i would recommend Paul’s Online Notes
#help-27
wind mason
wispy river
Questions available online
thorny rune
okay, I'll try Paul's online notes.
are there any other links/references i should check out?
wispy river
okay, I'll try Paul's online notes.
Also watch blackpenredpen videos on YouTube
thorny rune
thank you! 😊
wind mason
🫡
thorny rune
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mellow willow
Just want to check if I am doing this right before moving on
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Just want to check if I am doing this right before moving on
hollow merlin
I don't know which method was taught to you (especially when drawing the triangles), but the first one is good and the second one is wrong. Recall for cosine that you have to take the ratio of the adjacent side by the hypothenuse
mellow willow
I don't know which method was taught to you (especially when drawing the triangl...
We are using special triangles and making diagrams to do it. Isn’t cosine x/r and just realizes I wrote down y instead of x
hollow merlin
Yes, you took y instead of x, which is why your answer to (b) is wrong
winter torrent
yea that was your issue so you calculated sin(210º) instead 
mellow willow
Are these others ones correct? And quick question that is worded terribly since idk how to word it. When we do the triangle drawings sometimes the angle we are using is included for the original angle but sometimes it is outside of it. How does the at work? For example e and a has the angle outside of it while b and d have it inside/included
tender wharf
cos is positive in 1st and 4th quadrant
tender wharf
Are these others ones correct? And quick question that is worded terribly since ...
also i don't understand what you meant by excluded angle
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@mellow willow Has your question been resolved?
mellow willow
also i don't understand what you meant by excluded angle
So let’s say we have the angle 180 and th triangle we use has an angle of 30 degrees in the corners. Sometimes that 30 degrees is on the outside of that angle but sometimes it is included within the 180
robust bobcat
https://www.youtube.com/watch?v=CCa66RpxgQM can someone explain why at 7:14 he says lets not look at the endpoints. Wouldn't we want to show that f^-1 is continuous on J = [c,d] not (c,d) on our first go instead of showing it first on (c,d) and then trying to show it on [c,d]
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https://www.youtube.com/watch?v=CCa66RpxgQM can someone explain why at 7:14 he s...
@robust bobcat Has your question been resolved?
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pallid robin
i just needed help confirming the answer to this question. acc to me, it should've been 9, but the answer key says 4
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supple knot
i just needed help confirming the answer to this question. acc to me, it should'...
!show
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Show your work, and if possible, explain where you are stuck.
pallid robin
the roots of the quadratic in the numerator are 1 and 2. hence, when the quadratic in denominator has either 1 or 2 as a root, then f(x) can take all real values except 1.
then a could be 4 or 5
faint zinc
If a = 5, then we have (x - 1) (x - 2) / (x - 1) (x - 4). In particular this means that there is a pointwise discontinuity at x = 1
Therefore, the range of this is R - {1/3, 1}, not R - {1}
@pallid robin hope this help
pallid robin
oh right thanks
but how do we figure that out
does it occur to you in a step while calculating
faint zinc
Notice that in the denominator we have two points where we divide by zero
the first is when (x - 1) is zero, so x = 1, and the second is when (x - 4) is zero, so x = 4
So we know that there are two discontinuities.
The first is pointwise, because we also have (x - 1) in the numerator. The second is at (x - 4) which we knows goes to infinity.
However, for a = 4, the denominator factors as (x-2)^2, and because there is an (x-2) in the numerator, so this acts as a single pole and still goes to infinity in both directions (instead of just one for an even powered pole)
For values between 4 and 5, we have two single poles, so we do attain y = 1 between them.
and then finally for values above 5 we also have this behavior,
and values below 4, we don't have a discontinuity, due to there being no real roots in the denominator
@pallid robin
This was my thought process ^
pallid robin
yes i understand now thanks for your help
here, i got f(x)= (secx)^6. how to compute the number of solutions of the given equation ?
supple knot
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pallid robin
the answer should've been infinite in that case, but it's 7
supple knot
here, i got f(x)= (secx)^6. how to compute the number of solutions of the given ...
then your f(x) is wrong
supple knot
Show your work, and if possible, explain where you are stuck.
^
that means you show how you got f(x)
pallid robin
A inverse is just A transpose
det of transpose and matrix is same
as it is second order matrix so det of adj and matrix is also same
det(adjB) is then just det(A^3).
and detA is sec^2 x
supple knot
A inverse is just A transpose
why do you think this is true
pallid robin
i meant in this particular ques
faint zinc
i meant in this particular ques
same question, why do you think this is true for this particular question?
supple knot
i meant in this particular ques
show how you proved A inverse is the same as A^t
pallid robin
yes, i missed the division by det. sorry for the confusion and thanks for the help.
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pastel rose
Hi, can i have some help on this,
I need to show that this sequence is cauchy
i feel like its some telescoping argument right but idk how to use the sequence and |a_ n - a_m| < eps
inland carbon
I feel like you can just guess the limit and show it converges
pastel rose
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willow helm
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vernal terrace
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wicked turtle
your work looks ok i think, what's your answer?
vernal terrace
i wanted to use viettas but it won't come
wicked turtle
it's a quadratic, no?
vernal terrace
yes
wicked turtle
x^2 + 4x - 4 = 0, use the quadratic formula?
vernal terrace
yes i tried and im getting ungly answers
drifting sierra
Who says the answers aren't ugly?
