Show your work, and if possible, explain where you are stuck.
#help-17
vocal sleetBOT
summer urchin
Show your work, and if possible, explain where you are stuck.
idk what to do
<@&286206848099549185>
slate herald
what do u NOT understand?
summer urchin
how do i use it?
slate herald
in order to make two indivitual triangles simillar, u have to show that both have same angles
so like u have to show three angles
one is already given that angle 1 = angle 3
slate herald
since AB = BC
angle BAC = angle BCA
and the other one comes with this
summer urchin
ur saying measure angle A = C
how???!?!
wait i got it
since 2 sides are equal
right @slate herald ?
placid plover
How does this work? How are constants treated in the upper and lower part of the formula when taking a derivative of a function?
vocal sleetBOT
How does this work? How are constants treated in the upper and lower part of the...
hard atlas
the formatting might confuse you?
f(x) = (ugly term) + 5x_1 x_3 x_4
but from the perspective of x_3, the ugly term doesnt change (i.e. when you change x_3, the ugly term stays constant). so if you diff wrt x_3, the first part just turns to 0
just like if it was for example f(x) = 2 + 5x_1 x_3 x_4
placid plover
Do constants in the denoninator always get "erased" when the function is differentiated?
patent nymph
Do constants in the denoninator always get "erased" when the function is differe...
Can you give an example
placid plover
The numerator and the "ugly term" in the denominator cease to exist after the partial derivation
Or am I missing something?
vocal sleetBOT
@placid plover Has your question been resolved?
cobalt skiff
Can someone help me fully factor 1 - b - a^2 + a^3 b + a^2 b^3 - a^3 b^3
west raptor
I think you need to first test a few values
twin meteorBOT
northsteve
cobalt skiff
in the clue i was given, b=1 has been tested to give (1 - b)(1 - a^2 (1 + b + b^2) + a^3 b (1 + b))
ive tried a=1, which is also a root
west raptor
Do you know the remainder theorem?
cobalt skiff
yeah yeah
west raptor
So if a=1 is a root, what can you say about factoring the polynomial?
cobalt skiff
that (a-1) is a factor right
cobalt skiff
mhm okok lemme try
ok i can't seem to factor out the (a-1)
(1-a(a(1+b+b^2)+a(a^2b(1+b))
cobalt skiff
idk ive been doing it for 15 minutes and just... couldn't
cobalt skiff
what are the steps to getting there tho
west raptor
No idea
cobalt skiff
yk, gotta show working out ahaha
west raptor
I got $ba^2+b^2a^2-a-1$
twin meteorBOT
Math Is Fun
pallid gull
west raptor
?
cobalt skiff
how'd you get to that step???
cobalt skiff
you can do that here woah
west raptor
you can do that here woah
You mea list out the steps?
cobalt skiff
no i just didn't think about doing that method here
i tried to like take out the a's
okokok i got that result too through division
now its just ab(a)+ab(ab)-a-1
and it just becomes (ab-1)(ab+a+1)?
normal loom
Heyo
normal loom
I've got a question related to algebra
if a-b = X
b-c = Y
c-a = Z
Then how do i write a, b, c in terms of X,Y,Z
viral copper
You can do stuff like subtract the first equation from the third and then add the result to the second
that worked in my head
It just seems that it all ends up with x + y + z = 0
normal loom
Yes 😭
viral copper
Is this the original question
normal loom
There was no question tbh this just came into my mind
All i ended up with was x + y + z = 0
silk kindle
Well it looks like the system doesn't have an unique solution then 🤔
normal loom
How do i check if a equation is solvable or not idk about the matriz and stufz
silk kindle
I don't remember the conditions for that 😵💫, but we can find the rank (?
mild flower
actually wait yeah if we have x+y+z = 0 then it's not solvable for all xyz so it can't be full rank... I think
twin meteorBOT
silk kindle
,w rank of [[1,-1,0],[0,1,-1],[-1,0,1]]
twin meteorBOT
viral copper
,w det({X, -1, 0},{Y, 1, -1},{Z, 0 ,1})
silk kindle
:0
twin meteorBOT
normal loom
What r u guyz upto
silk kindle
I don't know enough linear algebra to interpret that and X+Y+Z=0
viral copper
I was just using cramers rule
silk kindle
Ohh
viral copper
Since we know X + Y + Z = 0, the system in a, b, and c has infinite solutions
silk kindle
Ok so in summary
silk kindle
if a-b = X
b-c = Y
c-a = Z
A system has an unique solution if all the equations are independent. That means that you can't get an equation by operating the rest of them: eq3 ≠ eq2+eq1, eq2 ≠ eq1 - eq3, etc.
normal loom
Since we know X + Y + Z = 0, the system in a, b, and c has infinite solutions
Ohk so what if someone doesn't know these matrix and stufz like i know for2 variable we can equal the slope of lines to get inf solution about about here ?
silk kindle
Yeah I'm trying to explain that
normal loom
A system has an unique solution if all the equations are independent. That means...
