wait so this is wrong bronx?
#help-28
neon rivet
noble spade
Isnt a side of the triangle called hypotenuse only when its opposite to a right angle?
turbid tinsel
Isnt a side of the triangle called hypotenuse only when its opposite to a right ...
yes you are correct
noble spade
wait so this is wrong bronx?
It is u cant add vectors like that unless they are in the same direction
turbid tinsel
wait so this is wrong bronx?
since its north east, the angle formed between the east and north is 45 on either side, so you take the sine of the angle to get the length
so it would be (10i + 0j + 0k) for the east one then the other length would be (5) (sin 45) which is 5/root2
prime pier
Isnt a side of the triangle called hypotenuse only when its opposite to a right ...
you are right, I'll be quiet
turbid tinsel
you are right, I'll be quiet
its no worries mate we all make mistakes, i once added -3 with -3 and wrote +6 as the answer
noble spade
Do you know the formula for magnitude of resultant vector
noble spade
you are right, I'll be quiet
Its ok bro ig u meant to say diagonal in the parallelogram sum thing prob
neon rivet
so it would be (10i + 0j + 0k) for the east one then the other length would be (...
How did you calculate?
noble spade
Do you know the formula for magnitude of resultant vector
@neon rivet ??
noble spade
neon rivet
given that a and b are vector themselves
noble spade
Perhaps this reminds u of it?
neon rivet
Yeah I’ve seen that
noble spade
Yeah I’ve seen that
Yeah you have to use it here
noble spade
Yeah I’ve seen that
Do you agree than north east makes 45° with east?
neon rivet
I agree
neon rivet
Okay, don’t worry now I know
noble spade
The angle opposite to a bar in the triangle would be 180-45 or 135 and if that was 45, 135+45 would be 180 making the other angle 0 which it obv Is not
Ok
neon rivet
The north east vector is the one in 5 cm so 45°
noble spade
Yes
neon rivet
Also, why do you need to write the modules a vector when the a vector already without the modulus is contained measurement and direction?
So with the other vectors as well
noble spade
Also, why do you need to write the modules a vector when the a vector already wi...
The a vector is 10i it is not 10.
neon rivet
I know that the modulus a vector is meaning length of a vector but still why is that the case?
noble spade
10i cap
noble spade
Also, why do you need to write the modules a vector when the a vector already wi...
Wait i didnt get ur question wdym
neon rivet
The absolute symbol in the vector
noble spade
More context?
neon rivet
You could’ve wrote it without the absolute symbol since the vector without the absolute symbol is already a vector quantity, which means it has direction and magnitude
noble spade
You could’ve wrote it without the absolute symbol since the vector without the a...
Bro this is a formulae i dont understand why you are asking me
Im not the one who derived it
Anyway u get this formulae when u assume the vector's magnitude as lengths and make a triangle and use some pythagoras
noble spade
using phythagoras ig but it comes from cosine rule or so
Ye vector decomposition of b vector and then do pythagoras
noble spade
Ye vector decomposition of b vector and then do pythagoras
bcosthetai+bsinthetaj
mossy stratus
Just use latex
glossy valveBOT
mercy
mossy stratus
Didnt talk to bro
glossy valveBOT
mercy
noble spade
Just use latex
Idk how to
full forumBOT
@neon rivet Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
naive walrus
can someone tell me the thought process for this question usign pigeon hole
torn jolt
can someone tell me the thought process for this question usign pigeon hole
what have you tried so far
naive walrus
what have you tried so far
okay well
so
i know that its true beacuse
if we assume worst case scenario where 10 people right
so 10x7 is 70where 10 is the pigeons
and 7 is the pigeon hole
that means +1 makes it so at least 1 of the 7 pigeon holes have like 11 people
71<75 so that means it will work for 75
brittle sun
What's the statement you're using for the pigeonhole principle
torn jolt
71<75 so that means it will work for 75
i too am confused about this
according to general php a hole will have atleat mathceil(n/k) where k is number of holes and n is pigeons
naive walrus
What's the statement you're using for the pigeonhole principle
wdym
i dont get that
naive walrus
i too am confused about this
no beacuse 71 people is needed for worst case scenario
that means like 75 meansit definetly will
is that right?
naive walrus
What's the statement you're using for the pigeonhole principle
wait but what does it eman id ont get this
torn jolt
oh hm.. that works
naive walrus
what statement do i need to give?
brittle sun
The theorem statement
naive walrus
whats that
heady heron
state your version of the pigeonhole principle, please.
naive walrus
what do u mean
what is my version?
thats what im confused abt
o do i state like
let the adluts in the room be the pigeons and let the 7 days of the week be the pigeon holes?
is that what u guys mean
brittle sun
Okay let's step back
naive walrus
ok
naive walrus
like that if u have more pigeons then pigeon holes that means that like
there will be a certain amount
like if n+1 or more objects palced in a hole, then some holes will have 2 objects
torn jolt
where did you learn php from
heady heron
from where have you learnt the principle? state the statement from that source exactly as you've learnt it.
naive walrus
where did you learn php from
our teacher spent like 10min through it in class bru
brittle sun
Does your book mention it at all
naive walrus
bro idk the exact meaning
brittle sun
You can't do maths by feel
naive walrus
okay let me go read
naive walrus
You can't do maths by feel
what is by feel
brittle sun
What you're doing right now
brittle sun
okay let me go read
Cool, let us know what the book says
naive walrus
if n+1 or more ojetcs are placed into n holes, then some holes contains at least 2 objects
what cambridge says
exact wording
brittle sun
Ah good, so not the general case
naive walrus
generalised pigeonhole principle is if at least mn+1 objects are placed into n holes, then some holes contains at least m+1 objects
naive walrus
Ah good, so not the general case
what
brittle sun
generalised pigeonhole principle is if at least mn+1 objects are placed into n h...
