also here n is odd
#help-23
ripe cove
proper vortex
And since the options are with the ≠ sign
ripe cove
if i remember correctly
proper vortex
Ahan
ripe cove
so now u got it :D
proper vortex
Thank you!!!
ripe cove
you are welcome :)
proper vortex
Can I dm I have a bunch of questions
proper vortex
Similar ones
ripe cove
sure, but i would suggest trying them out first
now that you know the method
if you still encounter some problems I am here for ya
do .close to close this
proper vortex
.close
safe radishBOT
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polar fossil
can I just say, for all n O_n = the set of real numbers?
cuz the real numbers are open and they are a subset of themselves
and a set's infinite intersection with itself is simple itself so thats just R again and R is also closed and nonempty? this seems like cheating
safe radishBOT
can I just say, for all n O_n = the set of real numbers?
cuz the real numbers ar...
solar hazel
yea
maybe an oversight from the question writer
a more realistic version of the question would be to require the set containments to be proper
but as stands that is definitely not what was asked
polar fossil
so I'm technically correct, my favourite type of correctness
solar hazel
i would not even call it technically
tough zephyr
How would you go about proving these
safe radishBOT
How would you go about proving these
tough zephyr
for i) would it be equal since u*(v x w) = 4 and w*(u x v) = -4, and then the det of each one is equal since its oppositve of each other? For the other two I'm not sure where to begen. Expect for ii im not sure if it has to do with cross product being communitative.
For iii) Im not sure what the property/ thereom for this is and how I can prove it to be T or F.
dreamy elk
i) Let $a = u, b=v, c = w$, then it matches, meaning by this that i) is false.
flat frigateBOT
Crystopher
tough zephyr
I see so the determinant has nothing to do with it, it just following the property
dreamy elk
for ii) you can use the following algebraic properties of cross product:
dusk nova
I see so the determinant has nothing to do with it, it just following the proper...
it does if u want
dreamy elk
for iii) try to recall when two vectors are orthogonal to each other.
Hint :
||It has to do with the dot product||
dusk nova
for iii) try to recall when two vectors are orthogonal to each other.
Hint :
||I...
cross product is more appropriate for formulating an argument for iii)
dreamy elk
I see, that's possible, the result of cross product is orthogonal, but I found it simple with dot anyways.
dusk nova
in fact if u think about it, | |w| |v + | |v| |w is exactly the angle bisector vector of w and v and so the rest is trivial
safe radishBOT
@tough zephyr Has your question been resolved?
tough zephyr
I see thank you guys
opal steeple
119 students took a test. We know that the highest score was 98% and that to place in the top 30 students, a student had to score 62%. The mean score was 48%. Assuming a normal distribution, what rank would you expect a student that scored 28% to place?
safe radishBOT
119 students took a test. We know that the highest score was 98% and that to pla...
grizzled fossil
119 students took a test. We know that the highest score was 98% and that to pla...
!status
safe radishBOT
119 students took a test. We know that the highest score was 98% and that to pla...
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
well I had a look around and found this: https://statproofbook.github.io/P/norm-cdf so I subbed in my values as mu=0.48, x=0.62 and set it equal to 1 - 30/119 in order to find the std dev
so that i could then use the normal distribution to find out the probability of a person getting 28%
but the standard deviation i get doesn't seem to be correct when i enter it into desmos, because it tells me that the probability of a student scoring above 62% is around 23% and not 30
should be 0.3 or very close
safe radishBOT
@opal steeple Has your question been resolved?
rough storm
I think you are overcomplicating it
opal steeple
i'm not sure how else i'd go about it
rough storm
try to think about going from the distribution you have N(.48,sigma), to a standard normal distribution N(0,1). there's a function called an inversecdf as well, which basically extracts a z-value given a probability<z
do you see how this helps?
rough storm
but the standard deviation i get doesn't seem to be correct when i enter it into...
why would it be around 30%?
if you're getting it from top 30, the top 30 doesn't mean top 30 percent
safe radishBOT
@opal steeple Has your question been resolved?
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hasty cairn
What did I do wrong solving $$ \int{sin^{-1}x dx} $$
safe radishBOT
What did I do wrong solving $$ \int{sin^{-1}x dx} $$
flat frigateBOT
Nerdy_Coder
kind forge
What did I do wrong solving $$ \int{sin^{-1}x dx} $$
,rotate
dammit is there no way to make it rotate the right message
,rotate
flat frigateBOT
obtuse plover
Is it possible for you to space out your work a little more
It’s tough to read that
Like write vertically instead of horizontally, but occupy more space
supple shore
ye a bit difficult to read
hasty cairn
Like write vertically instead of horizontally, but occupy more space
Wait write vertically?
Hold on how much space because I did space out my work more
As you can see bigger letters and more space
hasty cairn
This is the old work
new work
See how letters are bigger and more space
somehow this is not enough so how much more space
gusty trench
the integral in question is 1/sin^2?
hasty cairn
yea
gusty trench
you might have evaluated the integral of x/sqrt(1-x^2) incorrectly
of course you've still cramped everything together in your work so it's hard to follow exactly what you did
but you have the right idea, if u = 1 - x^2 then -2xdx = du so dx = du / (-2x), then your integral becomes -1/2 * u^(-1/2) du which becomes -u^(1/2) which becomes -sqrt(1-x^2)
yeah that's the part that's off
you should be getting x*arcsinx + sqrt(1-x^2) + C
,w integrate arcsinx
flat frigateBOT
hasty cairn
Is this what you guys expect of me?
obtuse plover
I mean, im sure your teachers will probably appreciate it too
It’s easier to follow along if the work is not difficult to read
hasty cairn
cool
didm’t know there was a standard
Is there a problem with the way I separate problems?
safe radishBOT
@hasty cairn Has your question been resolved?
full marsh
hidden lynx
what in the Egyptian scripture
safe radishBOT
@hasty cairn Has your question been resolved?
hasty cairn
Did I get it right now?
copper shadow
I am trying to solve question six but when I tested one even number and 2 odd numbers this results in z^2 being equal to an even number. How can I prove the proof then?
safe radishBOT
I am trying to solve question six but when I tested one even number and 2 odd nu...
empty gyro
I am trying to solve question six but when I tested one even number and 2 odd nu...
