail
that's how you find midpoints on a 2d graph in general
true grail
lemme look
oblique garden
true grail
ok for no 3 my immediate advice is draw a graph
and not just bc im on a phone and all my stuff is in a different house
oblique garden
and for no 1?
true grail
ngl i don't remember what that symbol means
i think it just means they're the same length?
oblique garden
Im pretty sure
true grail
in which case ur just being told that 8x-6=52, which is just elementary algebra
true grail
And how would I solve from that
add 6 to both sides, then divide by 8
the goal is to isolate x
oblique garden
Ahh I see, well tysm for the help I rlly needed it ur the bestt ttytyty
south ember
Hi, someone help me with this exercise pls? I'm making a mess to perform the hasse diagram
vocal sleetBOT
Hi, someone help me with this exercise pls? I'm making a mess to perform the has...
south ember
How do you recommend me to organize the diagram as I draw it? When there are several elements I start to have a hard time
vocal sleetBOT
@south ember Has your question been resolved?
manic gulch
What’s P(two 5’s before 4 and 6 in rolls of fair 6-sided die)? What’s the expected payoff if you get $1 for each pip in the face rolled until you get the 4 and 6, and pay $1 per roll?
The two 5’s part is what makes it difficult for me. P(5 before 4 and 6) is simply 1/3. Either using p = 1/6 + 3/6p where 3/6 is probability that none of the 3 cases occurred on first roll. Other way is symmetry (recognizing three possible events of 4 before 5 and 6, 5 before 4 and 6, and 6 before 4 and 5, so 1/3, or recognizing events of 465, 645, 564, 546, 456, and 654 are equally likely and counting to get 1/3)
vocal sleetBOT
What’s P(two 5’s before 4 and 6 in rolls of fair 6-sided die)? What’s the expect...
manic gulch
This is a quantitative finance interview question (labeled hard).
jovial rock
P(two 5s before 4 and 6) = 2/27. Expected payoff calculation is more involved, requiring analysis of a state machine with transitions based on each roll. The payoff depends on the number of rolls and pips before hitting the 4 and 6.
manic gulch
I see. How do you get to 2/27?
I assume for second, you mean finite-state homogenous markov chain where you can set the state for 1 to be 0, 2 to be 1, 3 to be 2, etc.?
jovial rock
We only care about rolls of 4, 5, and 6, Imagine rolling the die repeatedly, but only writing down when a 4, 5, or 6 comes up
We need two 5s to appear BEFORE either a 4 or a 6>>> The only two possible sequences are 554, 556
each roll has a 1/3 chance of being a 4, 5, or 6 (since we’re ignoring the other numbers),
So, the probability of getting 554 is (1/3) * (1/3) * (1/3) = 1/27
the probability of getting 556 is also (1/3) * (1/3) * (1/3) = 1/27
Since either of the two valid sequences satisfies our condition
we add their probabilities
1/27 + 1/27 = 2/27
manic gulch
I see ok thank you
jovial rock
np
manic gulch
Wait there’s also cases where you can get another number other than 4, 5, or 6 after the first 5. Not sure if 2/27 is correct. Seems too simple.
Since 5’s don’t have to be consecutive. Just both need to occur before 4 and 6.
jovial rock
then I think it should be solved with using geometric distribution
manic gulch
Also, 4 and 6 must both occur. Can’t just be 2 5’s than 1 of the two.
jovial rock
Since 5’s don’t have to be consecutive. Just both need to occur before 4 and 6.
In that case I assume it's 1/9
quick crag
let me get this correct, you're rolling 6 fair 6-sided dice sequentially, and you want to calculate the probability of rolling "two 5's before a 4 and a 6"
@manic gulch ?
manic gulch
let me get this correct, you're rolling 6 fair 6-sided dice sequentially, and yo...
1 fair 6-sided die
quick crag
so, 1 fair 6-sided die, rolled 6 times?
manic gulch
No can roll infinitely. Just need to find the probability that two 5’s occur (doesn’t have to be consecutive) before 4 AND 6.
