Sum(2k)=2sum(k)=2*(1/2)n(n+1)=n(n+1) though
#help-33
humble osprey
yeah
paper stirrup
Walk me through how you got that expression
paper stirrup
You're summing twice the sum of even numbers here
Also, can you explain the first equality
Second line of course
humble osprey
Also, can you explain the first equality
well the sum of all odds equals the sum of all numbers minus the sum of all evens
paper stirrup
If you use index k=1 to n of 2k-1 then by your logic you need to evluate
sum_1^(2n-1){k}-sum_1^k{2k}
Because sum of all numbers include numbers from 1 up to 2n-1
humble osprey
okey im confused
paper stirrup
So you wanted to calculate $\sum_{k=1}^n{2k-1}$ yes
elfin berryBOT
sunset
humble osprey
mhm
paper stirrup
And you interpret this sum as all natural numbers from 1 to 2n-1 (2n-1 because this is the n-th odd number in your sum) minus all of the even numbers between 1 and 2n-1
paper stirrup
Alr. So the previous sum is $\sum_{k=1}^{2n-1}{k}-\sum_{k=1}^{n-1}{2k}$
elfin berryBOT
sunset
paper stirrup
You see it gets messy
paper stirrup
Np
marsh citrusBOT
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surreal valley
ouh heya, do you mind helping me get the x y and z functions for this easy shape? thanky!!
marsh citrusBOT
ouh heya, do you mind helping me get the x y and z functions for this easy shape...
surreal valley
im guessing it is just some sort of tweaking of sin and cos but geniunely can't figure it out
lavish pelican
dude tf is this
surreal valley
um a basketball thing idk i fouhd it super cool :d
Instagram
im a programmer and i specialize in bending tools to build stuff with css only so i thought id build this :D
https://codepen.io/Cubiq-ish/pen/myVNNoe
like currently it's the easy meta shape but i wanna do this.. idk command button shape in 3D :D
hazy lion
its a little involved but hopefully it has the info you need
this looks like an implementation of the description in the paper
surreal valley
oh wow
absolutely!! thank you! ill figure out the rest, thank you so much you guys are amazing <3
muted lynx
can someone
marsh citrusBOT
can someone
wary kite
you don’t need an explicit form
red nimbus
what do you get when $\abs{(-1)^n\f{5^nn!}{11 \cdot 17 \cdot 23 \cdot \dots \cdot (6n+5)}}$ is simplified?
elfin berryBOT
marsh citrusBOT
@muted lynx Has your question been resolved?
muted lynx
Wouldn’t it be (5^n * n!) / (6n+5)!
red nimbus
No
(6n+5)! = 1 x 2 x 3 x ... x 6n+4 x 6n+5
They wrote the denominator as is intentionally
marsh citrusBOT
@muted lynx Has your question been resolved?
marsh citrusBOT
muted lynx
.reopen
marsh citrusBOT
✅ Original question: #help-33 message
muted lynx
what did i exactiy do wrng with this limit
cunning fiber
what did i exactiy do wrng with this limit
6n+5 cancels in the numerator and denominator
muted lynx
6n+5 cancels in the numerator and denominator
on which step
cunning fiber
The one where you cancelled with the red?
valid cape
$11 \cdot 17 \dots (6n + 5)(6n+11)$
elfin berryBOT
muted lynx
6n+5 cancells with 6n+11??
valid cape
you can cancel 6n + 5 with the second largest number in the multiplications
muted lynx
..
muted lynx
you can cancel 6n + 5 with the second largest number in the multiplications
i feel really lost wdym
valid cape
well the largest number in the multiplication is 6n + 11, yes?
muted lynx
yes
valid cape
what is the second largest?
muted lynx
6n+5
valid cape
yeah, and lo and behold the numerator also has 6n + 5
what should one do in this case?
wheat mauve
please help
muted lynx
.close
marsh citrusBOT
halcyon elk
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muted lynx
marsh citrusBOT
muted lynx
main idol
$(kn + k)! \neq (kn+k) (kn)!$
elfin berryBOT
riemann
marsh citrusBOT
@muted lynx Has your question been resolved?
muted lynx
**riemann**
what does it equal
marsh citrusBOT
@muted lynx Has your question been resolved?
main idol
what does it equal
(kn+k)! = (kn+k) * (kn+k-1)! From the definition
marsh citrusBOT
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wise oxide
marsh citrusBOT
marsh citrusBOT
@wise oxide Has your question been resolved?
wise oxide
are you asking which one 10 (a) is?
Ye
stray hound
well what have you tried
wise oxide
well what have you tried
2
wise oxide
2 or 4 idk which
stray hound
2 or 4 idk which
okay well do you know what phi represents
wise oxide
okay well do you know what phi represents
No
Is it 4
Cus d is graph 1 and it’s similar
stray hound
well that logic works i guess yeah
wise oxide
well that logic works i guess yeah
So it is 4?
marsh citrusBOT
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warm elk
marsh citrusBOT
warm elk
why is that question different from this one
the second one i sent it easier but supposedly they are the same thing
warm elk
i need help solving the equation
like the x and y on the first pic are separated while the second it’s easier bc the x and y are on the same side
pseudo flax
oh i see
y = -x -3
Add x to both sides of the equation
y + x = - x -3 + x
or, y + x = -3
quiet monolith
like the x and y on the first pic are separated while the second it’s easier bc ...
the first one is in y=mx+b form where m = -1 and b = -3
quiet monolith
like the x and y on the first pic are separated while the second it’s easier bc ...
you can make the 2nd like the first one by doing some basic algebra
marsh citrusBOT
@warm elk Has your question been resolved?
chrome jacinth
i don’t get how im supposed to turn the first pic into the second
Hi! The thing with the first equation is that y is by itself. So, ideally, you want to make y by itself as well!