Ah good, that's the general case
Are you allowed to use either
wraith hinge
where can i start with highschool math
brittle sun
Cool, then you have already solved it. Just make it a bit more explicit
naive walrus
what?
warped spire
where can i start with highschool math
!occupied, please move to another channel or use #study-discussion
full forumBOT
where can i start with highschool math
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
brittle sun
where can i start with highschool math
#study-discussion pls, this is an occupied channel
naive walrus
wait u guys asked me to like learn pfp or like theorem statement
what do i do with that?
brittle sun
71<75 so that means it will work for 75
What you said here is a solution
naive walrus
What you said here is a solution
ye but wasnt my above text like how i go tto the solution
brittle sun
Php is pigeonhole principle
naive walrus
ye
brittle sun
It's a theorem
naive walrus
yes
brittle sun
Formally you would make the argument more concrete is all
If you have ≥ mn+1 objects and n holes, one of the holes contains ≥ m+1 objects
Just say what your values are for m and n in this case
And you're done
naive walrus
If you have ≥ mn+1 objects and n holes, one of the holes contains ≥ m+1 objects
what is mn in this case
or like what would u sub in?
warped spire
you know n here
naive walrus
can i do
allow the adults in the room be the pigeons
allow the days of the weeks to be the pigeons hole
let each pigeon hole contain 10 pigeons so 7x10=70
the 71st pigeon can go into any 1 of the 7 pigeon holes
at least 1 of the 7 holes have 11 pigeons in it
so therefore as 71<75 that means at least 1 of the 7 holes will have at least 11 pigeons in it
what is i write that?
naive walrus
you know n here
i do
is n the number of pigeon holes?
and m is the worst case scenario?
warped spire
look back at your generalized statement
naive walrus
what on earth is my generalized statement bro
warped spire
generalised pigeonhole principle is if at least mn+1 objects are placed into n h...
^
naive walrus
oh ye what abt that textbook definition
warped spire
when I refer to n I'm referring to that statement's use of n
naive walrus
yes so what is it abt the use of n
warped spire
what is n in the statement?
naive walrus
what is n in the statement?
wait since im on a time crunch
warped spire
I was expecting you to define n as the number of holes but yes that's correct
naive walrus
my idea of this is correct right
warped spire
your idea is correct.
naive walrus
and like i would get full working if i just specify
like n value being n of holes whcih is 7
m being the worse cast scenario
warped spire
for marking stuff, ask your examiner or teacher, cuz none of us can answer that
naive walrus
shoot bruh my test is tomorrow
warped spire
cuz only they know what they want to see
naive walrus
okay ima guess its rightc uz my teachers working got like nothing
alr then ty guys
.clos
.close
full forumBOT
Available help channel!
dreamy anvil
full forumBOT
grand escarp
Write out all of the equations you can think of. For example, what do all of the angles of a triangle add up to? That’s one. Then what do 2 angles on a straight line (y and (w-13) for example) add up to?
From there you can use some of the equations to plug into the others to simplify and reduce the number of variables
full forumBOT
idle heart
if someone can send work too we would like that thanks
light sonnet
if someone can send work too we would like that thanks
We?
Also we don't do people's work
We can assist if needed
full forumBOT
@serene temple Has your question been resolved?
full forumBOT
@serene temple Has your question been resolved?
fickle shuttle
@serene temple hello
Do you need help w all 3?
Starting with 8, what have you tried? Where are you stuck? Do you know what all the terms in the question means?
Do you know what a basis is?
@serene temple
You seem very uhh nonchalant.
Do you think maybe you should try to learn the definitions for the concepts before trying the question?
Yes, but you can, you know, help us help you. If you need help with the concepts, ask about the specific concepts you don't understand. If you understand the concepts but need help with the question, then ask about the question
And when I'm trying to gauge what you understand, all I get is "nah" with no explanation
weak minnow
Do you expect us to tell you what the terms in the question mean? Have you read the definition of a basis and not understood it, or you did not read it and expect us to tell you the definition, which is no different from you reading the definition?
fickle shuttle
Look at the definition of a basis and basic results about bases
And tell us if you understand it
weak minnow
Read the definition of a basis. It's literally the best advice
fickle shuttle
Or ask about what you don't understand
Did you read the definition?
Let's say our vector space is $V$ (with field of scalar $F$) and we have vectors $v_1, v_2, \dots, v_n$.
A linear combination of the vectors $v_1, v_2, \dots, v_n$ is a vector of the form
[ a_1 v_1 + a_2 v_2 + \dots + a_n v_n, ]
where $a_1, a_2, \dots, a_n$ are scalar from $F$.
The span of the vectors $v_1, v_2, \dots, v_n$ is the set of all linear combinations of the vectors:
[ \text{span}(v_1, v_2, \dots, v_n) = { a_1 v_1 + a_2 v_2 + \dots + a_n v_n: a_i \in F }. ]
The set ${v_1, v_2, \dots, v_n }$ is linearly independent if
[ a_1 v_1 + a_2 v_2 + \dots + a_n v_n = 0 \implies a_1 = a_2 = \dots = a_n = 0. ]
Vectors are linearly independent if every vector in their span has a unique representation as a linear combination, by which I mean there is only one way you can choose the scalars to get that specific vector.
A basis for your vector space $V$ is a linearly independent set $B = { b_1, b_2, \dots, b_n }$ with $\text{span}(B) = V$.
