like -2-1012
#help-19
keen mirage
gilded shard
so if the x value is -4 how many units is it being translated by
keen mirage
but i only kinda understand that
gilded shard
but i only kinda understand that
the charts or this?
keen mirage
uh yes
gilded shard
well do more charts after this
but for the translation
because its -4 its being moved to the left as thats where negastive numbers are on a graph
so we would say its being translated 4 units left
got that?
keen mirage
oh so the h value determines where it lies on the x axis
gilded shard
correct
keen mirage
ok so the k value should represent the stretch on the x axis right?
gilded shard
no remember you said tyhat was the a value
K value representsd the Y point on the graph
keen mirage
so where it lies only the y axis
keen mirage
so a is the vertical stretch which is 1/2
and k is the y axis so that means its translated 7 units up
gilded shard
correct on which value but because its less then one its compressed
keen mirage
ohhh
gilded shard
0.1-0.9 is compressed
keen mirage
os it has a vertical compress of 1/2
keen mirage
and h is x so it is 4 units left
gilded shard
Correct
keen mirage
compression*
oh okay so a vertical compression of 1/2 or 0.5
gilded shard
either or is correct
keen mirage
is that the answer for 9a
gilded shard
gilded shard
is that the answer for 9a
yes
keen mirage
oh okay so for 9b
gilded shard
try this one now ok
keen mirage
it has a vertical compression of -4
it is translated 2 units right along the x axis
and is translated 1 unit down?
gilded shard
that was good but one was wrong ill explain
gilded shard
it has a vertical compression of -4
this
keen mirage
oh
gilded shard
because its not a decimal or a fraction its still going to be a compression i should have clarified that
so anyuthing like 0.whaver is going to be a compression
keen mirage
but if its a whole number its going to be a stretch
gilded shard
but if its a whole number its going to be a stretch
corect
so 4 is still a stretch
also
because its a negative value
remember it flips the porabola making it open down
keen mirage
wait it doesnt open up
gilded shard
no because its a negative A value the porabola opens down
anythign less then 0 opens down and 0+ opens up
gilded shard
yup
keen mirage
and the parabola opens down becuse the a value is negative
keen mirage
yes
are you okay with helping me with this one problem though?
or should i call another helper
gilded shard
i looked at 10 and its a Longer explanation i dont have enough time sorry i have a math exam tommorow morning and im a few questions off being done studying and then i need to sleep
gl on your work tho i hope this helped
keen mirage
oh okay tysm btw
gilded shard
for sure
dense summit
stinky poopoo
gilded shard
pretty sure idk i j jopined this server like 30 mins ago or smthn
gilded shard
😭 what did that guy j say
keen mirage
oh lol ok maybe ill start a new one then idk
odd edgeBOT
glass silo
rahhhh
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lost sky
anyone know the answer?
hardy panther
anyone know the answer?
use substitution
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@lost sky Has your question been resolved?
hardy panther
if i know i would already do it
I can tell you for sure that b > 4sqrt(595)
lost sky
I can tell you for sure that b > 4sqrt(595)
i know this but i dont know exact answer tho
hardy panther
i know this but i dont know exact answer tho
well, me neither
I may be on the cusp though
ok I got it
lost sky
so wut the answer?
hardy panther
dammit
nevermind
it's not integral
I have a typo somewhere
but look here's what I tried to do
,rotate
clever fjordBOT
hardy panther
where w=z^7
oh I got it now
um
I got b=0 :/
and if that were true,
then the factorization would be
$(\sqrt{34}w-\sqrt{70}i)(\sqrt{34}w+\sqrt{70}i)\
=(\sqrt{34}z^7-\sqrt{70}i)(\sqrt{34}z^7+\sqrt{70}i)$
...except then be isnt a positive integer and neither q or r are positive integers
I give up.
sorry
clever fjordBOT
Melvin Eugene Punymier
hardy panther
Fyi: the first thing I tried was doing long division with pq+r and using remainder thrm, but I tapped out since it was getting ugly and I thought I would need to guess-and-check
I got this far just now woth remainder thrm. That's really all the insight I have for this one, sorry
(and b is a multiple of 34)
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warped wharf
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warped wharf
wrong channel pal
static ocean
what channel do i go to
warped wharf
any channel without names
undone basin
can i get help
static ocean
ok thanks
undone basin
post there fast
warped wharf
nova galleon
what do we need to find
undone basin
this point?
warped wharf
what do we need to find
the equation of the tangent
wait i found it
just wanting to see if its correct
warped wharf
yeah just checked it and it seems all correct
low karma
ok well you need to go to a diferent channel
low karma
nice man if you close this channel then i can help Ahnaf
crimson agate
ok well you need to go to a diferent channel
in wihich chanel ?
odd edgeBOT
low karma
@crimson agate what do you need help with
crimson agate
@low karma
low karma
ok dude i actually have to go so if you @ helpers then more people will come to help you, and they will be here soon
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ebon badger
$\int_{0}^{\infty}\frac{\ln\left(\frac{1+x^{11}}{1+x^{5}}\right)}{\left(1+x^{2}\right)\ln x}dx$
clever fjordBOT
$.Night!
frigid canopy
!15m
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cursive field
not entirely sure, but reminds me of the gamma function.
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ancient crow
@frigid canopy can you help me
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<@796939110815629322> can you help me
ancient crow
If I can help, I will
Memorising how to work with fractions or can I understand
Which is best
Like adding fractions
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red ivy
So for my maths project I am attempting to fit a curve to a curved road using the least squares approach. My plan is to take a screenshot of the road from google maps and insert it into GeoGebra and generate co-ordinates . However, I am struggling with how to scale the road accurately. Any suggestions?
odd edgeBOT
So for my maths project I am attempting to fit a curve to a curved road using th...