9x + 5y = -20
We want y by itself.
What should we get rid of on the left side so that y is by itself?
pseudo flax
you could always plot a few points satisfying the line and then draw it
marsh citrusBOT
@warm elk Has your question been resolved?
cold idol
hey is this the correct?
marsh citrusBOT
hey is this the correct?
cold idol
marsh citrusBOT
@cold idol Has your question been resolved?
cold idol
no
marsh trench
Do you know how to check if it’s right?
cold idol
no
marsh trench
Differentiate your answer. Check if you get the integrand
cold idol
idk what that is
marsh trench
Your integrand is what you were integrating
cold idol
i havent learnt derivatation e
marsh trench
i havent learnt derivatation e
But you did it in this question?
cold idol
for lawn
marsh trench
for lawn
Ah. So remember that if $\int \frac{1}{x} dx = \ln x + C$ then $\frac{d}{dx} \ln x = \frac{1}{x}$
elfin berryBOT
Beth
marsh trench
For the record, your answer looks correct
cold idol
.close
frozen lava
I have a few questions that need clarification.
First is . What should I do with the statistical formula proofs..do I learn them or just understand and move on..?
I have started to learn statistics from a book but have no idea how to approach it, should I watch videos along with reading the book and just follow book source.
Chatgpt is giving vague answers
marsh citrusBOT
I have a few questions that need clarification.
First is . What should I do wi...
@frozen lava Has your question been resolved?
wicked cloud
I have a few questions that need clarification.
First is . What should I do wi...
Would like to see what book you're using. If you're doing it for a course then ask the lecturer what you'll be examined on.
If you're learning for fun, I don't think statistical proofs are necessary to memorize, and just use a learning style you typically use for other math subjects. Nothing to overthink
fading lotus
How do i find the surface area of this
marsh citrusBOT
How do i find the surface area of this
fading lotus
Oml im so jealous of people with good visualisation
calm harbor
Can you first find the area of this triangle?
fading lotus
Can you first find the area of this triangle?
7?
frail obsidian
How do i find the surface area of this
is that supposed to be a tetrahedron?
frail obsidian
3d shape with 4 faces, each face being a triangle
frail obsidian
if those dotted lines are supposed to represent out of plane lines then yeah lol
this is what you're looking at
marsh citrusBOT
@fading lotus Has your question been resolved?
wide sinew
hi, im unsure how to do part ii
marsh citrusBOT
hi, im unsure how to do part ii
amber birch
hi, im unsure how to do part ii
right, do you know the formula for tan(2 alpha)?
wide sinew
yes i do
i used that to get part 1 by using a/2 is a and a is 2a
and thats fine but i dont get the hence
amber birch
oh sorry, I was reading the wrong part
amber birch
hi, im unsure how to do part ii
I think it's pretty clear from $\cos \alpha \cos \beta + \sin \alpha \sin \beta = \frac{\sqrt 2}{10}$
elfin berryBOT
south
wide sinew
right but when you sub in cos a and sin a being like 3/5 and 4/5
amber birch
you put that into the form $R \cos (\beta + \theta)$
wide sinew
what do you do after
elfin berryBOT
south
wide sinew
can i see how
wide sinew
ohh wait
amber birch
the idea is that you compare coefficients, so $\frac{3}{5} = \cos \alpha, \frac{4}{5} \sin \alpha \implies \tan \alpha = \frac{4}{3}$
elfin berryBOT
south
wide sinew
i knwo what you're talking about
ill try that gimme a sec
ok i am stuck i think i did something wrong
thats where im up to
i just got what i had before
karmic hatch
All this for what lmao
wide sinew
All this for what lmao
thanks now i dont know what to do can i have a tip 😭
chrome jacinth
Hi! Let's look at the equation you already have: [ \cos\left(\beta-\cos^{-1}\left(\frac{3}{5}\right)\right)=\frac{\sqrt{2}}{10} ] Indeed, the left hand side alright has $\beta$, so we should start isolating for it. So, what might we do?
elfin berryBOT
Redfern Station
wide sinew
Hi! Let's look at the equation you already have: \[ \cos\left(\beta-\cos^{-1}\le...
i tried compound angle formula but it just takes me back
i will maybe draw a triangle
chrome jacinth
i tried compound angle formula but it just takes me back
Indeed, so is there anything else that we could do instead?
Hint: You already did the heavy lifting by drawing the diagrams, now we just have a bunch of algebra.
wide sinew
i have no idea
chrome jacinth
Out of curiosity, how would you solve cos(x) = sqrt(2)/10?
How would you solve for x?
wide sinew
with a calculator i dont know
by drawing a triangle maybe
then using cosine formula i dont rlly know
chrome jacinth
Out of curiosity, how would you solve cos(x) = sqrt(2)/10?
Hint 2: You can do something to both sides.
wide sinew
Hint 2: You can do something to both sides.
cos inverse both sides
wooden pendant
I think it is quite easy
chrome jacinth
cos inverse both sides
Yeah! That's it.
chrome jacinth
**Redfern Station**
So what might we do here to both sides to solve for beta?
wooden pendant
Just open lhs and then convert it into simpler sin and cos
wide sinew
So what might we do here to both sides to solve for beta?
cos inverse both sides
chrome jacinth
cos inverse both sides
Perfecto. Try that.
wide sinew
but this is a tech free test so i need it in exact form is there a way other than leaving it in cos-1(xxxx) form
well thats what i assumed
chrome jacinth
but this is a tech free test so i need it in exact form is there a way other tha...
Yep! There is.
So after you take the cos inverse of both sides,
What do you get for beta?
wide sinew
= cos^-1(sqrt2/10) + cos^-1(3/5)
chrome jacinth
= cos^-1(sqrt2/10) + cos^-1(3/5)
Good!