vernal terrace
i assumed
drifting sierra
So what do you get
wicked turtle
yea i just checked in wolfram, you should expect ugly numbers
vernal terrace
-2-2sqrt(2) and -2+2sqrt(2)
drifting sierra
Yeah, that's correct
vernal terrace
what about his problem here we have to find all integers a such that the number will be divisible by 9
and im not getting any
sand pumice
do you know the divisibility rule for 9
drifting sierra
and im not getting any
Maybe there aren't any
vernal terrace
of course add up digits and see if its divisible by 9
and when i add them up i get 35 +3a
sand pumice
and when i add them up i get 35 +3a
so you need (35+3a)mod9=0
drifting sierra
Yeah, and is that divisible by 9? Or even by 3?
sand pumice
what's 35mod9
vernal terrace
well 3 would have top be 1 or 10 or 19 or 28 and none of those are possible
vernal terrace
what's 35mod9
8
wicked turtle
35 is not divisible by 3, so can 35 + 3a be?
vernal terrace
well yes if a were 1/3
wicked turtle
a is a digit tho
sand pumice
so you need (35+3a)mod9=0
if you were to follow along with this, you'd get 3a mod9 is always either 0, 3 or 6 and that could never add to 8mod9 to give 0mod9
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inland carbon
what continuous functions from [-1, 0] to R can be approximated uniformly by polynomials with positive coefficients?
polar chasm
pretty sure it was all of them
inland carbon
but the coefficients need to be positive
polar chasm
oh, misread that, sorry
inland carbon
all good
supple knot
what continuous functions from [-1, 0] to R can be approximated uniformly by po...
is this a book problem or something you came up with
inland carbon
book problem
supple knot
what book
supple knot
what course
inland carbon
it's not a specific course like in uni but the chapter is about sequences of functions. this problem is in the "results about density" part of the sheet
I was wondering if something like f(x) = -x could be approximated
ocean scroll
The kth derivative would have to be positive at x=0
supple knot
well that f is differentiable and wouldn't match the polynomial's derivative
inland carbon
would the derivatives necessarily match?
like does uniform convergence imply convergence of the derivative? (in this case specifically)
stoic lotus
No, it does not
ocean scroll
It can’t have a root in the positive x right
ocean scroll
Oh I missed the domain
ocean scroll
we know that f(0) >= 0
f(0)>0?
polar chasm
one thing to notice is that for large n, x^n = -x^(n+1)
polar chasm
one thing to notice is that for large n, x^n = -x^(n+1)
this basically allows you to imitate negative coefficients
you could probably get a specific bound on the difference
inland carbon
The max difference is around 1/n
polar chasm
Yeah, now that i think about it again, its probably not sufficient. The coefficients could scale that difference massively
might be relevant
it has to be non-negative at 0, if that's satisfied, it can be approximated
inland carbon
But I could change the sign of the a coefficient by changing the value of f
stoic lotus
You can adapt this for [-1, 0]
So we have a continuous target function $f: [-1, 0] \to \mathbb{R}$.
Now I can define a new function $g: [0, 1] \to \mathbb{R}$ using the linear bijective map $t = x + 1$
$$g(t) = f(x) = f(t - 1)$$
woven radishBOT
a handsome russian dude
inland carbon
If you only approximate g then you will need to re-compose with x-1 which could invalidate the condition on the coefficients
I have to go so this will probably close by itself
Will ask my prof
stoic lotus
If you only approximate g then you will need to re-compose with x-1 which could ...
The thing is that you transform back to x
Basically instead of using x, you use x + 1
On [-1,0] it follows that $x + 1 \in [0,1]$ and $-x \in [0,1]$, which allows the positivity structure to be preserved when transforming the Bernstein polynomial
woven radishBOT
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@inland carbon Has your question been resolved?
stoic lotus
If I'm right, if it happens to be that a continuous function $f: [-1,0] \to \mathbb{R}$ satisfies $f(x) \geq 0$ for all $x \in [-1,0]$ and f is not strictly decreasing, then the adapted Bernstein polynomial will have positive coefficients and converge uniformly to f
woven radishBOT
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rocky arch
help please, should be simple but idk why it's not clicking
wicked turtle
any thoughts on how to start?
rocky arch
any thoughts on how to start?
kinda. I assume to move stuff around I just take inverse on both sides?
wicked turtle
yea, you have a C^T at the start of the left hand side and on the right hand side, so you can start by getting rid of those
(how?)
rocky arch
multiply both sides by C^(-1)?
wicked turtle
yes, specifically left-multiply
(since the side you multiply on matters, for matrices)
oops wait
not C^-1
what should it be instead?
rocky arch
C^-T ?
wicked turtle
well what will you have on the right hand side after doing this multiplication?
you have C^t and you're multiplying by its inverse
wicked turtle
yep correct
so that simplifies it a little bit
now you just want to do the same thing, multiply on the left and right by the inverse of whatever is there
chip away at the left hand side until all that is left is D
rocky arch
chip away at the left hand side until all that is left is D
hmm okay
would doing it in chunks work
so just (B^-1 A^2 B A C^-1)^-1
wicked turtle
sure, but you should then probably simplify that when you write it on the right hand side
(i assume that's what they want you to do)
rocky arch
(i assume that's what they want you to do)
yeah
how would you simplify in this case?
do you reverse the order?
so RHS = C A^-1 B^-1 A^-2 B ?
wicked turtle
yep exactly
rocky arch
okay and I understand the exponent isn't really an exponent
but like thinking of it as one in this case is fine right?
like -1*-1 = +1 so u just get C
etc
wicked turtle
yes it's fine indeed, with the understanding that A^-2 means (A^2)^-1, or equivalently A^-1 times itself
wicked turtle
like -1*-1 = +1 so u just get C
yep you won't run into any trouble using the usual exponent arithmetic
rocky arch
okay makes sense so we end up with D A^-2 B^T C^-2 = C A^-1 B^-1 A^-2 B ?