Ohhh i get it now
Oh yes
silk kindle
In this case, you can get a similar eq to eq3 by -eq2 -eq1
You'd have
c-a = -X-Y
c-a = Z
Depending on the values of x y z, this equations might be incompatible, so the system would have none solutions
normal loom
Yesss , so we apply the same thing for more than 3 variables too?
silk kindle
Because c-a can't be 2 values at once
normal loom
4 eqns 4 variable
silk kindle
Yes
silk kindle
You'd have
c-a = -X-Y
c-a = Z
If you want this to still have solutions, you need X+Y+Z = 0, which is what you got
Then you're only left with eq1 and eq2, because eq3 already comes from them
normal loom
So this has no solution or inf solutions
Omg i m sorry i understood everything you said but ...yes
if eqn is like
A-B = 4
B-C = 2
C-A = -6 so here the sum is 0
So if someone asks me find the value of a ,b c
I should say this has inf solutions?
silk kindle
yes
normal loom
What is one of those inf solutions
viral copper
Well I think you should say depends on x, y, z
It's only infinite if x + y + z = 0
Otherwise you have no solutions
normal loom
if eqn is like
A-B = 4
B-C = 2
C-A = -6 so here the sum is 0
For this
viral copper
Just write the other two variables in terms of A
Then you can insert a value for A and get corresponding values for B and C
viral copper
yes now just choose any A value you like
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
im trying to solve a function question where the function t is defined by t:x -> 5-2x
vocal sleetBOT
im trying to solve a function question where the function t is defined by t:x ->...
paper depot
which would be t(t)
t(t(x)), to be more precise.
vast shale
i was looking at the mark scheme and it was 5-2(5-2x) although i thought it would be 5-2x(5-2x) and im unsure why
paper depot
you're unsure why you thought t(t(x)) = 5 - 2x * (5-2x)?
or you're unsure why t(t(x)) = 5 - 2(5-2x)?
vast shale
or you're unsure why t(t(x)) = 5 - 2(5-2x)?
unsure why ^
im unsure why t(t(x)) = 5-2(5-2x)
paper depot
to calculate t(5-2x) you replace all x's in the formula for t with (5-2x)
vast shale
im not sure i understand
oh i understand hahaha
alright this makes sense as im substituting t into t
thank you
.close
onyx meadow
vocal sleetBOT
onyx meadow
Don't know how to start it
elder rampart
do you know the formula for calculating expected value?
onyx meadow
No I don't
elder rampart
you’ll need it
@onyx meadow so there’s a 3/10 chance of getting score -10, 2/5 for getting 5, 4/5 for getting 10 and 1/20 for getting 20 points
elder rampart
it’s sum{ n x P(score =n) } for all integers n
so for example P( score = -10) = 3/10 and P( score = -7 ) = 0
vocal sleetBOT
@onyx meadow Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
tidal shale
does this proof make sense
vocal sleetBOT
does this proof make sense
tidal shale
hard atlas
no
"every output element has an input element" is trivial
otherwise it wouldnt be an output element
you need to show that it has one input element
also, the proposition you are quoting only holds if V is finite dimensional
which V here isnt
oh and I didnt even look at the first four lines, those are nonsense
mild flower
why are we talking about np(n) at all
mild flower
so we have our set V, which is all polynomials of any degree
for instance, $3+2x \in V$; also $5+8x-9x^2+\pi x^{100} \in V$
twin meteorBOT
Hayley
tidal shale
i got that part
mild flower
the polynomials themselves are elements of the set, not the polynomials at any particular value
ok cool
so you're trying to show that it's injective, right?
this T relation
tidal shale
well im trying to answer the question
mild flower
sure okay
can you give an exemplar polynomial (just pick one) and the result of applying T to it?
tidal shale
let p(x) = 3 + 2x. Then T(p(x)) = x(3 + 2x) = 3x + 2x^2
tidal shale
surjectivity
mild flower
mmk, so does T hit every element of V? Or are there elements that it doesn't output?