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harsh gull
how to graph |y|=2|x+3|-5? I know I have to graph one for +y and one for -y but idk what to do after that
mystic saffron
i think the first step is to start making the graph of mod x-3
spice geyser
mod x-3?
mystic saffron
|x-3|
mystic saffron
bruh i mean there are so many methods how u can make it
harsh gull
what does modding even mean
summer cradle
pun pun meant modulus
spice geyser
i got confused because i thought mod |x-3| is looking at the restricted interval (0,|x-3|)
summer cradle
not "modding out" by something
mystic saffron
oh i thought mod and modulus the same thing
spice geyser
pun pun meant modulus
oh i searched it up never knew its called modulus function
frigid canopy
oh i thought mod and modulus the same thing
mod is different IMO
mystic saffron
like i know in higher studies mod is soemthing like 3 lines or smth like that
i mean like the symbol
harsh gull
isnt it casework on x+3>0, x+3<=0, y>0, y<=0
so y=2|x+3|-5 and y=-2|x+3|+5 is wrong? idk what you mean
summer cradle
i think the first step is to start making the graph of mod x-3
i mean i wouldn't have said it like that but i knew what you meant
mystic saffron
yea mb 😭
spice geyser
so y=2|x+3|-5 and y=-2|x+3|+5 is wrong? idk what you mean
can you split it into more cases? what happens when x+3>0 and y>0?
what happens when x+3<=0 and y>0?
etc
harsh gull
is that necessary? I know how to do the transformation
spice geyser
is that necessary? I know how to do the transformation
it is necessary as there is two absolute value you have to consider, which is pretty tedious work i know
harsh gull
damn alr
spice geyser
is that necessary? I know how to do the transformation
unless you know how to draw the function y=2|x+3|-5
harsh gull
yeah I do
spice geyser
unless you know how to draw the function y=2|x+3|-5
just note carefully y>0, you don't want to plot any points where y<0 for this case
spice geyser
unless you know how to draw the function y=2|x+3|-5
try to plot this case
harsh gull
try to plot this case
I did both
for y<0 too
but after checking the middle gets cut out for some reason
spice geyser
but after checking the middle gets cut out for some reason
yeah
harsh gull
why though
spice geyser
how to graph |y|=2|x+3|-5? I know I have to graph one for +y and one for -y but ...
plug in x=-3 here
you get |y|=-5
how could a positive value be -5
hence no points plotted
spice geyser
so you would expect (-5.5, -0.5) to be cut out
as those values of x gives a negative value for |y|, absurd!
harsh gull
so the only way to know that you have to cut out a part is just by checking?
spice geyser
so the only way to know that you have to cut out a part is just by checking?
know the region that is being cut out?
harsh gull
yeah
spice geyser
or you can just plot the graph like you did
every step you did in plotting the graph should be corrrect
spice geyser
plug in x=-3 here
this is just a intuitive explanation on why there is a gap
spice geyser
no worries
harsh gull
.close
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ancient crow
@frigid canopy I understood fractions but I doubting myself
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grave sail
There are 17 points on a plane and are connected by lines colored red, blue, and yellow. Prove that there is a monochromatic triangle.
grave sail
Given to me by my middle school math tutor, I believe it involves Ramsey's Theorem
odd edgeBOT
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grave sail
what if all points are collinear?
I forgot to say there are no three points on a straight line
<@&286206848099549185>
is finding the amount of lines and triangles a good stepping stone?
even then i dont even know what to do after
grave sail
i understand,
nova galleon
680
grave sail
i just am absolutely stuck after that point
nova galleon
yeah i am pretty sure it involves ramsey's theorem
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grave sail
<@&286206848099549185>
vivid girder
I don't know what your professor expects you to do / answer given that you are in middle school. One way that may be appropriate for you is possibly to show a coloring for a specific set of points and hand-wavily argue that similar can be done in any set of 17 points fulfilling the conditions given by the problem.
Apparently there are only two of these colorings, in this article the proof for the 17 points and 3 colors is given (your specific question), although I don't know how much of it you can understand.
grave sail
Apparently there are only two of these colorings, in this article the proof for ...
I might take some time to process this
grave sail
Apparently there are only two of these colorings, in this article the proof for ...
In the meantime; do those two colorings have the exact same number of red, green, and blue lines?
vivid girder
There was a misunderstanding. Those two are apparently the only colorings for 16 points where there are no monochromatic triangles (triangles with the same color in all edges.), there are 40 edges of each color, confirming your question. Using these one can prove that for 17 there must be some monochromatic triangles. This is basically done by taking any of these 2 colorings for 16 and placing another point, then proving that there is no way to avoid a monochromatic triangle when connecting this new point to the other 16 points.
grave sail
There was a misunderstanding. Those two are apparently the only colorings for 16...
If so, how can I prove to my tutor that there are only two possible colorings for 16 and no monochromatic triangles are made?
vivid girder
thats what's being explained in text accompanying the colorings in the image I sent. Once again I don't know what your teacher expects from you, does he expect you to know that these 2 colorings for 16 points exist and that they are the only ones, or does he want you to understand why there are only 2 of these?
grave sail
thats what's being explained in text accompanying the colorings in the image I s...