So, the fact that $\text{span}(B) = V$ means that every vector can be written as a linear combination of your basis vectors, and that the basis is linearly independent means that there is a unique way to write each vector as a linear combination of the basis vectors. So, for every $v \in V$, there is a unique choice of scalars $a_1, a_2, \dots, a_n$ such that
[ v = a_1 b_1 + \dots + a_n b_n. ]
So, because of there being a unique choice of scalars, we call those scalar "coordinates" and then coordinate vector with respect to B of v is just the column vector containing those coordinates, so
[ [v]_B = \begin{bmatrix} a_1 \ a_2 \ \dots \ a_n \end{bmatrix}. ]
@serene temple read, explain what you don't understand
glossy valveBOT
Lunasong the Supergay
full forumBOT
@serene temple Has your question been resolved?
fickle shuttle
@serene temple hello?
You are saying your question hasn't been resolved, but you are not replying either
onyx glen
clearly they are intentionally hogging the channel
fickle shuttle
simple totem
.close
full forumBOT
onyx glen
then close the channel lol
torn jolt
Yeah ?
onyx glen
if you need help, then why leave without a word for 2 hours?
either you want to get help now and stay in the channel and respond to things people tell you,
or you close the channel, take care of the shit you need to do, and only then come back
torn jolt
do you need help or do you want the answer
well we can only offer the former
so what concepts do you think you need for this problem
a coordinate matrix is like a "transition matrix"
if you multiply a matrix x by the coordinate matrix, you get x'
full forumBOT
@serene temple Has your question been resolved?
full forumBOT
@serene temple Has your question been resolved?
fickle shuttle
Can no one except the person who asked close the channel? 
winged geyser
helpers can
torn jolt
.close
full forumBOT
torn jolt
nice
full forumBOT
Available help channel!
fickle shuttle
Do I actually have to get the role now for this power? No, I'll just ping other helps to do it
full forumBOT
brisk nexus
**Lunasong the Supergay**
oh my god
full forumBOT
Available help channel!
full forumBOT
light sonnet
crimson sequoia
Hi,
Given a finite field F_p, if a root does not exist in F_p, can I conclude that it is also not in F_p^2? For example, sqrt(-5) may not exist in F_p, does it mean that it is also not exist in F_p^2?
crimson sequoia
<@&286206848099549185>
deep sigil
hi
crimson sequoia
hello!
deep sigil
do you want to talk about the problem
crimson sequoia
Yep, so I have a field F_p and it has no solution for the polynomial X^2 + 5
Now I am wondering if it has a solution for X^2 + 5 in the field F_p^2
deep sigil
do you want to come to the voice channel mathematics
crimson sequoia
Where elements in F_p^2 is (a,b) where a and b are in F_p
Alright
changing mic settints
still open for help, if anyone is available
full forumBOT
@crimson sequoia Has your question been resolved?
lavish island
My question is in french so I am doing my best to translate it:
What is the value of j(30.8) if j(x) = f(h(x))
f(x) = $-\sqrt(5) \sqrt(x+9) +10$
h(x) = $\frac{4}{x-10}+30$
glossy valveBOT
Yoyo
devout void
My question is in french so I am doing my best to translate it:
What is the val...
What have you tried?
lavish island
What have you tried?
i've tried using j(x)^2 in order to get rid of the sqrt. i also tried adding 30.8 to the entire equation as x
second try i got -4
devout void
There are two approaches you can take
1) Plug in j(30.8) and evaluate step by step
2) Find the general formula for j(x)
Also, I don't know the answer but I can check right now
lavish island
thank you
devout void
I don't think it's -4
devout void
Can you perhaps post an image of what you tried?
lavish island
yeah one sec
devout void
i tried first approach and got -3.99..
This is more probable, so the calculations here were correct
I had mistyped a root in the calculator, but I've corrected it and it does give -3.9986 and so on
devout void
Yes, this looks good
full forumBOT
fervent leaf
This method is a very bad way of doing this
full forumBOT
@untold umbra Has your question been resolved?
untold umbra
.close
full kayak
No idea how to sketch anti derivative graph
full forumBOT
No idea how to sketch anti derivative graph
full kayak
Only ever sketched derivative functions
jaunty chasm
Choose any starting point and go from there
thorn dock
No idea how to sketch anti derivative graph
the idea is that you pick a starting point
you are free to set that to 0 or maybe even something negative to be good with the limited space on the paper
then you just draw the curve and follow where the original graph is positive, negative or 0
jaunty chasm
+c moment
thorn dock
never forget the +c! (unless youre a physics student in which case you will always argue why that constant will become 0 anyways 
)
thorn dock
almost
but you shouldnt treat the local max to the left as a 0
it can get a little confusing at times but remember that the left graph shows the slope of the right one
thorn dock
extremal points of the derivative are inflection points of the next higher function, thats right ^^
but the slope shouldnt go to 0, at least not in this situation
its quite the opposite, the slope should be steepest there
full kayak
So on the anti derivative function is the highest point the local max from derivative?
jaunty chasm
The highest slope
thorn dock
id try something else before actually drawing the graph:
take note of the special points of the left graph and mark their respective x coords on the right side
full kayak
So x int at x=-3 local max x=-1 local min x=4
thorn dock
id try something else before actually drawing the graph:
take note of the specia...
and then consider the meaning of each of these points for the anti-derivative
thorn dock
So x int at x=-3 local max x=-1 local min x=4
local min and what else?