It’s labeled hard.
quick crag
if you can keep rolling it indefinitely, the probability will tend to certain that you will eventually roll a 6 and two 5s followed by a 4.
over an infinite number of random rolls, any finite sequence of rolls tends to certainty
manic gulch
…
That’s incorrect
There’s an actual probability
I remember seeing the answer (I don’t remember how to get it), and it’s very low
raven owl
Is this exactly two fives, or can there be three fives and then a 4 and a 6
manic gulch
Is this exactly two fives, or can there be three fives and then a 4 and a 6
Two 5’s
Exactly
I hope I don’t get this in quant trading interviews ngl
raven owl
I think you can do the approach of only looking at the first 4 rolls and ignoring any roll <= 3
manic gulch
I think I have an example of someone calculating it, but don’t know how they got numbers. 1 min.
quick crag
That’s incorrect
Are you sure you can roll the dice as many times as you want?
proof. Let N be the number of sides of the die, and B be the length of the sequence S you want to calculate the probability. Consider a X = N^B sided die where exactly one side of this die corresponds to the sequence S. Each roll of the dice has the probability 1 - 1/X of NOT rolling on the side S. After R rolls, the probability of not rolling S is (1 - 1/X)^R. Since the limit of this tends to 0 as R tends to infinity, it is certain to roll S given enough rolls.
manic gulch
This was correct
manic gulch
Are you sure you can roll the dice as many times as you want?
proof. Let `N` be...
Yes
I just don’t know how they got numbers
quick crag
The only way it's not certain is if rolling one number depends on what was rolled before.
I think you've misread the question.
raven owl
I don't think they have
manic gulch
I think you've misread the question.
No I didn’t lol
manic gulch
This was correct
This was correct/verified. I just don’t remember how they got it.
raven owl
This was correct
what does that sum come out to be
manic gulch
I would have to recalculate
raven owl
I think the approach is what I was talking about. You can just check the probability that the last number isnt a 5
vocal sleetBOT
@manic gulch Has your question been resolved?
raven owl
I think you can do the approach of only looking at the first 4 rolls and ignorin...
nvm I forgot about situations like if they just keep rolling 6s and no 4s
manic gulch
2/24 + 2/36 + 2/54 = (18 + 12 + 8)/216 = 38/216 = 19/108
That’s what it is
still not sure how to get the numbers, though
Probably a follow up that they would ask in addition to payoff questions I said is expected number of throws to get the desired sequence
this question really sucks
vocal sleetBOT
@manic gulch Has your question been resolved?
manic gulch
What is the simplest way to ask your question
Lol there is no simpler way
clear ivy
Then what is your question
manic gulch
What’s P(two 5’s before 4 and 6 in rolls of fair 6-sided die)? What’s the expect...
^ top part of this
clear ivy
Then what is it
manic gulch
This was correct
This was correct approach and was correct
Just not sure how they got it
manic gulch
2/24 + 2/36 + 2/54 = (18 + 12 + 8)/216 = 38/216 = 19/108
^
clear ivy
How do you know there right
manic gulch
How do you know there right
Because multiple senior quants said it was right in a quant Discord when the person posted it. Been a long time though. This is a quant finance interview question.
clear ivy
Probability of getting a 5 on a single roll: 1/6 (since there's one favorable outcome, 5, out of six possible outcomes)
Probability of getting two 5's in a row: (1/6) × (1/6) = 1/36 (since we need two consecutive 5's)
Probability of not rolling a 4 or 6 on a single roll: 4/6 = 2/3 (since there are four favorable outcomes, 1, 2, 3, and 5, out of six possible outcomes)
Probability of not rolling a 4 or 6 for two rolls: (2/3) × (2/3) = 4/9
Now, we need to find the probability of getting two 5's before rolling a 4 or 6. We can use the formula for the probability of event A happening before event B:
P(A before B) = P(A) × P(B' × A')
where A' is the complement of event A (not rolling a 5), and B' is the complement of event B (not rolling a 4 or 6).
