the answer would be just negative root10/10
#help-0
lilac jolt
yes!
silk lintel
hurray
i like to remember the ASTC rule by giving it a easy to remember acronoym
like all stations to central
but u do u
lilac jolt
so in every quadrant, there is a cos, sin and tan?
silk lintel
if we were to go back to the qn u tpyed wrong, where it was cosx>0, we know tan is postive and cos is postive and this will only work if its in the first quad, since both is postive, where the other 3 quad only one of them can be postive !
silk lintel
so in every quadrant, there is a cos, sin and tan?
yes
this rule jjust lets us know which of the cos, sin or tan is postive in which quad
ALL in first quad = ALL of them r postive
lilac jolt
idk why our teacher never taught us that
silk lintel
SIN in second = only sin is postive, so if u want to find cos or tan in the second quad itll be negative
silk lintel
idk why our teacher never taught us that
umm now u know!
lilac jolt
thanks to you!
silk lintel
no worries!
lilac jolt
can you give me a problem similar to this one and ill try to solve it? idk what these problems are called
silk lintel
SIN in second = only sin is postive, so if u want to find cos or tan in the seco...
so for ur types of qn weve been doing, u can find sin/cos/tan via sohcahtoa anf apply if its postive or negative by finding out what quadrants they r
and thats how ill get the answerr
silk lintel
can you give me a problem similar to this one and ill try to solve it? idk what ...
um i dont know what theyre called either
uhhh
if cosx=4/5 and sinx<0, find tanx
silk lintel
uhhh
it is in the 4th quad
altho mayve check over the 9/20 part
maybe theres been an algebraic mistake
this is my solution, i hope it makes sense
silk lintel
apologies for the handwriting im drawing with my finger
silk lintel
yeah -3/4!! just got it
hurray
lilac jolt
how do i know which one to use?
silk lintel
i used the identity instead of the right triangle
its okay! the more practice u do the more it’ll come naturally and you’ll avoid doing silly mistakes
silk lintel
how do i know which one to use?
know what to use?
lilac jolt
know what to use?
the sin²x + cos²x = 1 or the soh cah toa
silk lintel
for these types of questions, soh cah toa should work for all
personally if u dont want to get confused i would suggest just using soh cah toa all the time, so itll be consistent but probably quicker to do?
but its up to u
soh cah toa might be easier tho if u come across like a cot or sec or cosec?
this one u can also solve it with soh cah toa
but thats js me, do whatever ur more comforttable with
is there anymore last min qns? i will be sleeping quite soon now
sorry for ping @lilac jolt
lilac jolt
i dont mind!!
lilac jolt
personally if u dont want to get confused i would suggest just using soh cah toa...
alright
silk lintel
do u have any last min qns?
lilac jolt
does the soh cah toa progress make sense?
yes, and way easier
silk lintel
does the soh cah toa progress make sense?
as long as u know how to find the quadrants via ASTC and then apply soh cah toa and pythagrous depedning onthe qn u should get the answer, regardless if its finding cos sin tan or cot( same as 1/tan) sec(same as 1/cos) or cosec (same as 1/sin) just flip the fractions when needed
lilac jolt
find the exact value of $\cos\frac{11\pi}{6}$
ocean sealBOT
sterling
lilac jolt
iirc we use the unit circle
silk lintel
what quadrant do u think cos11pi/6 is
silk lintel
iirc we use the unit circle
mhm
lilac jolt
4
silk lintel
are you aware of like these rules with the unit circle, like first quad is angle X, second quad is pi-X, third pi+X, fourth 2pi-X
ill make this quick bc i really need to sleep (sorry!!)
lilac jolt
$\tan\frac{13\pi}{4}$
ocean sealBOT
sterling
silk lintel
are you aware of like these rules with the unit circle, like first quad is angle...
but basically X is 30 degrees or pi/6,
silk lintel
so cos11pi/6 is the same as cospi/6
so u can just cospi/6 with ur calculator and itll give exact
lilac jolt
but i get it now!!
silk lintel
it makes sense?
lilac jolt
yes, ive actually heard of it
you can go to sleep now, you've helped me plenty 😁😁
thank you!!!
silk lintel
lilac jolt
yes, ive actually heard of it
i didnt realize until u explained
silk lintel
i didnt realize until u explained
oh cool!!
one other thing to note
if u like tan(angle) it’ll be the same as tan(angle + 2pi)
works with cos and sin too
silk lintel
**sterling**
i like to convert this to degrees, this is 585 degrees, but if u minus/plus 360 degrees itll give the same answer
so we can minus 360 degrees
lilac jolt
minus, because?
silk lintel
and its the same as tan225 or tan5pi/4
silk lintel
minus, because?