$$ D A^(-2) B^T C^(-2) = C A^(-1) B^(-1) A^(-2) B $$
woven radishBOT
BK75
wicked turtle
okay makes sense so we end up with D A^-2 B^T C^-2 = C A^-1 B^-1 A^-2 B ?
yea this looks right
for the typesetting, use {} instead of () for exponents
rocky arch
okay so now how do I get D isolated?
wicked turtle
do the same thing with the stuff on the right hand side of D
except now you'll be right-multiplying both sides by the inverse of that
rocky arch
hmm okay
can you explain right and left multiplying please I don't really know what that means
wicked turtle
ah for example, if you have A = B and i say "right multiply both sides by C" i mean you should do AC = BC, not CA = CB
the order matters since matrix multiplication doesn't commute
rocky arch
the order matters since matrix multiplication doesn't commute
$$D=CA^{-1}B^{-1}A^{-2}BC^{2}B^{-T}A^{2}$$
woven radishBOT
BK75
rocky arch
okay yeah that right and left multiplying thing is important. I could easily see my self screwing up the order
I think that's the right answer then
wicked turtle
yea that looks correct
wicked turtle
yw
rocky arch
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willow cypress
im genuinely gonna die from probability, idk where to even start on something like this
"A bag has 9 tiles each with a number from 1-9, whats the probability of choosing the numbers 1, 2, 3, in that order"
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im genuinely gonna die from probability, idk where to even start on something li...
willow cypress
the notes made no sense and i feel like shes teaching it kinda weird
im pretty sure the denominator is 9x8x7
not sure how to find other stuff tho
uncut crow
you have a 1/9 chance of drawing a 1 first, then a 1/8 chance of drawing a 2 after that, then a 1/7 chance of drawing a 3 after that
willow cypress
the notes made no sense and i feel like shes teaching it kinda weird
i can show what i mean like its fractions on fractions
willow cypress
you have a 1/9 chance of drawing a 1 first, then a 1/8 chance of drawing a 2 aft...
but dont we have to do the distinguishable ways?
uncut crow
what
willow cypress
idek at this point
like ill show a practice problem i did
There are 4 boys, 8 girls on the debate team, the coach randomly chooses 3 of the students to participate, whats the probability that the coach chooses all girls"
uncut crow
notice how in the other problem a specific order was prescribed
willow cypress
willow cypress
notice how in the other problem a specific order was prescribed
im confused what do you mean
mild anvil
im genuinely gonna die from probability, idk where to even start on something li...
there are 9 tiles currently in the bag, so the first tile (1) has a probability of 1/9 to be selected
there is one less tile when selecting the second tile (2), so there is a 1/8 chance
uncut crow
there is no specification that the girls need to be chosen sally, then amanda, then kathryn
any three girls, in any order
sally then kathryn then amanda would also be just fine
in your other problem, picking 2 then 1 then 3 would have been no bueno
willow cypress
ohh so when order DOES matter then its just the easy like multiplication
uncut crow
hm sure
mild anvil
there are 12C3 ways to choose 3 students out of 12
uncut crow
not really
willow cypress
there are 12C3 ways to choose 3 students out of 12
she isnt teaching that 12 choose 3 stuff yet and i dont think at all
uncut crow
just about anyone would use the choose function instead of writing it like that
uncut crow
she isnt teaching that 12 choose 3 stuff yet and i dont think at all
yea you’re cooked then
sorry man
mild anvil
,,^nC_r = {n \choose r}= \frac{n!}{r!(n-r)!}
woven radishBOT
calvin
willow cypress
N is like what im trying to find right
woven radishBOT
calvin
willow cypress
well what is N and R
willow cypress
this is used when order doesnt matter right
willow cypress
do you understand what she is doing here?
mild anvil
so she basically simplified it
There are 4 boys, 8 girls on the debate team, the coach randomly chooses 3 of the students to participate, whats the probability that the coach chooses all girls"
,,\Pr(\text{picks 3 girls from picking 3 students}) = \frac{\text{no. ways to pick 3 girls out of 8 girls total}}{\text{no. ways to pick 3 students out of 12 total students}}
woven radishBOT
calvin
mild anvil
in the top
using the formula
how can we do that?
it would be something choose something
can you tell me what those ‘something’s are
willow cypress
3 choose 8?
mild anvil
not quite
willow cypress
oh uh
mild anvil
if n is the total number of objects
and 8 is the total number of girls
then it’s …?
willow cypress
can i send a question and try and work it out and tell me if im doing it right?
mild anvil
ill explain this to you first
willow cypress
okie
mild anvil
we had to find how many 3 girl combinations of 8 girls there were
so its 8C3
and plugging that in:
woven radishBOT
calvin
mild anvil
thats just the math behind it
willow cypress
okay thats makes more sense now
willow cypress
thats how many ways to choose 3 out of 12?
mild anvil
we have to find the number of ways to choose (…) students from (…) student
willow cypress
12c3
willow cypress
i know how to do the math part but im having hell of a time just setting it up if that makes sense, i feel like i would be doing better just doing the function
thick ledge
12!/3!(12-3)!
12!/3!9!
12 * 11 * 10/3!