So here's the dealio
We have beta = cos^-1(sqrt(2/10) + cos^-1(3/5)
wide sinew
yupyup
chrome jacinth
Clearly the right hand side is not so nice
But, there is a way to fix this
Notice how the right hand side is just a bunch of inverses.
wide sinew
yupyup
chrome jacinth
So, to fix this, yet again we should take the cosine of both sides!
That is, we have: [ \beta=\arccos\left(\frac{3}{5}\right)+\arccos\left(\frac{\sqrt{2}}{10}\right) ] So, we get: [ \cos\left(\beta\right)=\cos\left(\arccos\left(\frac{3}{5}\right)+\arccos\left(\frac{\sqrt{2}}{10}\right)\right) ]
elfin berryBOT
Redfern Station
wide sinew
okok i see
chrome jacinth
How would you simplify the right hand side?
chrome jacinth
Yep.
marsh citrusBOT
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distant girder
This one isn’t even solvable? Considering we don’t know whether or not the second triangle is a right triangle.
marsh citrusBOT
This one isn’t even solvable? Considering we don’t know whether or not the secon...
fast spear
This one isn’t even solvable? Considering we don’t know whether or not the secon...
what do we need to find?
distant girder
X
fast spear
ok did you try?
distant girder
I feel like too few values are known to start somewhere
fast spear
I feel like too few values are known to start somewhere
hmm.. there are values ig use trignometry here
both are right triangles
distant girder
I feel like cosine and sine law are both inapplicable here , and SOH CAH TOA can’t be used because the lower triangle is not right-angled.
slim shard
This one isn’t even solvable? Considering we don’t know whether or not the secon...
This is solvable. The second triangle is right-angled because 180 - 90 = 90. Even if it wasn't, a mix of cosine and sine law calculations should get you the answer.
distant girder
This is solvable. The second triangle is right-angled because 180 - 90 = 90. Eve...
Ok I’ll try
@slim shard
I feel like we need more variables to solve it
trim owl
Both r right angles triangles
distant girder
It says “Diagrams are not drawn to scale,” therefore I’m assuming the long side isn’t a straight line
.close
marsh citrusBOT
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timber imp
marsh citrusBOT
sacred nebula
Did u cleared it by urself?
marsh citrusBOT
Available help channel!
lime rose
got the wrong answer
marsh citrusBOT
got the wrong answer
main idol
you can save yourself a lot of steps and just split the sum in the beginning
sum( a_n + b_n) = sum(a_n) + sum(b_n)
lime rose
that is if the sum a_n or b_n exists ig
but i should've arrived to the same result so my solution is wrong
main idol
yea everything including this step and onward is wrong
lime rose
ap?
main idol
arithmetic progression
keen zodiac
arithmetic progression
lime rose
the sequence yes
keen zodiac
it is gp
lime rose
since i couldn't find a geometric
keen zodiac
you cannot apply the ap formula in a gp
main idol
you can save yourself a lot of steps and just split the sum in the beginning
yea do this and you will be able to
keen zodiac
yup
keen zodiac
yes
still temple
hi
still temple
when we talk about matrices spanning a space or polynomials spanning a space in linear algebra what does that really mean??
like geometrically
i know how it works in R^n
spanning in R^n makes sense but i dont get how it works with matrices, such as nxn matrices or mxn matrices or polynomials in P_n
same concern that i have for linear dependency/independency as well
hope someone can help me out on this
quick kindle
u wont find a good geometric representation of those spaces themselves but u can use the fact that any finite dim space is isomorphic to R^n and maintain the R^n geometric interpretation
marsh citrusBOT
@still temple Has your question been resolved?
scenic stirrup
when we talk about matrices spanning a space or polynomials spanning a space in ...
the span of a vector over a space is the set of all possible constant multiples of it
ie one of the axioms of a vector space is that it is closed under scalar multiplication
Well consider a vector, and the span of that vector is all possible scalar multiples of it. The span of multiple vectors is the set of the sum of all possible scalar multiples of each constituent parts
a set of vectors is said to span its spanning set, defined in this way
obsidian crater
sorry i need help solving the first
I could help
scenic stirrup
I could help
That's from a fair while ago^
scenic stirrup
no afaik it timed out
scenic stirrup
cta
warm elk
sorry it has tho thanks everyone
upper berry
I have gotten through some of it, but converting those limits of integration to spherical seems comlicated
marsh citrusBOT
I have gotten through some of it, but converting those limits of integration to ...
graceful elbow
<@&286206848099549185>
It appears to be correct, but I'm new to multivariable calculus. Starting with the third integral as it's easiest, x^2+y^2 is 64, so z would equal 64, which you also have. The projection covers the entire circle, so 2pi appears right as well (first integral). Therefore, the second integral, covering the radius of the base of the circle, would be 8. I may be wrong, however, so I would still recommend double checking if confused.
upper berry
It appears to be correct, but I'm new to multivariable calculus. Starting with t...
thanks, I got the same confirmation by ai, I am still trying the spherical conversion
graceful elbow
thanks, I got the same confirmation by ai, I am still trying the spherical conve...
You think you also need help with the spherical conversion?
upper berry
You think you also need help with the spherical conversion?
yeah mostly that one,
marsh citrusBOT
@upper berry Has your question been resolved?
graceful elbow
yeah mostly that one,
Now I'm a bit confused, actually. If all the lower bounds are zero, wouldn't the first integral just render the full thing as zero? The upper bound for p, remember, is the radius of the sphere, which would be 8. For phi, I think that would just be the hemisphere, or pi/2. And for theta, wouldn't that just be 2pi as it is representative of the full rotation within the xy-plane? I'm not the best at this. (another helper should take it from here)
silk sable
Do you understand the shape you are integrating?
upper berry
If I understand it correctly, the region is bonded by these surfaces
wait nevermind should not be a ^2 on z
wait wait
even harder to visualize now, but I believe the region is bounded by the cylinder, a thin paraboloid inside the cylinder, and z=64
silk sable
Yes, it is the bottom of a parabaloid.
silk sable
The issue with spherical coordinates is that there are two outer boundaries.
silk sable
upper berry
for the first integral, will the lower limit of rho be 64 and upper limit the length from the origion to the intersection of the 2 surfaces?
silk sable
On the inside of that cone, the outer boundary is the plane z=64.
