wait, what
#help-39
midnight haven
You mean the equation for f(u)?
autumn fossil
You mean the equation for f(u)?
we have f(u) = u^2 + u for u = 1/n for some natural number n
sharp smelt
why didn't I think of that ☹️ . thanks a lot though!
autumn fossil
we can take e.g. u = 1, 1/2 and 1/3
then we can calculate f(u) for these values
and there is one unique parabola passing through the points (u, f(u))
midnight haven
we have f(u) = u^2 + u for u = 1/n for some natural number n
Yeah and we want to prove something for f(x).
So we need to know what domain of x is so we can use appropriate substitution for f(u) or f(1/n)
acoustic path
why didn't I think of that ☹️ . thanks a lot though!
in general if ur given an expression involving f(1/n) it's a good idea to manipulate it into f(n)
(in this case that's the solution you want to take)
autumn fossil
and the one parabola is u^2 + u, because this one works and since there is just 1 unique parabola, no other parabola will work
sharp smelt
in general if ur given an expression involving f(1/n) it's a good idea to manipu...
got it, thanks!
autumn fossil
Yeah and we want to prove something for f(x).
So we need to know what domain of ...
I know, f(u) = u^2 + u isn't the complete proof. But the rest is trivial to see. f(u) gives us values of f(x) for at least 3 different values of f(x) (e.g. 1, 1/2 and 1/3), then there is only one possible parabola passing through those 3 points. And we know that the parabola x^2 + x definitely passes through those points. So we can just take this one unique solution and we're done
midnight haven
Cool but how do you know that f(u) =f(x)?
Or you just say that f(u) is special case of f(x)
Therefor lim of f(u) =lim of f(x)?
autumn fossil
Cool but how do you know that f(u) =f(x)?
Or you just say that f(u) is special c...
f(u) = f(x) for all u = 1/n, right?
midnight haven
Cool but how do you know that f(u) =f(x)?
Or you just say that f(u) is special c...
Sorry ment derivatives
midnight haven
f(u) = f(x) for all u = 1/n, right?
Yeah
autumn fossil
we also know that f is a parabola
or its graph
f is quadratic functions
thats what i meant to say
midnight haven
Yeah make sense, so you just take special case
autumn fossil
how many points on graph do you need to UNIQUELY define a parabola?
midnight haven
Thanks because was confused that we don't have range for x
midnight haven
how many points on graph do you need to **UNIQUELY** define a parabola?
2 or 3?
autumn fossil
You only need 3 points, f(u) = f(x) for all u = 1/n gives us infinitely many points
meaning that if there even is a parabola passing through all of f(u), it must be unique
midnight haven
You only need 3 points, f(u) = f(x) for all u = 1/n gives us infinitely many poi...
Yeah because we just concerned about limit so we can do thus
autumn fossil
and since f(x) = x^2 + x works for all u = 1/n, we can just take that
and then trivially find the limit
midnight haven
halcyon pagoda
I have a triangle with points A:(4,3), B:(0,0), and C:(4,-3). I solved the previous steps, but I need some help dilating this triangle by a scale factor of -4 about point A
marble sigil
I have a triangle with points A:(4,3), B:(0,0), and C:(4,-3). I solved the previ...
I'd write B and C in terms of their x-y distance from A, multiply by -4, then adjust it back to normal coordinates
halcyon pagoda
@marble sigil What do you mean by adjust it back to normal coordinates?
marble sigil
the first step is doing -4 to x and -3 to y, and in the end you do +4 to x and +3 to y to go back
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vagrant agate
Using Heine's definition of a continuity of a function, prove continuity at the given points
pearl pondBOT
Using Heine's definition of a continuity of a function, prove continuity at the ...
@vagrant agate Has your question been resolved?
elder plaza
hi how do i determine whether this sequence converges?
pearl pondBOT
hi how do i determine whether this sequence converges?
elder plaza
a.n = arctan(ln (n))
idk how to do the subscript
i havent tried much becuase im not sure where to start
but i know the domain of arctan is all real numbers
and domain of ln is 0 -> inf
and ln (infinity) is infinity
so we just have arctan(inf)
lavish portal
Do you know what arctan(x) looks like
lavish portal
Oh nvm I don’t think I understand this problem fully
Are you trying to find if the infinite term will reach a certain value
elder plaza
nw
lavish portal
is that important for this problem?
