its just all that stuff confused me
#help-27
dire forge
and also what is this?
do you know the sigma notation for sums? like for example
[\sum_{i \in \bN}\frac{1}{n^2}]
woven radishBOT
propERICly_embedded
feral sun
yes
dire forge
This is very similar
It's just saying "take the union of all the B_is"
where i ranges over all the elements of I
feral sun
**propERICly\_embedded**
doesnt this mean , the sum of 1/n^2 where i belongs to all natural numbers?
dire forge
So if (I = {1,2,3}), then
[\bigcup_{i\in I}B_i = B_1 \cup B_2 \cup B_3]
woven radishBOT
propERICly_embedded
dire forge
so the union of B_i where i ranges over I
dire forge
the advantage of the notation on the left hand side is that I can be infinite!
whereas if I is infinite, we can't use the notation on the right hand side
it only works for finitely many sets in the union
feral sun
ok i think ive got it all but i just want to know, when they put something like i belongs to I or i belongs to all natural numbers under an intersection or union or a summation like you showed me, is it just trying to show that there is an infinite amount of like possibilities?
dire forge
ok i think ive got it all but i just want to know, when they put something like ...
yup, just like how in the sum example I gave, i can be 1, 2, 3, etc, ranging over all the natural numbers
dire forge
yup yup, it doesn't have to be the natural numbers N, it can really be any set that you're taking the union over
feral sun
so if it said like i belongs to all natural numbers in the proposition, would it be all natural numbers as well as whats in A?
dire forge
i has nothing to do with A
i ranges over I
but if you chose I to be the set N of all natural numbers, then you would get one set for each natural number so B1, B2, B3, B4, ... (infinitely many sets B_i)
feral sun
yup yup, it doesn't have to be the natural numbers N, it can really be any set t...
what do you mean by it can be any set that youre taking the union over?
dire forge
what do you mean by it can be any set that youre taking the union over?
like I could be N, but it could also be the set R of real numbers, or the set {1, 2, 3, 4}, or really just any set you want
the important thing is that for each i in I, you have one set B_i
and you take the union of all the B_i's as i ranges over everything in I
feral sun
so you mean that i refers to anything in I?
dire forge
so you mean that i refers to anything in I?
it's just like how in
[\sum_{i=1}^5 \frac1{n^2}]
(i) goes over all of the different elements in the set ({1,2,3,4,5}), so (i=1), (i=2), etc.
woven radishBOT
propERICly_embedded
dire forge
we call i a "dummy variable" since it's just a notational convenience to express the sum
similarly i in this proposition is a dummy variable so we can give each of the sets B_i different names
feral sun
i see
so is the use of “dummy variables” only in stuff like propositions and theorems?
timber pebble
so is the use of “dummy variables” only in stuff like propositions and theorems?
its called dummy because it doesn't effect the result, it's not present
you could call it i or j or k or anything you like
feral sun
or would i come across this in a problem
timber pebble
i can see getting this problem in a basic proofs class
prove that the thing you posted is true
so sure
in math you see dummy variables all the time
feral sun
oh ok
well then i think thats all for now im too tired for more math but thank you both lots for the help
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vital hearth
Hi, I need help factoring out the numerator to where i can get an x-1 on both the top and bottom to find be able to find the limit.
vital hearth
chrome granite
Hi, I need help factoring out the numerator to where i can get an x-1 on both t...
Do you know how to factor a quadratic?
vital hearth
yes i do. but when i try to factor by forcing the (x-1) on one of the sides i dont get a number that adds up on the other. unless im just missing something entirely
vital hearth
oh i think i see what i did wrong.
so i assumed that since the bottom equaled 0 i had to start factoring the top, but since it all equals to 2/0 rather than 0/0 that would mean DNE?
winter torrent
yeah
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wooden axle
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wooden axle
I did not understand the question properly hence no idea to solve in which direction.