On the outside of that cone, the outerboundary is dictated by the parabaloid.
silk sable
The equation of the cone is irrelavent. I only put that there to demonstrate that the azimuthal angle determines the cutoff between the change in outer boundaries.
You will need to determine that angle.
upper berry
is the angle phi?
silk sable
Which angle are you referring to? There is the polar angle and the azimithal angle.
The polar angle is always theta while the azimithal is phi.
upper berry
the angle between the z axis and the line connecting the intersection of the surfaces to the origion
ok
Tan(phi) = 8/64
phi = arctan(1/8)?
upper berry
silk sable
The azimithal bounds look good.
upper berry
Not sure quite how to find upper limit for rho, my best guess is sqrt(4160)
silk sable
upper berry
oh
silk sable
I think the z on the RHS of the third equation is supposed to be r.
upper berry
I dont follow, on the second part of the spherical integral?
upper berry
oh right
I got this image from google
didnt notice until now
I would have done rcostheta anyway probably
One of the first times google has failed me
silk sable
Plug in the values you know into those equations and solve for r.
silk sable
You don't need to replace phi. That will be evaluated by the middle integral.
upper berry
OK
now just need to evaluate the integral
I rechecked with the jacobian, p^2 should be p^3 in the 2 right boxes
Now I just need to figure out what should be different with the 2nd upper limit Rho
upper berry
silk sable
Note that those two radii are calculated differently.
silk sable
yw
upper berry
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
ruby verge
This is an evt problem. Why is 0 a critical number?
marsh citrusBOT
This is an evt problem. Why is 0 a critical number?
honest creek
This is an evt problem. Why is 0 a critical number?
"a critical point is the argument of a function where the function derivative is zero (or undefined)"
emphasis on the bolded thing
ruby verge
"a critical point is the argument of a function where the function derivative is...
Ohh so done
Dne*
honest creek
sure
ruby verge
And I assume zero is an example of that because it’s not a <= but just a <?
honest creek
from the graph you can see there's a "cusp"
so that's that
or you can just consider the derivative from the left
as x-> 0-
and compare it with the derivative from the right
so basically x -> 0+
honest creek
And I assume zero is an example of that because it’s not a <= but just a <?
that's not really the reason, no
honest creek
because it's <= on the second equation
ruby verge
True
honest creek
from the graph you can see there's a "cusp"
^
ruby verge
How would I know without graphing it tho?
I don’t think we will have a calc on the test
honest creek
or you can just consider the derivative from the left
^
honest creek
and compare it with the derivative from the right
^
it's -1 from the left
and 4 from the right
clearly doesn't match
ruby verge
clearly doesn't match
So is the easiest way just graphing it and realizing “oh this is a critical number cuz derivative dne”
ruby verge
I wish there is like a math way to just be able to easily know that
Without having to graph it idk
ruby verge
look at what i quoted
I mean like how we found the other point
By setting the derivative to zero
That’s how we found one of the critical numbers
honest creek
well when you're transitioning from the first function
to the second function
you'll likely want to check if the transition was "smooth" or not
so it makes sense to check if the function is differentiable at the "transition point"
namely, x = 0
so it's all "formulaic"
ruby verge
Ehh
ruby verge
.close
marsh citrusBOT
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golden musk
Hello, I have a pretty specific question. I need to calculate minimum required steps required to solve hanoi tower with n-elements and m-places where elements are numered from 1 to n and are decreasing towards the bottom of the stack (and need to mantain such order in every stack) and you can move pieces from top of the stack to bottom of it. You always start with more than 1 tower already. (it may not be a pure math problem, but it's worth a try asking you guys)
marsh citrusBOT
Hello, I have a pretty specific question. I need to calculate minimum required s...
quaint elm
it's definitely worth finding solutions to some simple cases manually and maybe making a spreadsheet or something
you can move pieces from top of the stack to bottom of it
wouldn't this mess up the order of the stack though
golden musk
it's definitely worth finding solutions to some simple cases manually and maybe ...
I guess so... I think that it should be definietly recursive similarly to the regular 3-stack hanoi
But It's very confusing
I mean yeah, a spreadsheet may be worth trying, althoe I don't think it's a straigtup solution
golden musk
> you can move pieces from top of the stack to bottom of it
wouldn't this mess u...
I don't think so
cuz you already start with 2 stacks
because 1 stack is impossible
quaint elm
i don't understand. if you have a stack with [1, 3, 7, 9] then can you move the 1 to the bottom of the stack?
you'd end up with [3, 7, 9, 1] which seems invalid
quaint elm
no sorry
quaint elm
oh you can move it to the bottom of a different stack interesting
so they're more like queues than stacks
quaint elm
,rccw
elfin berryBOT
quaint elm
so if you ever have a blank stack then it's an easy solution
golden musk
so if you ever have a blank stack then it's an easy solution
Maybe, sorry it's 1 a.m. im thinking a bit slow
I mean yeah, it's necessary to complete the puzzle
otherwise you could not
Like in the second example
quaint elm
this seems to be an ongoing contest
quaint elm
I mean yeah, it's necessary to complete the puzzle
this isn't quite true
golden musk
this isn't quite true
depends on the stacks
quaint elm
the remote round is supposed to be "samodzielnym rozwiązywaniu zadań"
golden musk
if you finish the 3rd stage (offline) (this is 1st which that you write online) you have pretty much 95% guaranteed technical studies
golden musk
the remote round is supposed to be "samodzielnym rozwiązywaniu zadań"
it refers to coding
so not using chat gpt
you literally have forum on the official site
where people share tests etc
marsh citrusBOT
marsh citrusBOT
Available help channel!