when u plus/minus 360 degrees/2pi, when u tan/cos/sin itll give the same thing
bc like
one full rotation around the unit circle is 360degrees/2pi
wait
lets say our angle starts with the blue dot, then we go a 2pi rotation
the purple dot will technically lie in the same place as the blue dot
thus they are equal
silk lintel
if we go backwards, the pink dot will still lie in the same place as the blue/purple dot
the position, angle itll be the same
thus why if u have an angle and u like sin/cos/tan it,
if u sin/cos/tan that angle +/- 360 degrees itll sitll give the same answer
lilac jolt
mhmm
silk lintel
**sterling**
i personally find tan585 quite ugly so i can like “simply” or make it look nicer by doing 585-360 = 225, as tan225 will be the same as tan585
225 is in the 3rd quad
silk lintel
apply this, pi + angle
225 = 180 + angle, therefore the angle is 45
so u can tan45, and itll be positive too (since in 3rd quad where only tan is positive)
tan45=1
lilac jolt
mhm!!
silk lintel
does it sorta make sense? (sorry im rushing)
lilac jolt
yes!!
i think i can do it now, ill just check with my calculator if i got the right answer
thank you!!
silk lintel
if u try go 585 degrees around the unit circle
you’ll see u do one full rotation (360 degrees) then another 225 degrees
to get at the final spot
ie, the spot for 225 and 585 is the same so thats y i can tan225
silk lintel
thank you!!
ur welcome!
silk lintel
as long as u know how to find the quadrants via ASTC and then apply soh cah toa ...
summary 1
silk lintel
summary 2, these qns, try to simply the angle if possible it might make it look less intimidating (eg 585 degrees to 225 degrees), figure which quad its in and apply the rules from photo to find the angle and u can just sin/cos/tan that angle, then apply if its negative/postive if needed depending on what quad and which trig u used!
hope it makes sense and goodluck!
i shall farewell
lone heartBOT
@lilac jolt Has your question been resolved?
alpine sable
answer is 3 *2 * (9-2)!
lone heartBOT
answer is 3 *2 * (9-2)!
alpine sable
I dont understand the answer
dusk depot
the question is cut off not sure what it's asking
alpine sable
the question is cut off not sure what it's asking
the question is asking for how many probabilities are there if the pianist begins with 1 classical piece and ends with 1 contemporary piece
3 *2 * (9-2)!
here 3 is for one of the classical piece
2 is for one of the contemporary piece
(9-2)! is for the rest
does the answer also contain probability where the pianist does not begin with classical piece
alpine sable
no
okay 👍 can you explain
im also a little unsure whether to use combination or variation but the answer indicates that variation must be used
okay so order here is important therefore i have to use variation?
thorny root
I think the correct term would be permutation and yes you use permutations in ordered arrangements
alpine sable
i still dont understand why they used 3 * 2 in the answer
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
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frank widget
i still dont understand why they used 3 * 2 in the answer
the last statement is how many ways can he arrange the piano pieces if he begins with a classical piece and ends with a contemporary piece
we have 3 classical pieces
and 2 contemporary
think of it like a table
alpine sable
the last statement is how many ways can he arrange the piano pieces **if he begi...
does it also include the possibility of it beginning with a contemporary piece instead of classical
frank widget
excuse my artistic skills
also this is nowhere near accurate because
these can pair up like
c1 and o3 or c1 and o2
but its just for visualisation purposes
frank widget
does it also include the possibility of it beginning with a contemporary piece i...
no
no it doesnt lol
simply put
alpine sable
hmm
frank widget
the variation can be
(c1,o1)(c1,o2)(c1,o3)
and same thing for c2 and same thing for c3
thats where (9-2)! comes in
to mitigate that repetition
alpine sable
o is for contemporary right? but why are there 3 since there are only 2 contemporary pieces
frank widget
yes
my diagram prior just sucked so i told you the (9-2)! one
but great you understand now right?
alpine sable
but i dont understand how the answer indicates that classical begins
frank widget
well what does this table indicate?
alpine sable
the pairing of each classical and contemporary
alpine sable
couldnt it begins with romantic piece then the pairing of CO then the rest
frank widget
couldnt it begins with romantic piece then the pairing of CO then the rest
no which is why we're doing (9-2)!
you have a total of 9 pieces
for every piece you're going to have two pieces which will compose the end and the beginning
which is why we're subtracting 2
nvm thats not your question im must mansplaining
sorry
frank widget
but i dont understand how the answer indicates that classical begins
the diagram suggests the possible pairs right
alpine sable
the diagram suggests the possible pairs right
yes
alpine sable
like beginning with the contemporary then ending with classical?
frank widget
so how would you really know whether or not a composition begins with classical?
frank widget
like beginning with the contemporary then ending with classical?
yea
why couldnt it be reversed right?
alpine sable
yes
frank widget
i can write c1o1 as o1c1
alpine sable
but the reversed version has the same amount of posibility as the normal one
frank widget
exactly
wait lemme rewind rq
is your question about probability or just how we know whether or not the composition begins with classical?
alpine sable
is your question about probability or just how we know whether or not the compos...
i understand that whether it begins eith clasical of contemporary it has the same amount of possibilities but i dont understand why the paring of classical and contemporary cant be in the middle
alpine sable
so with this answer we can calculate the possibilities of the recital beginning with clasical or contemporary?