(this point has 2 properties)
full kayak
Is it an intercept?
thorn dock
yup!
thorn dock
thats still fine
full kayak
Okay now what
thorn dock
as long as it "touches" y=0 it counts as an intercept
thorn dock
now lets think of the meaning of each of these points for the antideriv
lets start with the intercept
what does an x intercept mean for its antiderivative?
full kayak
turning point?
thorn dock
hold up now i need to look up the correct names 😂 (english isnt my first language)
full kayak
oh I couldn’t tell ahah, you’re fluent
thorn dock
thanks ^^
okay so the x intercept of a function means that its antiderivative will have a local min, max or saddle point there
basically it just means that the graph is horizontal in that point
full kayak
Okay
thorn dock
okay so the x intercept of a function means that its antiderivative will have a ...
which of the 3 it is is determined by what the first graph does to the right and left of the intercept
so if we look at the first x intercept at x=-3
thorn dock
okay so the x intercept of a function means that its antiderivative will have a ...
which of these 3 would you say it is?
full kayak
negative then 0 then positive
thorn dock
correct!
moving on, the next point of interest is the local max at -1
or rather
before we move on
id draw a little segment of the new graph right where the local minimum is
(so we have a start)
thorn dock
now, what does the local max correspond to?
full kayak
A slant point?
I call it point of inflection where I’m from tho I think
I think they’re the same
full kayak
Okay
full kayak
Yep
thorn dock
next POI is the x-intercept + local min at x=4
full kayak
Is that higher or lower than the previous poi
thorn dock
since the first graph and therefore our slope isnt negative anywhere besides to the far left, the points will go higher and higher
thorn dock
well you still made the curve flatten out at the local max of your first function
the opposite is correct
this local max means the slope of the antiderivative has a local max in this point
so this part has to be steeper than anything else
the rest is correct tho
thorn dock
like this
full kayak
Ohhhh okay
thorn dock
well in your case the graph doesnt start to drop
but the points matter
its basically a local max of the slope
thorn dock
yes pretty much
full kayak
I fixed the curve towards the 3
So it’s not as linear
Abs the middle of it is max slope
Makes sense
thorn dock
if you have a teacher thats really strict, you might want to make the inflection point a little steeper (and a little clearer that its an inflection point)
but this already comes down to your drawing precision
full kayak
I pretty sure they said this was a bit out of my course so it’s okay
thorn dock
maybe just mark the point to say "here is the point of inflection"
thorn dock
np! 😄
full kayak
.close
torn jolt
Help
raven lake
full forumBOT
full forumBOT
@raven lake Has your question been resolved?
raven lake
<@&286206848099549185>
full forumBOT
@raven lake Has your question been resolved?
full forumBOT
@raven lake Has your question been resolved?
pseudo trellis
Write an equation for a line parallel to y = 0.25x − 5 that passes through the point (8, 5).
arctic yoke
y=0.25x+6.75 i think this is right but feel free to check me on that
i used desmos graphing to help find my answer
unborn quarry
y=0.25x+6.75 i think this is right but feel free to check me on that
Hello, this line passes through (5,8), not (8,5)
pseudo trellis
https://www.desmos.com/calculator
Thanks for it
pseudo trellis
right, i knew something was wrong
Is it wrong?
full forumBOT
full forumBOT
Available help channel!
twilit ridge
Is this right?
full forumBOT
Is this right?
torn jolt
full forumBOT
torn jolt
is this correct
because they are asking
equation of line that passes throught the point
so do I write the answer
or do I write an equation
ornate oriole
isn't the equation the answer
torn jolt
isn't the equation the answer
its correct right?
ornate oriole
yeah
static bronze
Anyone know what method I should use to find if this series converges or not? I messed around with the integral test but then looked at its graph which doesn’t decrease, so now I’m stumped :( if I had an idea of which method to use I could solve it but I’m drawing a blank right now
static bronze
Don’t think it could be a direct or limit comp either cause it’s not similar to a geometric or p-series. Don’t think it’s ratio or root either cause the general form doesn’t look right
Not alternating series test or divergence test
full forumBOT
@static bronze Has your question been resolved?
static bronze
<@&286206848099549185>
cobalt otter
blissful juniper
What is the slope of the line 4x - 5y = 20?
equation of line
blissful juniper
<@&286206848099549185>
blissful juniper
ohh ty
slow canopy
Happy to help
If you need to see an example I can show you in like 10 minutes
@blissful juniper did you get it?
shrewd copper
Hey , idk how to start on this , cause I'm very much confused on how to find the first term with just third term and eight term , can you guide me?
wide star
Hey , idk how to start on this , cause I'm very much confused on how to find the...
There's multiple formulas courses usually derive for arithmetic sequences. One looks sort of like $a_{n+1}=a_n + d$. For all of them you are given $a_0$ in advance.
glossy valveBOT
DootDooter
wide star
You can use that formula with what you know to find d an work ur way backwards to a_0
But there's also a nicer formula.
It looks something vaguely like a_n=a_0+(n-1)d
That one would be easier since you can just plug the info for the 8th and 3rd term into it and solve directly.
But you should use whatever specific versions of these formulas your course showed you rather than my hazy guesses because I could be remembering the formulas slightly wrong!
full forumBOT
@shrewd copper Has your question been resolved?
shrewd copper
Ouhhh i see , i think i could try it out , Thanks a lot for the suggestion @wide star
torn jolt
Hey, I am stuck on this step of a calculus 1 problem where I have to use l’hospital rule, can someone help me?
torn jolt
Well it says, “Find the limit. Use L’Hospital when appropriate” and since Webassign has videos I thought I could use that but I didn’t understand what steps they used to get the stuff they got after…
onyx glen
so what you have is $\lim_{x \to 0} \paren{4(1 + 8x)^{-1/2} + \frac{9}{2} (1 - 9x)^{-1/2}}$
glossy valveBOT
Ann
torn jolt
Yes yes😭
onyx glen
have you considered direct substitution?
torn jolt
Hold on
onyx glen
you can plug in x=0 with no harm here lol
torn jolt
Uhhh, did I rewrite the things correctly or am I confusing something😭
onyx glen
you're overcomplicating it.
i mean, sure, that's a valid way of rewriting the expression
but it doesn't change the fact that:
you can plug in x=0 with no harm here
torn jolt
So what would happen if I plugged it in where you said?😅
torn jolt
Okay let me try🤔
onyx glen
sam
you've solved limits before, right?
you know that 'doing algebra with the goal of being able to plug in the limiting value' is like, the most common technique when doing limits like this, right?
torn jolt
Yes but like I haven’t exactly been doing all my hw up till this point so I’m trying to fix my wrongs now by doing it now😭
Like I did know but the -1/2 exponent scared me for a sec that why😂
I plugged it in the calculator and it said error ;-;
I think it’s because it’s just 0+0
onyx glen
...