viral falcon
how have we gone from the RHS of first line to seocnd
marsh citrusBOT
how have we gone from the RHS of first line to seocnd
viral falcon
this was proposition btw
nvm
can just distribute the intersection
i see it now
.close
velvet yarrow
can someone help me understand bootstrapping
marsh citrusBOT
can someone help me understand bootstrapping
velvet yarrow
as in how to calculate confidence interval and p value
i dont understand how to calculate test statistic
marsh citrusBOT
@velvet yarrow Has your question been resolved?
velvet yarrow
<@&286206848099549185>
marsh citrusBOT
@velvet yarrow Has your question been resolved?
stone pelican
Z-test or t-test?
If it's the z-test (which it probably is) , type out the formula for test statistic here
velvet yarrow
wouldnt it be t test
stone pelican
wouldnt it be t test
Why would you think so
velvet yarrow
wait im lost
stone pelican
Are you testing a mean or a proportion?
velvet yarrow
bootstrapping is done wen original population is not normally distributed
so u take a sample
which u pretend is the population
stone pelican
Are you testing a mean or a proportion?
Just answer this
velvet yarrow
and take samples form the sample
velvet yarrow
Just answer this
mean
stone pelican
That means it's a t test
Okay then tell me what is the formula for the test statistic for a t test
velvet yarrow
im not sure
stone pelican
im not sure
Are you learning stats from a book?
velvet yarrow
wait lemem show u what i have written down
stone pelican
wait lemem show u what i have written down
Ok
stone pelican
Sample mean
velvet yarrow
which same
sample
i have written here that X_hat is sample mean for orignal sample taken from population
stone pelican
Oh hold up
velvet yarrow
and sigma_hat is SD of sample taken from original poplution
stone pelican
You're getting things mixed up
There's 2 main types of t-test ; hypothesis and confidence interval
velvet yarrow
This one is for hypothesis right?
oh right yeah
stone pelican
oh right yeah
That's why I was so confused for a moment lol
stone pelican
as in how to calculate confidence interval and p value
Well, now to this question
Do you know the way to find t* ?
stone pelican
Have you learnt about z* ?
velvet yarrow
nah
stone pelican
Okay
So can you tell me what the formula for the confidence interval is in your curriculum
stone pelican
wait can u let me explain what i think t* is
Okay
velvet yarrow
so in bootstratping you assume ur sample form the real population is a kind of 'fake' poplution
thats representative of the real one
from the 'fake' pop u take a bunch of sample with replacement, form which you find the mean and threby create a distribution
so would t* show how far ur observed sample mean (from original poplution is) from the mean of the bootstrapped distribution, in terms of SD
stone pelican
so would t* show how far ur observed sample mean (from original poplution is) fr...
That's not correct
velvet yarrow
hm ok
stone pelican
So, t* is the minimum z score to attain a certain confidence level
You know what a z score is right?
velvet yarrow
yeah
it standardises a point for the normal dist cruve right?
or something like that
stone pelican
it standardises a point for the normal dist cruve right?
Wdym
stone pelican
It's how far away a data point is from the mean, in terms of s.d
stone pelican
so would t* show how far ur observed sample mean (from original poplution is) fr...
Aka this
velvet yarrow
ik its something ab shifting the curve to N~(0,1)
stone pelican
Your previous understanding of t* is basically z-score
velvet yarrow
oh ok
velvet yarrow
nah
im a bit lost on that
i still dont get what t* mean
can u explain it in relly simple terms
stone pelican
i still dont get what t* mean
Ok remember the empirical rule?
velvet yarrow
yeah
stone pelican
Can you recall it and type it out
velvet yarrow
the 68 95 99.7
stone pelican
the 68 95 99.7
Yep
velvet yarrow
is 1sd 2sd and 3sd
stone pelican
If I want to be 95% sure that the proportion is in a certain interval
Then that interval would be $[\mu - 2\sigma , \mu + 2\sigma]$
velvet yarrow
o yeah
elfin berryBOT
Matcha
stone pelican
So 2 will be the z*
This is z* btw, not t* yet cause that's a bit more complicated
velvet yarrow
its z because we assume its normally distrubuted?
stone pelican
its z because we assume its normally distrubuted?
Z because it is a proportion that we are testing
T if it is a mean
velvet yarrow
oh
the reasoning i was given is that
we use z test when we know the pop sd and t test if we dont
velvet yarrow
and then use bootstrapping furhter more if the sample comes form a population tahts not normally distributed
which we check with a qqplot
or boxplot or histrogram
apprently yhe boostrapping dist creates something that rougly normal
so we can use t test for that
stone pelican
Yeah
stone pelican
as in how to calculate confidence interval and p value
Now back to this
You know the t-table and how to use it?
velvet yarrow
oh we just lreand to use r
this is what i haev got written down
i dont see where t* is here tho
stone pelican
Hold up I'm also confused
Sadly I think I haven't made it to this part on statistics yet
I can't help you any further 
velvet yarrow
noo
can u at lteaset explain
why when finding the p value
we find sum all the t_stats that are greater than our t_sat ( a calculated above) / bootstrap sample
still temple
How to find basis of question b? Why the answer is the first 2 vectors
chrome jacinth
How to find basis of question b? Why the answer is the first 2 vectors
Hi! There's a couple of ways to find the basis. Here's one way:
Remember that in the column space of a matrix A, the basis of the column space refers to the position of the pivot columns in the reduced matrix. I.e if you find that there's a pivot in column 1 and column 2, the basis vectors are the 1st and 2nd column vectors.