Alright so let me give some backstory I guess
It was a combinatorics class, he was teaching about the pigeonhole principle and stuff
Gave some examples and questions
And then pulled this one right out of nowhere and assigned it as homework
This isn't middle school btw, I'm in a math camp.
grave sail
Alright so let me give some backstory I guess
So, going into this I have no understanding of Ramsey's Theorem and I only understand the PHP.
vivid girder
I see, there's a version of Ramsey's theorem for 2 colors proven using pigeonhole , maybe that's a better starting point, since its result is used on the 3 colors one I presented you with before.
grave sail
I see, there's a version of Ramsey's theorem for 2 colors proven using pigeonhol...
Okayy
The 2 colour case is clear as day for me
Where should I go from here?
vivid girder
I think I somewhat understand the proof for 3 colors. We start with 16 points, and select a vertex $v$ among them
clever fjordBOT
Crystopher
vivid girder
now let's draw some red edges from $v$ to other vertices $w_1,w_2,...,w_m$, in this case let's say that $m=6$
clever fjordBOT
Crystopher
vivid girder
these vertices $w_1,w_2,...,w_6$ are called the 'red neighborhood' of $v$ in the proof.
clever fjordBOT
Crystopher
vivid girder
Now we take these 6 vertices, obviously there cannot be any red edges among them, otherwise some red triangle would form like shown in this image where $v,w_4,w_5$ form a red triangle
clever fjordBOT
Crystopher
vivid girder
This means that edges between $w_1,w_2,...,w_6$ must either be blue or green
clever fjordBOT
Crystopher
vivid girder
This sounds very familiar to Ramsey's Theorem for 2 colors, using that result you may notice something's amiss here
namely that there are 6 vertices and 2 colors to color their complete graph
this is impossible as shown in the case of 2 colors
so there can at most be 5 vertices in the red neighborhood of $v$, that is there are at most the vertices $w_1,w_2,...,w_5$ which have a red edge with $v$.
clever fjordBOT
Crystopher
vivid girder
The same argument can be made for the green and blue neighborhoods of $v$ (they can have at most 5 vertices)
clever fjordBOT
Crystopher
vivid girder
this gives at most 5 + 5 + 5 + 1 = (red neighborhood+green neighborhood+ blue neighborhood + v itself) = 16 vertices for there to be a coloring without a monochromatic triangle.
using pigeonhole maybe you could say that if you have 17 vertices then from any vertex there are at least 6 edges with the same color, and then the subgraph formed by the vertices these connect to would always give a monochromatic triangle, as shown by Ramsey's theorem for 2 colors.
odd edgeBOT
@grave sail Has your question been resolved?
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sonic pollen
really struggling with e
odd edgeBOT
really struggling with e
dawn tiger
it's exactly cos(a - b)
latent quiver
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sonic pollen
there has to be an easier way to do f that what im thinking right? does this not js become an abomination real quick
drowsy root
use trig identities
sonic pollen
yh but surely it become a hugge mess using identities
drowsy root
in particular, double angle formulas
drowsy root
yh but surely it become a hugge mess using identities
no, its makes it simpler
odd edgeBOT
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dusk abyss
Hello, I need some help with this question. Not sure if I'm just being an idiot rn or what but my brain is not mathing, thanks!
dusk abyss
Like, I've done these before but they've been consecutive (like FG+GH instead or something similar) not sure how exactly to go about this one
dusk abyss
yea
lethal pond
furthermore, E,G,F,H are midpoints
so AE = EB
and DG=GC
as vectors
so magnitude and direction
dusk abyss
so it would be EF?
lethal pond
match up
wait
furthermore AE = GC
cuz they're parallel and the midpoints themselves are forming a parallelogram
so FG + AE = FC
now that's not amongst the options
but HD is
which again matches up because its parallel to FC
dusk abyss
oh because their parallel it doesn't matter?
lethal pond
and again has same magnitude
yeah so parallel vectors will have same direction
if their length/magnitude is same
dusk abyss
ok, wasn't sure if that's how it worked. That makes sense though, thanks
dusk abyss
.close
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drifting junco
I ask wise ones of this server: radians.. god what are they
drifting junco
(you can tell im studying precalc)
drifting junco
when radius = arc length?
royal herald
Wow \sum AC you just taught me something cool
tall veldt
when radius = arc length?
Yup quite literally the angle you get when you shove the radius onto the circle
forest sky
we get the formula
s = r θ
where s is the arc length, r is the radius, and θ is the angle in radians
drifting junco
I'm sorry, whats the name of the greek letter?
forest sky
θ is theta, which is often used for denoting angles
drifting junco
then what's the difference between pi.diameter and 2pi?
both seem to be for circumference
go send that in a available channel
forest sky
the circumference of a circle is
c = πd = 2πr
where d is diameter, r is radius. note that d = 2r
drifting junco
ye so circumfrence is pi.d
forest sky
(note that this shows that there are 2π radians in a full circle)
drifting junco
ah
im sorry: I meant to ask this means 2pi.r = 2pi.rad?
(also do I just copy paste pi symbol)
forest sky
we said earlier that the arc length (length of a part of a circle) is given by
$$s = r \theta$$
where $r$ is the radius, and $\theta$ is the angle. the arc length of a full circle is its circumference. we know that the circumference is given by
$$c = r (2 \pi) = r \theta $$
therefore the angle of a full circle is
$$\theta = 2\pi$$
clever fjordBOT
cloud
drifting junco
hm
ok.
but why is it considered negative when counter clockwise?
sorry clockwise*
forest sky
on a number line, negative is in the opposite direction (left) from positive (right), so we just adapted that to the unit circle
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vale compass
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vale compass
confused on derivation of the thing i circled
i dont understand how N cancels out on right side but not left
it shouldnt cancel out on both sides.
odd edgeBOT
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@vale compass Has your question been resolved?
quiet berry
ancient tinsel
I'm a little stooped, can someone let me know where I went wrong?