Are you sure z is still an integer in that case?
hardy lion
consider the remainder when dividng by 4
icy sonnet
x,y,w are evens ⇒ z even:
this one should be simple
z even ⇒ x,y,w evens
you can use contraposition
meaning one of x,y,w is odd implies z is odd
not sure if this is exactly whats asked of you tho
solar hazel
there is no way you found a solution with one of w,x,z even and the other 2 odd because that implies you found a square that's 2 mod 4
safe radishBOT
@copper shadow Has your question been resolved?
copper shadow
Are you sure z is still an integer in that case?
Ye just realized it's not
copper shadow
x,y,w are evens ⇒ z even:
this one should be simple
z even ⇒ x,y,w evens
you ca...
I need to solve by case
Assuming I need to make 8 cases right?
icy sonnet
yeah
copper shadow
Ok
safe radishBOT
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lone arch
How do you solve the system \begin{align} x_1^2 + (x_2 - 7)^2 + (x_3 - 8)^2 &= 20 \ (x_1 - 2)^2 + (x_2 - 5)^2 + x_3^2 &= 20 \ x_1 + x_2 &= 7\end{align} which is essentially \begin{align*} x_1^2 + x_2^2 + x_3^2 - 14x_2 - 16x_3 &= -93 \ x_1^2 + x_2^2 + x_3^2 - 4x_1 - 10x_2 &= - 9 \ x_1 + x_2 = 7?\end{align*} Subtracting the first from the second, we get \begin{align*} x_1^2 + x_2^2 + x_3^2 - 14x_2 - 16x_3 &= -93 \ 8x_2 + 16x_3 &= 84 \ x_1 + x_2 &= 7\end{align*}
safe radishBOT
How do you solve the system \begin{align} x_1^2 + (x_2 - 7)^2 + (x_3 - 8)^2 &= 2...
flat frigateBOT
Kepe
lone arch
Though that's not very helpful either
@obtuse jackal Since you just typed, is there an approach you'd use over doing what I did here?
obtuse jackal
no
I never really studied quadratic forms
so I don't know how quadratic systems and the potential theorem for solving them
lone arch
so I don't know how quadratic systems and the potential theorem for solving them
Yeah, though this is in a high school book so I guess we don't need any of that. The solutions just say "the solution to this system is [...]". This system arises from "mirroring" a point on a plane with given conditions
The system is correct, it's given in the solutions too
They just don't say how they solve it
They will end up with two solutions, involving square roots
obtuse jackal
**Kepe**
the bottom 2 express x2 with x1 and x3
Then the top one is a quadratic in x1 and x3, so express x3 as a function of x1
Then maybe the bottom 2 let you solve for x1 ?
Seems painful to brute force it that way
lone arch
the bottom 2 express x2 with x1 and x3
Then the top one is a quadratic in x1 and...
x2 = 7 - x1
8(7 - x1) + 16x3 = 84 so - 8x1 + 16x3 = 28
obtuse jackal
another silly option is to take it as a linear problem with 6 variables, get a 3D kernel and then see which points verify x4 = x1², x5=x2², x6=x3²
lone arch
another silly option is to take it as a linear problem with 6 variables, get a 3...
I think at this point the author just didn't really think the system was going to turn out like this
And then in the solutions he was like "screw it, I'll just enter this into WA"
lone arch
the bottom 2 express x2 with x1 and x3
Then the top one is a quadratic in x1 and...
How will the bottom two let me solve for x1
There is x1, x2, x3 involved and only two equations
obtuse jackal
if x3 = f(x1) and x2 = g(x1, x3), then x1 + g(x1, f(x1)) = 7 is an equation in x1
lone arch
Btw, one solution turns out to be $(x_1, x_2, x_3) = \Big(1 - \frac23 \sqrt 2 \mid 6 + \frac23 \sqrt 2 \mid 4 - \frac 13 \sqrt 2\Big)$
Which is surprisingly nice?
flat frigateBOT
Kepe
obtuse jackal
could definitely be worse
lone arch
could definitely be worse
Maybe in the end, there really is some nice cancellation or something?
obtuse jackal
who knows
lone arch
who knows
Would you continue trying to search for something here or just conclude the author didn't intend this? The topic is kinda completely different (analytic geometry; planes, lines, mirroring along them, ...) and this exercise belongs to one of the easier ones
obtuse jackal
if it's the only nontrivial quadratic system in the book yeah it's weird
lone arch
if it's the only nontrivial quadratic system in the book yeah it's weird
Yeah it is, there has been nothing like this before
obtuse jackal
what about after?
lone arch
what about after?
Nope, neither
obtuse jackal
what was the original problem?
lone arch
what was the original problem?