So, what you might do is put all the vectors into a matrix (as column vectors) and row reduce!
stone pelican
(2 7 4 1) is 3•(2 1 0 -1) + 4•(-1 1 1 1)
chrome jacinth
Or you can recognise the above :)
marsh citrusBOT
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Available help channel!
dusty kite
In a corner bordered by two stone walls is a rectangular chicken yard enclosed with a 10-meter fence, and its area is y , \text{m}^2.
(diagram: one side of the rectangle has length x, the top side has length 10 - x)
What values can
a) x take?
b) y take?
marsh citrusBOT
In a corner bordered by two stone walls is a rectangular chicken yard enclosed w...
dusty kite
I don’t understand this
hybrid gull
Think about (a) first — is there an obvious lower bound? an obvious upper bound?
still temple
,ask plot 10x - x^2
elfin berryBOT
still temple
weird y values in this plot 🤣
still temple
,ask plot 10x - x^2
but this is the formula for the area, you can take the derivative, make it equal to 0 and find the point of maximal area, which i think is 25
and as x->0+ you can see that the area is becoming 0, so yea i think it's the minimal u can get
(0,25], not 0 really because you cannot have x = 0
hybrid gull
!nosols
marsh citrusBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
marsh citrusBOT
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mossy garden
i'm stuck trying to understand the logic of an algebraic function. Why is the vertex of the parabola in the function y=(x+2)^2 on the - side of the x-coordinate instead of the + side?
marsh citrusBOT
i'm stuck trying to understand the logic of an algebraic function. Why is the ve...
fervent rampart
the vertex is where the thing inside the square = 0
so vertex is where x + 2 = 0
mossy garden
didnt very understand, does it mean x always ≤0?
when square with him or he inside the square
fervent rampart
well for example the vertex of y = (x - 6)^2 + 8 is given by x - 6 = 0, or x = 6
mossy garden
well for example the vertex of y = (x - 6)^2 + 8 is given by x - 6 = 0, or x = 6
but why x is 6 or equals 0?
fervent rampart
if you write a parabola in vertex form, as y = (x - h)^2 + k, then the vertex is where the part in the square (x - h) is equal to 0
mossy garden
if a function squared is 0, doesn't that mean the vertex will be at the center? (0 coordinate)
(like (x-2)^2)
or you means it's <0
mossy garden
or you means it's <0
if used on the function graph
marsh citrusBOT
@mossy garden Has your question been resolved?
viscid violet
if a function squared is 0, doesn't that mean the vertex will be at the center? ...
What do you think vertex of parabola means
mossy garden
What do you think vertex of parabola means
that thing where i drew an arrow but i cant describe that
mossy garden
oh ye exactly
elfin berryBOT
flynger
plain heath
and $(x-a)^2 \ge 0$
elfin berryBOT
flynger
mossy garden
(x-a)^2 is nonnegative so where do you think the minimum is?
at 0?
elfin berryBOT
flynger
plain heath
we can take square root to get $x-a=0$
elfin berryBOT
flynger
plain heath
so $x=a$
elfin berryBOT
flynger
plain heath
For any other value of $x$, $x-a \ne 0$, so $(x-a)^2 > 0$
elfin berryBOT
flynger
plain heath
But for $x=a$, $(x-a)^2=0$
elfin berryBOT
flynger
plain heath
Does it make sense why the minimum is acheived at $a$ now and not $-a$?
elfin berryBOT
flynger
mossy garden
because x-a=0 and x=a?
mossy garden
**flynger**
and what do you mean any other value of x?
viscid violet
and what do you mean any other value of x?
Any value of x that is not a
Any real value
plain heath
Yeah I meant $x \ne a$
elfin berryBOT
flynger
mossy garden
Any value of x that is not a
like
if x not equal a, then (x-a)^2 not equal 0
if x equal a, then (x-a)^2 equal 0?
viscid violet
like
if x not equal a, then (x-a)^2 not equal 0
if x equal a, then (x-a)^2 equa...
Yeah
But we can also say (x-a)^2>0 for real x not equal to a
mossy garden
in which situations number a can be not equal to 0?
viscid violet
in which situations number a can be not equal to 0?
You if a is zero you get the parabola touching x axis
mossy garden
You if a is zero you get the parabola touching x axis
oh ye it makes sense, but i dont know how to apply this information to for understanding when y=(x+2)^2 (when vertex of the parabola touches x axis on the - side and not on the + side)
plain heath
$(x+2)^2 \ge 0$
For $x=-2$, you have $(x+2)^2 = 0$
For $x \ne -2$, you have $(x+2)^2 > 0$
elfin berryBOT
flynger
plain heath
$x+2 = x - (-2)$
elfin berryBOT
flynger
plain heath
$(x- (-2) )^2$ has $a=-2$
elfin berryBOT
flynger
marsh citrusBOT
mossy garden
But I'll better continue to trying understand it out tomorrow
marsh citrusBOT
Available help channel!
somber panther
marsh citrusBOT
somber panther
How do I know when this function hits 9?
I tried putting y as 9 then solving but looking on desmos it’s wrong
slim shard
what is the function? $f(x) = 4.3\cos\left(\frac\pi6\left(x-\frac 12\right)\right) + 12.5$?
elfin berryBOT
slim shard
i think you have to consider for $0 \leq x \leq 24$
elfin berryBOT
marsh citrusBOT
@somber panther Has your question been resolved?
wind hare
Your bracket expansion from the 3rd to 4th line is not correct, and I would recommend not rounding before you get to the final answer. There is also more than 1 solution in the 24 hour domain (four solutions, in fact) due to the periodicity of cosine
somber panther
Your bracket expansion from the 3rd to 4th line is not correct, and I would reco...