Yea I guess
Arctan is the inverse of the tan graph so it is reflected across y=x
do you know what tan(x) looks like
lavish portal
ok reflect is across y=x and then you get arctan(x) but remember that functions can only have 1 value
elder plaza
period pi
lavish portal
actually do you just want to see what arctan(x) looks like then it will be obvious
graph it on Desmond
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wind solstice
Hello, I was wondering how to find the limit of a linear recurrence with variable coefficient ?
wind solstice
More precisely for the following sequence:
$a_{n+2}=\frac{n+1}{n+2}a_{n+1}+\frac{n}{(n+2)^2}a_n$
jolly parrotBOT
Louis
wind solstice
with a_1 = 1 and a_2 = 0.75
marble sigil
in general you just have to guess a function that sort of matches the recurrence, here it's going to be something involving factorials
oh apparently OEIS says it's about derangements, so you can't really do this algebraically and would want a combinatorial proof
you sort of just have to know it. but the derangement recurrence is a(n+2)=(n+1)a(n+1)+a(n)
wind solstice
I'm sorry but I don't really understand how is this suppose to help me
marble sigil
the answer is going to look like (factorial times or divided by other factorials)*(degrangements !n)
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bleak rivet
pearl pondBOT
tiny jay
-_-
bleak rivet
I thought that standard form was in descending order, but none have that
fluid root
Shouldn't it be 3?
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midnight haven
Hi, the formula for the sector of a circle is theta times radius squared times half correct? However, in this answer sheet I don't see the 1/2 in the first part where it says pi times 12 squared over 4 and I don't know if I'm wrong or if this is a misprint.
versed remnant
Hi, the formula for the sector of a circle is theta times radius squared times h...
pi r^2 is area for circle
u know its a quartar of circle so area of that is pi r^2/4
midnight haven
but wheres the 1/2
isnt there supposed to times 1/2
so its pi times 12^2 over 4 times by 1/2
right?
nvm i got it
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indigo prawn
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indigo prawn
I have this question
i did the first step
i know u have to do polynomial divison
i did some of it
im on the 2nd part of it
this is also college algebra
vast solstice
what is the 2nd part?
indigo prawn
i did like the first step in the divison were the x goes on top
but i nvr finished the rest
vast solstice
im not sure what you mean, the oblique asymptote will be the quotient without the remainer
thats all that is asked in the question
indigo prawn
im not sure what you mean, the oblique asymptote will be the quotient without th...
i know what u mean but like the question im trying to ask is that like
can i show you my work?
vast solstice
sure
indigo prawn
alr
this is what i have so far for the division
ik its simple but idk what to do next😭
vast solstice
The same thing you did for the first line
you need to find a term to multiply by x to get -17x
vast solstice
i think the bot would say something
indigo prawn
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pearl pondBOT
light helm
has to be unedited, editing a message to .close has no effect
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fossil warren
whats the logic behind this question? how would i do this if i dont know what g(y) is
pearl pondBOT
whats the logic behind this question? how would i do this if i dont know what g(...
@fossil warren Has your question been resolved?
midnight haven
whats the logic behind this question? how would i do this if i dont know what g(...
@fossil warren
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midnight haven
It's a
g(y) for any y give you positive Therefor look at x^2-1
When x=1 or - 1 we have 0
Horizontal line
When x<1/x >-1
We have negative gradient
Other cases are positive gradient Therefor it should be A
@fossil warren
pearl pondBOT
@midnight haven Has your question been resolved?
sharp smelt
is there any quick way to do this?
pearl pondBOT
is there any quick way to do this?
sharp smelt
Other than finding A^2, A^3 etc
last summit
My Sir @tepid ether can help
tropic saddle
its not like the powers are hard to compute
tepid ether
It likely comes down to how x^5-1 factors and then computing A^2
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midnight haven
Okay I can solve both questions individually but I don't understand why 1 leads to 2
midnight haven
The reciprocal of 1/3 is 3/1. Therefore, $3/19= 27/1$
The reciprocal of 7/3 is 3/7. Therefore, $3/79=27/7$
jolly parrotBOT
zeinvincible
midnight haven
So both answers are correct by doing them individually, however, the second answer is apparently meant to be derived from evaluating the first answer
pearl pondBOT
@midnight haven Has your question been resolved?
midnight haven
<@&286206848099549185>
sweet forge
midnight haven
yes
prisma forge
I think it’s trying to get you to see that if you are given a numerator other than one you use the numerator at your new denominator after dividing
prisma forge
Okay I can solve both questions individually but I don't understand why 1 leads ...