frank widget
we're just generating the number of possibilities all these pieces can be arranged together where one composition isn't the same as the other
frank widget
so with this answer we can calculate the possibilities of the recital beginning ...
you'd have to have a program that generates that, with the calculation we just derived we're actually just looked at the different variation where out of the 3x2 ending and beginning pairs, there are different contents on the inside
alpine sable
you'd have to have a program that generates that, with the calculation we just d...
what do you mean by different contents?
alpine sable
yes
frank widget
and then you're multiplying the 6 ways into the rest of the ways you can order the entire ensemble
where, each composition is different from the others and not equal to any other
lone heartBOT
frank widget
alright i get it now
happy to help
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light bone
Why can’t I simplify from 2000/6 to 1000/3 in this case? Thanks in advance.
cerulean zealot
is answer right?
light bone
is answer right?
If I would use 2000/6, yes. If 1000/3, no.
cerulean zealot
can u show
light bone
Oh bruh I’ve made a mistake, my bad. From 2000/6 simplifies indeed to 1000/3. This times 2 u^1/2 makes it 2000/3 * 6 which makes 4000
.close
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prisma night
How can they use the sum of complex numbers and a complex number as the sides of triangle, like if it was mod then it can be length and side, or the they should have been the vertices but how they used them as sides
cerulean zealot
i think they are using vertice
prisma night
i think they are using vertice
How would I know which vertice is which complex number in the figure
prisma night
i think they are using vertice
And if they using them as the vertices then the sides should mod of difference of constant numbers but it's not like that here
cerulean zealot
consider P as origin(0,0)
hushed locust
the complex numbers represent the sides of the triangle here
prisma night
consider P as origin(0,0)
Why? It's not given to consider it as origin
hushed locust
if you're familiar at all with vector addition, we can treat complex number addition in the exact same way
prisma night
the complex numbers represent the sides of the triangle here
But in the figure they haven't included mod while representing sides
dusk depot
Why? It's not given to consider it as origin
you can translate vectors anywhere without changing them
hushed locust
the length of the sides is the absolute value/modulus of the complex number and its direction is the argument/angle
lone heartBOT
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obsidian scarab
4 (1 point) Circle the letters of the statements that are true for the implicit form of curve representation.
A. In many cases, the conversion to the explicit form is not possible.
B. Conversion to the explicit form is always possible.
C. Describe by so-called coordinate functions. ´
D. we make the function in y = f(x) form.
E. A closed shape can be created.
obsidian scarab
A- True
B- False
C- True
D- False
E- True
is this correct, or there are some questions i should think about again
lone heartBOT
@obsidian scarab Has your question been resolved?
obsidian scarab
<@&286206848099549185>
i don't think these are hard questions, is there something that i wrote that needs to be clarified?
lone heartBOT
@obsidian scarab Has your question been resolved?
lone heartBOT
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novel crystal
So for 3b, I know how to construct an orthonormal basis using the G-S algorithm. My question is what do I use for span(S) in this context? Is it something like span(S)={a0+a1x+a2x^2 | a0,a1,a3 in R}?
vale crag
they do tell you what S is yes
novel crystal
Okay but i'm asking if I'[m constructing the spanning set for S correctly
vale crag
yes it's correct
it's not like you need to write it out though
you just need S itself to perform G-S
novel crystal
oh okay so itd be like f1=1, f2=x, and f3=x^2 for the original basis? and then just use those elements for the GS process?
vale crag
yes
lone heartBOT
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umbral arrow
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hard oasis
what’d you come up with
umbral arrow
what’d you come up with
i think i need to expand aTx = b?
vale crag
#help-39 message asked you a few questions before you left earlier
umbral arrow
what does it mean for x and y to be in the hyperplane?
what does it mean for (1-t)x + ty to be in the hyperplace ?
vale crag
yes these two
umbral arrow
what does it mean for x and y to be in the hyperplane?
what does it mean for (1...
- 2x + y = 3
- ???
vale crag
I meant in general, not for the specific 2D thing I talked about
you're looking for a general proof yes?
umbral arrow
ye
vale crag
look how the hyperplane is defined
what's the condition for something to be in that set
umbral arrow
x, y in R^n and for all a in [0,1 ] ax + (1-a)y in Rn
vale crag
that's all I'm asking really
umbral arrow
a^Tx = b
vale crag
yes
vale crag
what does it mean for x and y to be in the hyperplane?
what does it mean for (1...
ok can you answer these questions now ?
using the general defn
umbral arrow
- a^T x = b
- Idk yet how to substitute x and y
i know t is in [0, 1]
and x and y is in R^n where n is random ?
umbral arrow
using the general defn
wait is this not similar to the 2d case?
because i just expand the same formula
And get it in R^n too
Like, I just add one more row
whenever i add a dimension
and it is same thing
ends up in R
for each row
for n times so R^n
example x+2y = 3 case we want to show its in R^2
and we end up [ax1 + (1-a)x2 ; ay1 + (1-a)y2]
vale crag
[ax1 + (1-a)x2 ; ay1 + (1-a)y2] ok that's your convex combination of (x1, y1) and (x2, y2)
what do you want to show about it though ?
umbral arrow
what do you want to show about it though ?