I would be able to get the other 3 by adding the difference in hours from 3:45 am right
marsh citrusBOT
somber panther
.reopen
marsh citrusBOT
✅ Original question: #help-33 message
pine wolf
marsh citrusBOT
sacred idol
i guess you remember what $\cos(\alpha + \theta)$ expands to?
elfin berryBOT
sacred idol
$\cos(a+b) = \cos(a)\cos(b) - \sin(a)\sin(b)$?
elfin berryBOT
sacred idol
what would you get here then
sacred idol
did you do any trig problems before this
pine wolf
easy ones like this one lol
marsh citrusBOT
@pine wolf Has your question been resolved?
marsh citrusBOT
@pine wolf Has your question been resolved?
marsh citrusBOT
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Available help channel!
worthy delta
What should I do in this inequality and why
|2x -3| < |x+2|
I tried to do this
|2x-2| < |x+2|
|2x| - |2| < |x| + |2|
|2x| - |x| < |2| + |2|
|2x-x| < 2+2
|x| < 4
-4 < x < 4
But chat gpt said that's wrong
So what is the correct solution and ((why))
latent mirage
Divide into cases
amber birch
What should I do in this inequality and why
|2x -3| < |x+2|
I tried to do this...
is it 2x - 3 or 2x - 2?
but anyway, you should know that |a - b| is not |a| - |b|
stoic saddle
!noai
marsh citrusBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
stoic saddle
but anyway, you should know that |a - b| is *not* |a| - |b|
this stands
amber birch
for example, |5 - (-1)| = 6 but |5| - |-1| = 5 - 1 = 4
amber birch
yes, so they're not equal in general
worthy delta
yes, so they're not equal in general
Ok if this not work what should I try?
amber birch
Ok if this not work what should I try?
if you had to solve |2x - 3| = |x + 2| with the =
what would you do first?
amber birch
mhm, that could work
there's another method where you can do 2x - 3 = x + 2, 2x - 3 = -(x + 2)
worthy delta
there's another method where you can do 2x - 3 = x + 2, 2x - 3 = -(x + 2)
And solve both ?
amber birch
And solve both ?
yes
worthy delta
Ok but if it was < instead of =
amber birch
Ok but if it was < instead of =
the idea is to make a sign diagram based on the equality case
worthy delta
-(x+2)<2x-3<x+2
amber birch
there's another method where you can do 2x - 3 = x + 2, 2x - 3 = -(x + 2)
from here, x = 0, 2
worthy delta
-(x+2)<2x-3<x+2
I should do this?
amber birch
|2x-2| < |x+2|
btw you said it was this
worthy delta
the idea is to make a sign diagram based on the equality case
If I made any sign diagram then I can take one value less than 0
And one value greater than 2?
worthy delta
no actually it works
How?
worthy delta
it's a big coincidence
Can you suggest a YouTube video teach me how to solve an inequality with absolute on both of it sides?
worthy delta
give me time ok
Ok
amber birch
so you know that |x| < a means -a < x < a of course
so you have that you have that -|x + 2| < 2x - 2 < |x + 2|
worthy delta
Can you suggest a YouTube video teach me how to solve an inequality with absolut...
I searched for smth similar but I got nothing
worthy delta
so you know that |x| < a means -a < x < a of course
so you have that you have t...
Yes
amber birch
Can you suggest a YouTube video teach me how to solve an inequality with absolut...
https://www.youtube.com/watch?v=iAbyLWe9qQo
what I'm suggesting is method 2
latent mirage
The way I approach absolute value inequations is often to just break em into cases.
|2x-3| < |x+2|
can have 4 different regions in space (space over which x ranges) that change the function behavior.
Trace them out
Case 1: 2x-3, and x+2 both >0
Case 2: one > one < 0
And so on. There'll be 4 cases.
And then in each region you have a simple linear function comparison. Then union all ranges of x where the LHS < RHS
amber birch
search for 'double absolute value inequalities'
worthy delta
Thx so much
Idk why should I study absolute value when I'm a computer science student
Any way tysm bro
.close
marsh citrusBOT
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still temple
I wanted to ask how you could identify the different kinds of probability questions and why these formulas work
marsh citrusBOT
I wanted to ask how you could identify the different kinds of probability questi...
gloomy merlin
I wanted to ask how you could identify the different kinds of probability questi...
There is no panacea of an answer
You gotta narrow down your question's scope if you want any meaningful responses
agile iron
I wanted to ask how you could identify the different kinds of probability questi...
To be exact, it all comes down to good intuition and instinct.
The more problems you do, the more you'll recognize the techniques needed to solve them.
So, I would recommend practicing with all sort of questions.
still temple
.close
marsh citrusBOT
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thin spire
Hello, I dn't understand what is the respond of this vector product. It implies 2 vectors that are in different space and my teacher didn't explain this
marsh citrusBOT
Hello, I dn't understand what is the respond of this vector product. It implies ...
@thin spire Has your question been resolved?
calm grove
Do you wanna explain your ideas? Is there some other context regarding x, y, z (like the space they are coming from)?
thin spire
My teacher use this method to have the third vector, to have a direct orthonormal base and this is the website that my teacher gave to my class
calm grove
So they all exist in R³?
thin spire
yes
calm grove
Okay, so do you want to try to explain the task to me? Or do you just have no idea at all? (You could try a geometric interpretation of the problem)
thin spire
The task is to find the result of the vector product in the image and the method behind this
For information this engineering science not pure maths problem, it's my engineering science that gave me this
calm grove
The symbol indicates a wedge product, at least as far as I know. A vector product could also be the cross product. Which one do you mean?
thin spire
I didn't even know that represent two thing. I learn that the symbole means for example : z and y = vector norm x vector norm x sin(angle between them)
calm grove
My teacher use this method to have the third vector, to have a direct orthonorma...