i guess that's the same question as you were already asked
tidal shale
I believe so
mild flower
what does T do to a polynomial like $a_0+a_1x^1+a_2x^2+a_3x^3$?
twin meteorBOT
Hayley
tidal shale
$xa_0+xa_1x^1+xa_2x^2+xa_3x^3$ = $xa_0+a_1x^2+a_2x^3+a_3x^4$
twin meteorBOT
submergedduck
mild flower
okay great, now do you think you can write all polynomials in V in the form of the RHS?
tidal shale
RHS?
mild flower
right hand side
mild flower
yep exactly
tidal shale
so it's not surjective
mild flower
so we can find an element in V that isn't in the range of T (and you'll have to write down some kind of explanation as to why)
correct, it's not surjectie
but it might still be injective
tidal shale
mhm to prove injective you have to prove that the codomain of T(p(x)) can't have multiple inputs?
mild flower
Let's be slightly more precise. For that, we take two elements of V and assume they have the same result, then prove that they are the same element
so we can use $p(x)$ and $q(x)$ for our example, and maybe $a_i$ and $b_i$ for our coefficients
twin meteorBOT
Hayley
mild flower
so like $q(x) = b_0 + b_1 x^1 + ... + b_m x^m$
twin meteorBOT
Hayley
tidal shale
Let's be slightly more precise. For that, we take two elements of V and assume t...
prove they are the same element?
mild flower
we assume their images are the same (so apply T to both of them and set them equal) and prove that p = q
ie $T(p) = T(q) \rightarrow p = q$
twin meteorBOT
Hayley
mild flower
p=q -> t(p) = t(q) is not the same thing that's just what it means to be a function
mild flower
$p \neq q \rightarrow T(p) \neq T(q)$ would work though
twin meteorBOT
Hayley
mild flower
if a = b then a^2 = b^2 but f(x) = x^2 is definitely not injective
because 3^2 = (-3)^2 but 3 != -3
mild flower
they're different polynomials yeah
tidal shale
and we apply T
mild flower
and we should get a different result
or maybe there are two polynomials that map to the same output
mild flower
yeah like two different inputs that T takes to the same output
tidal shale
so it's not injective?
mild flower
if you find an example of two different inputs that go to the same output, it's not injective
have you found such an example?
mild flower
well, do you want to try showing it is injective then?
start with $p(x) = a_0 + a_1x + a_2x^2 + \cdots + a_n x^n$ and $q(x) = b_0 + b_1x + b_2x^2 + \cdots + b_m x^m$
twin meteorBOT
Hayley
mild flower
apply T to both of them, and set $T(p) = T(q)$
twin meteorBOT
Hayley
tidal shale
right
mild flower
then show that p must equal q
mild flower
we want to show that same output means same input
also remember that they might not be the same length
tidal shale
tidal shale
also remember that they might not be the same length
what
do you mean by same length?
mild flower
same degree; like if we have $p(x) = 3 + 2x$ and $q(x) = 4 + 7x + 9x^2$
twin meteorBOT
Hayley
mild flower
well you've asserted that p(x) and q(x) are both degree n
tidal shale
then would i remove n
mild flower
make q(x) go up to m instead
mild flower
and show that n has to equal m for the polys to be equal
for the uh
for the images to be equal
lyric fossil
that shows injectivity yeah
mild flower
✅
onyx meadow
vocal sleetBOT
onyx meadow
I picked A and H
For this
But B and G are also correct
Can you please explain why
I just used the answer choices
And plugged them into the 5 numbers
To see if the standard deviation was greater than 6
viral copper
What did you get as the standard deviation
lyric fossil
What did you get as the standard deviation
answer this
viral copper
7?