It is in R^2
Which it is
because alpha is in R
vale crag
no
ofc it's in R^2 it's a completely trivial fact
what you want to show is that this convex combination is still in the hyperplane
umbral arrow
Oh shit i mistook the subset sign for equals LMAO
i saw C = R^n
for the convex set definition
hard oasis
will the solution require you constructing an a and an x st the convex combination is equal to aTx?
umbral arrow
what you want to show is that this convex combination is still **in the hyperpla...
Still satisfies 2x + y = 3?
vale crag
yes
vale crag
what do you get
snow geyser
lone heartBOT
@umbral arrow Has your question been resolved?
umbral arrow
what do you get
Let x, y be in the general hyperplane. This means aTx = b and aTy = b. Test now with ax + (1-a)y. We want to show that this is also equal to b?
vale crag
the problem with your notation is that you have a that means two different things now
umbral arrow
the problem with your notation is that you have `a` that means two different thi...
Let x, y be in the general hyperplane. This means aTx = b and aTy = b. Test now with alphax + (1-alpha)y. We want to show that this is also equal to b?
vale crag
alphax + (1-alpha)y, that's a vector
how do you expect that to ever equal b (which is a real number) ?
umbral arrow
basically, we want to add two rando points in the hyperplane and this addition should be equal to b?
because of the equality
Let x, y be in the general hyperplane. This means aTx = b and aTy = b
vale crag
I'll ask the question again
what does it mean for alphax + (1-alpha)y to be in the hyperplane ?
umbral arrow
must be inside the set {x: aTx = b}
vale crag
yes
hard oasis
platypus could I send you my solution and you just let me know if I’m right or not
vale crag
if you want, dm is open
umbral arrow
Im stuck what to show alphax + (1-alpha)y is equal to hmm
vale crag
@hard oasis I might look at it later though
umbral arrow
Let x, y be in the general hyperplane. This means aTx = b and aTy = b
alpha x + (1-alpha) y
vale crag
must be inside the set {x: aTx = b}
and what does it mean to be inside the set {x : a^Tx = b} ?
umbral arrow
alpha aTx + (1 - alpha) aTy
vale crag
you're already simplifying a ton of stuff but yes
vale crag
$a^T(\alpha x + (1-\alpha)y) = b$
ocean sealBOT
aPlatypus
umbral arrow
Wait is that it
vale crag
yes it's not a hard question
vale crag
it means what it means, any convex combo of two elements of the hyperplane stays in the hyperplane
umbral arrow
it means what it means, any convex combo of two elements of the hyperplane stays...
is the alphax + (1-alpha)y basically like adding two elements of the hyper plane?
the first element alphax
second (1-alpha)y?
vale crag
is the alphax + (1-alpha)y basically like adding two elements of the hyper plane...
alpha x + (1-alpha) y is some random element on the line segment linking x and y
umbral arrow
you know what i wont bother asking
i'll just write the theorem down
definition, theorem whatever
vale crag
"if you draw a line between two elements in the set, then the whole line stays in the set"
umbral arrow
yeah thats obvious
vale crag
that's the more geometric way of understanding convexity
umbral arrow
the problem is when they give you a 360 dimensiuonal hypeplane
vale crag
well just imagine it's a line in 360 dimensional space now
there's no way of really visualizing that obviously
but using the usual terminology for low dimensional spaces helps a bit better understand what's going on
even when you work with 42 dimensional crap
umbral arrow
Ohhh wait i think i get the solution now
since we got it to be eequal b
basically ax + (1-a)y = b right
and we want to show thats in the hyperplane
but we got b
which is the same as aTx and aTy?
so is is?
vale crag
basically ax + (1-a)y = b right
you still forgot the a^T in front
but that's the rough idea yes
you know a^Tx = b and a^Ty = b (x and y are in the hyperplane)
and that helps you show that a^T(alpha x + (1- alpha)y) is also b
which means that alpha x + (1- alpha)y is in the hyperplane
lunar dragon
i need to find 2 different equations that model the path of a ball. one in feet and one in yards. its a writen question, so the information is: max of 12 yards in height reached by the ball. 52 yards from point of origin/where the ball started. goal post is 45 yards from the point of origin.
lunar dragon
the vertex is (26,12)
but i am unsure what the A value for an equation in vertex form would be
<@&286206848099549185>
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lunar dragon
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subtle delta
you are given the y value of the vertex which you've found
what else do you know
"max of 12 yards in height reached by the ball. 52 yards from point of origin/where the ball started."
this wording is very weird
does it mean that the max is achieved 52 yards from the point of origin?
if it does your vertex should be (52,12)
not (26,12)
lunar dragon
no, it lands at 52 yards
subtle delta
ok then your vertex is correct
what do you know about when the ball touches the ground then
it touches the ground at two points
which two points?