Plugging in the values, we get:
P(two 5's before 4 and 6) = (1/36) × (4/9) = 1/81
So, the probability of getting two 5's before rolling a 4 or 6 is 1/81.
manic gulch
Probability of getting a 5 on a single roll: 1/6 (since there's one favorable ou...
This is just not correct though. 19/108 is correct. It’s a standard quant finance interview question. It’s categorized as hard for a reason.
clear ivy
Then what do you want for an answer if you already have it
manic gulch
I don’t want an answer… I want an explanation. I don’t know how the person got the numbers.
clear ivy
How long do you have to get an explanation?
manic gulch
Going to apply for quant trading intern positions mid September or so, so a while.
clear ivy
Ok ill work on it tonight I could add you so it's easier contact if that's ok
I don't really have paper rn
Lol
manic gulch
Ok ill work on it tonight I could add you so it's easier contact if that's ok
Ty 🙏
All good lol
clear ivy
Ok
vocal sleetBOT
@manic gulch Has your question been resolved?
vocal sleetBOT
@manic gulch Has your question been resolved?
vocal sleetBOT
@manic gulch Has your question been resolved?
muted anchor
What’s P(two 5’s before 4 and 6 in rolls of fair 6-sided die)? What’s the expect...
I'm not seeing this from just skimming the chat: Are both x,x,4,6 and x,x,4,x,6 complete sequences or just the former?
I actually tried to monte-carlo both options and neither gives 19/108, so it may be categorised as hard because the interviewer is wrong
golden bloom
someone can explain me the basics of math distribution?
vocal sleetBOT
someone can explain me the basics of math distribution?
hushed nebula
Are you doing an introductory course on statistics right now?
velvet zephyr
someone can explain me the basics of math distribution?
distribution means how things are placed
like suppose I have 100 pens
I give it to 5 people
so each gets 20 pens
golden bloom
Are you doing an introductory course on statistics right now?
no, just for fun
i like to learn random stuff
velvet zephyr
it's like division
golden bloom
oh
velvet zephyr
you must know the distributive property of number
a(b+c) = ab+ac
(a+b)(c+d) = ac + ad + bc + bd
hushed nebula
What
velvet zephyr
Each number distributes over the other numbers of the other bracket
golden bloom
so i have a calculator, there are 7 distribution modes, why?
velvet zephyr
can you ggive an example
golden bloom
normal pd, normal cd, inverse normal, binomial pd, binomial cd, poisson pd and poisson cd
hushed nebula
That's one nifty calculator
golden bloom
normal pd have x, $\sigma$ and $\mu$
twin meteorBOT
TLauncherGD
hushed nebula
This is not related to the distributive property tho
At least not immediately
Sadly I'm kind of busy right now, but I do know that 3b1b has started a "the essence of statistics" series which is worth checking out
velvet zephyr
normal pd, normal cd, inverse normal, binomial pd, binomial cd, poisson pd and p...
bro what
velvet zephyr
This is not related to the distributive property tho
oh
hushed nebula
In this setting a distribution is essentially just a function that says something about how likely something is to occur
Like coin flips
Say you toss a coin until you get heads
How will the probability of you throwing it no more than n times look like
hushed nebula
When you've figure out this relation you've essentially derived what is known as a geometric distribution
golden bloom
my youtube is soo bad
hushed nebula
Oh
hushed nebula
That sucks to hear
vocal sleetBOT
vocal sleetBOT
Available help channel!
wicked tundra
Remainder when 7^90 + 9^90 is divided by 64 is.
vocal sleetBOT
Remainder when 7^90 + 9^90 is divided by 64 is.
hard atlas
do you know modulo?
muted anchor
I take it you want to do it by hand and not with a calculator?
kind light
yes
wicked tundra
how do I use it here
split wind
let's take an easier example
7=7(mod 8)
but also
7=-1(mod 8).