Count how many sets of 7 colored blocks there are
midnight haven
4
midnight haven
I think it’s trying to get you to see that if you are given a numerator other th...
why do i use the new numerator as my denominator
midnight haven
6, why isnt the last filled?
prisma forge
If the last was filled we would get to 28/3 looking at the number line
But 27/3 is 9
The colored blocks represent 7/3s, it changes color after each 7/3
So in 9 we have 3 and 6/7 7/3s
I believe you just need to rewrite 3 and 6/7 as an improper fraction
I believe it’s trying to get you thinking of 1 leading to 2 as 9 / 1/3 is 27/1 which is also 9 * 3/1
Then when you get to question 2 9 / 7/3 should be 9 * 3/7
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analog girder
for this question, the x axis starts from 20. would it be the okay if i start at like 150 instead? or is there a specific reason on why its starting at 20
midnight haven
for this question, the x axis starts from 20. would it be the okay if i start at...
你的数学老师用英语教你吗
woeful stump
for this question, the x axis starts from 20. would it be the okay if i start at...
it starts at zero, it just isn't marked
starting at 150 would be ok too
analog girder
你的数学老师用英语教你吗
是。？
analog girder
it starts at zero, it just isn't marked
thank you
midnight haven
啥國家
analog girder
为什么
analog girder
我留学生，不在中国
midnight haven
好我不打擾你了
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midnight haven
!status
pearl pondBOT
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
jolly parrotBOT
deltaG
midnight haven
where (h,k) is the vertex
winged lance
you know how the general parabola equation is right
i don't know how to find the value of a
i found h and k
winged lance
**deltaG**
y-k? isnt it just y
midnight haven
i don't know how to find the value of a
you can see in the graph that it passes through (0, -1) right
winged lance
you can see in the graph that it passes through (0, -1) right
yeah
midnight haven
y-k? isnt it just y
yeah you can throw the k to the right hand side and get the same
winged lance
yeah you can throw the k to the right hand side and get the same
ok
midnight haven
g(x)=a(x-4)^2 -3
can you show me the equation you got
midnight haven
where is y lmao
winged lance
idk how to continue
jolly parrotBOT
deltaG
midnight haven
you should get this
midnight haven
because thats how parabolas are defined?
the most basic one
y^2 = 4ax
a is the focus
winged lance
ok
winged lance
you can just put (0, -1) here
can't get the answer
i got 1/32 while the answer is 1/8 for a
midnight haven
i got 1/32 while the answer is 1/8 for a
i guess yall use a different notation
use without 4a and you'll get 1/8
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clear sinew
Just making sure is the answer here C?
pearl pondBOT
Just making sure is the answer here C?
@clear sinew Has your question been resolved?
worthy whale
I got b, how u got c
this is just
let distance = x
tan40=15/x, no?
or am i wrong
<@&286206848099549185> can verify?
clear sinew
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native acorn
pearl pondBOT
native acorn
<@&286206848099549185>
light helm
!status
pearl pondBOT
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
1
light helm
for convenience, introduce three variables for the
height, length, width
of the cuboid
and also draw in the line segments BH and BG
native acorn
light helm
and introduce 3 variables for the height, width, length of the prism
its not needed but it'll make things a little easier
native acorn
light helm
ok good
now <GBH can be determine from cos rule if you know all three sides of the triangle GBH
currently you know two, with b currently unknown
so the next step would be to determine that
now, do you know pythagoras' theorem
as well as how it applies in 3D?
light helm
pretty similar
p^2 + q^2 + r^2 = d^2
from how you defined a,b,c here that'd give you
a^2 + b^2 + c^2 = 36^2
a^2 + c^2 = 24^2
which lets you determine b^2 and b
native acorn
pretty similar
p^2 + q^2 + r^2 = d^2
@light helm
Can someone please help me
<@&286206848099549185>
I seriously give up with this question
pearl pondBOT
@native acorn Has your question been resolved?
unkempt rapids
how to find derivative of this
pearl pondBOT
how to find derivative of this
prime bramble
with respect to y?
sharp smelt
apply the antilog to both sides and proceed from there
tepid mauve
apply the antilog to both sides and proceed from there
Does that mean exponentiating with e?
sharp smelt
yes
tepid mauve
Ight just curious
pearl pondBOT
@unkempt rapids Has your question been resolved?
warm echo
pearl pondBOT
warm echo
determine x
pearl prism
are you trying to find the equation?