lunar dragon
(0,0) and (52,0)
subtle delta
ok and are you familiar with x-intercept form
specifically speaking
y = a(x-r)(x-s)
where r,s are the two roots of the quadratic
in this case what is r and s
lunar dragon
no i have been trying to convert it into vertex form
lunar dragon
no, we were not taught that one in my class
subtle delta
in vertex form
how do you express everything
you know the vertex
so how woudl you express your equation
(vertex form is y = a(x-h)^2 + k)
lunar dragon
0=a(0-26)^2 +12
subtle delta
yes you skipped a step but thats precisely what you do to solve for a
y = a(x-26)^2 + 12
then sub in either (0,0) or (52,0)
to find a
and then you are finished
subtle delta
12 is not a like term with a(0-26)^2
lunar dragon
oh
subtle delta
write what as -3?
lunar dragon
sorry, with -3 at the top, or with the neagtive beside the line
subtle delta
the equation would be y = (-3/169)(x-26)^2 + 12
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fervent spire
I know the radius of the base, but I can't seem to wrap my way in getting to AP, is it a triangle and do I use pythagorean, it says surface so that's make ir hard
lone heartBOT
I know the radius of the base, but I can't seem to wrap my way in getting to AP,...
@fervent spire Has your question been resolved?
fervent spire
So like a triangle?
tardy stag
yeah
wintry pewter
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hushed locust
are you more likely to get a nice view on the side of a steep cliff or a gentle hill?
wintry pewter
erm
ive never gone rock climbing so i wouldnt know
a gentle hill i guess
so B?
hushed locust
let's say you don't want to see the side of the hill itself. for which one would you see less of the hill (and therefore, more of the surrounding countryside)?
hushed locust
consider that how much the hill takes of your vision is proportional to how far away the bottom of the hill is
wintry pewter
but if you follow along either path wont you end up at the same elevation point after some time?
or is it because one is higher than the other?
wintry pewter
ok so its path A then for part b?
hushed locust
now that i say that, i think they are going for something different than what i was thinking of
on one path, you have the hill to your left and right, whereas on the other path, you have open space to your left and right
hushed locust
i think that makes sense
wintry pewter
but for C i have no idea
idk how streams flow 😭
probably A cuz its more steep
id assume water tends to flow down in a roughly perpendicular direction
hushed locust
water tends to flow downwards. so if you have more hill on either side it will concentrate towards the middle and form a stream, whereas if you have open air on either side, it will scatter and not form a stream there
wintry pewter
so A
hushed locust
yes
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trim solstice
anyone know how?
lone heartBOT
anyone know how?
trim solstice
answer is there on the mark scheme but doesnt show how it got there
lofty gorge
use the scale to figure out the real diameter of the cell (physically measure the length of the scale), and then use the formula for the volume of a sphere V = (4/3)*pi*r^3, where r is the radius
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@trim solstice Has your question been resolved?
trim solstice
use the scale to figure out the real diameter of the cell (physically measure th...
on my laptop the image is 7 cm across and the scale is 1.5 cm across
i did all that before
and is still the wrong answer
lone heartBOT
lofty gorge
on my laptop the image is 7 cm across and the scale is 1.5 cm across
was this question originally supposed to be on paper?
I have no idea how screens work in terms of scaling
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tardy venture
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@tardy venture Has your question been resolved?
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@tardy venture Has your question been resolved?
scarlet root
Looks good to me, maybe just mention you are using similar triangles for clarity
scarlet root
yhea sure bro
tardy venture
Yeah Ik my handwriting sucks
tardy venture
Ty for help
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@tardy venture Has your question been resolved?
rare nimbus
Hello, good morning, anyone help me understand the Weierstrass Function and its relation in the time domain and frequency domain, I don't have any clue about it but I need to understand it for my curiosity, I'm serious about it and am a speedy learner, could someone tell me sources to consume and how to visualize using Mathematica or any other tool!
rare nimbus
https://en.m.wikipedia.org/wiki/Weierstrass_function
saw it and a couple of yt videos but yet didn't get it and it's relation to the time domain and freq domain!
tacit arch
Because its definition has nothing to do with time or frequency
Functions are agnostic to units
rare nimbus
Functions are agnostic to units
okk so can be applied to any context, whether time, frequency, or other domains.
tacit arch
Sure
rare nimbus
when we talk about applying the Weierstrass function in certain contexts, such as signal processing, wave propagation
In signal processing, the time domain -as a signal evolving over time- and transformed it into the frequency domain via a fourier or laplace transform
This is what I mainly thinking of and trying to visualize but I'm missing the core pieces of information on how to do it exactly and how would I modify the context of using it, if u have some materials or sources I can rely on to find some understanding on how to use it I would appreciate it.
what I'm trying to do is I'm a trader in the foreign exchange market who has a weird theory about the market and its fractality and its relation to the WF they share a lot of similarities and i don't mainly believe in coincidences.
thx in advance
lone heartBOT
@rare nimbus Has your question been resolved?
rare nimbus
@tacit arch if u kindly have anything to provide :)
going to sleep rn i will check the channel when i wake up 
lone heartBOT
@rare nimbus Has your question been resolved?
lone heartBOT
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cedar juniper
,rotate
ocean sealBOT
feral trellis
I could rewrite this as x³-x² but what next
cedar juniper
$x^2(x-1) = 0$ Could you solve this?
ocean sealBOT
Adarsh
feral trellis
x³-x²=0
cedar juniper
I mean find the x values
feral trellis
I mean find the x values
Is that even possible
Or we're to just substitute them with numbers I can think of, to then graph them.