<@&286206848099549185>
empty flame
hey arjunn how are you
empty flame
ohhh ok
wooden axle
How are you doing?
wooden axle
Ahh I am reading, learning each day
Random stuffs
Some graduated topics and some high schools topics
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wooden axle
If three points are given in 3d what will be the shortest way to find in what ratio second point is dividing if they are collinear?
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If three points are given in 3d what will be the shortest way to find in what ra...
wooden axle
grizzled yew
Distance formula is easy
pseudo basin
find distances AB and BC and divide one by the other
it takes a total of:
- 6 subtractions
- 4 additions
- 6 multiplications
- 1 division
- 2 square root extractions
dire forge
damn, you actually counted lol
dire forge
you could also divide just the change in one of the coordinates, if you know they're colinear
pseudo basin
you could, yeah.
i assume myself not to.
but if you trust that, then it's only 2 subtractions and 1 division.
which is about six times quicker at the expense of reduced certainty.
quaint citrus
it takes a total of:
- 6 subtractions
- 4 additions
- 6 multiplications
- 1 div...
U a real one for that
pseudo basin
@wooden axle
wooden axle
Yes i am
wooden axle
it takes a total of:
- 6 subtractions
- 4 additions
- 6 multiplications
- 1 div...
What are these 6,4,6?
pseudo basin
that is how many times you will have to do each operation.
i counted it up for you.
it is not relevant for your work.
pseudo basin
divide distance AB by distance BC.
i mentioned two things, then the words "one" and "the other" refer to those same things in the same sentence.
i guess you are also learning some English on top of the math.
wooden axle
√56/√126
I got this
AB/BC
Let me simplify
√28/63
What next should I have to do with this?
I don't think you have dropped enough information for me to do even you are fluent in English
wooden axle
it takes a total of:
- 6 subtractions
- 4 additions
- 6 multiplications
- 1 div...
I guess people were active just for fun here. To find some funny moments in each channel
No problem. Have fun
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chrome badger
hii, is C a proper subset of A if
C={ 2} and A={1, {2}, √2}? it is, right?
wooden veldt
is every element of C, also an element of A?
chrome badger
it should be C= {{2}} to make it proper?
wooden veldt
that would be a proper subset of A yes
wooden axle
A proper subset of a set A is a subset of A that is not equal to A.
wooden veldt
your original C is not even a subset
wooden axle
it should be C= {{2}} to make it proper?
Yes
vestal notch
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vestal notch
Can someone help me don't know where to start
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winter patrol
questions are cut off,
also seems like clear explanations of the answers are given
gilded wigeon
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gilded wigeon
am lost
weak cove
Tangent is pi periodic
gilded wigeon
im not sure what that means
lyric hornet
im not sure what that means
$\tan(\pi+\theta)=\tan\theta$
woven radishBOT
MrFancy
gilded wigeon
ohhh right so its the same, and 2pi + theta is also the same no?
lyric hornet
ohhh right so its the same, and 2pi + theta is also the same no?
$\ldots=\tan(2\pi+\theta)=\tan(\pi+\theta)=\tan\theta$
woven radishBOT
MrFancy
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lyric hornet
thank you sm mrfancy
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restive river
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restive river
@open portal
Sorry for my ugly hand writing
I used the elimination method
Did i do anything wrong
coarse crow
For this type of question
devout snowBOT
For this type of question
coarse crow
why are the answers always 1 term
like this
Shouldnt it be sqrt(z) = sqrt(|z|)cis(x/2) or sqrt(z) = sqrt(|z|)cis(x/2 + pi)
I can think of 1 explanation, however i don't know if it is right:
the argument being x/2 shows that for any real values substituted for 'theta,' or x in my case, both roots undergo this division of 2. In summary, the angle shown that is divided by 2 represents the all of the angles from all of the roots.