I chose to have all the equations =to A based off the first solution.
2nd solution: 2a=HB1+B2------> A=(HB1+B2)/2
3rd solution: B1=(2a/h)-B2--->(B1+B2) x H divided whole things by 2
4th solution: B1=given----> H(B1+0.5HB2) divide whole by 2
leaden widget
I'm a little stooped, can someone let me know where I went wrong?
I chose to hav...
recheck 2nd and 3rd
ancient tinsel
Oh I'm dumb, for the second one, its a=(HB+B2) /2?
I still get the same answer for the third one though
pearl cargo
I still get the same answer for the third one though
if you know that 1 and 3 are equivalent to each other, but not equivalent to 2, there's only one more place to check
ancient tinsel
Ohhh from the way he was saying it, I thought the solution I had for the third one was also incorrect and kept doing it hahaha
Thank you guys
.close
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charred current
I only need help determining the interval, I'm not entirely sure what it's asking for this question.
charred current
I assume it needs to be answered in interval notation
which isn't an issue I know how to do that, but I'm not sure what numbers exactly I'm looking for
this is also instructor created so there's not an example included in mathXL which is what I have been using to learn this stuff
which sux...
odd edgeBOT
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charred current
<@&286206848099549185>
I don't know if I provided enough information, but the equation I'm working from is there
if you need anything let me know
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outer wadi
Why is the answer to this B and D?
odd edgeBOT
Why is the answer to this B and D?
outer wadi
I got B C D
I did x^2 - y^2 >= 0
y <= -x, y <= x
wouldn't c be under both the line y=x and y=-x
nimble blaze
how did you get
y <= -x, y <= x
outer wadi
I added y^2 to both sides
then took the square root of both sides
sqrt(x^2) >= sqrt(y^2)
nimble blaze
can't square root like that for inequalties
i mean you can, but that'll give you
|x| >= |y|
and from there you can apply definition of the abs val and do some casework
personally i would do
(x+y)(x-y) >= 0
and consider when both factors are positive
or when both are negative
outer wadi
ok i'll try that
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steel tartan
I think the one I picked is correct but I’m not sure
steel tartan
.close
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steel tartan
.reopen
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✅
steel tartan
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lofty patio
$$Hi, I am having issues evaluating a quotient with imaginary numbers.
Question: Evaluate the quotient, and write the result in the form a + bi.
\frac{8-3i}{1-8i}$$
clever fjordBOT
kxli
lofty patio
Hi, I am having issues evaluating a quotient with imaginary numbers.
Question: Evaluate the quotient, and write the result in the form a + bi.
$$\frac{8-3i}{1-8i}$$
clever fjordBOT
kxli
glossy perch
multiply the top and bottom by the complex conjugate of the denominator
which is 1+8i
lofty patio
multiply the top and bottom by the complex conjugate of the denominator
got the answer, thanks!
.close
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elfin bear
left of the coma is set 1, right of it is set 2
how do i check if one set is a subset of another here? since there is cartesian product im not sure
elfin bear
taking $x \in$ subset 1 or subset 2 is something im not sure how to do exactly
clever fjordBOT
Ayanokoji
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elfin bear
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pastel orbit
fastest doubt cleared in the west
normal niche
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solemn tinsel
How would u calculate surface area for a can that has one side open??
latent scaffold
So a cylinder without one of the bases?
solemn tinsel
Yeah
desert marlin
find the surface area of the cylinder first
and then find the area of the base you remove
strong jewel
How to solve the inverse of 9/4-x^2
red portal
why arent +-1 also critical points?
odd edgeBOT
why arent +-1 also critical points?
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fair remnant
Hi, question about probability. Taking two cards from a deck in a row, two events are dependent. I want to find the probability of the first card being an ace OR second card being ace.
So I know we use addition rule
P(A or B) = P(A) + P(B) - P(A and B)
P(A) = 4/52 = 1/13
P(B | A) = 3/51 = 1/17
P(A and B) = 1/13 * 1/17 = 1/221
But I'm stuck at P(B) because it's dependent on whether A was an ace or not
I suppose it would be either:
-
second card is an ace given first card wasn't an ace: 4/51
plus second card is an ace given first card was an ace: 3/51
equals 7/51 -
4/52 = 1/13 because we're counting it's individual probability
but wouldn't 1) be more correct because those two events are mutually exclusive so we can use addition rule
Someone please enlighten me. I don't have the answer because this is something I just thought up on my own
pearl cargo
Hi, question about probability. Taking two cards from a deck in a row, two event...
P(B) = P(A and B) + P(-A and B)
fair remnant
wdym by -A and B
pearl cargo
[not A] and B
i.e. split on the cases
check the probability for when the first card is an ace and the one when the first card isn't, and sum them up
it actually simplifies though, with your [- P(A and B)]
odd edgeBOT
pearl cargo
Hi, question about probability. Taking two cards from a deck in a row, two event...