marsh silo
determine x
u know its gotta be something divided by x since its undefined at a point. If u subtract x in the denominator by the value of that point itll move it from 0 to the point (which here is 1)
-1 / (x - 1)
and since at x = 0 this is 1, you just add 5 to it
f(x) = -1 / (x-1) + 5
looks about right
nvm this is wrong
just noticed 💀
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grizzled tundra
Guys I need help
pearl pondBOT
Guys I need help
grizzled tundra
In the triangle with a 30 degree angle,the altitude relative to the hypotenuse divides it into two segments measuring m and n units,respectively,where m is greater than n.We know that the ratio of m to n is greater than 1. Formulate a conjecture specifying the value of the ratio m to n in this type of triangle
If you could help I would really appreciate it ¡
clever pewter
so first off you should find all of the angles (easy part)
then find cos 30 (for bigger triangle) and cos (find it) (for smaller triangle) then you got it pretty much.
pearl pondBOT
@grizzled tundra Has your question been resolved?
grizzled tundra
so first off you should find all of the angles (easy part)
then find cos 30 (for...
I tried(thank you tho),problem is that I have to invent values and find the link between my values and the question but I don’t know how
clever oxide
i don't think your going the right way...
tbh i have no idea what im doing either
clever pewter
tbh i have no idea what im doing either
not that complicated find cos30 and cos60
clever oxide
not that complicated find cos30 and cos60
oh yeah i get it now
clever pewter
so base on that we have
$M/x=√3/2 , N/z=1/2$
jolly parrotBOT
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jolly parrotBOT
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icy pasture
I have Proof question.
I'm currently working on Proofs by Jay Cummings (amazing book, hilarious). Exercise 1.2 is "Explain the error in the following "proof" that 2=1. Let x=y. Then,
icy pasture
I made a proof and while it seems right, I can't help feel like I did something wrong and still misunderstanding the idea on writing proofs.
For some context, Im on a math journey from Algebra to Linear Algebra while learning Pure Math concepts.
Im currently in Algebra 1, therefore at the start of this personal journey, so "proved" this exercise with Algebra. Would it be a good idea to share my scratch work? And to keep it short:
I defined
x=2, y=1, because it looks like 2=1 denotes x=y based on the question. - (maybe i have yet to prove this?)
x^2=xy returned 2=1 so true
x^2-y^2=xy - y^2 returned 2=1 so true
(x+y)(x-y)=y(x-y) returned 3=1 so false
x + y = y returned 3=1 so false.
To me, that proves 2=1 wrong. But is there a better more efficient way of proving this? did i do algebra poorly and were the results i got wrong? I guess thats where im hung up. perhaps "solving" the proof algebraically doesnt actually prove anything?
compact veldt
I have Proof question.
I'm currently working on Proofs by Jay Cummings (amazing...
well if x = y
then x - y = 0
and you're dividing by 0
rough stream
I have Proof question.
I'm currently working on Proofs by Jay Cummings (amazing...
This line is the last correct line
icy pasture
I think im still stuck on algebra. If I remove y from the right side and move it to the left, wouldnt the equation come out to be -y + x = 0. Oh. That is also 0. OH I GET IT NOW.
rough stream
Note it reads "0 = 0"
deft pivot
why DF:FA:BH = 5:6:3?
icy pasture
I got my wires crossed a bit and tried to solve this in a weird way when it was much more simple than I thought. I didn't have to plug anything in.
Thank you!
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magic ermine
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magic ermine
<@&286206848099549185>
ancient locust
yeah
magic ermine
Thanks.
magic ermine
So there are 3 rectangles and to triangles
Just show me the work and the answer. ❤️
magic ermine
I still don’t understand.
The answer that im getting it not the same with that.
<@&286206848099549185>
fluid root
you need to wait 15 minutes
fluid root
@frozen summit
magic ermine
Why changing the topic?
fluid root
<@&268886789983436800>
frozen summit
<@1199060542904598670>
Hi
fluid root
accidental istg
frozen summit
Ok
fluid root
mb g
magic ermine
Can sometime help me now?
frozen summit
Can sometime help me now?
How
fluid root
find the total surface area
fluid root
wow, you want a kiss on the cheek with that too
fluid root
what is the 21 cm connected to
magic ermine
9
magic ermine
Im not sure man
frozen summit
9 is the measure in cm of the other side I think
So it wouldn't be height
ancient locust
2*(21.5)^2 + 2(21) + 21.5*(9)
frozen summit
The backside
Why does it have a exponent there?
I think it would be
2 x (21.5• 21 ) + 2 x ( 21.5 • 9)
frozen summit
I think it would be
2 x (21.5• 21 ) + 2 x ( 21.5 • 9)
I think it would be this
magic ermine
But like that answer is 614.7 cm^2
frozen summit
Oh that 614 is already the answer?
magic ermine
Oh that 614 is already the answer?