Please ping btw
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copper hatch
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grizzled yew
Covert 1 to log
copper hatch
10?
grizzled yew
Now use the addition rule
copper hatch
ohh
grizzled yew
log(3/2)+log(10)=??
grizzled yew
Yep
grizzled yew
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untold crow
$z^{3}=-1+i$, $z=\sqrt[3]{-1+i}$
devout snowBOT
$z^{3}=-1+i$, $z=\sqrt[3]{-1+i}$
woven radishBOT
HqppyFeet
untold crow
hmmm.. haven't done this type of cube root before... I know that one of the cube roots of -1 is -1, but... -1 + i? That's a different thing... can someone give me a hint as to what to do?
round lava
first you want to find one root
untold crow
yup
round lava
so you need to find a complex number (a+ib) so that (a+ib)^3 = -1+i
where a,b are real
wihch you can hopefully just do algebraically
actually converting it to polar coordinates might be easier
sry
winter torrent
polar coordinates will make this substantially easier
untold crow
i was thinking that xD
untold crow
i was like... am i really going to do a+ib)^3
round lava
not an analyst :)
untold crow
xD anyway, yeah i am familiar with z = r(cis(x))
winter torrent
instead of writing it like that
untold crow
I found the modulus and argument. 2 and -pi/4 respectively
winter torrent
write it as $z = re^{i\theta}$
woven radishBOT
hayley!
winter torrent
uh -pi/4 isn't right for the angle
untold crow
yeah both ways work, i tend to use cis but yeah
winter torrent
yeah both ways work, i tend to use cis but yeah
writing it with the exponential makes it clearer how to take the root
but cis is easier to write in text so
and neither is 2 right for the radius
untold crow
hm-? $arg(-1+i) = tan^{-1}\frac{1}{-1}=-45\circ$
woven radishBOT
HqppyFeet
untold crow
-45 degrees in rad is -pi/4. what did i do wrong?
winter torrent
ok this is why blindly applying arctan is bad
consider what -1 + i looks like on the complex plane
winter torrent
yeah
untold crow
woops
ok im getting a bit confused as to when i can use arctan here--- simply copied a text book, apologies
winter torrent
my recommendation? until you're very comfortable with it, just draw a quick sketch
so what angle should you actually have?
untold crow
135, or 3pi/4, right?
round lava
👍
untold crow
and the modulus is sqrt(2) i realized
winter torrent
yeah
untold crow
well nice, with e^(ix), argument, and modulus, I can simply do (re^(ix))^(1/3) and adding 2pi after each answer will give me the three roots. aight this sounds good
winter torrent
well nice, with e^(ix), argument, and modulus, I can simply do (re^(ix))^(1/3) a...
hmm
careful with that 2pi
untold crow
Yeah.
r^(1/3) * cis(pi/4) for first root.
r^(1/3) * cis(3pi/4) for second root.
r^(1/3) * cis(5pi/4) for third root.
Is this correct?
untold crow
cis(pi/4) was acquired through cis(3pi/4)^(1/3), then applying de Mouivre's theorem, => cis(3pi/12) => cis(pi/4)
(I hope my thinking is correct lol, this feels like familiar territory)
nvm, found out that r^(1/3) is 2^(1/6)
wait a minute, answer sheet says " $2^{\frac{1}{6}}(cos(\theta)+isin(\theta))$ where $\theta = \frac{\pi}{4}$, $\frac{11\pi}{12}$, $\frac{19\pi}{12}$ "
woven radishBOT
HqppyFeet
untold crow
bruh what... do they add 2pi into theta before the (1/3) exponent is applied in cis(3pi/4)^(1/3)?