Next
9=1(mod 8)
then
7+9=-1+1(mod 8) = 0(mod 8).
next
7²+9²=(-1)²+(1)²(mod 8) = 2(mod 8)
so in this example,
the remainder when 7²+9² is divided by 8 is 2.
vocal sleetBOT
@wicked tundra Has your question been resolved?
hot mauve
vocal sleetBOT
meager shoal
are u calculated the curve along the x-axis
hot mauve
yes?
hot mauve
what does that mean
bitter pilot
what does that mean
Find a parameterization for this curve too
hot mauve
.close
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orchid osprey
How to differentiate f(x) = 3x^(2/3) using first principles?
vocal sleetBOT
How to differentiate f(x) = 3x^(2/3) using first principles?
devout kindle
How to differentiate f(x) = 3x^(2/3) using first principles?
you will have to apply binomial
devout kindle
also the question says to use difference of cubes
tell me till what step have you reached yet
granite quiver
I need help with the questions given
equation of graph is x^3/3 -x^2 +1, ss of graph in desmos is here
vocal sleetBOT
I need help with the questions given
equation of graph is x^3/3 -x^2 +1, ss of g...
bitter pilot
parallel to the x-axis means horizontal tangent line, one where the slope is 0
loud walrus
You say x^3/x but in the edercise i read x^3/3
granite quiver
oops mb
granite quiver
parallel to the x-axis means horizontal tangent line, one where the slope is 0
so i js draw lines at the point of curves?
bitter pilot
You wanna determine the tangent equations
empty wave
uhh can someone help, i forgot when u use permutation and combination.. isit u use permutation when u arrange something and permutation when u select randomly?
bitter pilot
To get the slope you would need the 1st derivative and set it to 0
bitter pilot
uhh can someone help, i forgot when u use permutation and combination.. isit u u...
!occupied
vocal sleetBOT
uhh can someone help, i forgot when u use permutation and combination.. isit u u...
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).
bitter pilot
cause as you can possibly see on the graph
These are extreme values
So ideally you already found them from a) and then you would compare your minimum to the borders f(0) and f(3)
and then conclude the smallest value
granite quiver
wait so i just
do smth like this
and find the value?
the value for where the line is located at??
bitter pilot
no you calculate f(0) and f(3)
With the given function and compare it to your minimum value
Which looks like is at x = 2
bitter pilot
if you do what i say you will see
granite quiver
f(0) and f(3)****
they both result as 1
bitter pilot
Yea good
granite quiver
so lowest point of y is -0.33 on the graph for the equation
thats correct i think
ok yeah i think thats it
thanks
stark viper
I need to prove this
vocal sleetBOT
I need to prove this
stark viper
I've been trying to fit this into the binomial theorem, but I haven't been able to make it work
hard atlas
split it into two sums
half imp
the left yes
stark viper
What exactly do you mean? What sums? I've tried doing it with even and odd since it seems to become zero when k is odd
But it didn't work exactly
I might be missing something
stark viper
Ah you mean with the division?
hard atlas
well the /2 you can just move in front of the sum
stark viper
This is what I tried to do (I know the last row isn't exactly right, it's not complete)
Do you think I have the right idea here...? Or I should go in a completely different direction?
hard atlas
writing out the sum actually makes it harder this time
hard atlas
whatever that is supposed to be
let me give a min to type out more explicitly what I mean
stark viper
What level is it?
I don't know what that is. I'm a student for software engineering. Bachlor
craggy mauve
Uni?
stark viper
Yes
hard atlas
$\frac12\left(\sum 1^k \binom n k 4^k+\sum (-1)^k\binom n k 4^k\right)$
twin meteorBOT
Denascite
stark viper
So you want me to take the 1/2 out? I'll try that
stark viper
**Denascite**
That's actually sort of what I was going for after I wrote the sums, I tried bringing them together into 2 sums, if you look at my picture again. But I don't understand exactly what you did here
How did you split it into 2 sums?
Ah I think I see it
vocal sleetBOT
@stark viper Has your question been resolved?
stark viper
Ah I think so. Still working on it though. Do I need to mark it as "yes"? 😅
raw trellis
i need help understanding set-builder notation and interval notation as its for my algebra class
vocal sleetBOT
i need help understanding set-builder notation and interval notation as its for ...