lyric fossil
the standard deviation should be in terms of c
onyx meadow
Yes
viral copper
It should have Cs in it
onyx meadow
Yes I got 7
lyric fossil
chewie do you have organized work for this question
onyx meadow
Sorry I just plugged in the answer choices into c
And determined if the standard deviation was greater than 6
lyric fossil
And determined if the standard deviation was greater than 6
you should be solving for the standard deviation before plugging in c
otherwise you’ll have to solve for the standard deviation like 10 times
onyx meadow
But it said it's greater than 6
Why do you need to know the exact deviation
It said could be
Not must
lyric fossil
what
viral copper
Ignore what I sent before
lyric fossil
they’re asking you which values could work
what me and neon are saying
is you should solve for the standard deviation as is
and get it in terms of c
viral copper
yes
lyric fossil
if you plug in c first
and then find the standard deviation
you’ll be doing the standard deviation calculation 10 different times
as opposed to just once, and then plugging in a small value
viral copper
just to be clear what you did might not have been wrong but it's not particularly efficient
onyx meadow
Actually I don't know how to find it in terms of C
viral copper
Can you get the mean of the data
lyric fossil
what
onyx meadow
Like 2, 4, 6, 8
lyric fossil
do you know what standard deviation is
onyx meadow
The sd is 2
Idk probably need to review sd again
From my understanding I thought it was that
lyric fossil
it is not
onyx meadow
I guess how far it lies from mean
lyric fossil
$\sigma = \sqrt{\frac{\sum (\overline x - x_i)^2}{N}}$
twin meteorBOT
maximofs
lyric fossil
x with the bar is the mean
N is the number of data points you have
x_i is each data point
it’s literally right above the problem in your picture
it’s the square root of (s/n) where s is the sum of squared differences between the mean and each value
onyx meadow
Okay so mean would be 20-2c+20-c+
....
The sum of the 5 numbers
Divided by 5
So when I did that I got 100/5
For the mean
Which is 20
lyric fossil
yes
onyx meadow
The maximum and minimum?
lyric fossil
what
lyric fossil
would i be giving you that equation if there was
vast shale
vocal sleetBOT
vast shale
How come B isn't an inflection point
slope goes from positive 0 positive
hence
double derivative is negative 0 positive
bitter copper
Imagine you have a car. We have a graph that shows acceleration. At point B acceleration is 0, the car is therefore before and after going from deceleration to acceleration. This therefore does not have to be an inflection point as if the car was moving up a hill and only turned on it’s engine after 1 meter so it was briefly decelerating, it still has a positive velocity and thus positive displacement. So on the displacement graph it could look like a simple increase in the gradient as the gradient for a displacement graph is velocity and since velocity was initial positive, it is not an inflection point.
Wow that is a scuffed explanation
vast shale
Wow that is a scuffed explanation
thanks for detailed explanation
I still don't get it though sorry
From my understanding inflection point has to do with the double derivative which can be interpreted as acceleration where f(x) is displacement
you mentioned that since the velocity was initially positive, it is not an infleciton point
but can't this logic be applied to c
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
lean osprey
how did they get 253.9 at the very end?
vocal sleetBOT
how did they get 253.9 at the very end?
indigo jay
i looked up the definition of bearing
it means you start at the positive y axis and measure your angle clockwise
so going down to the south is 180, and then you can add (90-16.1)
lean osprey
so going down to the south is 180, and then you can add (90-16.1)
wait then whats that calculation their doing with 16.1 + 180? whats the point of that
indigo jay
that's with respect to the standard angle measurement from the positive x-axis
going counterclockwise
there's different ways to do it in different fields like navigation
in math you'd go with 196.1, but maybe in a naval academy or something you'd report it as 253.9
hushed cipher
Mapping notation: ( x - 2, y - 6)
F(x): | x - 3 | - 4
What would the function be after the transformations
vocal sleetBOT
@hushed cipher Has your question been resolved?
vocal sleetBOT
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Available help channel!
light lantern
Hey, so i have a question where I get 3 points on a number plane and have to find the 4th one so that pqrs is a parallelogram
vocal sleetBOT
Hey, so i have a question where I get 3 points on a number plane and have to fin...
lime gorge
Are any of the sides parallel to an axis
light lantern
Are any of the sides parallel to an axis
these are the points given
(-9,9),(5,-1),(1,-5)
now I need to find where point S goes
slim citrus
right so
light lantern
PR // QS
slim citrus
i can't see the labels of the points
so it's a little hard to explain
can you put labels on em
light lantern
flat leaf
You can write an algebraic expression saying that RQ = PS and that the slope of RQ = PS
light lantern
so in the example our teacher gave us where we had to prove that 4 points are a parellelogram she did AB // DC and AD // BC
flat leaf
you can also use symmetry and see that from R its down 4 left 4 so do the same with P
light lantern
oh yeaa
flat leaf
S is going to be down 4 left 4 of P
light lantern
a gradient of 1
flat leaf
it is
light lantern
i should draw a graph first next time
vocal sleetBOT
@light lantern Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
stone vault
vocal sleetBOT
stone vault
I don't know
what to start with
I just know the value of x
(10-31) when x=3
that is about it
mild flower
Looks like you've evaluated (f + g)(3) and gotten -21, which is good! Let's move onto the next one
stone vault
(-4-3) when x=1
mild flower
so we take (f - g)(1), now we know that's equal to f(1) - g(1)
mild flower
whoa slow down
we're not done with (f - g)(1) yet
so f(1) - g(1) is (-4) - (-3)
and what's the value of that?