Sure looks like it
cos(3pi/4), so that cos(3pi/4 + 8pi/4).... mhm
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narrow jolt
How do i do this
devout snowBOT
How do i do this
devout snowBOT
How do i do this
Show your work, and if possible, explain where you are stuck.
jaunty musk
You replace x by x+h in f, subtract it with f(x), then divide the whole result by h
If you tend h to 0, you unfortunately don't get the derivative, so there is a mistake somewhere for sure
Now it's for you to find it. Look back at your computations
There should be something wrong
narrow jolt
oh okay
narrow jolt
I don't get it, I think I do (x+h)^2 and -5(x+h) +6 which gives me x^2+h^2-5x-5h+6 and then subtract by f(x) which makes it h^2-5h over h
winter patrol
(x+h)^2 isn't x^2 + h^2
ripe finch
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chrome granite
Which one
ripe finch
i dont understand d h and j
chrome granite
i dont understand d h and j
they’re right
chrome granite
there is a hollow circle at -3 on the graph of h
that means -3 isn’t in the domain of h
so h(-3) doesn’t exist
can you see why h(2) also doesn’t exist?
ripe finch
ohh
there is a circle there too
and doesnt exist in domain
what about h(1) theres a jump here
chrome granite
what about h(1) theres a jump here
Then you have to look for the solid circle
chrome granite
what about h(1) theres a jump here
you mean h(0)?
chrome granite
also if there are two circles there it means it wouldn't exist
you have to see if the circles are hollow or solid
ripe finch
hollow circles
chrome granite
also if there are two circles there it means it wouldn't exist
are we looking at the same graph
I don’t see 2 hollow circles at the same y coordinate on the graph
ripe finch
yes
like IF
there were on h(0)
two hollow circles except one filled and one hollow
then the answer should be DNE
restive river
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ripe finch
in geometric its multiplied here in the question
1 4 9 16
+3 +5 +7
+2 +2
so i assume its arithmetic
ripe finch
damnn how tho
ripe finch
ur right
main gull
i asked chat gpt
First, do not use chatgpt for math
restive river
First, do not use chatgpt for math
why
main gull
Because chatgpt is garbage at math
main gull
no its not
Yes it is
silver fjord
it's not meant to do math. gpt4 may be better than the free version but it was not intended to do math problems
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dire forge
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dire forge
Don't know if its arithmetic or geometric
How do you know it's arithmetic or geometric? What if it's neither?
Do you know the definitions of arithmetic and geometric?
restive river
Do you know the definitions of arithmetic and geometric?
yes?????????????????????
dire forge
Okay so is the sequence arithmetic? What do you think
dire forge
what's not fixed?
restive river
the difference in terms
restive river
Could be
dire forge
How could you check?
restive river
equation
dire forge
what equation?
dire forge
can you write out what equation you mean?
woven radishBOT
intracatholic
dire forge
Yup, how can we check if this sequence satisfies that equation?
dire forge
Try it out
dire forge
what about the ratio? ratio of what?
restive river
of two terms
dire forge
what can you say about the ratio for this sequence?
restive river
it aint the same for every consective term
dire forge
yup, what ratios do you get?
dire forge
right so the important thing is 4/1 and 9/4 are not the same
so is the sequence geometric?
restive river
it quadratic
dire forge
that's true, but is it geometric?
restive river
nuh uh
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frozen dune
why is n^2 = -0 (for n ≠ 0) on the sedenion multiplication table
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why is n^2 = -0 (for n ≠ 0) on the sedenion multiplication table
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finite briar
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finite briar
<@&268886789983436800> deal with this
I was just about to do this
zenith jacinth
bro is mad
red turret
we are not entitled to help you.
finite briar
STOP FUCKING SPAMMING
zenith jacinth
bro thinks we are paid to help
finite briar
!community
restive river
we are not entitled to help you.
Hi lmao yes
true dew
Hi
finite briar
!volunteer
zenith jacinth
if we dont want to help you, we wont lol
red turret
!volunteers
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Helpers are just people volunteering their time to help you. Be polite.