Do you have a link to the website (or is it private, don't share if you don't think it's okay)
calm grove
I didn't even know that represent two thing. I learn that the symbole means for ...
Well that is a start.
That's probably just a very geometric interpretation of the wedge product, which is just the area/volume of something.
calm grove
Just for your information: I am trying to understand your definition, but I don't French, so it's going to take a while. If you have a useful link, that would help me a lot. (I am currently here: https://www.jdotec.net/s3i/)
thin spire
A useful link to understand my definition of vector product ?
calm grove
I've found your definition, all good
thin spire
Don't worry I already sent a mail to the teacher about that, I will just wait for his respond I think and ask him monday
thin spire
I mean I think that my teacher method is just weird, I don't where he has found this
.close
marsh citrusBOT
thin spire
Thank you for your time
marsh citrusBOT
Available help channel!
muted palm
Part of a bigger maths question, but the video says that when u factorise it its 2x - 5 and x - 2 but they dont add up to -9?? maybe its because of the 2x² its doing something but i cant see what. I have no problems solving normal quadratics like x²+ whateverx+whatever number
marsh citrusBOT
Part of a bigger maths question, but the video says that when u factorise it its...
slim shard
Part of a bigger maths question, but the video says that when u factorise it its...
what doesn't add up to 9?
rose mural
Part of a bigger maths question, but the video says that when u factorise it its...
Hi Bambietta, you know that when roots are added, they give -(b/a). Therefore, 5/2+2=9/2
muted palm
Hi Bambietta, you know that when roots are added, they give -(b/a). Therefore, 5...
I dont rlly understand sorry
💀
rose mural
I dont rlly understand sorry
Do you know quadratic rules?
rose mural
Ok
cold tulip
Part of a bigger maths question, but the video says that when u factorise it its...
hi, have you found the answer to this yet?
I can help you if you’d like.
muted palm
I can help you if you’d like.
would appreciate it lol
fast spear
Op there?
marsh citrusBOT
marsh citrusBOT
Available help channel!
hard root
What is the general strategy for finding the limits of integration for polar area?
marsh citrusBOT
What is the general strategy for finding the limits of integration for polar are...
@hard root Has your question been resolved?
marsh citrusBOT
Available help channel!
echo scaffold
Am I doing this wrong
marsh citrusBOT
Am I doing this wrong
echo scaffold
Wait
It says on my worksheet I need to do ling devision for 8 and 10 but idk where I would do that
echo scaffold
Ok I think I got it but I don’t think 10 is right but I don’t have an answer key so jdk
maiden edge
Ok I think I got it but I don’t think 10 is right but I don’t have an answer key...
wait what is the doubt?
because the graph is not correct
echo scaffold
wait what is the doubt?
10 I’m confused on because it’s 4-3x and the X is not first
And for this one number 35 would it be a translation 4 left or 4 rigjt
maiden edge
Ok I think I got it but I don’t think 10 is right but I don’t have an answer key...
10 is correct
maiden edge
And for this one number 35 would it be a translation 4 left or 4 rigjt
u can rewrite it as -1/x-4
echo scaffold
Ok this does not make sense I found an answer key but it said half of them are wrong but the tick marks on the graphs do not match the functions
echo scaffold
u can rewrite it as -1/x-4
Huh
Like this is the correct matches but they don’t make sense at all
maiden edge
Ok this does not make sense I found an answer key but it said half of them are w...
well ur graphs are wrong 😭
echo scaffold
For example for 33 it says it is a . And on the X axis it is correct . But we are supposed to be going up two units. And on this graph we are going up 4 units
echo scaffold
well ur graphs are wrong 😭
Wait which question sorry
maiden edge
Wait which question sorry
6,8
maiden edge
For example for 33 it says it is a . And on the X axis it is correct . But we ar...
we are looking at the behaviour
if we look at question 33
we get the function as 2 + sth positive right?
so it will be above x axis
echo scaffold
It just doesn’t make sense how we are supposed to know what graph to match it to if the tick marks are wrong
Even for the answer key for question number 10 the tick marks are wrong
maiden edge
wdym by tick marks
echo scaffold
Like the marks on the axises of the graph
marsh citrusBOT
@echo scaffold Has your question been resolved?
maiden edge
@obtuse umbra bro help here
i don't understand this stuff as its not in my education system
obtuse umbra
💀
tiny bear
Let $A$ be a proper subset of $X$ and $B$ a proper subset of $Y$. If $X$ and $Y$ are connected, prove that
[
(X \times Y) - (A \times B)
]
is connected.
elfin berryBOT
Halex
marsh citrusBOT
Let $A$ be a proper subset of $X$ and $B$ a proper subset of $Y$. If $X$ and $Y$...
tiny bear
Working with topological spaces, not math analysis
stoic saddle
you may consider making a picture in the case that X, Y, A and B are all intervals -- at least for intuition's sake
tiny bear
you may consider making a picture in the case that X, Y, A and B are all interva...
X-A would turn into an union of semi open intervals
stoic saddle
true but your problem is talking about X × Y - A × B
marsh citrusBOT
@tiny bear Has your question been resolved?
tiny bear
true but your problem is talking about X × Y - A × B
Product of unions of semi open intervals
stoic saddle
i did say to draw a picture btw
humble nebula
Product of unions of semi open intervals
For example, consider X = Y = [0,3], A = B = [1,2]
Then your picture should look like || 回 ||
marsh citrusBOT
@tiny bear Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
torpid pawn
how do we use the texit bot?
marsh citrusBOT
how do we use the texit bot?
brave marsh
Do you know any LaTeX? That’s the language it recognizes.
If you do then it’s pretty much just writing as you would normally in a LaTeX document.
proud ice
how do we use the texit bot?
#latex-help may be a better play to ask
marsh citrusBOT
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Available help channel!
still temple
hello