A plane contains the points P(2, 5, 0), Q(0, 7, 8) and R(0, 5, 4). First, set up a coordinate equation of the plane. Now, the plane gets rotated by 90° along the line PQ and this generates another plane F. Determine the coordinate equation of F (which turned out to be x1 + x2 = 7). Now, the point R goes over to another point R' during this rotation. Determine possible coordinates of R'
The Ansatz is to let R' = (x1, x2, x3)
And then set up these equations
obtuse jackal
2 solutions for clockwise and anticlockwise right?
lone arch
2 solutions for clockwise and anticlockwise right?
Yeah, probably, though we don't really need to think about it when setting up the equations. We just make sure the distances are still the same
|PR'| = |PR|
|QR'| = |QR|
And it needs to lie on the plane
So x1 + x2 = 7
Then, you get these 3 equations above (after squaring the first two so the square roots vanish)
lone arch
2 solutions for clockwise and anticlockwise right?
So yeah, I think the topic doesn't have to do much with solving quadratic systems or anything like that..
lone arch
other simplification: do R1 <- R1 - R3² to make the only square be x3²
Though then we have x1x2
obtuse jackal
oh nvm
safe radishBOT
@lone arch Has your question been resolved?
lean otter
How do I solve this?
Calculate how many elements are included in the sequence 3, 6, 12, 24, ... if the sum of the numbers in the sequence is 196605.
safe radishBOT
How do I solve this?
> Calculate how many elements are included in the sequence ...
tardy pivot
This is a geometric sequence
There is a formula for the sum of a geometric series, which you should memorise if u havent
lean otter
There is a formula for the sum of a geometric series, which you should memorise ...
I haven't
can you send it to me
lean otter
Thank you
Imma search it up and come back if I need any further help. This is the first time I have seen the formula.
tardy pivot
kk
tardy pivot
when the nth term takes the form ar^(n-1)
your sequence takes the form 3(2)^(n-1)
3(2)^(1-1) = 3, 3(2)^(2-1) = 6 etc
when each term is multiplied by a number to get to the next term
that is a geometric sequence
safe radishBOT
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Available help channel!
fallen pier
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desert pasture
,rotate
flat frigateBOT
fallen pier
Q1 idk what to do
desert pasture
1a?
desert pasture
are you familiar with viteas formula?
or the relation between the roots of a quadratic and the coefficents ?
flat frigateBOT
ƒ(Why am. I here)=I don't know
desert pasture
then $\frac{-b}{a} = \alpha + \beta$
flat frigateBOT
ƒ(Why am. I here)=I don't know
desert pasture
and $\frac{c}{a} = \alpha \beta$
flat frigateBOT
ƒ(Why am. I here)=I don't know
fallen pier
Ok I get the rule but how do I apply it
desert pasture
$\alpha + \beta =\frac{6}{5}$
flat frigateBOT
ƒ(Why am. I here)=I don't know
desert pasture
$\alpha\beta = \frac{-56}{5}$
flat frigateBOT
ƒ(Why am. I here)=I don't know
fallen pier
So simultaneous equation?
desert pasture
$\alpha + \gamma = \frac{14}{3}$
flat frigateBOT
ƒ(Why am. I here)=I don't know
desert pasture
I think so
desert pasture
the second root of the equation 3x^2-14x+a
alternatively
find the roots of the first equation
and substitute them into equation 2
fallen pier
So I could quadratic equation first one
flat frigateBOT
desert pasture
oo
this helps a lot
do it by yourself
and use the fact that equation 1 has only one integer root
fallen pier
Does a=8
desert pasture
,w 3(4)^2-14(4)+a=0
flat frigateBOT
safe radishBOT
@fallen pier Has your question been resolved?
bronze pilot
safe radishBOT
bronze pilot
I only know about the angles inside, which is n-2 x 180
so it has 6 sides so its 720 in total , now I dont know what to do
☠️
thin bridge
what are the sizes of each angle in a regular hexagon
bronze pilot
what are the sizes of each angle in a regular hexagon
120 right? 720 divided by 6
bronze pilot
1 sec
bronze pilot
and from there you can apply basic angle sums
alr I've wrote it down , just to be sure, the angle of S , its 90 , so the one on the left is 30 right? 120-90
thin bridge
if you're referring to <TSW, yes
bronze pilot
soo 360-50 ? for the rest of W ?
thin bridge
yes
bronze pilot
so how do we know the angle sum for STUMVW? we don't have the value of x yet
thin bridge
count the number of sides
bronze pilot
oh I thought the formula only works on a regular polygon ?
thin bridge
not limited to regular shapes
bronze pilot
dang I see so its n-2
6-2
4x180
720-(100+120+120+30+310)
40
so x is 40
ty
tysm 😭
cerulean crane
Do you have a math question
thin bridge
<@&268886789983436800> non-math self promo
warped roost
.close
craggy sundial
how to be better at math
safe radishBOT
how to be better at math
desert pasture
practice
light shoal
practice
lime dust
Studying and working.