0+0 should not give any errors.
please show exactly what you put into the calculator.
torn jolt
Wait I changed the minus 1/2 exponents to negative 1/2 and now it gives me 17/2
Is that correct?😅
Im trying here man😭💀
onyx glen
yes now it's correct
i'm still a bit puzzled what you could've put in the calculator originally
but whatever
pulsar gale
you mean "the negative symbol instead of putting minus symbol"
torn jolt
Yeah that🤧
pulsar gale
minus symbol is interpreted as an operation, after all
torn jolt
So umm, can I get help with another problem or do I have to wait or?😭
I literally just joined this server like 1 minute ago :/
pulsar gale
until you're satisfied, then .close
torn jolt
Oh okay!😁
pulsar gale
read #❓how-to-get-help if you haven't or have forgotten
torn jolt
I’m glad I decided to put “math” in the discord server invite link thingy😂
So for this problem, I’m kinda stuck on how to take the derivative of the e to the x…
L'Hôpital's rule
hmmm
onyx glen
@torn jolt e^x is its own derivative
torn jolt
Ahhh😭
pulsar gale
-x is a separate function
pulsar gale
no
glossy valveBOT
torn jolt
So just take the derivative of -x then?
pulsar gale
this is the chain rule
torn jolt
So like this?🥲
pulsar gale
sure
pulsar gale
mind your signs
torn jolt
.close
full forumBOT
full forumBOT
Available help channel!
sharp igloo
can someone confirm that all quadratic equations that are also a perfect square trinomial always have 0 as the discriminant?
torn gust
that's right
sharp igloo
thanks
torn gust
wait let me check
sharp igloo
wait but is it the same reversed?
torn gust
this is only true if the zeroes are real
sharp igloo
like all quadratic equations with 0 for a discriminant are perfect square trinomials?
torn gust
that's right
sharp igloo
okeee thanks
torn gust
the discriminant is like the distance between zeroes
but if it's square then the zeroes are the same and the distance is 0
sharp igloo
the discriminant is like the distance between zeroes
wdym by that, isnt it just b^2-4ac
torn gust
like for the quadratic formula
it's like -b/2a plus or minus sqrt(discriminant)/2a
so if the discriminant is big the zeroes are far apart
full forumBOT
full forumBOT
Available help channel!
untold solar
Hi, how would I go from the left-hand-side of the equation to the right-hand-side of the equation for the following problem:
untold solar
chrome sapphire
5n^2 is a little less than 5 times as big as (n^2+2), the -10 is remaining after doing long division
chrome sapphire
no problemo
untold solar
.close
ripe summit
This has to be wrong, right? It’s a function composed of its inverse function so the answer should be x…. I think.
ripe summit
gentle sparrow
check your denominator - something happened in the process of expanding it
but yeah your intuition is right, should have been x
full forumBOT
@ripe summit Has your question been resolved?
ripe summit
@gentle sparrow thank you! I’ll re do my denominator and see what happens. This inverse function stuff is kinda dumb lol
.close
spiral ore
Hot water at 80 C is mixed with cold water at 12 C. After thermal equilibrium is reached the final temperature is 32 C. The total mass of the water is 4.50 Kg, so what is the initial mass of the hot water? OK so how do i start with the formula.. Qgained=Qlost?
spiral ore
.close
full forumBOT
full forumBOT
Available help channel!
wheat umbra
I'm having a really hard time comprehending how the radius of convergence works for power series. I keep on looking at examples and not getting it. I think my brain is broken.
I understand the center of convergence well enough, it's pretty self-evident to me. This image is just an example problem from an image search.
full forumBOT
I'm having a really hard time comprehending how the radius of convergence works ...
@wheat umbra Has your question been resolved?
polar mica
alright so
glossy valveBOT
A Fellow Human
polar mica
so essentially as long as $x$ is a distance $\lim_{n\to\infty}\left|\frac{a_n}{a_{n+1}}\right|$ away from $a$ then the series converges
glossy valveBOT
A Fellow Human
polar mica
you can imagine a sort of circle around $a$ and radius $\lim_{n\to\infty}\left|\frac{a_n}{a_{n+1}}\right|$ and if $x$ is in that circle then the series converges
this help?
glossy valveBOT
A Fellow Human
polar mica
**A Fellow Human**
yeah typo here the limit is upside down sry
wheat umbra
**A Fellow Human**
This is where I'm getting a bit lost
wheat umbra
I know that the convergence on the ratio test depends on whether the limit is <, = or > 1
polar mica
good
now because $|x-a|$ is independent of the limit we have $|x-a|\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|<1$ instead
glossy valveBOT
A Fellow Human
wheat umbra
I see that you can factor out the X and constant terms because they're irrelevant to the function of the variable n
polar mica
yes
now you can divide both sides of the inequality by $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|$
glossy valveBOT
A Fellow Human
polar mica
clearly because $\left|\frac{a_{n+1}}{a_n}\right|\geq 0$, so $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|\geq 0$
glossy valveBOT
A Fellow Human
polar mica
which means we dont need to flip the inequality sign
you still there?