12 - 3 = 8 
mild anvil
i know how to do the math part but im having hell of a time just setting it up i...
you should remember the function
mild anvil
12 - 3 = 8 <:KEK:586240877358350341>
shit
woops
i mean i did just wake up
so now we have
willow cypress
okay real quick, so numerator is basically just "how many ways to find whatever you gotta find" but denom is "how many ways to do the total amount"
willow cypress
can i try and explain how to set up this one and check if its right/wrong
"John has 3 of each red, blue, and green marbles, all the same size, how many ways can the 9 marbles be arranged in a row?"
mild anvil
do specifically 3 girls/ no. ways to pick 3 students
mild anvil
can i try and explain how to set up this one and check if its right/wrong
"John ...
ight
willow cypress
alr lets do denom
i think since we are using all 9 marbles its gonna be 9! yeah? then divide that by 3!?
willow cypress
oh fart
mild anvil
because all the marbles are the same
i mean
each marble has 2 duplicates
so we’re overcounting
willow cypress
the teacher explained that as like multiply the number of repitions in the denom
so 3 repitions of 3 each i think i get that
mild anvil
yeah
mild anvil
that’s for the top
willow cypress
i think i was thinking of the probability questions
mild anvil
yh
willow cypress
so when its how many they switch
so yeah total is 9! boom
uh
i think i did it wrong
willow cypress
yo what the sussss
willow cypress
okay real quick, so numerator is basically just "how many ways to find whatever ...
what happened to this
is that only for probability??
mild anvil
yeah
willow cypress
so when its just how many i do total/reps
yo im about to cook
ramon has 10 cards each with numbers, the numbers are
1,2,3,4,4,6,6,6,6,6, how many different ways can he order the row
since its NOT probability we just do 10!/4!6!
mild anvil
are you gonna attempt this?
mild anvil
not quite
willow cypress
2!6!
mild anvil
we have 10 cards so the total ways to arrange it is 10!
willow cypress
yes
mild anvil
we have 2 reps of 4 and 5 reps of 6
willow cypress
i see the 4 and 6 repititions
ohhhh is that how it works?
i think i get it
just focus on how many times smt repeats not what it is
mild anvil
its divided by the number of eeps
willow cypress
10!/(2!5!)
mild anvil
rep
mild anvil
10!/(2!5!)
yes
mild anvil
ty
willow cypress
The letters, G, E, O, M, E, T, R, Y are on 8 tiles in a bag, basically whats the chances of placing one by one and it spelling out geometry
Ima do top part first
wait
no
bottom
okay so
8 ways yeah
8!
then i see just the 2 reps of E?
so numerator/ 8!/2!
wait @mild anvil is this going so far so good
mild anvil
not quite
willow cypress
okay is it bc i switched the numerator and denom
mild anvil
uhm no
stiff thicket
why do u think it's 8 ways?
mild anvil
basically
willow cypress
why do u think it's 8 ways?
8 letters idk
willow cypress
yes
mild anvil
not quite
stiff thicket
sillybilly
willow cypress
wait what
mild anvil
its the same as my answer i jusr swapped it
willow cypress
1 is there since its only 1 way to spell it right
ocean scroll
Two ways
ocean scroll
You can draw the first e or second e
willow cypress
i think thats how it works
stiff thicket
yes
ocean scroll
The answer is 2!/8!, yes
stiff thicket
sillybilly u did it
willow cypress
heh
mild anvil
1 is there since its only 1 way to spell it right
you were righr about the 8!/2!
but for probability you just needed to swap it
1/(8!/2!)
sorry i didnt think properlh
mild anvil
there r 8!2! ways to arrange the word geometry
8!/2!
stiff thicket
ty
ocean scroll
Each way of spelling the letters is equally likely, because you use all the letters
stiff thicket
i think the more intuitive way is to just do 1/8 * 2/7 * ... * 1/1
mild anvil
yh i did thay
willow cypress
okay ty guys so much, ima try and do the rest and there MAY be a chance ill be back soon 🥹
mild anvil
that
mild anvil
okay ty guys so much, ima try and do the rest and there MAY be a chance ill be b...
bye
willow cypress
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lethal fractal
I need help with question 7, I’m solving the sigma notation part first and then multiplying but I’m not getting the correct answer if someone could please explain how to do this correctly, thank you
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I need help with question 7, I’m solving the sigma notation part first and then ...
lunar harbor
I need help with question 7, I’m solving the sigma notation part first and then ...
In the future, please use the ,rotate command.
,rotate
woven radishBOT
lethal fractal
sorry thank you so much, im new to this discord channel
lunar harbor
did you use it on 5/y + y in its entirety
because 5/y + y doesn't define an arithmetic sequence
try calculating it for y=1,2,3 and calculate the differences
(you can also see this by the fact that 5/y isn't a polynomial)
lunar harbor
do i delete the channel?
!done
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do i delete the channel?
If you are done with this channel, please mark your problem as solved by typing .close
lunar harbor
no rush tho
you can also do .solved instead of .close
no real difference between the two tbf
lethal fractal
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calm tinsel
devout snowBOT
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
I know how to get the eq but half of the time it is wrong and a lot of the time the final answer I get is wrong
I havent started this power reg but I have tried a bunch and havent got any right
granite venture
what is a "power regression"
calm tinsel
Power Regressions
bitter ledge
are you trying to fit a $y = ab^x$ equation to the data
woven radishBOT
snowflake
bitter ledge
okay cool
hollow ice
I know how to get the eq but half of the time it is wrong and a lot of the time ...
why dont you write out the steps here, and we can help you spot where you mess up
calm tinsel
not a polynomial?