empty gyro
craggy sundial
studying never helped, cause i never understand
lime dust
Studying helps you understand
proud belfry
studying never helped, cause i never understand
What do you mean you never understand
desert pasture
ask for help here
lime dust
That is what studying means
desert pasture
and online too
proud belfry
like wym by that
prisma karma
studying never helped, cause i never understand
you need to find good resources that are thorough in their explanation
craggy sundial
like in general never really understood almost anything in math😭
prisma karma
you need to find good resources that are thorough in their explanation
and if u r stuck at any point seek help here
empty gyro
studying never helped, cause i never understand
Then you need to ask questions about what you don't understand
lime dust
That is vague
proud belfry
like in general never really understood almost anything in math😭
do you understand addition? Well then atleast theres some things you understand
prisma karma
like in general never really understood almost anything in math😭
take your time to understand the concept will help,
prisma karma
take your time to understand the concept will help,
it might take hours before things click
craggy sundial
do you understand addition? Well then atleast theres some things you understand
yee but i started detriorating in grade 5 when i changed countries and then grade 6 covid and from then on things have been lagging
craggy sundial
take your time to understand the concept will help,
yes ill do this👍
empty gyro
So it's on you to try harder now
craggy sundial
im so behind it feels hopeless
prisma karma
yee but i started detriorating in grade 5 when i changed countries and then grad...
you should go to the first point where you are starting to get lost, and go from there
prisma karma
im so behind it feels hopeless
dont feel rushed by the schedule that school goes at, if u take ur time its not too hard to catch up
gentle edge
dont feel rushed by the schedule that school goes at, if u take ur time its not ...
i can relate
craggy sundial
you should go to the first point where you are starting to get lost, and go from...
bet in this discord i can ask math questions right
empty gyro
bet in this discord i can ask math questions right
as many questions as you want, so long as you follow the rules
prisma karma
bet in this discord i can ask math questions right
yeah this is what help channels is for
craggy sundial
thank you i feel motivated
gentle edge
@craggy sundial i reccomend after you learn basic addition subtration and stuff focus a lot on fractions
fractions are very confusing at the start but very usefull later
empty gyro
It won't be easy, but if you care and try and really put in the work, you can do it
craggy sundial
fractions are very confusing at the start but very usefull later
ye i was so lost in grade 5 cause of fractions
empty gyro
So do you have fraction questions?
empty gyro
i didn't even know they did math
thin narwhal
its new
empty gyro
khan academy is the popular reccomendation here
craggy sundial
i didn't even know they did math
ye they do math
prisma karma
i didn't even know they did math
maybe they consider first order logic as a language 
craggy sundial
i didn't even know they did math
lol i just learnt they had one when tryna login to do music
craggy sundial
Do khan academy imo
ye alr where should i start
prisma karma
ye they do math
keep multiple resources just in case one resource is unclear, i suggest ur school textbook, khan and what u r using right now
gentle edge
@craggy sundial is say watch indian guys on youtube
proud belfry
ye alr where should i start
grade 5 or 6 math course
proud belfry
<@890079554494939156> is say watch indian guys on youtube
Username checks out
gentle edge
Username checks out
bruh
thin narwhal
just start at the point where you got lost
gentle edge
Username checks out
but still indian ppl know how to teach
craggy sundial
<@890079554494939156> is say watch indian guys on youtube
wdym?
thin narwhal
or a little before the point you got lost
prisma karma
Username checks out
but indian guys on youtube do be somewhat clear though
proud belfry
but indian guys on youtube do be somewhat clear though
yes but its unhelpful advice
empty gyro
This sounds like a good start if you have fraction trouble
https://www.khanacademy.org/math/arithmetic/fraction-arithmetic
craggy sundial
just start at the point where you got lost
gotchu ye ill do that
i also got summer school if i fail am going to dash 2☠️
prisma karma
honestly if you have a grade 5,6 question and u search your question on the web, thered be a indian guy on youtube who explains it
craggy sundial
i been trying youtube for a while i never got anywhere so ill try active recall and actual practise, cause i always watch youtube video but it be completely different outcome when the test comes cause i get like 50-60
prisma karma
i been trying youtube for a while i never got anywhere so ill try active recall ...
well if you have any question in any concept u can always come here. u just gotta make sure u 100% understand the concept with 0 gap in knowledge
craggy sundial
yess ok thank you
supple bramble
can someone expalin this proof to me my brains not working
safe radishBOT
can someone expalin this proof to me my brains not working
safe radishBOT
supple bramble
.reopen
safe radishBOT
✅
supple bramble
.close
safe radishBOT
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Available help channel!
odd widget
Really struggling with these critical point and absolute extrema problems. (Sample problem I'm trying to follow along with and my notes forthcoming). Thanks in advance for helping make this make more sense...
safe radishBOT
Really struggling with these critical point and absolute extrema problems. (Samp...
odd widget
Sample problem I'm trying to follow along with.
My scratch so far.
I'm wondering if my f'(x) is wrong, but I don't see any mistakes in my quotient rule. Did I simplify it too far?
rough storm
My scratch so far.
$(-1)(6x^2+1)=-6x^{2}+\mathbf{-1}$
flat frigateBOT
🫎 Moosey 🫎
rough storm
there's more
odd widget
Argh. That'd do it. Thanks. Let me see if I can recalc and figure it out now
Oh jeez.