@raw trellis Has your question been resolved?
surreal basin
i need help understanding set-builder notation and interval notation as its for ...
do you have an example
raw trellis
do you have an example
for example i have a graph labeled at -2 and 8. what would those look like?
surreal basin
for example i have a graph labeled at -2 and 8. what would those look like?
thats not enough, isnt there something on top of the number line?
raw trellis
no, its a number line that stretch from -inf to -inf but points labeled on -2 and 8
im using -2 and 8 as an example because its not in my homework and once i understand it then i get the rest
surreal basin
you should take a picture
raw trellis
does
(-4,0) U (1,infinity) help?
raw trellis
thats for a different problem
im giving one of the questions because it seems i dont know how to make math problem
surreal basin
im giving one of the questions because it seems i dont know how to make math pro...
you should take a picture of the question then
raw trellis
like, help me understand it so i can actually solve it. left column is set-builder notation, middle is interval notation, and right is the line graph
vocal sleetBOT
@raw trellis Has your question been resolved?
silent lion
hi
shrewd moth
hello
silent lion
i thought this was negative infinity but it said thats wrong so im lost
twin horizon
i thought this was negative infinity but it said thats wrong so im lost
Divide the numerator and denominator by x³
shrewd moth
so why did you think it was negative infinity?
silent lion
basically i learned that u chop everything in the num and denom off besides the highest power
so i got to jus those 2 numbers
and since u end up with a negative x
thatd be to -infinity
twin horizon
Divide the numerator and denominator by x³
.
silent lion
ok
dull bear
(Also be very careful: if u is negative, then sqrt{u^2} = -u)
shrewd moth
hes just using a placeholder variable for whatever
silent lion
so isnt it still jus -infinity
shrewd moth
anyways
twin horizon
(Also be very careful: if u is negative, then sqrt{u^2} = -u)
I thought √x² =|x|
dull bear
I thought √x² =|x|
and |u| = -u when u is negative (using u as per above, for a particular reason!)
(of course, that's meant to hint that u should probably be x^3, but anyways, that's my input for now 
)
silent lion
yall im lost
twin horizon
i got it down to x^2/-4
Are you sure?
silent lion
Are you sure?
yes
shrewd moth
Are you sure?
youre kinda over complicating this lol
shrewd moth
do out the numerator, highest power is x^3, highest power denominator is -4x^3
x^3 / -4x^3
However, since we're taking the square root of x^6 in the numerator, we should actually end up with |x^3| (absolute value of x^3). This is because the square root of a positive number is always positive.
So what does that leave us with?
twin horizon
$\frac{1}{x^3}\sqrt{x^6 + x^2}=?$
twin meteorBOT
David
twin horizon
@silent lion
silent lion
uh
twin horizon
Simplify
silent lion
thats jus x^6+x^2 all over x^3
twin horizon
thats jus x^6+x^2 all over x^3
No.
silent lion
sry\
shrewd moth
oh good lord...
shrewd moth
oh great heavens
twin meteorBOT
David
shrewd moth
david im not gonna lie rn, even i dont even know what youre doing
twin horizon
david im not gonna lie rn, even i dont even know what youre doing
Lol
silent lion
i think im more confused than when i started
shrewd moth
do out the numerator, highest power is x^3, highest power denominator is -4x^3
...
if you wanna be less confused look at:
twin horizon
i think im more confused than when i started
Sqrt(1/x⁶)=1/x³
I only put sqrt so you can bring 1/x⁶
gn
silent lion
So what does that leave us with?