??
calm tinsel
why dont you write out the steps here, and we can help you spot where you mess u...
alr
calm tinsel
I dont think so
granite venture
reason i ask is because this is an extremely overdetermined question
calm tinsel
i was never taught power regressions
granite venture
and so one might just not exist
calm tinsel
idk why this is on my hw
bitter ledge
my first thought was that this is a least squares problem but more context would be helpful
hollow ice
i was never taught power regressions
its pretty simple, you need to fit a curve as closely as possible to the given set of values
the common way is to take log of both sides
so you turn it into a linear regression problem
calm tinsel
so i put the values into l1 and l2 on my ti 84
hollow ice
so y=ax^b becomes log(y) = blog(x) + log(a)
calm tinsel
the common way is to take log of both sides
what sides
granite venture
i think itll help if you push the show examples button and post it here
just so we have the question pinned down
calm tinsel
sry its rlly wonky
granite venture
ok yeah just throw it into the calculator
i would whip out excel and see the thing you get makes sense
calm tinsel
the eq i got was 76.538*x^0.625
granite venture
or like plug in the x values
calm tinsel
i would whip out excel and see the thing you get makes sense
idk how to use excel
granite venture
the eq i got was 76.538*x^0.625
ok lets test that with the existing x values before continuing
granite venture
idk how to use excel
thats okay i realized we can just brute-force this
bitter ledge
what sides
we're assuming the data follows a y = ax^b relationship, and we want to fit the data to find a and b
but linear regression needs a linear equation
if we take the log of both sides of the equation for this relationship, we get log(y) = blog(x) + log(a)
that means that if we fit a linear regression for log(x) and log(y), then the slope will be b and the intercept will be log(a)
granite venture
plug in 1, hopefully the answer is not too far from 80
plug in 4, hopefully we get near 167
continue
calm tinsel
we're assuming the data follows a y = ax^b relationship, and we want to fit the ...
so log the eq i got
bitter ledge
sry its rlly wonky
does your calculator have a direct power regression function?
how did you calculate it?
granite venture
i think it does
calm tinsel
does your calculator have a direct power regression function?
i dont see it
granite venture
or is expected to
granite venture
4 is 182.04
whats 11
calm tinsel
i just put it in "PwrReg" on ti 84
bitter ledge
that sounds like a power regression function LOL
bitter ledge
okay i guess there isn't anything to this problem beyond plugging the data in
granite venture
ok im comfortable with calling that the right answer
testing the extremes usually gives you a good barometer
not perfect but you know
hollow ice
this is what I get, which looks close enough to what you have
calm tinsel
so to find out what the hour when the diameter is 618 i set the eq equal to 618 right
granite venture
yeah
calm tinsel
why did you take a log there?
idk what to do when the base is unknown
shut trail
idk what to do when the base is unknown
take the root of the power. For example. x^2 = 10. You take the square root.
calm tinsel
alr
fossil locust
is that 1/0 * 625
no, 1/0.625
fossil locust
why did you take a log there?
do you understand this step?
if so, type the value of x into your calculator and you're done
fossil locust
you don't get $(618/76.538)^{1/0.625} = x$?
woven radishBOT
south
fossil locust
okay
fossil locust
take the root of the power. For example. x^2 = 10. You take the square root.
if you go back to this idea
to solve x^2 = 10
you can also raise both sides to the power of 1/2
$(x^2)^{1/2} = 10^{1/2} \implies x^{2 (1/2)} = 10^{1/2} \implies x = 10^{1/2}$
woven radishBOT
south
calm tinsel
you don't get $(618/76.538)^{1/0.625} = x$?
im more confused on what you did to the right side of the eq
fossil locust
im more confused on what you did to the right side of the eq
so the logic is similar, where you take the reciprocal of the exponent
$(618/76.538)^{1/0.625} = (x^{0.625})^{1/0.625}$
woven radishBOT
south
calm tinsel
so were just multiplying it my the recp. of the exponent
fossil locust
so were just multiplying it my the recp. of the exponent
this is not multiplication
this is exponentiation
fossil locust
so i just put that in my calc
yes
really the main thing is to understand $(x^2)^{1/2} = x, (x^{-3})^{1/-3} = x, (x^{0.625})^{1/0.625}=x$
woven radishBOT
south
fossil locust
well it's a bit harder than that for when the exponent is even, actually $(x^2)^{1/2}$ is the absolute value of $x$
woven radishBOT
south
fossil locust
but that's the idea
calm tinsel
so the answer is 28.3
fossil locust
,calc (618/76.538)^(1/0.625)
woven radishBOT
Result:
28.273409595352
yeah
calm tinsel
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night rune
i did not use the notio of rate=60 here.
devout snowBOT
i did not use the notio of rate=60 here.
night rune
is the info about rate trivial ?
devout snowBOT
@night rune Has your question been resolved?
void fox
I think the only important information is that the speed is constant
night rune
can we ignore it i this scenario ?
seems like the answers i chose without using R were right
void fox
well actually you need it for the second part don't you
night rune
but , why would they put it in then as a fact
stoic lotus
How did you know it's gonna take an hour less if you didn't calculate distance over speed?
night rune
speed can cancel out since its constant for both
most expesive trip is: 20+ 50 + 50 + 60 = 180
leaste xpe: 150
stoic lotus
Oh, I calculated the distances instead of cost
night rune
hold on
stoic lotus
90 and 150 miles respectively
night rune
i forgot how i solve this
stoic lotus
90 and 150 miles respectively
Then I found the difference in time (in hours)
And it matches your answer
So I guess that's what they wanted you to do
stoic lotus
I guess you can subtract 90 from 150
Because 60 mph = 1 mile per minute
But you still would need the rate to know that
night rune
yeah you are right thaks for that
fossil locust
yeah you are right thaks for that
(if you're done type .close)
night rune
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robust ermine
hippity hoppoty
this channel is now my property
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hippity hoppoty
this channel is now my property
robust ermine
sending the stuff
wait
so what im thinking ill do is
ill fine the V of one pyramid
double it to get the V of the entire thing
so i need the height
ajnd
hold on
neon folio
so what im thinking ill do is
ill fine the V of one pyramid
double it to get th...