stone vault
-1
stone vault
0*-13=2
stone vault
yes
mild flower
so i'm not sure where you're getting 2 from
mild flower
$(fg)(2) = 0$
twin meteorBOT
Hayley
stone vault
yes
mild flower
"f times g, evaluated at 2, is equal to 0"
stone vault
ok
mild flower
okay and the last question? We're looking for (f/g)(0)
so your answer should be in the form $\frac{f}{g}(0) = ___$
twin meteorBOT
Hayley
mild flower
(if you think of functions as machines, you put -1 in on the left, pass it through g, then take that output and pass it through f)
formal herald
Need a little help here, i suck at word problems
vocal sleetBOT
Need a little help here, i suck at word problems
@formal herald Has your question been resolved?
formal herald
Help
stiff sandal
Need a little help here, i suck at word problems
are ya winning son?
formal herald
No
flat kindle
So we know the rate the contaminated water is going into tank and the rate it is leaving tank
and the amount of contamination in the replenish water
formal herald
Yeah 1kl and 1kl
Amount of contamination is 1.25mg/kl
Change in metals is 1.25- concentration*1kl
But dont know how to find A(t)
flat kindle
A(t) is amount of heavy metal at some time t
We know that dA(t)/t is 1.25mg*1000 per day
formal herald
Wouldnt some of the contaminated water be pumped out
flat kindle
- some amount that’s lose from drinking yeah
flat kindle
Depends on how you model the contaminates (e.g are they distributed evenly through the water )
Because we also know that tank is 3/4 full
So if metals are distributed roughly evenly then the amount of metal leaving tank would start off small and increase
formal herald
It says you may assume metals are evenly distributed
flat kindle
That’s useful
I said that A(0) is 0 because there’s not really another way I see to put that bit
formal herald
I think the equation should be something like dA/dT = 1.25-(A(t)/7.5)
flat kindle
Yeah that’s the idea
A lot goes in and then it’s mixed evenly and then taken out
Can you solve that?
flat kindle
This part depends on your skill with Differential Equations
formal herald
Yeah seperation of variables
flat kindle
Im not sure you can separate the variables in this case
formal herald
How would you do it
flat kindle
I think this is a case of first order DEs
formal herald
Oh wait i think the equation might be dA/dT=1.25t-(A(T)/7.5)t?
flat kindle
Why the ts?
flat kindle
Not sure that days changes much
formal herald
Dy/dx with no x on the other side though
flat kindle
Oh I think I found it
It’s pretty close to the IVP for Newtons law of cooling
So use that method ( kinda just separation of variables again )
formal herald
Yeah pretty much, wouldnt need the t’s then
flat kindle
Nope
vocal sleetBOT
@formal herald Has your question been resolved?
vocal sleetBOT
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unborn elm
GUYS CAN ANYONE TELL HOW POINTS CAN BE PUTTED IN DIVISON? EXAMPLE 7divided by 8 =
vocal sleetBOT
GUYS CAN ANYONE TELL HOW POINTS CAN BE PUTTED IN DIVISON? EXAMPLE 7divided by 8 ...
unborn elm
this .
paper depot
IF YOU'RE LOOKING FOR HOW TO WRITE THE DIVISION SYMBOL ON DISCORD, USE A SLASH: 7 / 8
paper depot
you wrote your question in allcaps. when you write in allcaps, it reads as shouting.
unborn elm
.....
tepid plinth
WHAT WOULD THIS BE, THEN?
unborn elm
paper depot
is there a problem you're looking at
unborn elm
this server is not helping me
paper depot
bc idt anyone knows what you mean by "put points in division"
unborn elm
im hell out of here
paper depot
maybe if you were solving a problem from a textbook/online homework system or whatever then we could look at it
unborn elm
useless server
paper depot
and see what you want/need
ok yeah bye you won't be missed
kind of entitled behavior on your part
but yknow
aint for everyone
tropic canopy
left alr
unborn elm
fuck
tropic canopy
or not
paper depot
user threatens to leave
user does not leave
vocal sleetBOT
@unborn elm Has your question been resolved?
unborn elm
no
vocal sleetBOT
@unborn elm Has your question been resolved?