What do you mean? Sorry?
ancient locust
i feel the 21 is the area of the triangle
im wrong its hte height
frozen summit
What do you mean? Sorry?
I thought it was of another question, sorry
magic ermine
I thought it was of another question, sorry
.
magic ermine
We’re working on this. ^^
frozen summit
OK so as I understood, the red 614.7 is the answer ?
magic ermine
OK so as I understood, the red 614.7 is the answer ?
Correct.
magic ermine
isthe 21 a height?
I’m not sure, that’s why I’m struggling on this.
fluid root
we dont need a quick example
we need to see the figure better to understand the 21 is about
frozen summit
This alone doesn't make that much of sense
magic ermine
That’s pretty much it then.
magic ermine
we need to see the figure better to understand the 21 is about
I think 21 is the height
frozen summit
Let's suppose is the height
magic ermine
Here are a quick example.
frozen summit
Ok
magic ermine
Anything yet?
frozen summit
I'm only getting similar results
But not the same
One thing I tried :
2(½ • 21.5 • 9 ) + 2(½ • 21.5 • 21 )
But it resulted 645 cm²
Not the same
magic ermine
One thing I tried :
2(½ • 21.5 • 9 ) + 2(½ • 21.5 • 21 )
But it resulted 645 cm...
So, what’s your saying is that the answer they gave it is wrong?
frozen summit
I'm not saying with 100% sure, but based on our results it is to be wrong
frozen summit
Try asking your teacher
magic ermine
Okay.
pearl pondBOT
@magic ermine Has your question been resolved?
pearl pondBOT
@magic ermine Has your question been resolved?
proper harness
Idk how to do this
proper harness
<@&286206848099549185>
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proper harness
<@&286206848099549185>
proper harness
<@&286206848099549185>
proper harness
<@&286206848099549185>
proper harness
<@&286206848099549185>
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<@&286206848099549185>
distant raptor
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proper harness
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unkempt yacht
A class has 5 female students and 6 male students. Line them up, calculate the probability for there are no female students adjacent to each other
unkempt yacht
i figure the only configuration for this to happen is MFMFMFMFMFM
so what i did was
cinder flower
how is that the only configuration
unkempt yacht
$\frac{A_6^6\times A_5^5}{A_{11}^{11}}$
jolly parrotBOT
unkempt yacht
what about MFMFMFMFMMF
oh youre right
cinder flower
i’m always right
unkempt yacht
im not sure how to calculate exactly how many of possible configurations?
cinder flower
you need to have a male between each female but if you just put one that still leaves 2 males “free”
and you can insert them anywhere
unkempt yacht
you need to have a male between each female but if you just put one that still l...
right, so the base config is FMFMFMFMF, which i have 2 M left
cinder flower
sure
unkempt yacht
there are 10 available slots for a M
once that M joins, there will be 11 available slots for another M
so, 10*11?
unkempt yacht
the space between people that i can insert another male in
for example, i can insert a M between the first F and first M, that a slot
cinder flower
just think of the slots as between the Fs
and at the beginning and end
so 6 of them
unkempt yacht
oh
cinder flower
and 6^2 ways to place down Ms
unkempt yacht
so a total of 36 possible configs to satisfy the initial condition?
cinder flower
36 permutations of FFFFFMMMMMM fit the problem specifications yes
unkempt yacht
right, so my final answer would be
$36\times\frac{6!5!}{11!}$
which gets me 6/77?
seems wrong, it isnt listed in one of the options
cinder flower
never seen this A notation
unkempt yacht
yeah in my place its used as A, combination counts that order matters
cinder flower
lol you could just say 11! instead of P_11^11
unkempt yacht
oh yeh i forgot
jolly parrotBOT
unkempt yacht
which gets me 6/77?
but anyway
cinder flower
unkempt yacht
seems wrong, it isnt listed in one of the options
if it helps, the options are:
- 65/66
- 1/22
- 1/66
- 7/99
i eliminated the first and last options; the last implies the configurations amount is non-integer, while the first is wayyyyy too high realistically
unkempt yacht
youre welcome to do so if it helps
final horizon
A class has 5 female students and 6 male students. Line them up, calculate the p...