1/-4
silent lion
so the limit is just -1/4
silent lion
oh
shrewd moth
"However, since we're taking the square root of x^6 in the numerator, we should actually end up with |x^3| (absolute value of x^3). This is because the square root of a positive number is always positive."
did you just not read the second part lol
silent lion
i didnt
shrewd moth
.-.
shrewd moth
always gotta consider the original function
silent lion
yea
withthat same logic why isnt this -infinity
bc it ends up being 5/-6x
@shrewd moth
shrewd moth
1s let me try something rq
silent lion
ok
shrewd moth
$lim_{x\rightarrow-\infty}\frac{5x^{3}+2x}{2x^{2}-6x^{4}}$
twin meteorBOT
thecrumbeler2
silent lion
W
shrewd moth
alright anyways
$lim_{x\rightarrow-\infty}\frac{5x^{3}+2x}{2x^{2}-6x^{4}} = lim_{x\rightarrow-\infty}\frac{\frac{5x^{3}}{x^{4}}+\frac{2x}{x^{4}}}{\frac{2x^{2}}{x^{4}}-\frac{6x^{4}}{x^{4}}}$
twin meteorBOT
thecrumbeler2
shrewd moth
simplify:
$lim_{x\rightarrow-\infty}\frac{\frac{5}{x}+\frac{2}{x^{3}}}{\frac{2}{x^{2}}-6}$
twin meteorBOT
thecrumbeler2
shrewd moth
As x approaches negative infinity, the terms with x in the denominator approach zero. Therefore, we can evaluate the limit by ignoring these terms:
silent lion
isnt the first step just to chop off everything but the big one on top and bottom
shrewd moth
$lim_{x\rightarrow-\infty}\frac{\frac{5}{x}+\frac{2}{x^{3}}}{\frac{2}{x^{2}}-6} = \frac{0+0}{0-6} = 0$
twin meteorBOT
thecrumbeler2
shrewd moth
isnt the first step just to chop off everything but the big one on top and botto...
i mean that works too
In this case, the highest power term in the numerator is 5x^3 and the highest power term in the denominator is -6x^4. So, we can simplify the limit to:
$lim_{x\rightarrow-\infty}\frac{5x^{3}}{-6x^{4}} = lim_{x\rightarrow-\infty}\frac{5}{-6x}$
silent lion
so jus 5x^3 over -6x^4
twin meteorBOT
thecrumbeler2
shrewd moth
As x approaches negative infinity, 1/x approaches 0, so the limit becomes:
silent lion
isnt that just -infinity
shrewd moth
$lim_{x\rightarrow-\infty}\frac{5}{-6x} = 0
Therefore, the limit is indeed 0.$
twin meteorBOT
thecrumbeler2
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
shrewd moth
isnt that just -infinity
how lol
keen moat
I keep getting .94 for Sin /37 for cot/ 1.07 for csc . It keeps saying it’s wrong can someone help me ?
vocal sleetBOT
I keep getting .94 for Sin /37 for cot/ 1.07 for csc . It keeps saying it’s wron...
lone linden
I keep getting .94 for Sin /37 for cot/ 1.07 for csc . It keeps saying it’s wron...
it never said to round, leave your answer in exact form (that means use radicals)
keen moat
So what do I do a when I get a square root .8775
lone linden
I wouldn't even do that (decimals aren't that helpful when you're working with fractions and radicals, and are extra useless when they're not finite or have an exorbitant number of digits)
$\sqrt{1-\left(\frac{7}{20} \right)^2}=\frac{1}{20} \sqrt{20^2-7^2}=\frac{1}{20} \sqrt{27 \cdot 13}=\frac{3}{20} \sqrt{39}$
twin meteorBOT
Civil Service Pigeon
vocal sleetBOT
vocal sleetBOT
Available help channel!
late mist
Need some help
vocal sleetBOT
Need some help
lost lake
if you input k into P() you should get 0 as the output
So k might be any of the roots really
k=2 works I just realized (just try small numbers)
divide P(x) by (x-2) and you’ll get a second degree polynomial (then you will factor that into two factors which you can easily do, even if you can’t find a way to factor you can just find the roots doing quadratic formula and then factor using those)
somber portal
Need some help
if (x-k) is a factor, k is a root.
If k is an integer, it has to divide the last term, in this case, 6. So you should try the divisors of 6 first.
for 1 to be a root, the coefficients must add up to 0. This does not happen.
for -1 to be a root, the alternate sum of the coefficients must add up to 0. This does not happen.
so you'd start with +2, -2, +3, -3, +6 and -6 for root checking
somber portal
divide P(x) by (x-2) and you’ll get a second degree polynomial (then you will fa...