Oh wait sorry I'm too late to understand
1³-1²=0
cedar juniper
If $A*B = 0$ then $A = 0$ or $B = 0$ in our case $x^2 = 0$ or $x - 1 = 0 $
feral trellis
If $A*B = 0$ then $A = 0$ or $B = 0$ in our case $x^2 = 0$ or $x - 1 = 0 $
hold on what type of rule is that
ocean sealBOT
Adarsh
feral trellis
yeah but I first thought that x³-x²=0 could mean x=1
but I don't understand why x²(x-1) where x²=0, when we're just multiply x by itself
cedar juniper
Yup
feral trellis
I mean technically it is still correct...
cedar juniper
Yes
feral trellis
how do we get y?
cedar juniper
Y = 0 for both?
cedar juniper
,w plot y = x^2
ocean sealBOT
cedar juniper
This graph is tangent at x = 0
feral trellis
what other words could you use for tangent
ocean sealBOT
ocean sealBOT
cedar juniper
This is tangent at x = 0 again
feral trellis
Oh so tangent is just the point or the center of the graph?
pale pawn
**Adarsh**
1?
feral trellis
I do not have an idea what touches, but not intersecting mean
cedar juniper
Let me think of an example 1 sec
feral trellis
How does the lines touch
because right now I'm thinking that a straight line itself could be a tangent itself
cedar juniper
,w plot (x-1)^2
ocean sealBOT
cedar juniper
,w plot (x-1)^2
When is the y value 0 for this function? @feral trellis
feral trellis
1
cedar juniper
Take a value of x just before 1
feral trellis
0
cedar juniper
Say 0.99
feral trellis
oh
cedar juniper
Is the y value positive or negative
feral trellis
Positive
feral trellis
Positive
cedar juniper
Is it positive or negative
Okay
So it just touches the y axis and then goes back up?
It doesn't go through the y axis
feral trellis
Oh so when y=0, is the tangent line?
cedar juniper
,w plot y = x
ocean sealBOT
feral trellis
,w plot x³
ocean sealBOT
feral trellis
this isn't tangent I believe?
cedar juniper
It is not tangent
feral trellis
Oh, so the tangent is when the lines have the same value of sign intersecting at x?
like + value to x?
feral trellis
oh
ocean sealBOT
cedar juniper
This is also tangent at x = -1
alpine sable
hey guys im only good at algebra basics and i wanna learn math
alpine sable
im new here hoping for help
alpine sable
<#488120190538743810>
alright thank you
ocean sealBOT
ocean sealBOT
feral trellis
Is 1, not a tangent?
lone heartBOT
lone heartBOT
Available help channel!
halcyon marten
lone heartBOT
halcyon marten
I just don’t understand what I’ve done wrong and what to put as the last proof
lone heartBOT
@halcyon marten Has your question been resolved?
lone heartBOT
@halcyon marten Has your question been resolved?
alpine sable
I just don’t understand what I’ve done wrong and what to put as the last proof
Start by describing the question
halcyon marten
Ok so here
Are the insteuxtions
It’s all right except the last line and idk what symbol I’m missing
alpine sable
Ping helpers since I don't know this topic 
patent hawk
um ok
blissful chasm
Are the insteuxtions
what topic is this 💀
halcyon marten
It’s logic
blissful chasm
i see
patent hawk
its logic
halcyon marten
can someone help me
lone heartBOT
@halcyon marten Has your question been resolved?
shadow ermine
How do I factorize a expresion I dont understand
lone heartBOT
@halcyon marten Has your question been resolved?
frail stirrup
can someone help me
First time I ve seen to prove through a program, can I see a proof for reference
I might help
alpine sable
try
A ∧ (A → I) : PR
A : ∧E 1
A → I : ∧E 1
I : →E 2,3
(A ∧ (A → I)) → B : PR
B : →E 1,5
cant type some of the symbols so replace
∧ represents logical AND
→ represents logical implication
PR stands for premise
∧E stands for AND elimination (simplification)
→E stands for implication elimination (modus ponens)
frail stirrup
∧ represents logical AND
→ represents logical implication
PR stands for premise
...
For what stands for E 2,3 and E1,5?
halcyon marten
Ok let me try
lone heartBOT
@halcyon marten Has your question been resolved?
analog cave
(statistics question)
I am conducting a research on the feasibility of d-Limonene as solvent in shoe polish compared to commercial shoe polishes, and in it I am going to test the shine quantitatively between two groups with 15 samples each (d-Limonene applied to one group, and commercial applied to the other).