This is the question right?
unkempt yacht
yes
final horizon
For these types of question i generally like to split the condtions and then solve
First total number of ways to arrange all of them is 11! agree?
unkempt yacht
yeah, go on
final horizon
No female should be adjacent to each other
so we create gaps which can be filled in
unkempt yacht
right
final horizon
so we have 7 gaps
so 7C5 ways of arranging the female
and then for male
its simple
6 male 6 factorial ways
unkempt yacht
7? i only see 6 on the diagram
unkempt yacht
but its still possible that there is 2 adjacent males
FMFMFMFMFMMF is a valid combination
final horizon
alright gotchu your doubt
now lets say out of 7 spots
i fill 5 spots
like this
sorry for bad handwriting
now see there is two gaps between male?
those are empty
so that means they will sit together
so the combination here is FMFMFMFMMMF
Since we are choosing 5 spots out of 7
final horizon
The rest spots can be filled by men
ok onto next part
we got the seats ready
now the male does not have any restriction
so 6! ways
And obviously since we placed the FEMALE seats 2 F wont sit together
unkempt yacht
we already got the number of possible configs, then we can just multiply it to 6!5!/11! ya?
unkempt yacht
same result can also be yielded by 7C5 * 5!
unkempt yacht
so that gives me 1/22
unkempt yacht
right i get it now, thanks @final horizon @cinder flower
final horizon
btw
unkempt yacht
final horizon
just one more tip
unkempt yacht
hi
final horizon
This method is called gap
gap method
whenever you see adjacent word
in the question
you pop this in
always works👍
final horizon
Glad i could help!
unkempt yacht
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pearl pondBOT
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arctic cave
I've been struggling with this question and I can't understand the solution. How many integers $n$ are there in ${ 1,\ 2,\ 3, \ldots , \ 2022} $ such that $ \left \lfloor{\sqrt[3]{n}}\right \rfloor $ is a factor of $n$?
jolly parrotBOT
everything_addict
smoky musk
Just find how many numbers in ${n^3, n^3+1, ... (n+1)^3-1}$ that is divisible by $n$
jolly parrotBOT
Xwtek
pearl pondBOT
@arctic cave Has your question been resolved?
arctic cave
Just find how many numbers in $\{n^3, n^3+1, ... (n+1)^3-1\}$ that is divisible ...
huh
jolly parrotBOT
Xwtek
smoky musk
What do you know about divisibility?
(Also, please do ping me, I might be lost in way and forget to check this thread.)
arctic cave
alright
smoky musk
I know.
arctic cave
so no calculators or anything
smoky musk
If you're prepared for olympiad, you should've been taught about divisibility
smoky musk
**Xwtek**
Then, for this question, what is the answer?
And no, there is a simpler answer than "calculate one-by-one"
arctic cave
for k an integer right?
smoky musk
Natural number
smoky musk
Lemme test
$$\left \lfloor{\frac{n}{k}}\right \rfloor$$
arctic cave
$\lfloor{\frac{n}{k}}\rfloor$
smoky musk
TeXit was just drunk
arctic cave
im a bit new to latex
smoky musk
But that's right.
jolly parrotBOT
everything_addict
smoky musk
I think you missed a term.
arctic cave
@smoky musk
smoky musk
Can I show your calculation?
arctic cave
$\frac{\left( (n + 1)^3 - 1 \right)}{n}= n^2 + 3n + 3$
jolly parrotBOT
everything_addict
arctic cave
$\frac{n^3}{n} = n^2$
jolly parrotBOT
everything_addict
jolly parrotBOT
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smoky musk
Correlation?
smoky musk
So, what is the possibe values of x such that
$n = \lfloor \sqrt[3]{x}\rfloor$
for a specific n?
jolly parrotBOT
Xwtek
jolly parrotBOT
everything_addict
arctic cave
i sort of get the connection but t doesnt work out somehow
sorry about that
could u guide a bit more
smoky musk
Divide the range to several categories:
${{1,..., 7},{8,...,26}, ..., {1331, ..., 1727}, {1728, ..., 2022}}$
And calculate the valid integer for each case.
jolly parrotBOT
Xwtek
smoky musk
Be careful. 2022 is not 13^3-1
arctic cave
oh yeah
so for 1 through 11 ill do that
then for 12 i have to calculate
😦
right?
jolly parrotBOT
everything_addict
jolly parrotBOT
everything_addict
smoky musk
**everything\_addict**
Wait, you made a mistake on 4
jolly parrotBOT
everything_addict
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halcyon plank
Hi, can someone give me the hardest SATs math questions
pearl pondBOT
Hi, can someone give me the hardest SATs math questions
halcyon plank
hardest beyond
sharp smelt
which topics? I don't have any hard SAT questions,but I do have hard questions on various topics
pearl pondBOT
@halcyon plank Has your question been resolved?
halcyon plank
which topics? I don't have any hard SAT questions,but I do have hard questions o...
eh
pearl pondBOT
halcyon plank
well
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polar badge
hi in this question theorganichcemistrytutor solved it graphically
polar badge
but how do we solve it without graphs? this is rolles thereom, the step where we try to determine c
pearl pondBOT
@polar badge Has your question been resolved?