P(A) + P(B) - P(A and B) =
P(A) + P(A and B) + P(-A and B) - P(A and B) =
P(A) + P(-A and B)
i.e. it's the probability that the first card was an ace, plus the probability that the first card wasn't an ace but the second card was
hopefully that makes sense when you think about it
those are mutually exclusive events, and what you want is equivalent to knowing when either one happens
so just sum the probabilities
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atomic zinc
Hi guys, I need to solve example 2
odd edgeBOT
Hi guys, I need to solve example 2
nimble blaze
partial fration decomp
frigid canopy
Hi guys, I need to solve example 2
partial fractions
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atomic zinc
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rough lantern
What is the length of AB? <A=<BOD and <COD=<DBO
odd edgeBOT
What is the length of AB? <A=<BOD and <COD=<DBO
rough lantern
I keep getting 13 but the answer is 12
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grave geode
i never did sin cos tan shit
google says get the angle, with the angle get the length of the base
grave geode
u already have like half of it u can do this on ur own fr
fickle coral
It is congruency question
grave geode
with what may i get the angle
the two sides with known length i guess
grave geode
It is congruency question
here this dude knows
rough lantern
It is congruency question
what?! 🔥
fluid tundra
I keep getting 13 but the answer is 12
12 is right
rough lantern
12 is right
amazingly so but idk why
Or this one
an amount of white baloons is x
an amount of blue baloons is 3x
1 costs 1.5$
and the answer
is 6x
but
hollow quarry
amazingly so but idk why
Like square said, it's a congruency question. You just need to show both triangles share another angle (they already share one angle and a side)
by share, I mean "they have both have"
odd edgeBOT
odd edgeBOT
Available help channel!
elfin bear
if I have given;
1/x < x < 1-1/k
can I say;
0 < x < 1?
icy kindle
only if k and x are both positive, nvm x has to be positive for this to hold.
since k is usually positive in these types of things, yes you can (probably) say that
elfin bear
only if k ~~and x~~ are both positive, nvm x has to be positive for this to hold...
why? and both are positive
icy kindle
well... maybe this could work with negative x...
if x = -.5
Then 1/x = -1/.5 = -2
So 1/x < x but x < 0, so unless you know they're positive this may not hold.
and obviously, if k is negative then 1 - 1/k > 1 so there's nothing to guarantee that x < 1
So you need to know those are positive to begin with.
If you know x and k are positive, then you already have 0 < x
And then 1 - 1/k < 1, so you have 0 < x < 1
elfin bear
and obviously, if k is negative then 1 - 1/k > 1 so there's nothing to guarantee...
I see, ty mate
.close
odd edgeBOT
odd edgeBOT
Available help channel!
random yew
I need help
odd edgeBOT
I need help
random yew
unreal pawn
Just put x=8 and y=-3
unreal pawn
its not that hard 😉
random yew
I Dont have a calculator
unreal pawn
💀
random yew
thick island
I Dont have a calculator
It should become the same number
random yew
you guys should just tell me the answer. I'm being timed and u guys are sitting here taking 50 hours
once the timmer is over, that will be my score
unreal pawn
if u cant to this, then u should fail this exam
molten palm
So if you don't understand what's happening. T is a function that takes in x and y, and uses them in the function to spit out new answers. For example if i have f(x) a function that takes in only x. and set it equal to f(x)=x+1. In this case the outcome of a coordinate x like x=2 the function does as follows. f(2)=2+1=3. Now to look at the question if we take our function T(x,y) and set the values to the values of the point we get new coordinates according to the "translations" or calculations inside the function. A translation are operators and an image is the outcome when a point is inserted into a function. For example the image of x=2 in the funciton f(x)=x+2 will be 4 because f(2)=2+2=4
molten palm
if u cant to this, then u should fail this exam
Dont be rude
unreal pawn
bruh
random yew
calculate T(8,-3)
( 8,-3)t?
random yew
if u cant to this, then u should fail this exam
Your the one who cant give me the dam question
How hard is that
molten palm
@random yew u know what an image is?
thick island
T is a function and when you put (x,y) it spits out (x-4,y+7)
random yew
<@1224935735350526003> u know what an image is?
No
unreal pawn
we wont give u just an answer
thick island
So if T(8,-3) we get (8-4,-3+7)
unreal pawn
I hope so we wont
frigid canopy
This is a test ?
random yew
This is a test ?
YES DUMBY
thick island
I see
random yew
THE HELL ARE EXPLAING FOR
upbeat hearth
help him
thick island
In that case I can’t answer
upbeat hearth
xd
random yew
I'M BEING TIMED
unreal pawn
In that case I can’t answer
<333
molten palm
If I have the function T(x,y)=(x+5,y+3) and I enter x=2 and y=3 for example. Then the translation is (2+5,3+3)=(7,6) Now apply this logic to your form
@random yew
upbeat hearth
What old lady
old lady with a job
random yew
idc abt that
upbeat hearth
idc abt that
molten palm
You are not getting the answers. You have to calculate it yourself. It is not that hard if you take a good look at what is being asked
random yew
mystic saffron
you don't want to risk it
random yew
You are not getting the answers. You have to calculate it yourself. It is not th...
That not what helpers
are
bye bitch
unreal pawn
helpers help
random yew
your non helper
molten palm
Yes we help with steps
random yew
steps by taking so long
unreal pawn
cause there was one step
molten palm
Helping someone is not giving the answers. If i did im not a helper but rather just a cheat for you
unreal pawn
and it was too much for u xd
molten palm
when have you learned anything by just getting the answers
random yew
I'LL GUESS THE ANSWER IS 4,4
frigid canopy
<@&268886789983436800> cheating in a test
mystic saffron
rude to people who were trying to help too
upbeat hearth
any mods here?
upbeat hearth
https://tenor.com/view/spongebob-rainbow-imagination-meme-idc-gif-17331659
no one cares about u xd
random yew
haughty scaffold
for someone whos being timed mid exam she sure has enough time to argue on discord
random yew
for someone whos being timed mid exam she sure has enough time to argue on disco...