This homework is killing me lol.
flat frigateBOT
🫎 Moosey 🫎
rough storm
and you can't simplify it further
odd widget
That fixed it! I got it figured out! Thank you for your help 🙂
rough storm
np!
odd widget
.close
safe radishBOT
safe radishBOT
Available help channel!
safe radishBOT
safe radishBOT
@safe belfry Has your question been resolved?
safe radishBOT
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Available help channel!
lavish gyro
safe radishBOT
lavish gyro
(a) and (d)
In A i am getting that it converges
it will be less than 2/n^2
but I am unsure if it is true as the sign changes
also (d)
I could prove that |u_n| is divergent
rough storm
i feel like |u_n| will go to 0
lavish gyro
i feel like |u_n| will go to 0
in A or D?
lavish gyro
i am confused as it is oscillating
rough storm
use alternating series test
lavish gyro
yeah i know this
but i am unable to get the 2nd argument, like unable to show that it is decreasing or increasing
brain lag
rough storm
you could use lhopitals and f'(x)<0
rough storm
to say a function is decreasing on an interval is to say f'(x)<0 on that interval
rough storm
oh wait
lavish gyro
you could use lhopitals and f'(x)<0
lhopitals for condition 1 right?
rough storm
condition two just requires you show f'(x)<0
lavish gyro
yeah, i now see that
rough storm
or in this case u'(n)<0 for all n>=1
lavish gyro
In (a), is what i did good?
but i fear that sign changes affect it
how to tackle sin functions while testing different series
@rough storm just curious, which grade are you in
rough storm
i've graduated uni
lavish gyro
ok damn
rough storm
for the sin(ntheta) one
lavish gyro
@rough storm wait i think in (a), I can check the absolute value and if that converges, the orginal series also converges
is this correct?
rough storm
use complex formula for sin(ntheta)
rough storm
<@114875468959842306> wait i think in (a), I can check the absolute value and i...
that also works
lavish gyro
use complex formula for sin(ntheta)
ok in this case it does converge but what if it diverged?
rough storm
if original sum diverged you could use complex formula for sin(ntheta)
lavish gyro
like how should i then try to prove that it diverges or converges
rough storm
lavish gyro
I am not comfortable with complex, with time i will be
rough storm
i just noticed your book mentioned complex numbers
lavish gyro
oh yeah, but i am uncomfortable like it takes me time to do stuff with complex numbers
I have less exposure
rough storm
it would be helpful to get comfortable with them, especially if you're going further with math/stem
lavish gyro
I am doing maths from a physics book so it is haphazard
lavish gyro
it would be helpful to get comfortable with them, especially if you're going fur...
I havent decided, I just gave my 10th boards in India
rough storm
aight
lavish gyro
thank you
rough storm
np
lavish gyro
@rough storm which book would you recommend for calculus, that is not too hard
rough storm
i didn't really use any books, but i heard stewart is pretty universal. there are resources pinned in #book-recommendations as well
pauls online math notes is pretty concise resource to refer to
safe radishBOT
@lavish gyro Has your question been resolved?
kind tinsel
<@114875468959842306> which book would you recommend for calculus, that is not t...
probably better to learn from lectures than from books at this level
the youtube channel professor leonard has some lectures on calc 1
and paul’s online math notes has supplements for calc 1 that aren’t so textbook-y
bronze pilot
TOQ and POR is a straight line
safe radishBOT
TOQ and POR is a straight line
bronze pilot
:
I know that both of the Y's are ( 180 - 72 ) most likely because a straight line is 180
apart from that, I don't know anything else or what to do
rough storm
use vertical angles
on TOP and QOR
you know angle POR because it is supplementary with QOR
use vertical angles again
:3
@bronze pilot
rough storm
I know that both of the Y's are ( 180 - 72 ) most likely because a straight line...
they can't both be 180-72
,calc (180-72)
flat frigateBOT
Result:
108
Oh sorry I was away for a second
bronze pilot
use vertical angles
So x = 90-60 = 30?
bronze pilot
alright I can see that, but I don't see a line like this tho or am I just blind
safe radishBOT
@bronze pilot Has your question been resolved?
rough storm
so x is 12
yes
now, you know angle POQ is supplementary to angle QOR, this means POQ=180-72
and you know POQ and ROT are vertical angles
magic tusk
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magic tusk
why is 1/f(x)
drawn like that
especially that one near parabola
this bit
i thought 1/f(x) would need to start at the turning point
but it clearly didnt
i know its following the asymptotes of x = 3 and x = -1
but in an exam, how would i sketch it
where would i start it from
ohh
if parabola is under the x-axis, that has to be under the x-axis
thats a rule i learnt
rightt
but like
why does it start from the turning point
makes no sense
.close
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faint seal
$\int\frac{a\cos x+b}{(a+b\cos x)^2} dx$
safe radishBOT
$\int\frac{a\cos x+b}{(a+b\cos x)^2} dx$
flat frigateBOT
kheerii
faint seal
$\int\frac{a\cos x +b}{b\sin x}\cdot \frac{b\sin x}{(a+ b\cos x)^2} dx$
desert pasture
maybe double angle indentities ?
faint seal
$$\int \frac{b\sin x}{(a+b\cos x)^2} dx = \frac1{a+b\cos x}+C$$ and $$\frac{d}{dx}\left(\frac{a}{b}\cot x+\csc x\right)=-\left(\frac{a}{b}\csc^2 x+\csc x\cot x\right)$$ so we get $$\frac{a\cos x +b}{b\sin x(a+b\cos x)} +\frac1{b}\int\frac{a\csc^2 x+b\csc x\cot x}{a+b\cos x} dx$$
faint seal
maybe double angle indentities ?
how?
desert pasture
cos(x) in terms of tan(x/2_
faint seal
that seems tedious
desert pasture
it should work
faint seal
$$\int\frac{a\csc^2 x+b\csc x\cot x}{a+b\cos x} dx=\int\frac{a+b\cos x}{\sin^2 x(a+b\cos x)} dx = -\cot x + C$$ so the final answer I get is $$\frac{a\cos x +b}{b\sin x(a+b\cos x)} -\frac{\cot x}{b}+C=\frac{\sin x}{a+b\cos x}+C$$
but this doesn't match wolframalpha, I don't think?