urban obsidian
vocal sleetBOT
https://cdn.discordapp.com/attachments/903481102591750184/1119555503018749982/HQ...
urban obsidian
@sharp lynx
you were talking about my question but i didn't get a chance to respond
from your response, you have said they mean slightly different stuffs but technically they are equivalent right?
you said a is a an "easy" value to use but
in that case, t_0 should be too?
sharp lynx
a and t_0 would take on the same role yes
urban obsidian
a and t_0 would take on the same role yes
so you mean they're technically just the same i guess?
and the choice of which form i want to write it as depends on me?
sharp lynx
sure
sharp lynx
the first comes up more in math classes, the second is more common in applied/science settings
from what I've seen
vocal sleetBOT
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hushed atlas
part a?
light thistle
Binomial distribution question
hushed atlas
oh i think i get it now
hushed atlas
yh bc its probability of toast not landing butter side up, its 1-p
and then theres two toasts so its (1-p)^2
light thistle
Yeah nice one
hushed atlas
.close
vocal sleetBOT
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peak shard
is a function continuously differentiable if the function is continuously differentiable in every component?
vocal sleetBOT
is a function continuously differentiable if the function is continuously differ...
vocal sleetBOT
astral needle
thats not my question
sorry for misunderstanding
peak shard
.reopen
vocal sleetBOT
✅
peak shard
sorry for misunderstanding
for example a function f(t) = (sin(t) , cos(t) , e^t)
from R->R^3
my question was is that function continuously differentiable if the function is continuously differentiable in every component?
which is obv the case here but in general
or did I misunderstand you
astral needle
Nah
If every component of the jacobian matrix (in this case the gradient) exists and is continuous, then f is is differentiable
But I don't think that implies f' continuous
I'm thinking of a case where it is not continuous
vocal sleetBOT
@peak shard Has your question been resolved?
hot lark
Let (xn) be a cauchy sequence in a normed space, then (||xn||) is convergent series of real numbers:
vocal sleetBOT
Let (xn) be a cauchy sequence in a normed space, then (|\|xn\||) is convergent s...
hot lark
I am stuck because i dont really know how i can go from a cauchy sequence to the normed sequence
hasty pulsar
voor welke vak is het
hasty pulsar
ik haat theoretisch wiskunde vakken
hot lark
ik haat theoretisch wiskunde vakken
bedankt voor je hulp
hasty pulsar
dankuwel
heady ibex
Let $\left( x_{n} \right){n \in \mathbb{N}{0}}$ be a cauchy sequence in a normed space, prove that $\left( ||x_{n}|| \right){n \in \mathbb{N}{0}}$ is a convergent series of real numbers?
is that the question?
twin meteorBOT
kathlijn
heady ibex
don't you mean sum?
vocal sleetBOT
@hot lark Has your question been resolved?
hot lark
don't you mean sum?
convergent sequence
heady ibex
ok
heady ibex
right so the original sequence will land on some value in the end because the points will be closer and closer together because it is a cauchy sequence
but that doesn't necessarily mean that the norms will go to 0
as it could land on the point (0, 1) and then the norm will always be 1 for n going to infinity
so i must have something wrong
would the second part not suggest that the original sequence goes to 0 when n goes to infinity
hot lark
but that doesn't necessarily mean that the norms will go to 0
no it doesnt the norms will go to a certain value right?
heady ibex
yes
that's how i understand it
that the norm will only be 0 if the point is 0, 0, ...., 0
hot lark
yes
heady ibex
so somehow a cauchy sequence in normed vector space will always have to go to the origin
in order for the second part to be true
hot lark
so somehow a cauchy sequence in normed vector space will always have to go to th...
what suggest that?
heady ibex
otherwise the part you have to prove is false
i'm dumb
i'm so dumb
it doesn't say the sum
you said it said the sequence right
hot lark
yes i did :)))
heady ibex
this means that a cauchy sequence in the original normed vector space
ends up at some point when n goes to infinity
hot lark
ends up at some point when n goes to infinity
yes
heady ibex
but that point has a finite norm
as in the norm of that sequence converges to the norm of that point
sorry the sequence of the norm converges to the norm of that point
hot lark
ends up at some point when n goes to infinity
wait what does it mean for a cauchy sequence to be confined in a normed space that the norm of every sequence exist?
hot lark
as in the norm of that sequence converges to the norm of that point
yes that makes sense in words but honestly I don't get how you would write that down mathemathically
is saying it in words also a proof?