ok good
dividing both sides by $\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|$ gives $|x-a|>\frac{1}{\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|}$
glossy valveBOT
A Fellow Human
polar mica
RHS is equivalent to $\lim_{n\to\infty}\frac{|1|}{\left|\frac{a_{n+1}}{a_n}\right|}$
glossy valveBOT
A Fellow Human
polar mica
what
wheat umbra
denied
polar mica
let me try again
applying absolute value laws gives $\lim_{n\to\infty}\left|\frac{1}{\frac{a_{n+1}}{a_n}}\right|=\lim_{n\to\infty}\left|\frac{a_n}{a_{n+1}}\right|$
glossy valveBOT
A Fellow Human
polar mica
you good so far?
wheat umbra
**A Fellow Human**
trying to figure out what happened after this
wheat umbra
idk what's wrong with me today, nothing is making much sense to me, it's pretty frustrating
wheat umbra
I'll keep looking though your notes, thank you very much
polar mica
yw
wheat umbra
.close
primal vigil
The sum of the digits of a two-digit number is 3. When it is multiplied by a number composed of the same digits in reverse order, the number 252 is obtained.
tough marsh
@primal vigil You seem to already have a another channel open?
primal vigil
.close
full forumBOT
primal vigil
i m new to this so
full forumBOT
Available help channel!
mellow cedar
full forumBOT
full forumBOT
Available help channel!
fallen gale
full forumBOT
fallen gale
.close
full forumBOT
full forumBOT
Available help channel!
fluid trench
Hey
fluid trench
can anyone help with a problem
I could use a little help on the math work, below I attached the problem I’m stuck on. Can you tell me what I multiply my GCF (4) by to get the answer?
full forumBOT
@fluid trench Has your question been resolved?
torn jolt
<@&286206848099549185> I need assistance with this problem. The approach I took was finding the derivative of the function, however, when I set it to 0, I get +sqrt(4/3) & -sqrt(4/3). Is there any other approach I can take to finding the local maxima and minima?
swift snow
<@&286206848099549185> I need assistance with this problem. The approach I took ...
you should not post the question and ping helpers right away
read #❓how-to-get-help
knotty moth
And stop posting the same question all over the server @torn jolt
torn jolt
And stop posting the same question all over the server <@456226577798135808>
do i just wait another 15mins?
knotty moth
It's fine now. But don't do the same mistakes again
torn jolt
It's fine now. But don't do the same mistakes again
alright then. I wont. Are you available to help me?
full forumBOT
@torn jolt Has your question been resolved?
torn jolt
<@456226577798135808> Has your question been resolved?
no
torn jolt
need assistance with this problem. The approach I took was finding the derivative of the function, however, when I set it to 0, I get +sqrt(4/3) & -sqrt(4/3). Is there any other approach I can take to finding the local maxima and minima?
@timid heart
timid heart
<@!159004388944379905>
yeah idk too advanced for me. wait until the bot prompts u and then click the X and ping helpers ig
full forumBOT
@torn jolt Has your question been resolved?
tight wyvern
Google it?
If u can do the math u just need anotuwr equation/method
What did u get for derivation
full forumBOT
torn jolt
What did u get for derivation
for deviration
full forumBOT
Available help channel!
torn jolt
$g'(x)=3x^2 -4$
full forumBOT
$g'(x)=3x^2 -4$
glossy valveBOT
King T
torn jolt
If u can do the math u just need anotuwr equation/method
.close
full forumBOT
full forumBOT
Available help channel!
torn jolt
Can someone help me solve this please
full forumBOT
Can someone help me solve this please
torn jolt
I need to prove that the LHS is = to the RHS
shell flint
Can someone help me solve this please
use trigonometric identities on LHS to reach RHS
start by changing tanx and build your way from there gl
full forumBOT
@torn jolt Has your question been resolved?
torn jolt
use trigonometric identities on LHS to reach RHS
start by changing tanx and bui...
does this look alright? apart from the fact the last “sin^2 x should be just sinx
shell flint
looks good
full forumBOT
@torn jolt Has your question been resolved?
torn jolt
full forumBOT
torn jolt
I'm doing a half angle trig identity
And I'm confused on how my answer is wrong rn?
Bc I plugged in costheta as the correct value and then simplified
Did I go wrong in my math?
There should be sqrt around every step but I forgot
But still confused asf
.close
thin sun
Hi I’m stuck with this question
A body moves in a straight line so that its acceleration, a m/s^2, after time t seconds (t ≥ 0) is given by a = 2t − 3. If the initial position of the body is 2 m to the right of a point O and its velocity is 3 m/s, find the particle’s position and velocity after 10 seconds.
tranquil zenith
i think it's initial velocity is 3
so the velocity would be t^2 - 3t + 3
then integrate it to find the position
so $\frac{1}{3}t^3 - \frac{3}{2}t^2 + 3t + c$
glossy valveBOT
Tra-Guy
tranquil zenith
and since it's initial position is 2 metres to the right
we know that c is 2
so it becomes $\frac{1}{3}t^3 - \frac{3}{2}t^2 + 3t + 2$
glossy valveBOT
Tra-Guy
tranquil zenith
this is the position equation
so know just sub in t = 10
to find the position and veloicty
velocity
@thin sun
thin sun
Ohhh ya, I think I missed that point v=3 at the beginning
tranquil zenith
ye
thin sun
I’ll try first
tranquil zenith
ok
tranquil zenith
nice
thin sun
Thank you so much for your help:)))
tranquil zenith
np
thin sun
.close
open swift
heya, can some1 help me out with this?
i think it's trivial but the solution i'm seeing is more involved and i'm not sure why
fathom saddle
What could I possibly say that the solution doesn't say?
open swift
why it takes what seems like the scenic route
so it seems trivially true to me that the lim to inf of x^n/e^x = 0 so all polynomials belong in V
but the solution i'm seeing splits the integral between (0,X_0) and (X_0,INF) and does the limit for e^x/2... i don't see why all this is necessary
fathom saddle
"It's true because I feel like it" isn't exactly an answer, haha.