I'm not sure what tests I should use to interpret the results, but I'm leaning on doing a t-test, but I read that that only determines if there is a significant difference between groups, what should I use instead if I want to know which of the means of the groups is greater than the other?
lone heartBOT
(statistics question)
I am conducting a research on the feasibility of d-Limone...
@analog cave Has your question been resolved?
analog cave
<@&286206848099549185>
lone heartBOT
@analog cave Has your question been resolved?
barren bolt
How do you measure shine?
Luminance?
After the treatment
A t-test definitely works here
To determine the bigger one just look at the sample means
If there is a significant difference then the group with the larger sample mean has a larger population mean to significance level alpha
Or I guess it has a 1-P value probability of having a greater population mean
lone heartBOT
@analog cave Has your question been resolved?
wild belfry
Evaluate the Limits
lone heartBOT
Evaluate the Limits
@wild belfry Has your question been resolved?
Available help channel!
edgy merlin
How many topologies are there on a set with 3 elements?
lone heartBOT
How many topologies are there on a set with 3 elements?
somber crest
How many topologies are there on a set with 3 elements?
quite a few actually, but not too many
edgy merlin
I wrote down 29 of them
somber crest
that number sounds right, yeah
edgy merlin
Wikipedia says there are 29
somber crest
yes
edgy merlin
thank you
somber crest
there is no known closed form for the number of topologies on sets of size n
if I remember that right
edgy merlin
I wasn't looking for a formula. I had to find all of them and I just wanted to check if I found enough
sturdy bear
hi
sturdy bear
Can i please have some help!! 🙂
alpine sable
hi
sturdy bear
hi
Hello
Well can you check my answers for first page is it
6
24
Then for the table its 1, 2, 6, and 24
alpine sable
its correct
sturdy bear
Then the pattern is the factorial of the number of people (or chairs.) to predict the number of possible photos with 10 people and chairs, it would be 10!???
alpine sable
right
sturdy bear
So 10 people and 10 chairs there would be 3628800 different positions???
alpine sable
yeah
alpine sable
whats ur answ
sturdy bear
I dont get it sorry
alpine sable
there are 6 ways the cleaner would have arranged the label....
alpine sable
ACB
BAC
BCA
CAB
CBA```2/6 for what?
sturdy bear
All 3 names are correct
alpine sable
no
alpine sable
theres only one way (ABC) all name is correct
alpine sable
um no
sturdy bear
How?
alpine sable
how 2?
alpine sable
yeah
sturdy bear
How would you explain why it is impossible to have exactly 2 correct name lzbels
I know why
But idk how to explain it
It is impossible to have exactly two correct name labels because, if two names are placed correctly, the third name must also automatically be placed correctly, meaning all three are correct.
Is this correct?
alpine sable
Yeah
alpine sable
for two either it is correct or not
sturdy bear
Im assuming correct??
alpine sable
wait but what it asking?
alpine sable
u know no. of arrangement of lebels....?
sturdy bear
No i do not
alpine sable
its just like chair seating
sturdy bear
Mhm
alpine sable
n! Ways to arrange n labels....
alpine sable
i think just like we did for 3 label we have to do
sturdy bear
I just dont understand what question is saying though
What are we supposed to write???
alpine sable
you will explore number of CORRECT MATCHES(0,1,2,3,4)
alpine sable
for each
sturdy bear
I get that, but what do i write in the blanks
Do i write whether it’s correct or incorrect?
alpine sable
i think we have to write 0,1,2, to the left and no. of correct mathes to the right corresponding to it
i am not sure
sturdy bear
Ye its confusing me
So lets try it out i guess
It’s fine, you seem busy, ill open another ticket, ty for ur help tho 🙂
.close
lone heartBOT
lone heartBOT
Available help channel!
hexed basin
How
lone heartBOT
How
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
@hexed basin
hexed basin
1
alpine sable
okay
let's try to find the value of a and c
Try to use completing the square for ax^2 + 4x + c
lone heartBOT
@hexed basin Has your question been resolved?
winged isle
@hexed basin
Let’s start with trying to find the vertex
And breaking down the question
We know that k is negative
So the vertex lies under the x axis
And it tells us it opens upwards
So a is positive
If we use the fact that f(-9)=f(3)
And equate them when we sub it in
And you solve for a
You get a = 48/90
So therefore II is invalid
Now
Since we know at -9 and 3 the y values are the same
And because it’s a parabola
If we average the values
We get the x value of vertex
Which is -3
And now you solve for c
And done
lone heartBOT
@hexed basin Has your question been resolved?
final wyvern
how is the answer (a) I just don't get something
lone heartBOT
how is the answer (a) I just don't get something
fresh wedge
how is the answer (a) I just don't get something
Easiest way to remove the root terms from denominator is multiply numerator and denominator with same term
a/√b = a/√b × √b/√b
Like this
final wyvern
wow. lol.. that was simple
yet I could not wrap my head around it before
thanks
.solved
lone heartBOT
lone heartBOT
Available help channel!
urban storm
Hello
alpine sable
hi
'
urban storm
I need help in this
One sec
It's the 8th question
...