btw thank you for helping
heady ibex
for example $\left( x_{n} \right){n \in \mathbb{N}{0}} \rightarrow \begin{pmatrix} 3 \ 1 \ 5 \end{pmatrix}$ then $\left( |x_{n}| \right){n \in \mathbb{N}{0}} \rightarrow |\begin{pmatrix} 3 \ 1 \ 5 \end{pmatrix}|$
twin meteorBOT
kathlijn
heady ibex
which is not infinity
hot lark
owh man sometimes i keep forgetting the only difference with cauchy sequence and convergent sequence is that the point it approaches is in the space or not
heady ibex
since the original sequence is cauchy sequence it 100% goes to some point in the space
that is finite
not infinite
as otherwise the distance between the subsequent values in the sequence doesn't go down
meaning the norm has to be finite too
hot lark
since the original sequence is cauchy sequence it 100% goes to some point in the...
but the norm can be infinite at a point no?
hot lark
i genuinely don't know
thanks for giving me a general idea
i'll close this since this isnt that important for my exam
.close
obsidian ore
the question is related to trig substitution, i have tried wolfram alpha but all i got was a really large function, no idea what to do lmao (im only grade 8 so i didnt learn much about this in school) tysm
vocal sleetBOT
the question is related to trig substitution, i have tried wolfram alpha but all...
obsidian ore
nope never heard of that sorry
heady ibex
double angle
heady ibex
i'm not sure about the specifics
obsidian ore
oh
heady ibex
try x = cos(2t)
obsidian ore
try x = cos(2t)
but wouldnt that yield dx = -4sintcost dt..?
obsidian ore
okay ill try that thanks
eternal delta
vocal sleetBOT
eternal delta
I would like some help with e
what i found was she invests 15000 every month she gets 0.4 interest
so i wrote 15000(1.004)^n
and she withdraws 1000 every year so i wrote a arithmetic sequence which equates to (-250/3)n -2750/3
but i mustve wrote something wrong or gotten something very incorrect
vocal sleetBOT
@eternal delta Has your question been resolved?
eternal delta
aint nobody help
ok first one i fully understand
but the next part
why is this a geometric sequence
like the minus 1000 stuff
she withdraws 1000 every year
then why is there a common ratio
vocal sleetBOT
@eternal delta Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
random vortex
Here what happened between y’ and y’’
vocal sleetBOT
Here what happened between y’ and y’’
paper depot
,rccw
twin meteorBOT
paper depot
@random vortex stick to this channel.
p sure they just differentiated 1 - 2xy with respect to x...
random vortex
Oh then they have continued it till y”’
paper depot
yes
paper depot
yes
lapis niche
It's just the chain rule and the product rule
random vortex
That’s what I don’t know
vocal sleetBOT
@random vortex Has your question been resolved?
woven stratus
How come
woven stratus
3tg^2(3x) = 1
Gives you solutions
+-(PI/18) + kPI/3
Like I do get the + solution
But how the minus?
hard atlas
what are you solving for? t? g? x?
woven stratus
tg is tan(x)
I just used different terminology
tg(x) = tan(x), just different words
woven stratus
Yes
But that
Doesn't yield me the solution
The solution to + is PI/18 + kPI/3
The other one gives me 6PI/18 + kPI/3
That's not what I wanted to get
hard atlas
not sure how you got that?
remember that tan is odd. tan(-x)=-tan(x)
so if you know that tan(3x)=something, then tan(-3x)=-something
woven stratus
I mean I wanted to sovle
3tan(x) = -sqrt(3) / 3
And then I thought if for 30 degrees tan(x) = sqrt(3) / 2
Then for PI - PI/6 (180 - 30 degrees) has tan(x) = -sqrt(3)/2
hard atlas
yeah lets mix degree and radians what can go wrong
woven stratus
Misspelled, my bad
woven stratus
and why do you car about sqrt(3)/2 ?