WAIT IT DOES
I can't even simplify a fucking trigonometric expression
jeez
okay but still, is there a better method for this?
flat frigateBOT
kheerii
mortal ingot
**kheerii**
Ono what is this
faint seal
Ono what is this
what?
mortal ingot
It seems scary, just that.
eternal carbon
okay but still, is there a better method for this?
better method? yeah guess it's a quotient rule
faint seal
better method? yeah guess it's a quotient rule
💀
eternal carbon
usually when you have numerator/(something)^2 that's a good thing to try
desert pasture
**kheerii**
$\int \frac{a\left(1-\tan^2\left(\frac{x}{2}\right)\right)+b}{\frac{\left(1+\tan^2\left(\frac{x}{2}\right)\right)}{\left(a+\frac{b\left(1-\tan^2\left(\frac{x}{2}\right)\right)}{1+\tan^2\left(\frac{x}{2}\right)\left(\right)}\right)}}dx$
helps a bit IMO
flat frigateBOT
ƒ(Why am. I here)=I don't know
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glass field
how
glass field
final halo
Context?
glass field
spice wing
Multiplying both sides with 3√p
dark cargo
is this ctpcm
glass field
is this ctpcm
yes
glass field
is this ctpcm
have u read it?
dark cargo
parts of it
glass field
which parts?
dark cargo
like the first half + the last two chapters
glass field
oh
im currently at like the 14th page
so can u help me in the future incase im confused a bit?
dark cargo
put your questions here somone will help you out
glass field
put your questions here somone will help you out
cuz i think that being explained by a person whose read the book will be easier
dark cargo
im not necessarily always free to help.
dark cargo
also since i assume your prepping for olys you might want to ask stuff like this in the oly server.
glass field
also since i assume your prepping for olys you might want to ask stuff like this...
is that better?
dark cargo
idk it might just be useful if your prepping for olys
also, off topic
ping me in #discussion if you want to ask smt else.
haughty yarrow
how to divide equally among 3 people who paid different amounts?
lapis current
how to divide equally among 3 people who paid different amounts?
you mean , you give more to the person who paid more?
haughty yarrow
you mean , you give more to the person who paid more?
Like person a paid 100, person 2 paid 200, person 3 paid 300
Now We have to split the correct amount according to the person /3
How do we do it?
lapis current
(person 1)/(total money paid) * (money to be paid)
similarly for person 2 and person 3
haughty yarrow
(person 1)/(total money paid) * (money to be paid)
Sorry I don't understand 😔
Imma rephrase it
Let's say A,B,C are friends
A paid 300 that has to be divided by 3
B paid 400 that also has to be divided by 3
C paid 100 that as well has to be divided by 3 at the end of the day
So what's the best method to find out who has to pay how much to whom
safe radishBOT
@haughty yarrow Has your question been resolved?
safe radishBOT
@haughty yarrow Has your question been resolved?
buoyant shadow
Sorry I don't understand 😔
Imma rephrase it
Let's say A,B,C are friends
A paid...
C pays 34 to A, then C pays 133 to B
haughty yarrow
C pays 34 to A, then C pays 133 to B
Pls explain
buoyant shadow
800/3 is 266
C pays 166, and the other take from it
i can;t explain it
there's nothing interesting happening
in real life you wouldn't try to track who pays to whom, you would take money from people who owe it, and then people who are owed woult take money from this pile
safe radishBOT
@haughty yarrow Has your question been resolved?
haughty yarrow
800/3 is 266
But this method isn't the most efficient one
So r u saying there isn't a better method than this?
buoyant shadow
i don't understand what you're talking about
safe radishBOT
@haughty yarrow Has your question been resolved?
safe radishBOT
haughty yarrow
i don't understand what you're talking about
Nah ur good lol i was just thinking too much
sacred wagon
?
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@sacred wagon Has your question been resolved?
sacred wagon
.close
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white yew
can you please check over my work tell me if my answer is correct?
lean otter
yeah u good
white yew
.close
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wheat stag
How do I do this
safe radishBOT
How do I do this
wheat stag
I don’t know how I would solve this, I’m stumped
prisma karma
How do I do this
firstly can you solve f(u)=(1+sqrt 2)/2?
wheat stag
What is u
prisma karma
So u mean if f(x) but a different x equals the surd fraction
yeah
robust forum
you can see under which values of x - f(x)=(1+sqrt(2))/2, then state that the said value is equal to x^2-4 and solve for x
robust ocean
How to take the derivative of this
junior smelt
(that handwriting 
)
robust ocean
Sorry about that
lean otter
How to take the derivative of this
theyre all numbers?
the derivative is 0
wheres the variable
lean otter
WHY ARE U EXPLAINING PASCALS TRIANGLE
Just do the product rule twice
they both take the same time to do tbh
was v’ given or did u have to work it out bcs it looks wrong ngl
might just be me seeing things
wait nvm i was reading it as 60s
all good
u done killed her off
robust ocean
.close
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frigid ocean
How would I answer if the CFG is regular?
safe radishBOT
How would I answer if the CFG is regular?
placid oak
try write a regular expression for it
ah, actually, this will always generate at least 1 a
frigid ocean
Ah okay, so that’s sort of the thought process. You just try and write a regular expression?
frigid ocean
Okay, I wasn’t sure if there were any smart methods you could use to see directly this can be
placid oak
where the first + matches 1 or more of the character
placid oak
Okay, I wasn’t sure if there were any smart methods you could use to see directl...