But I also have no clue what they're doing. Why do I care about that limit?
open swift
well they need to show that the integral is finite for all polynomials, that's the requirement for the vector space
*for them to belong
fathom saddle
Right
open swift
i'll post the rest of the solution for context
so what is the significance of this X_0? and why is it incorrect to just state the same limit but for e^-x instead of -x/2 and then you're done?
thoughts? feelings?
fathom saddle
x0 is the x-value where e^x/2 is greater than x^2n
They take that limit to say "this will eventually happen, so x0 exists"
Then they do a fuq ton of algebra to worm their integral into it
It's a clever way to say "if you believe that x^2n < e^x/2, then the integral is finite"
open swift
but why i all this necessary?
couldn't i just show that the lim of x^n/e^x goes to 0 as x->INF, and so the original integral is finite for all polys, no additional tinkering required?
fathom saddle
1/x goes to 0, but ∫ 1/x dx is still infinite
open swift
ok,
but not 1/xe^x, right ?
or am i missing somethin
fathom saddle
What about x^(1000000)/e^x?
open swift
that sure is a scary number, but i don't see how the answer above does a better job of showing that it's bound.
wouldn't there be some lim (x->0) expression if that's what's being established here?
i assume you mean that as x^-(1000000)
cos any positive power is already taken care of by the lim to INF
i mean, unless i'm forgetting my limits (quite possible) lim (x->0) x^n/e^x=0 should be just as self evident as lim (x->INF) x^n/e^x=0
am i making some massive nono with this ?
fathom saddle
You're making a jump in logic. "The integrand goes to zero, therefore the integral is finite"
Which is just generally not true
open swift
i'm saying it's bound at both ends of the integration range and has no discontinuities within the range, so it should be finite
is this not a correct statement?
wait no it's not bound towards 0, i AM being a dumdum
but then how is this solution dealing with it? it does some meandering but it seems to me like it just kinda states that it's finite at the end anyway
wait is this even relevant? question state the space of of all continuous functions on [0,INF)
1/x isn't continuous at 0, which is within the range.
sounds like negative polynomials are defined out of the space from the get go, no?
but that'd imply a mistake in the question, which i doubt
torn gust
I haven't read the whole chat but I see the e^-1/2x so I'm going to guess what the strategy is
eventually e^cx beats any polynomial as you know from limits
to show an integral isn't infinite, you just need to show the tail is finite (assuming no asymptotes or whatever)
so split the integral into a random finite part and its tail, at the point e^1/2x beats the polynomial
then the tail integral is of e^-1/2x which is finite
open swift
heya Plurmorant,
but how does this split deal with the vertical asymptote?
i mean does it matter that you split the integral? you stil need to show the problematic part of it is bound somehow
torn gust
oh I thought the tail was the problematic part but yeah the asymptote at 0 matters just as much hmm
wait the asymptote for e^-x is fine
integral of e^-x from 0 to inf is finite
open swift
ok i desmosed it. it IS bound, my intuition was right (yay)
kaynex got me to self doubt XD
torn gust
xd
open swift
but if that's the case why is the solution above necessary?
did you see the start of this discussion?
torn gust
uh can you fill me in on how the solution differs from what I said
open swift
oh so basically:
this seemed really trivial to me. i mean all polys will tend to 0 when you take lim to INF right?
so just state lim(x->INF) x^n/e^x=0
that means the integral is bound. and call it a day
seems trivial
but i have a solution here
and it looks like this
torn gust
the main part of the proof is showing the tail gets small fast enough
open swift
and this whole convo is trying to figure out why it takes so long
torn gust
just tending to 0 isn't enough
open swift
to prove what that 1 limit does
torn gust
because like 1/n diverges
sort of like how the e^-x vertical asymptote is fine, but others wouldn't be
open swift
that's exactly what Kaylex said, but that's not true for 1/xe^(1/x)
that's a bound function around 0
he picked away at my confidence but desmos has my back now
so we have a function that is bound around 0 (in range) has no asymptotes, and is trivially shown to approach 0 at inf.
so why all that fancy prancing around in the solution?
torn gust
I'm not sure I get your argument
integral of 1/x from 1 to inf diverges, so it's not enough that the limit goes to 0
open swift
goddammit, it's not f(x)^2e^-f(x)
it's f(x)^2e^-x
torn gust
x_x
torn gust
it's showing the tail looks like e^-cx which is fine
open swift
like, it splits the integral, sure, but it doesn't do much with the problem area around 0
open swift
how not? it's where the function explodes
isn't that exactly where you need to show that the integral is bound ?
torn gust
,w integral of e^-x from 0 to 1
open swift
it's the tail that's trivial
glossy valveBOT
torn gust
I'm saying it's the opposite
it's unbounded but on such a narrow interval that the integral is finite
,w integral of 1/x from 0 to 1
glossy valveBOT
open swift
- that sounds kinda handwavy
- the solution doesn't seem to adress that
torn gust
is this pic the whole solution?
torn gust
yeah it'd be better if it explained why the 0 to x_0 part was finite
torn gust
yeah so for that you say x^k < M for some max
and it turns into Me^-x which has bounded integral because you can just calculate it
open swift
how is that not false?
lim(x->0) x^-1 -> INF
multiplying by e^-x does nothing to change that
torn gust
k is positive
torn gust
nah, polynomials have nonnegative exponents
open swift
wait that's just a definitional fact?