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@polar badge Has your question been resolved?
onyx mica
A bit confused here.
I wrote
ai) 4!=24 aii)(3P3)(2P1)=12
bi) 4^4=256 bii)(5P3)(2P1)=120
onyx mica
Or do I use permutation?
trail shoal
4+4•3+4•3•2+4•3•2•1
onyx mica
4P4+4P3+4P2+4P1
But for bi
nvm got it
Can I for the ii sections say because there're 2 even cards and 2 odd cards, so there're just 1/2 of it being even?
Or do I have to expand that?
got them
thanks
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torpid mica
hello. Is this channel available
pearl pondBOT
hello. Is this channel available
sharp smelt
yes
torpid mica
oh. oki
can someone help me with this
according to the available choices, approximately 0.029 ft per hour is correct. but I don't understand how it got up to that point
midnight haven
aight illl try
looks like its related to applications of derivatives
@torpid mica what was your final equations?
for dh/dt?
torpid mica
<@506020915390447619> what was your final equations?
hello. what do meant by that
midnight haven
hello. what do meant by that
what was your approach to this question?
torpid mica
what was your approach to this question?
the formula for this would be V=1/3pi r^2 h.
midnight haven
the formula for this would be V=1/3pi r^2 h.
yes
now radius will change as per height am i right?
torpid mica
now radius will change as per height am i right?
yes
torpid mica
do u know similarity between trinagle?
heard of it but not in actual application
midnight haven
heard of it but not in actual application
aight so
now imagine 2 traingles
basically they are said to be similar if the ratio of their any 2 corresponding sides are equal
for eg
abc
and prq
pqr*
2 triangle
now if ab/bc = pq/qr
they are said to similar
and lets say they share 1 common angle
or should i say
angle abc = angle pqr
this might seem a bit complicated at first
but all gotta do is visualize the cone
look
can u see the inner and outer trinagle
both fo them are similar
of the condition above is statisfied
now
torpid mica
both fo them are similar
so, uh -- the bottom one requires attention?
midnight haven
so, uh -- the bottom one requires attention?
both of them does
wait a sec im drawing smth
tell me do u see the 2 traingles?
triangles which are similar
torpid mica
yes
torpid mica
I understand the 15 and 10 but not so much with the 5
midnight haven
I understand the 15 and 10 but not so much with the 5
well
the tank is 10ft wide
right?
now what that means is the diameter of the tan
tank
the conical top
is 10m
so the radius will be 5m
torpid mica
ohhh.
torpid mica
so u understand this much
I get it now
midnight haven
now due to similarity between the 2 traingles
x/5 = 10/15
right?
and x is raidus so lets denotes by
r
and
that 10
is the height
at that exact moment
but we want to generalize it
so we'll just take h
so
r = h/3
now u know
that at any random time
when h is lets say 6ft
the r will be 2ft
now u already know the formula
v = 1/3 pi r^2 h
put value of r as h/3
now differentate both wrt t
and youll have value of dh/dt
torpid mica
and youll have value of dh/dt
I tried to input the values in the calculator and it worked. Thank you
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ripe needle
If I integrate 1/2x can I integrate 1/x and multiply the answer by 1/2?
ripe needle
like factor out one half
but it's not really working
bc one way you get .5lnx
the other 0.5ln(2x)
glad falcon
Well you can split 0.5ln(2x) into 0.5(ln(2) + ln(x)) so the 0.5ln(2) becomes part of the constant of integration thus you get left with 0.5ln(x) +c as before
But yes it just makes a bit more sense to take the 1/2 out first haha
pearl pondBOT
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midnight haven
a soccer tournament is played until A or B wins 4 rounds
pearl pondBOT
a soccer tournament is played until A or B wins 4 rounds
midnight haven
what is the probability A wins in the 6th round
i got this:
probability of the score being 3-2 in 5 rounds:
5 C 3 * 1/2 ^ 5
probability A wins in the 6th is 1/2
so its 5 C 3 * 1/2 ^ 6
pearl pondBOT
@midnight haven Has your question been resolved?
void grail
Is an equation an equivalence relation?
pearl pondBOT
Is an equation an equivalence relation?
void grail
For example, d/dx c = 0 is an equivalence relation or an equation?
tropic saddle
an equivalence relation can sometimes be defined by an equation if thats what you mean
but this is just an equation
void grail
an equivalence relation can sometimes be defined by an equation if thats what yo...