That's one solution
I forgot about the tan property
.close
vocal sleetBOT
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Available help channel!
shadow spindle
is 0^inf and indeterminated form?
vocal sleetBOT
is 0^inf and indeterminated form?
lyric fossil
no
shadow spindle
how can one justify it?
lyric fossil
for any x in (-1, 1), the limit of x^n as n goes to infinity is 0
shadow spindle
I used this function and I get a no also
lyric fossil
are you taking the limit as x goes to infinity
shadow spindle
yep, that limit is 0
lyric fossil
yeah
shadow spindle
for any x in (-1, 1), the limit of x^n as n goes to infinity is 0
I don't get his at all
lyric fossil
do you understand what x in (-1, 1) means
shadow spindle
-1 < x < 1 ?
lyric fossil
yes
what happens when you multiply a number in that range by itself
does it get bigger, smaller, or stays the same?
shadow spindle
smaller
lyric fossil
so we're going to get another number in that range, smaller than the last one
as you do this over and over, you tend to 0
shadow spindle
Oh yeah, I was asking cause we know 1^inf is in fact an indeterminated form
lyric fossil
what i just said, that for any x in (-1,1), x^n goes to 0
is to say that 0^inf is not indeterminate, because it is very much determinable
shadow spindle
can we tell that limit is 0?
lyric fossil
are you asking for a proof?
lyric fossil
Oh yeah, I was asking cause we know 1^inf is in fact an indeterminated form
i felt like here you were saying it already made sense to you it went to 0
shadow spindle
not really, cause a proof would require the definition of limits
I just need a way to tell that it is not indeterminate, that's why I tried using that function
lyric fossil
define indeterminate
shadow spindle
we can't be sure what the value of some "expression" or limit in this case is
lyric fossil
so you want to prove that $\lim_{x\to\infty} f(x)^{g(x)} = 0$ granted that $\lim_{x\to\infty} f(x) = 0$ and $\lim_{x\to\infty}g(x)=\infty$
twin meteorBOT
maximofs
shadow spindle
yep
vocal sleetBOT
@shadow spindle Has your question been resolved?
distant eagle
not really, cause a proof would require the definition of limits
Don't you know the definition of limit?
shadow spindle
Sorta
distant eagle
I just need a way to tell that it is not indeterminate, that's why I tried using...
You can follow the following reasoning: since lim g(x) is infinite, g(x) must from some point always be greater than 1, and since lim f(x) = 0, f(x) must from some point always be between -1 and 1. After those two points, f(x)^g(x) < f(x) because f(x) is in (-1,1) and g(x) > 1. When computing the value of lim f(x)^g(x), you can just consider that x is greater than the two points of before, so lim f(x)^g(x) < lim f(x) = 0
shadow spindle
That's a good reasoning
lyric fossil
i was going to suggest something similar
if f(x) -> 0
then at some point f(x) is less than, say, 1/2
so f(x)^g(x) < (.5)^g(x)
as g(x) goes to infinity, .5^g(x) also does, so f(x) must clearly tend to 0 as well
vocal sleetBOT
@shadow spindle Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
upper iron
Did you find p first?
upper iron
Yes right
vast shale
Now what
upper iron
How do I find the frequency
q is not the frequency
q is actually the angular frequency
upper iron
Let me just give you its formula
vast shale
Kk
upper iron
$q= \frac{2 \pi}{T}$
twin meteorBOT
LUNA
vast shale
But I also don’t have the period there?
vast shale
It completes a full wave from x = 0 to x = 8
So 8?
Since it completes half a wave from 0 to 4
Idk if that made any sense
upper iron
Right!
But I wanted to say earlier is that this q
its unit is not Hertz
it is not a frequency
it is an angular velocity
its unit is rad/s
vast shale
I’m so confused cause some formulas I see that it’s frequency
upper iron
Loosely speaking, just frequency
vast shale
Like this?
upper iron
Yes
mild flower
it's just the difference between do we shift it and then stretch it or the other way around
upper iron
Yes
vast shale
Icic
upper iron
what about r
upper iron
Right!
vast shale
Also for this, how do u get 1/6 as frequency? I just guessed 💀
mild flower
look for the half-frequency
or double frequency? whatever, measure between peak and trough
you know that's half of the distance between two peaks
vocal sleetBOT
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Available help channel!
urban obsidian
vocal sleetBOT
urban obsidian
n = 1 (mod 2)
n = 2 (mod 3)
n = 3 (mod 4)
n = 4 (mod 5)
how to find first hit without listing everything out
vocal sleetBOT
@urban obsidian Has your question been resolved?
urban obsidian
<@&286206848099549185>
urban obsidian
what your question?
i just wrote the question above though
coarse karma
this?
urban obsidian
yes and right underneath is my attempt
well not attempt i rewrote question and i want to find first hit
thin vale
just an fyi,
vocal sleetBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
urban obsidian
kid named <#486128019652476939>
umm ?
mild flower
umm ?
not you - I was about to tell PRO player that he shouldn't just put things into GPT and give that as an answer
thin vale
I was thinking the same thing lol