Yall arent helping me
random yew
no its not
upbeat hearth
Yall arent helping me
no one will
random yew
its helping like my teacher said
atomic cape
.close
proven cape
$\int \frac{x^3}{x^3 -1}$
odd edgeBOT
$\int \frac{x^3}{x^3 -1}$
clever fjordBOT
Penaldo
proven cape
How do I get out of here?
frigid canopy
$\int \frac{x^3-1}{x^3-1} + \frac{1}{x^3-1}dx$
clever fjordBOT
ƒ(Why am. I here)=I don't Know
frigid canopy
use partial fractions for the second part
proven cape
use partial fractions for the second part
Can i do $\int \lim_{x\to \infty} \frac{x^3}{x^3 -1}=1 ,\int 1 dx = x$
frigid canopy
what's the og question?
clever fjordBOT
Penaldo
proven cape
what's the og question?
?
frigid canopy
why do you want to do the limit
proven cape
Can't I do this to fix it?
proven cape
The integral
frigid canopy
no need to fix it
frigid canopy
**ƒ(Why am. I here)=I don't Know**
integrate this
proven cape
I used limits, is it the same?
frigid canopy
no, because this is an indefinite integral
proven cape
Lebesgue Dominated Convergence Theorem
I use this
Comb
With
Monotone Convergence Theorem
frigid canopy
If you need to use those, I'm not sure, never heard of any of them
proven cape
Can I use your method?
clever fjordBOT
Penaldo
proven cape
$x+\int \frac{1}{(x-1)(x^2 +x +1)}dx$
clever fjordBOT
Penaldo
green elm
now do partial fractions
proven cape
$x+\int \frac{A}{x-1}+\frac{Bx+C}{x^2 +x +1}$
clever fjordBOT
Penaldo
proven cape
$x+\int \frac{(Bx+C)\cdot(x-1)+(x^2 +x +1)\cdot A}{(x-1)\cdot(x^2 +x +1)}dx$
clever fjordBOT
Penaldo
hollow ginkgo
Don't spam here
fluid tundra
$x+\int \frac{(Bx+C)\cdot(x-1)+(x^2 +x +1)\cdot A}{(x-1)\cdot(x^2 +x +1)}dx$
right so expand the numerator and set it equal to 1
odd edgeBOT
@proven cape Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
light gazelle
Hey, I need help with an important task. I have to set up a cone placed at a defined point as an equation using a set of functions ("Funktionsschar" in German). The uppermost point, the apex, is the position vector. This position vector should then create a circular cone with the help of direction vector(s). Unfortunately, I'm really unsure how to do this. I might have thought of a circular equation (or similar) as the x,y value of the direction vector, i.e. with cos(a) and sin(a) as x,y. The Z value is already clear. The Z value is already clearly defined, as the gradient is always the same, negative.
wanton bison
Hey, I need help with an important task. I have to set up a cone placed at a def...
Kannst du einfach die Aufgabe posten
lethal spoke
Kannst du einfach die Aufgabe posten
Nice bio BTW 🙂
wanton bison
Nice bio BTW 🙂
thank you, you too 🙂
light gazelle
Hab keinen richtigen Zettel dafür. Ich soll aber einfach einen Kegel in einem 3d-Koordinatensystem durch eine Geradenscharr darstellen. Dabei soll dieser Kegel Vertikal stehen, also wie ein normaler Kegel auch. Unten soll er sozusagen einen Kreisbilden. Verstehst du?
Nehmen wir an der OV liegt bei (0,0,0) Dann soll nach unter ein drei Dimensionaler Kegel "strahlen"
odd edgeBOT
@light gazelle Has your question been resolved?
light gazelle
<@&286206848099549185>
wanton bison
Hab keinen richtigen Zettel dafür. Ich soll aber einfach einen Kegel in einem 3d...
Meinst du so in etwa (man müsste noch das Interval zwischen lambda 0 und 1 berücksichtigen)
und für x²+y²=1 müsste man z=0 berücksichtigen
odd edgeBOT
@light gazelle Has your question been resolved?
open crown
Have u heard about intergral?
Do it then?
?
Yeah
You just need get the antiderivative of y=20 - x -x^2
Then F(a) - F(b) = intergal(f(x)) {from a to b}
💀
Aint no way you're 13
And study calculus
LMAO
light agate
just find the roots of the polynomial
open crown
just find the roots of the polynomial
He already done that
light agate
right those are the limits
open crown
Then F(a) - F(b) = intergal(f(x)) {from a to b}
Combine with this
F(a) is this
Cap
🧢
light agate
$-x^2-x+20=0$
$-x^2-5x+4x+20=0$
$-x(x+5)+4(x+5)=0$
$(-x+4)(x+5)=0$
$x={-5,4}$
clever fjordBOT
esca (@ with reply)
open crown
$-x^2-x+20=0$
$-x^2-5x+4x+20=0$
$-x(x+5)+4(x+5)=0$
$(-x+4)(x+5)=0$
$x=\{-5,4...
He's not finding the limit, he probably doesnt even understand what's limit even is
light agate
He's not finding the limit, he probably doesnt even understand what's limit even...
where did i mention a limit
light agate
He's not finding the limit, he probably doesnt even understand what's limit even...
oh i see. by limit he meant boundary of the region
open crown
Bro, you should learn Numerical Analysis
Nah Real Analysis is even better
Bro is capping so hard
💀
Remember me when u get the Fields Medal dude
Honestly, I could teach u calc 1 and 2 for fun
Then real analysis
Then numerical analysis
Too old to be cool, too young to be wise
This is approximation method
AKA Riemann sum
Nope
Approximation never gives you the correct answer
Unless the iteration goes on infinity
But irl, no approximation method could give u the exact answer
There's 3 well known approximation methods
Riemann Sum
Trapezoidal Rule
And Simpson rule
The sigma?