torn gust
yeah rip
open swift
XD XD XD so again i'm back to why the hell is all this necessary
i figured the only reason to do this is because of asymptote when k<0
torn gust
nah the whole reason is the tail, the part from x0 to infinity
the proof wanted to show the function behaves like a negative exponential at some point
if the function instead looked like 1/x, the the integral from c to infinity would be infinite
open swift
ok i see what you're saying.... well that was 2 hours well spent
thanks m8
while i got you can i hit you with another one?
i keep asking it but i'm not getting any traction
torn gust
I'll try, I don't have much time today
open swift
i remember asking you something yesterday/day b4 but i've completely lost track
might be this one, let me know
was that it?
open swift
oof, well i tried
well, thanks for the timely rescue
i'mma keep chewing on the rest of the excercise
.close
full forumBOT
open swift
.reopen
full forumBOT
✅
open swift
WAIT!
so there was this question:
@torn gust can that question being so tricky have something to do with the p norm not being strictly convex for p=INF?
Prob 3.3 is the problematic one above
torn gust
oh I thought the only nonunique part was p=1, but I don't think I know this subject
open swift
yeah i had to work though that before this part of the question.
well i wont keep torturing you if this isn't your wheelhouse.
thanks for the prev one.
i'll try and bother BillyElKidd he seemed quite comfortable with this stuff
.closed
.close
.close
full forumBOT
full forumBOT
Available help channel!
deep pilot
help
old vessel
full forumBOT
old vessel
How do I begin to solve this
I am trying to isolate the y
the y's and x's
but i cant
full forumBOT
@old vessel Has your question been resolved?
old vessel
<@&286206848099549185>
full forumBOT
@old vessel Has your question been resolved?
full forumBOT
@old vessel Has your question been resolved?
full forumBOT
@grizzled night Has your question been resolved?
haughty gull
Hi, I'm currently working on this problem from a practice exam.
full forumBOT
@haughty gull Has your question been resolved?
haughty gull
<@&286206848099549185>
full forumBOT
@haughty gull Has your question been resolved?
haughty gull
.close
fathom dock
This is a special relativity question:
If Alice and Bob witness two light flashes $E1$ and $E2$, and Alice and Bob measures the distance between the position of the two light flashes as $\Delta x_A$ and $\Delta x_B$ respectively, and they also measure the time that elapsed between witnessing the two events happening as $\Delta t_A$ and $\Delta t_B$ respectively, then
$$(\Delta x_B)^2 - c^2(\Delta t_B)^2 = (\Delta x_A)^2 - c^2(\Delta t_A)^2$$
This, I think, is the spacetime interval. But it seems like something is wrong here.
Lets assume that Alice observes these flashes at each end of a measuring stick, both at the same time in her reference frame. Then $\Delta t_A = 0$, and we get
$$(\Delta x_B)^2 - c^2(\Delta t_B)^2 = (\Delta x_A)^2$$
$$(\Delta x_B)^2(1 - \frac{c^2}{v_B^2}) = (\Delta x_A)^2$$
$$(\Delta x_B)^2 = (\Delta x_A)^2\frac{1}{(1 - \frac{c^2}{v_B^2}) }$$
$$(\Delta x_B)^2 = (\Delta x_A)^2\frac{v_B^2}{(v_B^2 -c^2) }$$
$$(\Delta x_B)^2 = (\Delta x_A)^2\frac{v_B^2}{-c^2(-\frac{v_B^2}{c^2} + 1) }$$
$$(\Delta x_B)^2 = -(\Delta x_A)^2\frac{v_B^2}{c^2}\gamma^2$$
But this implies that
$$\Delta x_B = i \Delta x_A\frac{v_B}{c}\gamma$$
That doesn't make any sense!
Where did I go wrong?
glossy valveBOT
wikiemol
fathom dock
In this example, Alice is in motion relative to Bob, but the measuring stick is at rest relative to Alice
full forumBOT
@fathom dock Has your question been resolved?
full forumBOT
@fathom dock Has your question been resolved?
tough lion
Hey! I need help with this question, I'm just not sure where to start:
Person 1, 2, 3 complete a task in 5 minutes
Person 1, 3 complete a task in 7 minutes
Person 1, 2 complete a task in 15 minutes
How long does it take Person 1 to complete a task?
azure shoal
Hey! I need help with this question, I'm just not sure where to start:
```
Perso...
create a set of simultaneous equations
tough lion
I'm getting 2 answers and I don't know which one
17 or 21
tough lion
create a set of simultaneous equations
how would I do this? ;-;
I wrote
15/C = 5
C = 3
A/3 = 7
A = 21
where A, B, C are people 1, 2, 3 respectively
but I'm not even sure if this is right
tough lion
create a set of simultaneous equations
what simultaneous equations are these?
azure shoal
aight if you minus top equation from the top one, eg ( 1 + 2 + 3 = 5) - (1 + 2 = 5) you can prob guess that person 3 is zero minutes yeah
cos they dont add anything
azure shoal
oh right
tough lion
my bad :(
azure shoal
hahaha yeah it wouldnt have made sense otherwise
tough lion
I'll repost the question
azure shoal
ok so same thing (1 , 2, 3 = 15) - (1, 2 = 5)
tough lion
Hey! I need help with this question, I'm just not sure where to start:
Person 1, 2, 3 complete a task in 5 minutes
Person 1, 3 complete a task in 7 minutes
Person 1, 2 complete a task in 15 minutes
How long does it take Person 1 to complete a task?
sorry for the confusion! :w
tough lion
uh are negative times alright
negative?
are you doing A+B+C = 5 etc?
bc I'm pretty sure that isn't right
since if you have 2 people that can each complete a task in 5 minutes, when they both do it, they will complete it in 2.5 minutes, not 5 - 5 = 0 minutes
spare rivet