another way is to find another language such that intersecting it with this given language is non-regular
or any other closure properties of regular languages
just try reduce it to a known non-regular language
frigid ocean
just try reduce it to a known non-regular language
Reduce it to a known nonregular language? I’m not sure I follow?
placid oak
as in, you know regular languages are closed under intersecction
so you can show that a language X is nonregular by intersecting it with a regular language Y, and showing that X n Y is non-regular
or with any other operation that regular languages are closed under
whether this is helpful or not will depend heavily on the given language
frigid ocean
Ahh, okay thanks I will go watch a video upon this cause I don’t remember intersecting languages, but it sounds needy
placid oak
I had an example somewhere
frigid ocean
What do you reckon? Is it easier to just try and write a regular expression and come to a conclusion that way
placid oak
maybe I can dig it up
placid oak
What do you reckon? Is it easier to just try and write a regular expression and ...
yeah, for simpler languages, trying a regex is easier
frigid ocean
maybe I can dig it up
Yes, that would be nice if it’s not too much of a hassle
frigid ocean
How would I answer if the CFG is regular?
But isn’t it also because you can infinitely go between a+ and then the terminal plus and back to A and you can keep doing this, which you can’t describe using regular language or am I completely wrong?😂
placid oak
A is always on the left of the +
frigid ocean
Oh yes, I see
placid oak
so the language consists of a non-empty string of as followed by a (possibly-empty) string of +s
actually this feels like you should be able to construct a DFA for it now
placid oak
(NFA, but same thing)
yeah, this language doesn't really require "counting" per se, so it feels like it should be regular
frigid ocean
So it’s because the P production has the non-terminal A as a left recursive that it will appear on the left side, right?
placid oak
yeah
frigid ocean
And so it would just be a+(+)+
frigid ocean
Like one or more a followed by one or more +
Ohhh Tessa
Because it also derives epsilon
P
placid oak
yeah
placid oak
kind of annoying that they made + an alphabet symbol as well 😅
but yeah, that regex works
I just forgot what symbols were valid regex characters
frigid ocean
Yeah, exactly when I wrote that one above as well I was like that looks weird😭😭
a+(+*)
Would that be valid?
a++*
placid oak
if I were writing it on paper, I would just underline the alphabet + or something
make it clear that it's a different symbol
frigid ocean
Even this? It’s just weird when the plus is now an alphabet symbol
Yeah, I agree
I will do that as well
How would you use the plus symbol in normal regex?
How does it know that it’s the symbol and not the one or more occurrences?
placid oak
if you mean using them as in on a computer, you can escape characters with a backslash
placid oak
a+\+*
frigid ocean
Wait, my backslash disappeared
placid oak
yeah, backslash is also a control character in markdown
so you need to escape the backslash in plain text on discord
i.e. double backslash
frigid ocean
😂😭gotcha it’s just hard doing backticks on an iPad
frigid ocean
Yeah, makes sense. I just thought it was easier to read, but I see.
Anyway, thank you again for helping♥️
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gleaming oriole
what is a null hypothesis?
safe radishBOT
what is a null hypothesis?
gleaming oriole
"The null hypothesis in statistics states that there is no difference between groups or no relationship between variables."
but what does that actually mean
in a problem like,,
"A computer company claims that the lifespan of its batteries is 2.7 years. The population standard deviation is 0.85 years. A sample of 25 batteries was tested, and their mean lifespan was 3.1 years. Using a 95% confidence level, determine if the company's claim is correct."
how would i use the concept?
safe radishBOT
@gleaming oriole Has your question been resolved?
gleaming oriole
<@&286206848099549185>
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@gleaming oriole Has your question been resolved?
little glacier
diophantine equations: is there a more efficient way to calculate this?
little glacier
this is part of a puzzle game i play called KTaNE
the context isnt too important, but what i want is to find the most efficient way to calculate those 4 equations
and i believe that matrices are what can be used, the problem being, i dont know how matrices work or how to rephrase an equation to be a matrix multiplication problem.
more context: https://ktane.timwi.de/HTML/Diophantine Equations.html
my best guess would be to have this matrix
but when evaluating it with an example
it does not output the same
this setup outputs 3/4 correct ones, but fails at the last
OG MT GOSH
THATS GENIUS
how do i close
.close
sterile egret
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sterile egret
5 as the minimum but because of it being a “corner” it doesn’t qualify
light shoal
it does qualify, doesn't it?
sterile egret
We’ve tried it beforehand and it hasn’t worked, we assumed it was because technically the slopes before and after don’t follow the rule
light shoal
there's no "hollow circle" at the point (5,0), so i assume that point is included in the graph
it would be both a local minimum and a global minimum
the real question is how did you get 4.99 for the maximum?
and what is the actual value of the function at x=0? it isn't shown in the graph
sterile egret
It’s a hole
light shoal
well then how can you talk about the max or min on the interval [0,8]
if the function is not defined at x=0
in fact it won't even have a global max
sterile egret
Idk man I didn’t make the thing, it’s been really annoying bc it’s contradictory
But wouldn’t the absolute max just be a number incredibly close to 0?
light shoal
so it's telling you that you are wrong if you put 2 and 5 for the second question?
light shoal
But wouldn’t the absolute max just be a number incredibly close to 0?
to 5 you mean?
the supremum would be 5 but there is no actual max
sterile egret
X=0
light shoal
the function never takes on the value 5 but it takes on arbitrarily close values as x approaches 0
sterile egret
Marked it as incorrect :/
light shoal
Marked it as incorrect :/
cursed problem
light shoal
sure, gl
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hazy field
What is the exponential function for my example on the bottom right? Use (0,4) to plug into f(x)=abxto find a, then use your newly found a ANDf(x)=abxAND (1,12) to figure out the final exponential equation.