Its addition
Basically, a small delta X * Y = the area of 1 rectangle
Kid game
Do ur homework buds
You probably haven't get to quadratic
Bruh
Capping
dawn tiger
why is bro competing with how fast someone's learning math 😭
open crown
why is bro competing with how fast someone's learning math 😭
Its not competing, rather, you should not skip progression to learn too advance stuff
lethal spoke
Wait you only study math ?!
lethal spoke
Its not competing, rather, you should not skip progression to learn too advance ...
Tell that to hsf
Ah thank God
You are not one of them
dawn tiger
i think it's cool that bro is trying to get into more difficult mathematics, even if he doesn't necessarily have the most thorough background for it
open crown
i think it's cool that bro is trying to get into more difficult mathematics, eve...
Real?
dawn tiger
i found myself much more motivated and interested when i studied ahead on my own, even if i didn't fully understand everything that was going on
open crown
For example, in this case, he didn't fully understand what's root and limit means
dawn tiger
i don't see too much harm in covering basic RA while learning calculus
if it's already going to be new to you, might as well formalize it along the way
so you don't have to ask as many "why"s
open crown
Fair
But skipping from basic algebra to calculus is....not that useful, I think the effort would be better use for geometry or trig then pre-calc
dawn tiger
no that makes sense fs cause if you don't know basic trig and you don't have your algebra fundamentals down then calc is pretty useless
open crown
How many root does sin(5x) have?
light agate
judging from their work here they seem fine
dawn tiger
i mean math is math everywhere, even if we call it different things lol
light agate
by "limit" kaccha means the boundaries of the region
limit has a different meaning, so you should probably use the term "boundary"
that doesnt mean he doesnt know basic algebra or anything
mhm
dawn tiger
yeah we usually call that "boundary" or "endpoints" to avoid confusion with an actual limit
open crown
that doesnt mean he doesnt know basic algebra or anything
He said it himself that he's 13 and he's learning basic algebra at school 💀
light agate
He said it himself that he's 13 and he's learning basic algebra at school 💀
and? i havent seen any evidence that his algebra skills are lacking
dawn tiger
do you not find it a little silly to be so concerned with how fast a 13 year old is learning math?
i'm personally impressed that he's even trying to learn it compared to what most 13 yos are doing
lethal spoke
i'm personally impressed that he's even trying to learn it compared to what most...
Help 17 looks odd(pun intended)
open crown
Why are u guys not seeing the problem? The problem is not he's learning calculus, the problem is he doesnt have the basic skill for calculus, you guys should encourage him to study thing like geometry and trig then precalc
light agate
Why are u guys not seeing the problem? The problem is not he's learning calculus...
youre assuming he doesnt have the basic skill
lethal spoke
Learn the basics is what he means
light agate
its not our place to police what he should or shouldnt learn anyway
dawn tiger
what's the formula for the volume of a cylinder? what's sin(pi)?
light agate
mhm so thats something youll wanna learn
dawn tiger
he seems fine
though review unit circle lol
would sin(pi) not have fallen under trig values?
kinda hard to learn trig without a unit circle
kind frigate
lilac bluff
can someone check if my explanation is bad?
odd edgeBOT
can someone check if my explanation is bad?
clever fjordBOT
odd edgeBOT
@lilac bluff Has your question been resolved?
dawn tiger
neon badge
odd edgeBOT
@lilac bluff Has your question been resolved?
radiant shell
I have X ~ Bin(n = 100, p = 0.3)
odd edgeBOT
I have X ~ Bin(n = 100, p = 0.3)
radiant shell
I need to find upper bound of P(X > 40) using Markov's inequality
That's P(X >= 40), but since this is discrete, we need to take care of the P(X = 40) case right? So, we should do P(X >= 40) - P(X = 40) to get P(X > 40)? So, using Markov's, we get 3/4 - dbinom(40, 100, 0.3) = 0.7415098
However, what I am thinking is that it should also be the same if I try to find the upper bound of P(X >= 41) using Markov's inequality, but that gives me 30/41 = 0.7317073, which obviously is not the same
why is that so?
green elm
because the markov bound isn't necessarily tight
both bounds are in fact true
P(X >= 41) is less than both 0.7415098 and 0.7317073
P(X >= 41) is 0.0125, assuming this calculator i found online is correct
radiant shell
i guess, what would be the more correct way to write it though
would it be P(X >= 41) since it gives a tighter bound?
green elm
depends on what you want
both are correct
but the markov bound would be 30/41
any number greater than 0.0125 is a valid bound
odd edgeBOT
odd edgeBOT
Available help channel!
pulsar pond
Can anyone help me solve this question? I understand that you must use the binomial distribution to calculate the probabilities from 18-27 but it doesn’t specify how many decimals to input and I’m not even sure if I’m right
pulsar pond
I used this calculation
proven beacon
wow extrasensory perception
pulsar pond
Yeah lol
thin geyser
Are you given no tools to do this problem? That is kind of annoying if you are expected to write it out by hand without software for that many terms
zinc glacier
they are using wolfram tbf
pulsar pond
We have a formulas sheet with a table but it 1) doesn’t provide the precision the question is asking for, and 2) doesn’t go up to n=27
thin geyser
In any case, your proposed answer is not close
zinc glacier
you dont have to put the 0.5^9 and the like because its accounted for in the 0.5^27 in the front
pulsar pond
Right
zinc glacier
we get (1/2)^x(1/2)^(27-x)
pulsar pond
So the 0.5^27 can be factored since it is common to each of the terms
zinc glacier
yup
zinc glacier
no, you factored out the .5^whatever stuff alreafy
pulsar pond
But I haven’t though
zinc glacier
whats the probability of getting 9 heads?