I just learnt that the two sides of an equation symbol are never the same, unless it is x = x, I'm trying to understand this concept.
As I understand it now, there are relationships, or arrows of categories, and there are equivalence relations, and there are equations.
tropic saddle
oh you want to do this from the level of category theory?
then I'd rather not answer
void grail
Okay. I have very basic understanding of this, but it seems very interesting.
Thanks anyway!
pearl pondBOT
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pearl pondBOT
jolly parrotBOT
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past hound
however apperantly this isnt the answer. and I dont quite understand why this isnt the approach. I have read the answer is the following:
jolly parrotBOT
BeeGass
past hound
which is confusing because isnt this not possible because:
$$
\begin{align}
3s_{11} + 0s_{12} + 0s_{13} &= b_{11} \
3s_{21} + 4s_{22} + 0s_{23} &= b_{21} \
3s_{31} + 4s_{32} + 3s_{33} &= b_{31} \ \
\end{align}
\begin{align}
3s_{11} &= b_{11}
3s_{21} + 4s_{22} &= b_{21}
3s_{31} + 4s_{32} + 3s_{33} &= b_{31}
\end{align}
$$
jolly parrotBOT
BeeGass
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orchid fog
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orchid fog
Have I made any errors, if not how to proceed with my numbers being squared:0
<@&286206848099549185>
I'm not sure if it's just my phone, but when I open a channel at a time, it seems to not be visible to me when I exit it to browse through ><
merry carbon
<@&286206848099549185>
I'm not sure if it's just my phone, but when I open a ch...
Make sure that the help channel section is expanded so you can see all channels, including ones where you've read everything 
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onyx verge
I don't really understand what they want me to do here, or how to find their answer.
The second image is part of the example that they gave me to understand how to do it
pearl pondBOT
I don't really understand what they want me to do here, or how to find their ans...
@onyx verge Has your question been resolved?
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@onyx verge Has your question been resolved?
spring oar
I don't really understand what they want me to do here, or how to find their ans...
are you still there?
onyx verge
are you still there?
yes, sorry for the late reply
onyx verge
what is 7pi/2 approximately equal to?
~10.996
onyx verge
no worries.
i was more confused as to where they got the x coordinate's location from, honestly
spring oar
so in the example, 12 would be to the right of that, yeah?
onyx verge
yes
spring oar
and in your problem, you're trying to find the approximate answer for when theta = 6, yeah?
onyx verge
and in your problem, you're trying to find the approximate answer for when theta...
yup
spring oar
so what is the closest value on the number line to 6?
onyx verge
so what is the closest value on the number line to 6?
This, right?
But that's assuming each tick is an increase of x by 1 and not some other number
onyx verge
it looks like you took a pic of 3pi/2?
is that not what you're looking for?
Sorry, i got distracted, hence the late reply
spring oar
when you multiply 3*pi and then divide by 2, what do you get?
onyx verge
~4.71
spring oar
ok, so that's less than 6, yeah?
onyx verge
yes
spring oar
is there another number closer to 6 on the number line?
onyx verge
2*pi gets ~6.28
spring oar
which is closer. so that means that your value must be a little to the left of 2pi, ya?
onyx verge
correct. But where do i go from here?
spring oar
so what is the approximate value of the function just to the left of 2pi?
i'm not sure how exact the answer needs to be
onyx verge
i'm not sure how exact the answer needs to be
the example's answer was -0.5, so maybe just by approximations of .5?
spring oar
note that the value has to be negative, because just to the left of 2pi, the function is negative
oh, i see what you mean
yeah
onyx verge
note that the value has to be negative, because just to the left of 2pi, the fun...
interesting
so something between 3Pi/2 and 2Pi.
i dunno, so i just draw lines and hope one sticks?
spring oar
i don't see the rest of the instructions, so that seems about right
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ancient locust
yes
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toxic cliff
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toxic cliff
I'm not sure how they went from the first expression to the second
with the summation and the dx
Isn't f^(n)(0) always zero
merry carbon
Using $e^y = \sum_{k = 0}^\infty \frac{y^k}{k!}$ and setting $y = -x^2$, then simplifying
jolly parrotBOT
@merry carbon
toxic cliff
Using $e^y = \sum_{k = 0}^\infty \frac{y^k}{k!}$ and setting $y = -x^2$, then si...
oh okay, thank you!
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