Hello @alpine sable u online???
alpine sable
,rotate
ocean sealBOT
alpine sable
circles 9th?
urban storm
Yeahhh
alpine sable
Let ABCD be the trapezium in which AB || CD.
AD = BC (given)
In quadrilaterals you had done a question in which you had to prove angle A = angle B and angle D = angle C.
Refer to that and you'll be able to solve.
urban storm
Oooo okok
Let me try
Ohhh shittt
Sorry my brain not function properly
Thanks a lot 🙏🙏
. Close
.close
lone heartBOT
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Available help channel!
raw jetty
lone heartBOT
raw jetty
ABC is an acute triangle where D and E are on AB and AC, BCDE are cocyclic, prove that the line thats perpendicular to BC and passes trough A (like the height of the triangle with base BC) passes trough the circumcenter of ADE
im not sure what path i should try to look for to prove this
like what should i try to prove? is there anything i should try to find? ect
alpine sable
ok
raw jetty
heres a better image
lone heartBOT
@raw jetty Has your question been resolved?
fickle heath
You should fix the point labels
raw jetty
wdym?
fickle heath
heres a better image
F here is supposed to be A in your problem statement
B and C are swapped
raw jetty
oh yea i havent changed it
fickle heath
and so on
raw jetty
eaugh gimme a sec
here
ive been messing on trying to swap B and C but its not working
weather it just doesent change or everything falls apart D:
fickle heath
raw jetty
yay ty
fickle heath
Well, I have no clue how to solve it, but I can see some angle equalities
raw jetty
ADE=BCE and AED=DBC i found these
lone heartBOT
@raw jetty Has your question been resolved?
raw jetty
sorry gotta go to sleep, gn
midnight nest
no hopital
lone heartBOT
no hopital
gritty bramble
no hopital
valid spire
Tanx/x and sinx/x will be 1 then use l hopital
midnight nest
we cant use it
gritty bramble
$\frac{tanx-sinx}{x^3} + \frac{x^3}{x^3}$
ocean sealBOT
Astar777
valid spire
Holup u need help or complete solution?
gritty bramble
Holup u need help or complete solution?
!nosols, even if they need complete solution
lone heartBOT
Holup u need help or complete solution?
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.
midnight nest
help how to solve it
valid spire
Alr
gritty bramble
**Astar777**
.
mental schooner
Ya
valid spire
Ull be left with x³/x³
mental schooner
Divided = 1
midnight nest
well is anyone gonna help then i dont need just the answer
i need to understand it
mental schooner
Ok
gritty bramble
Sinx/x too
you dont put limits in middle like this
gritty bramble
well is anyone gonna help then i dont need just the answer
first split it $\frac{tanx-sinx}{x^3} + \frac{x^3}{x^3}$
ocean sealBOT
Astar777
gritty bramble
the latter term is just 1
and the first term: $\frac{1}{x^3}\left(\frac{sinx}{cosx}-sinx\right)$
ocean sealBOT
Astar777
valid spire
**Astar777**
Take tanx common
Ull have (1-cosx)tanx/x³
1-cosx can be written as 2sin²x/2
Then use the property
Of tan and sin
I did it this way and got the answer
mental schooner
I did it this way and got the answer
So whats the final?
valid spire
So whats the final?
1.5
valid spire
.close
lone heartBOT
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Available help channel!
sonic sedge
hi
hardy trench
Being introduced to the euler lagrange equations and im told to follow along doing the calculation for an example myself. The example is an atwood machine with a rope of length l, masses m_1 and m_2, and distances from mass to pulley of x_1 and x_2=(l-x_1). I'm a bit lost though since my proccess has given me this:
Where did I go wrong? Did I misunderstand something?
And I have to get this
sonic sedge
dude this is my channel
sonic sedge
.close
lone heartBOT
hardy trench
Being introduced to the euler lagrange equations and im told to follow along doing the calculation for an example myself (the first image). The example is an atwood machine with a rope of length l, masses m_1 and m_2, and distances from mass to pulley of x_1 and x_2=(l-x_1). I'm a bit lost though since my proccess has given me this:
Where did I go wrong? Did I misunderstand something?
lone heartBOT
Available help channel!
torn breach
I am doing a problem on binomial distribution, where n=30, p=0.1 and q=0.9. I need to find P(X is less than or equal to 4) but I don’t know how to calculate with less than or greater than signs. Have a test on this topic tomorrow and I still don’t grasp this.
raven cipher
lone heartBOT
@torn breach Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
junior kernel
if "SELECTION" is coded as 45 and "UNIVERSITY" is coded as 46 then how will "TOPPER" be coded?
(options are: 33, 47, 24, 51)
junior kernel
ive tried but i just cant find a logic for this question
the sum of selection is 102 and university is 162
tardy stag
you could make an argument for all of these
junior kernel
and what is that?
btw, i dont think theres any rigorous way to do this
u just gotta find a random logic that holds
tardy stag
you can literally make up anything
azure needle
I think
lusty token
the sum of selection is 102 and university is 162
what does that mean