Sounds good
hazy lark
Its a simple trig problem yet one Im currently stuck at, it says:
What is the value of the following expression 96sin⁵(10) +16sin⁴(10) -52sin(10) + 10
A) 1
B) 2
C) 3
D) 4
E) 5
devout snowBOT
Its a simple trig problem yet one Im currently stuck at, it says:
What is the va...
hazy lark
Ive tried some identities, the sin3x formula, but ive got nowhere
I couldnt find a integer value like in the alternatives
pseudo basin
do you know complex numbers
hazy lark
Yes
pseudo basin
right ok
hazy lark
tchebschev polinomial?
pseudo basin
let z := e^(i pi/18) and try to express this thing in terms of z
pseudo basin
tchebschev polinomial?
chebyshev polynomials might be a good thing to look at yeah
hazy lark
let z := e^(i pi/18) and try to express this thing in terms of z
Using cis, right? I havent tried that
pseudo basin
Using cis, right? I havent tried that
sure if you wanna write it like that
boreal helm
Could i be guided can we analyse this type of graph pattern using z or fourier transforms
devout snowBOT
Could i be guided can we analyse this type of graph pattern using z or fourier t...
boreal helm
I was just doing some research and found this to be cool like it looked to me like the weirestrass graph we see so is there any way to analyse this like using some transforms like z or fourier?
vital sedge
<@&268886789983436800>
boreal helm
Wait what is the problem atleast guide me
i am genuinely curious
like have i broken anything??
vital sedge
No wasn't u there was a bot in here
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boreal helm
<@&286206848099549185>
dusk mango
I was just doing some research and found this to be cool like it looked to me li...
use z if you want analyzing the function as a sequence of data points in a system
and fourier is for the specific harmonics used to build the curve
based on your needs
frozen aurora
are you counting the number of ones in the binary form of each number?
this operation is called "popcount" btw maybe there are some properties online about it
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neon wagon
hello
woven radishBOT
neon wagon
So in D) It says it first hit on the tenth attempt
and so its basically 0,6^9 * 0,4 but
what if the first hit isnt on the tenth attempt
supple knot
what if the first hit isnt on the tenth attempt
that would be a different probability
neon wagon
that would be a different probability
yes but
supple knot
and so its basically 0,6^9 * 0,4 but
different from this i mean
supple knot
what is "it"
neon wagon
that it doesnt exactly hit in the 10th hit, i mean it can also hit in the 1st 2nd 3rd and so on
once
supple knot
those all have equal probabilities, so they also equal 0.6^9 * 0.4
neon wagon
those all have equal probabilities, so they also equal 0.6^9 * 0.4
right cuz itbdoenst even matter
when i think about it
its so fucking stupid how did i forget this i literally did the exact problem like yesterday
supple knot
P(hit on 1 and miss on 2-10) = P(hit on 2 and miss on 1, 3-10) = ... =P(hit on 10 and miss on 1-9)
eternal forge
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eternal forge
Is ai right about the working out
Because im trying to use it to understand how to do this
Only got 1/6 from this in my test
past sedge
?
glossy dew
seems right
eternal forge
the mark was from converting 300g into 0.3kg
eternal forge
seems right
i thought mass and weight were different tho
eternal forge
oh
thought i had to rearrange the weight=mass x gpe
how do u close this
.close
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neon wagon
hello i dont understand on the d) part
is it 1-0,9^n >= 1/16
or
because i think thats wrong but i cant think of anything else
devout snowBOT
hello i dont understand on the d) part
ocean scroll
,rccw
woven radishBOT
ocean scroll
neon wagon
bro uve been helping me alot u must be thinking how stupid i am
devout snowBOT
is it 1-0,9^n >= 1/16
polar chasm
What was your probability for reaching A?
neon wagon
What was your probability for reaching A?
1/16
polar chasm
yeah, makes sense
polar chasm
not every field is equally likely
valid iron
uh is there a problem with the bot?
polar chasm
In fact, except for the last 5 positions all the fields have 0 probability of ending on them
neon wagon
i mean why is it 1/16 and not 1/15
polar chasm
do you know pascals triangle?
devout snowBOT
because i think thats wrong but i cant think of anything else
polar chasm
hm
neon wagon
do you know pascals triangle?
no
polar chasm
aw, lets do it the normal way then
neon wagon
with bernouli
polar chasm
so after first move, the probabilities look like this
neon wagon
so after first move, the probabilities look like this
i just put it in my calculator to get 1/16
ocean scroll
<@&268886789983436800>
ocean scroll
and one more thing, bot keeps pinning random mssgs
I think it's when you unpin its message
polar chasm
i just put it in my calculator to get 1/16
oh, so you didnt actually solve it by hand
polar chasm
okay, lets look at least one row further then, thatll help you understand
the probabilities will look like this
you're more likely to get to the center row than to the boundaries
so the last 5 positions will have probabilities
1/16, 4/16, 6/16, 4/16, 1/16
polar chasm
there is a nice way to see this via pascals triangle, but that'd prolly take too much time
so can we go back to d now?
neon wagon
yes
polar chasm
is it 1-0,9^n >= 1/16
Yeah, this is slightly off
lets start by finding the probability of getting to A after <= n games
polar chasm
lets start by finding the probability of getting to A after <= n games
do you know how to calculate it?
neon wagon
do you know how to calculate it?
uhhh
polar chasm
If you want a hint, try instead calculating the probability of never getting to A during the first n games
neon wagon
If you want a hint, try instead calculating the probability of never getting to ...