safe radishBOT
What is the exponential function for my example on the bottom right? Use (0,4) t...
hazy field
obtuse plover
What have u tried
hazy field
I haven’t tried because I’m stuck on where I’m inputting the numbers
It gives the formula
But I’m not sure how to input the numbers into the formula to find my answer
Like where I plug in (0,4)
hazy field
Yes
hazy field
Y=ab^0?
obtuse plover
Yes, but we also know the value of y
hazy field
yes it would be 4
obtuse plover
Right, so what’s the equation
hazy field
4=ab^0?
hazy field
4=ab
hazy field
I’m not sure
obtuse plover
Any number to the power of 0 is 1
obtuse plover
Yes
So now u can put that in our original equation
What’s our new original equation
hazy field
12=4b^1
obtuse plover
Ok now what
hazy field
if b^0 is 1 what is b^1
hazy field
1331
proud belfry
if b^0 is 1 what is b^1
if b^0=1 then b^1 is B
hazy field
121
obtuse plover
And then what’s 11^1
hazy field
just 11
obtuse plover
Yea
hazy field
Okay
obtuse plover
Any number to power 1 is itself
Did u see the pattern btw
11^3 = 1331
1331/11 = 11^2
hazy field
Yes
hazy field
so 3=b?
obtuse plover
Yea
hazy field
11/11 = 11^0
yes I just was confused with the “b”
Okay thank you very much
Danimal profile is cool
hazy field
😂
obtuse plover
Appreciate it
hazy field
peacw
obtuse plover
Not many people recognize it
hazy field
✌️
obtuse plover
Pce
obtuse plover
Lol
U know gogurt
U remember those
Gogurt was peak
Except when it splattered all over u
obtuse plover
Bro r u early gen z
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robust ocean
What did I do wrong
safe radishBOT
What did I do wrong
cyan monolith
the second derivative is less than 0 for concave downards
robust ocean
Wdym
cyan monolith
f''(x)<0 meanwhile the interval you have checked for is the first derivative
take the derivative again and then check the interval where its negative that will give concavity
cyan monolith
no first derivative gives you increasing and decreasing tendency lol
robust ocean
What’s is wrong with me
cyan monolith
its fine i made mistakes like this as well XD
robust ocean
Thanks man
cyan monolith
no probs
robust ocean
.close
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lean otter
What "level" of probability do i need to tackle this question?
safe radishBOT
What "level" of probability do i need to tackle this question?
old chasm
I think the bare minimum is combi
like, you can do a random walk on graph too but I don't think you need to go that far
I have not solved this so I might not be like... know what you really need. But I think it is combi. You want to solve the equation x + y = 7 (well, you have to do 7 hops) where you want to count how many solution y is 1 or something ...
but with ordered
I don't know...
dreamy elk
Another way is considering different orderings of numbers 1 through 7, like (1,3,2,5,4,6,7). How many right and left hops does the rabbit do in this ordering (you can read it as rabbit starts as 1, then hops to 3 , then to 2 and so on)?. Then how would a ordering representing only one left hop look like?
old chasm
My train of thought at first is like, you have to do 7 hops to reach all the stones. Let x be the number of right hop and y be the number of left hop. We want to find the non-negative integer solution for x + y = 7
the order does not matter... but why I think this would overestimate :/
lean otter
I think the bare minimum is combi
well i do know combinatorics
old chasm
and counting number of that solution will yields the probability
well will yields you two number to make probability
lean otter
My train of thought at first is like, you have to do 7 hops to reach all the sto...
dont you have to do 6 hops ?
1 to 2
2 to 3
3 to 4
4 to 5
5 to 6
6 to 7
lean otter
the order does not matter... but why I think this would overestimate :/
so youre saying x + y = 6
i am a bit dull in probability rn so correct me if i am wrong, but in our case, y MUST be 1 right?
old chasm
yes...
lean otter
i think i need to revise probability
old chasm
but that would oversimplified the positional-wise
like RRLRRR would be the same as RRRRRL
lean otter
is this a hard question?
lean otter
Another way is considering different orderings of numbers 1 through 7, like (1,3...
i did read this
dreamy elk
Depends on the perspective you want to give it, but then again so are most combinatoric problems.
lean otter
Depends on the perspective you want to give it, but then again so are most combi...
youre right, solving probability after a lot of time
dreamy elk
so 6! total ways
That's the amount of total orderings, since 1 is always 'locked on' the first position.
lean otter
That's the amount of total orderings, since 1 is always 'locked on' the first po...
yes that is what i meant
old chasm
you can't really do left turn on the first one
dreamy elk
Now we want amount orderings representing only one left hop.
lean otter
i was thinking, for just one left hop i would do all hops - all right hops
but i am sure it is VERY wrong
includes more than one left hop
dreamy elk
Yes, that's the problem, you also count 2, 3, etc. left hops doing that.
We can consider some ordering, then we can read from left to right. For each number, we look at the next one. If the next is higher than the current, then the rabbit made a right hop, else it made a left hop.
For instance, in (1,3,2,4,6,5,7) we begin on 1:
- 1, next is 3, right hop
- 3, next 2, left hop
- 2, next 4, right hop,
And so on, there would be 4 right hops and 2 left hops in this case.
lean otter
if we make a left hop on 3, how do we reach 2..