And then this
vocal sleetBOT
@late mist Has your question been resolved?
vast shale
Im not quite sure on how to solve this (excuse my supidity i bit off more then my brain can chew with college alg)
vocal sleetBOT
Im not quite sure on how to solve this (excuse my supidity i bit off more then m...
dark rune
Im not quite sure on how to solve this (excuse my supidity i bit off more then m...
what are you confused about?
vast shale
From what I understand I need to find the value of N but Im not sure where to begin since N seems to change
dark rune
I thought I did 😭
what do you believe a function is?
dark rune
it can be, but more precisely we can say that a function is a mapping
it does not necessarily need to follow a logic
we can define a function f(x) = 2x with the possible values of x being {1,2,3}
this would map 1 to 2
using function notation this would be f(1) = 2
dark rune
we can define a function f(x) = 2x with the possible values of x being {1,2,3}
this is defining the function with a rule
but we do not need a rule, we can just specify the mapping instead
we can say g(x) has possible values of x being {1,2,3}
we can manually define each mapping
g(1) = 2
g(2) = 4
g(3) = 6
this is the same thing the problem does
vast shale
How do we find the function though?
dark rune
we don't need to
vast shale
Im so lost
dark rune
a rule doesn't need to exist
dark rune
Im so lost
we can define a function with pairs of inputs and outputs
vast shale
so n(10) would be 18.4?
dark rune
yes, the table gives a mapping from 10 to 18.4
vast shale
Ok wait that makes alot of sense now, the reason I was so confused on that was I thought I had already answered that and it was wrong 😭
Thank you I understand a function a little better now, I will probably be back though because i have a decent amount of stuff left tho
dark rune
ok, good luck
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dapper hearth
I'm finding the limits of polynomial functions for Calculus. I'm not having issues with that. However, I don't remember how to apply trigonometric functions such like in these problems. I just remember it has to do with the unit circle.
lim (5 sin x - 3) =
x->0
lim sec x =
x->0
vocal sleetBOT
I'm finding the limits of polynomial functions for Calculus. I'm not having issu...
heavy yoke
most trig functions are continuous, so you can find the limit by plugging in
you can remember the value of trig functions with the unit circle
dapper hearth
Okay, so I could do something like 5 * sin(0) - 3 using the polynomial theorem? That's helpful to know
Thinking about it, I think what I'm really struggling with is remembering how something like
5 * sin(pi) -3
plugs in. I think that would become 5 * -1 -3?
dapper hearth
I'm seeing that I just need to review trig identities until it clicks again. It's been too long, lol. Thanks for looking at it for me.
.close
vocal sleetBOT
remote sinew
What are my next steps after this I do my U-subsititutiojn
harsh canopy
open a channel for this
harsh canopy
this one will close soon
vocal sleetBOT
Available help channel!
hidden hollow
solicito ayuda temprana
vocal sleetBOT
@hidden hollow Has your question been resolved?
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
1
lone linden
Let B=(0,0), A=(0,a), C=(c,0) and coordbash
vocal sleetBOT
@hidden hollow Has your question been resolved?
hidden hollow
Let B=(0,0), A=(0,a), C=(c,0) and coordbash
aja
vocal sleetBOT
@hidden hollow Has your question been resolved?
vocal sleetBOT
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vale frigate
From the formula, V(t) = 4/3pi[r(t)]^3, how do you differentiate this
vale frigate
with respect to t
bitter pilot
chain rule
vale frigate
I'm having trouble doing it in r(t)
bitter pilot
Consider $\frac{\dd}{\dd t} r^3(t)$
twin meteorBOT
bacc
vale frigate
My current answer rn is dV/dt = 4pi[r(t)]^2 * (dr/dt) (t)
bitter pilot
ok good
vale frigate
My current answer rn is dV/dt = 4pi[r(t)]^2 * (dr/dt) (t)
Is this correct?