thats
15/16
right
or 14/16
polar chasm
(15/16)^n is the probability of never getting to A during n games, yeah
polar chasm
nope, we only care about A
polar chasm
if you are asking for probability of getting heads, do you also include tails because they have the same probability on a fair coin (50%)? Nope
polar chasm
hm i dont get whats your point
yeah, it is the same
thats because 15/16 was calculated as 1 - 1/16 (the probability of NOT getting to A, which was 1/16)
polar chasm
alright, now 1-(15/16)^n is the probability of getting to A at least once during n games
is that clear?
polar chasm
(15/16)^n is the probability of never getting to A during n games, yeah
(15/16)^n is the probability of never getting to A during n games
1-(15/16)^n is the probability of getting to A at least once during n games
neon wagon
(15/16)^n is the probability of never getting to A during n games
1-(15/16)^n is...
yeah i get it
this atleast stuff confuses me
im not good at it
so that = 0,9
then solve for n
yeah
polar chasm
yep
polar chasm
the most important part of all this is that the negation of "at least once" is "never"
and never can be calculated easily
never A is just (not A)^n (where n is the number of games)
polar chasm
nope
A either happens or it doesnt
A either hapens at least once, or it never happens
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Available help channel!
late void
check: bool = False
def sua(a: str) -> int:
try:
k: list = a.split(' ')
m: int = 0
for i in k:
m: int = m + int(i)
except ValueError:
print('Just counting numbers, please!\n')
mainProg()
finally:
check = True
return m
# splits a string into numbers to add
def mainProg() -> None:
g_in = input('Add numbers with a space in between: ')
g = sua(g_in)
closure(g, check)
# the main program
def closure(g, ch) -> None:
if ch == True:
print(f'{g} is your sum.')
else:
print('Something went wrong!\n')
mainProg()
# closes the program
mainProg()
I made this program just so that I wouldn't get rusty but I keep on getting "Something went wrong!" apparently
late void
idk if this counts as math help tho
zealous nebula
check variable is false so it'll always say something went wrong
oh wait i didn't see that line
late void
oh wait i didn't see that line
just moved the check to right before I call closure(), solved my own problem
thanks speedy
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dull rivet
Howdo i do a double absolute value
devout snowBOT
Howdo i do a double absolute value
void fox
,tex $\norm{v}$?
woven radishBOT
dull rivet
,tex $\norm{v}$?
?
void fox
What did you mean by double absolute value
dull rivet
this
void fox
The absolute value map is idempotent so applying it twice is the same as applying it once
graceful cosmos
That's often used for a single absolute value. Depends on the author.
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gleaming hill
hi, i wanted to know whether a Bi-Directional edge is a parallel edge.
burnt steeple
can anyone help me i am in desperate need of help
soft umbra
can anyone help me i am in desperate need of help
Claim your own channel
Check out #❓how-to-get-help for further details
burnt steeple
ok
gleaming hill
.close
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magic bramble
Quick question. If a function is bounded by an interval [a,b] is it possible for a local minimum or maximum to be at f(a) or f(b).
From what i can find a global max and min is possible at those location but not a local
devout snowBOT
Quick question. If a function is bounded by an interval [a,b] is it possible for...
stone stump
definitions you can find online are sometimes messy
but to me it would be stupid to say that f(x)=x on [0,1] has a global max at x=1 but not a local max
young spade
the definition of local max and min doesnt exclude the bounds of the interval
magic bramble
Thats what i thought too. Thats why im so confused on
young spade
But you prob have seen that local max and min are also defined as the points with no derivative or derivative 0 in the interval (a,b)
More than defined, explained that way
magic bramble
Yes ive heard it that way
young spade
just to clear it up i guess
On layman terms, f(x*) if all x's near x* have a smaller f(x), aka they go lower
stone stump
no, thats the bad def
cause at the boundary you cant have an open interval containing it
stone stump
f has a local max at x* if there exists an epsilon such that forall x in the domain, if |x-x*|<eps, then f(x)<=f(x*)
but this is too hard for school
so the open interval version is chosen
without being precise about the domain
young spade
yea i was thinking of it but i think an epsilon delta might be a bit overkill
stone stump
leading to a mess
you could also say "intersection of open interval with the domain" or something along those lines
but either way, you have to go a bit more into the details and most teachers dont do that and that results in a mess
and bs statements like f(x)=x on [0,1] not having a local max
magic bramble
Ok so to sum it up, yes a local max or min is possible at the edge of the interval
Thank You for the confirmation
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velvet coral
For this problem why are we allowed to fix the position of Balan in the bracket before computing the probability? Don’t we need to consider all the possible positions of Balan as well?
devout snowBOT
For this problem why are we allowed to fix the position of Balan in the bracket ...
pseudo basin
do you mean like we're allowed to fix Balan at position #1
velvet coral
do you mean like we're allowed to fix Balan at position #1
Yes
pseudo basin
yeah that's simply bc the bracket is symmetric
steel sage
WLOG?
velvet coral
Or specifically choose a set position Balan is fixed at
pseudo basin
wrt swapping at any level of the tree
it's like if you were seating them at a round table
you can fix one seat WLOG to put balan in
velvet coral
Ah okay, but don’t we still need to account for the probability of Balan being in that specific position?
velvet coral
you can fix one seat WLOG to put balan in
Ah, because regardless of the position we place Balan in, the process of computing the desired probability of event (Balan and Balin meet) is the same. Or in this case because of symmetry no position Balan is fixed in is more special than another?
velvet coral
Ah okay, but don’t we still need to account for the probability of Balan being i...