pulsar pond
.5^9
zinc glacier
out of 27 flips*
pulsar pond
Oh I mean it would be 27 choose 9 times .5^27 times .5^18 no?
zinc glacier
show me how you are using the formula
pulsar pond
zinc glacier
youre welcome
pulsar pond
.close
odd edgeBOT
odd edgeBOT
Available help channel!
heady plover
how do they know the maximal size of Jordan block from the dim of kerspace?
heady plover
And when ker(A-3I), why isnt the maximal size of block equal to 1? It said "greater 1" , i dont understand
odd edgeBOT
@heady plover Has your question been resolved?
heady plover
<@&286206848099549185>
spare kelp
That null spaces is basically the eigenspace for the eigenvalue 3. By definition, jordan blocks are n x n matrices having eigenvalues on the diagonal, where n is the multiplicity of the said eigenvalue. That is the dimension of the eigenspace.
If it is known that the space with dimension 1 is certainly not the full space, the jordan block should be bigger than 1, otherwise a 1x1 matrix would suffice. However, it shouldn't given that the space is not the full space.
heady plover
if the jordan block is 1*1, then it will be diagonalisable so it wouldnt be jordan , am I understanding right?
spare kelp
Yeah,a 1x1 is literally just an entry, but it is technically a matrix.
A related fact that is that, a matrix is diagonalisable if and only if its jordan form consist of only 1x1 blocks.
heady plover
and only when >1, the eigenspace is full space ?
spare kelp
and only when >1, the eigenspace is full space ?
That is the assumption you are given I suppose, the jordan form can't tell you that. It can only tell you that it can't be full if it is just 1, so it should be greater.
What value that should be depends on the question.
Here, it is 2, if I understood correctly.
spare kelp
It happened to be like that for this question, but that is not a general fact. You may have a 10x10 matrix, and 4 different eigenvalues as well, right ?
So, the maximal size of the jordan block is equal to the dimension of the biggest eigenspace
whatever that value happens to be
you would need to check them all, here it is straightforward
heady plover
wait ,the dim of ker(A-\lambda I) is the dim of eigenspace?
spare kelp
Yeah, it is just a different way of saying it.
To put it shortly, an eigenvector means that when you multiplu this matrix with that said vector, you get the same vector, but scaled by a constant, we call this the eigenvalue. So, eigenvectors for a matrix are values that satisfy this equation:
$A \cdot v = \lambda v$
Now, you rearrange this equation, to get a set of vectors that can satify this equation. This is basically the definition for the eigenspace, it is like this:
$E = {v: (A-\lambda I)v = 0}$
clever fjordBOT
banana of rivia
spare kelp
A cooler way to say this in linear algebraic terminology is $ker(A- \lambda I)$.
clever fjordBOT
banana of rivia
heady plover
I see !
Lemme disgust the original question a bit, but thank you very much for this !!
spare kelp
Oh wait I made a typo in the above equation. it is supposed to be this, my bad:
clever fjordBOT
banana of rivia
heady plover
So, the maximal size of the jordan block is equal to the dimension of the bigges...
Just need to confirm a little things, the biggest eigenspace is ker(A-3I)^2, right?
the dim of ker(A-3I) also happen to be 2
but maybe it can be 1?
spare kelp
Just need to confirm a little things, the biggest eigenspace is ker(A-3I)^2, rig...
That is the whole space, no ? The eigenspace if the kernel space like what we talked above. Taking its square is not really realted to the eigenvalue itself.
spare kelp
but maybe it can be 1?
It is generated by two different vectors, right? The spanning set has 2 elements, the dimension can't be one at that point.
odd edgeBOT
odd edgeBOT
Available help channel!
placid hamlet
Hello
placid hamlet
Anyone here
south plume
ask your question
placid hamlet
Ok
For the second question
@south plume
<@&286206848099549185>
<@&286206848099549185>
south plume
<@&286206848099549185>
!15m
odd edgeBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
placid hamlet
Oh ok this is really important that’s why
south plume
note that CE is a shared side and is hence equal in two triangles BCE and DCE
you are also given that they have the same angle
i.e. 1 and 2 are congruent
south plume
additionally, in a kite diagonals intersect and right angles so these two angles are right and the same
so you have two angles and a side
south plume
what have you tried
placid hamlet
Yea
I have tried drawing a triangle
And then I got stuck on the second part
The reasoning on where the circle pool is placed as well as yes
Can u help me figure this out
<@&286206848099549185>
Helpers
Come on
bold kayak
Try to remember something you studied that can help in this scenario
Or try to visualize it
unreal quiver
If I remember right. This involves the intersection of lines in a triangle
odd edgeBOT
@placid hamlet Has your question been resolved?
gaunt pilot
guys pls help me, i play robloz pls pls pls i need the errrm acturaly head
gaunt pilot
<@&286206848099549185>
dawn tiger
!15mins
odd edgeBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
mystic saffron
guys pls help me, i play robloz pls pls pls i need the errrm acturaly head
Roblox : smirk :