bitter pilot
yes
vale frigate
With the t beside dr/dt?
bitter pilot
well just dr/dt is fine or d(r(t))/dt
bitter pilot
bruh
yea your notation is off but I knew what you meant
,, \frac{\dd r}{\dd t} = \frac{\dd r(t)}{\dd t} = \frac{\dd}{\dd t}r(t)
twin meteorBOT
bacc
bitter pilot
The (t) should be with the r
vale frigate
I got (dr/dt) (t)
vocal sleetBOT
@vale frigate Has your question been resolved?
vale frigate
I got (dr/dt) (t)
So is this also the same on above
bitter pilot
No it's just weird dont do that
vale frigate
Then my answer is wrong then ig
vale frigate
This is how I got it
bitter pilot
I dont get that
vale frigate
K wait basically I did chain rule
bitter pilot
what is dx doing
vale frigate
vale frigate
what is dx doing
It's dt I wrote it wrong
bitter pilot
It is
bitter pilot
YEA
vale frigate
Then (dr/dt) (t) is correct then?
bitter pilot
it looks weird but,yea
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grizzled root
how to solve both of these?? plss help
vocal sleetBOT
how to solve both of these?? plss help
twin horizon
The distance between opposite triangles is the diameter
And the diameter=2×the height of one triangle
vocal sleetBOT
@grizzled root Has your question been resolved?
forest rock
and then that distance = height of 2 triangles
u should be able to fniish it from there
twin horizon
And the diameter=2×the height of one triangle
.
finite hatch
excuse me
dense cedar
z²+3z +9/4
forest rock
(z+n)^2 + c = 0 is what u should be left with after completing the square
dense cedar
Try to make whole square
forest rock
*try not to give out answers straight away, dw sometimes i cant find ways to express how to work stuff out
maths is hard
forest rock
yea u want to create a squared term with z in it
finite hatch
how
forest rock
(z+n)^2 = z^2+2zn+n^2
finite hatch
ye
forest rock
you reverse the process
finite hatch
how
forest rock
to make (z+n)^2
u just group the terms like uve done now
z^2 + 3z + 9/4 u can convert nto a square that is (z+n)^2
quick vigil
did I do this one right
NAH
finite hatch
wat
hybrid flicker
huh
golden sierra
It looks fine to me?
quick vigil
Do you know the formula?
hybrid flicker
it looks good
finite hatch
Do you know the formula?
theres a formula?
quick vigil
It looks fine to me?
He wants to complete the square I think ;-;
quick vigil
theres a formula?
like of the (a + b)^2
finite hatch
a^2 + 2ab + b^2
quick vigil
Yea
golden sierra
He wants to complete the square I think ;-;
He's trying to factorise by using that method
quick vigil
He's trying to factorise by using that method
Oh 😭
golden sierra
And then find the solution using that
quick vigil
And then find the solution using that
Mb mb
finite hatch
how do i use the quadratic formula for dis
cus my teacher did this
wait
lemme send his method
quick vigil
How have you been taught to solve this
warped lion
so basically u can memorise this method if u dont understand
- ensure no coefficient before x^2, if have ,factorise it
ex: 2x^2 + 3x = 2(x^2+3/2x) - after first step, consider the coefficient of x as b, u +(b/2)^2 - (b/2)^2 inside the bracket from step 1
- take bx and +(b/2)^2 into perfect square, and other as constant
example:
2x^2-3x+8
=2(x^2 -3x/2) +8 [first step]
=2(x^2 -3x/2 +(3/4)^2 -(3/4)^2) +8 [second step]
=2(x-3/4)^2 -2(3/4)^2+8 [third step]
=2(x-3/4)^2 +55/8
finite hatch
quick vigil
Yea this is the formula
golden sierra
You divide the whole expression by 2 and you can just apply what you did prior
Whenever you have a number next to z^2, you can divide it all with that number
golden sierra
It means that t is your variable
finite hatch
o
quick vigil
how do i respect time
It's like what you are differentiating with respect to
quick vigil
It means that t is your variable
Ye