But I still think we need to consider this
steel sage
Because they are all the same? Two players A,and B. Node P is their most direct ancestor, with children P1 (ancestor of A), P2 (ancestor of B). The probability is just probability of A rises up to P1 times probability of B rises up to P2, right? Irrelevant with the initial position but layer of P, their direct ancestor
pseudo basin
Ah, because regardless of the position we place Balan in, the process of computi...
yes the first
velvet coral
Because they are all the same? Two players A,and B. Node P is their most direct ...
Oh okay. I think I understand that part, but what I mean is why don’t we take the probability of a specific position Balan is in into account?
steel sage
And you can rename things. If your player Balan is at position x, you just rename x as 1, and the one sharing a direct ancestor 2, the two nodes whose direct ancestor’s ancestor is the same as direct ancestor of ancestors of 1 and 2, rename them 3,4… on and on
pseudo basin
Oh okay. I think I understand that part, but what I mean is why don’t we take th...
would you like to try a simpler example
velvet coral
would you like to try a simpler example
Sure
pseudo basin
you and i each roll a d6. what's the chance we roll the same number
heavy token
i totally understand you guys
pseudo basin
we can just assume i rolled a 1 bc all the numbers are equally likely and the possibilities are symmetric
or failing that you can use the law of total probability like
sum[k=1..6] P(match | i roll k) * P(i roll k)
velvet coral
you and i each roll a d6. what's the chance we roll the same number
I think it should be 6/36, Becuase I am counting favorable outcomes
pseudo basin
only it's gonna just be 6 copies of the same term
and P(i roll k) is 1/6
so it all cancels out
velvet coral
sum[k=1..6] P(match | i roll k) * P(i roll k)
Oooo
Wait
Is the symmetry argument the LOTP argument you presented here?
Basically in this case
We have P(event) = sum[i=1,…n] P(event | Balan in position i) P(Balan in position i)
And by symmetry we know P(event | Balan in position i) are all equal.
So we can “take it out of the sum” and then the sum[i=1,…n] P(Balan in position i) = 1
steel sage
I think I can describe a renaming better. Say your player is at position x, if x is odd, you just replace every y with y+1-x mod 8. If x is even, replace x and x-1 with 1,2 and replace any y with y doesn’t equal x, x-1 with y+1-(x-1) mod 8. This way whatever x is, by a renaming it’s exactly like Balan is at position 1
velvet coral
I think I can describe a renaming better. Say your player is at position x, if x...
Ah okay yeah that makes sense, but would that still work if say Balan is more likely to be placed in the first 4 positions?
steel sage
Like follow the procedure. x=4, even
Replace x, x-1 with 1,2, namely replace 4,3 with 1,2
Replace y with y+1-(x-1)=y+2-x mod 8, like y=5, replace 5 with 3
(Replace 5,6,7,8,1,2 with 3,4,5,6,7,8)
Any x, you can rename so that x becomes 1
Oh ancestors change
I will stick to my previous renaming, or probability only depends on how many layers (or say how many predecessors) the most direct ancestor of two players A , B have
(Like position 2 and 4, most direct ancestor is the nod between second round and final, 2 layers (or say 2^2 predecessors), like position 1 and 6, most direct ancestor is the nod between Final and winner, 3 layers, (or say 2^3 predecessors). Only this quantity matters
velvet coral
Ah ok, I thought maybe the probability would stay the same since if we use LOTP it doesn’t matter if say Balan is more likely to be placed in the 4 higher positions of the initial bracket
steel sage
Only how many layers matter
For example, A at 1, B at 7. Direct ancestor the green nod. With children blue P1 and P2. The probability is probability that A rises up to P1 times probability of B rises up to P2
These subtrees with root P1, P2, with two layers (having 2^2 predecessors) matter, any one of its predecessors, like subtree with root p_1, any one of its predecessors, 1 or 2 or 3 or 4, have the same probability to arrive on top, P_1
((1/2) to the power of layers)
(Only who is the direct ancestor of A and B matters, so we can fix A and make B relatively different )
(1/2 probability highest node is their direct ancestor, 1/4 probability a second highest node is their direct ancestor, 1/8 probability a third highest node is their direct ancestor… …)
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tidal viper
Hey guys, I'm stuck with this Venn Diagram Problem, if anyone wants to try and help. The questions are:
- How many uses all modes of transpo?
- How many uses only a Jeepney?
But I'll appreciate it if you guys give all values for the Venn Diagram. Thanks
devout snowBOT
Hey guys, I'm stuck with this Venn Diagram Problem, if anyone wants to try and h...
devout snowBOT
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
Have you made the diagram
hi 
tidal viper
Have you made the diagram
First step apparently, I just can't seem to understand how it could work
And I tried to make the diagram but I don't have anything on it
wraith wing
i have a normal but slow way to solve venn diagram problems
first draw a venn diagram containing 3 circles and name them accordingly
then start slapping letters for each indiviual space
a , b , c ...... till the end
after that use the information that was given to make equations
stark parcel
@tidal viper can u try to draw something first?
then at least we can see what you're getting and what you're not
red grove
You should have something like that (numbers reference the whole circle, not only the excluded part, and it’s blank + big circles that makes 90, not just blank)
tidal viper
then at least we can see what you're getting and what you're not
I tried drawing but it's kinda pointless at this point since i don't have anything on it. That's how puzzled i am. I have three circles and that's it
stark parcel
bruh u have ALOT OF INFO
stark parcel
then start slapping letters for each indiviual space
have you tried this?
wraith wing
I tried drawing but it's kinda pointless at this point since i don't have anythi...
so you have this right?
stark parcel