restive river
Go google
finite briar
!volunteers
Thank you
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mystic scarab
<@&268886789983436800>
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restive river
@valid fern
red turret
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zenith jacinth
he thinks he will get help like that lol
restive river
Beo gone mad
mystic scarab
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red turret
dont feed him
restive river
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west ridge
What a degen
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true dew
I need help in math
zenith jacinth
buoyant furnace
what just happening
karmic abyss
I need help in math
Please refer to #❓how-to-get-help
restive river
😂😂
zenith jacinth
aight bye dude
true dew
Please refer to <#488120190538743810>
Thanks
buoyant furnace
dude
restive river
10 year old mindset
red turret
already banned
west ridge
He came Into my help box spamming his shit to lol
buoyant furnace
same lol
red turret
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zenith jacinth
I wanna be greeennn
look for the roles
restive river
I mean yeah have to help MORE 🙆
restive river
Why doesn't the bot detect this convo as a new question?🤔
red turret
the channel's not open yet
red turret
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ionic swift
given f(x) I am supposed to determine if f is a pdf. Now I know that it is but I dont understand why it satisfies the condition that the integral from -inf to inf of f(x)dx = 1.
In my books solution it says because the sum from 0 to inf of 2^(-x) = 1. But how does this explain this ?
devout snowBOT
given f(x) I am supposed to determine if f is a pdf. Now I know that it is but I...
ionic swift
thats what's in my book regarding that exercise
ionic swift
I understand that convergence and I have already seen it before. I just dont understand why that is the explanation to why said criteria is satisfied
ionic swift
oh lol sorry I thouhgt you graphed the sum
pseudo basin
i graphed the actual function
whose integral is composed of rectangles of width 1
so its integral is the sum
ionic swift
ohhhhh
now I understand
but like
no wait
I am just a bit confused because I feel like in order to solve this I had to be familiar with that exact function to know how it behaves
but in my book they just taught to take the integral
and I wouldve done something like this (one second)
ionic swift
it's 2^-ceil(x) essentially
I am sorry I dont understand that
pseudo basin
$2^{-\ceil{x}}$
woven radishBOT
Ann
vernal monolith
Well notice that your function is in terms of k not and x @ionic swift
Its 2^(-k)
And ceiling of x gives k, thats why
ionic swift
Well notice that your function is in terms of k not and x <@547149221598461973>
hows that different from saying
f(x) = 2^(-x) for x in N ?
ionic swift
And ceiling of x gives k, thats why
I dont understand that
ionic swift
oh so
vernal monolith
When input to 2^(ceil[x])
ionic swift
because in general x would be in R ?
oh damn
right
now I understand
big thanks to both of you
vernal monolith
I did nothing but you're welcome
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heady coral
Hi, I'm trying to solve this linear congruence, I watch a bunch of videos and I still don't understand the final step :c
This is what I did, I don't know how to continuous, I find the value of s which solve this equation 1 = 1993 * s + 990 * t, where 1993 is the result of 9965/5 (5 = gcd(9965,4950)), and 990 is the result of 4950/5
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Hi, I'm trying to solve this linear congruence, I watch a bunch of videos and I ...
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heady coral
<@&286206848099549185>
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fluid laurel
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fluid laurel
Hello I need help with solving this equation , but I can't understand how to start
heady current
u can start by getting both the terms on the same denominator
fluid laurel
what do you mean by that
heady current
try to get the denominator of 3/x to 5x
fluid laurel
I get it
heady current
like how u add fractions
heady current
np
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heady current
what, is there another way to do it
nono, ur method is fine
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heady current
np
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frozen dirge
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frozen dirge
Could u help me with this please
warped relic
Hey did you try it out?
frozen dirge
Yea I've been unable to do it tho
warped relic
Well your goal is to make T alone on the left hand side
frozen dirge
I've tried by first expanding the bracket but idk how to get it on its own
warped relic
I suggest you treat the question like an onion
You start by peeling the first layer
Which right now looks to be the r multiplied by the squared brackets
How do you get rid of a number being multiplied?
frozen dirge
Divide it by itself?
warped relic
Yep and to keep the equation from changing, what do you do to the right side when you divide the left side by r?
frozen dirge
Wouldn't it just be r^2 x r at the bottom of the right side then
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vast violet
do i take sq root of it
winter torrent
difference of perfect squares
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silent briar
Can someone help me prove this
devout snowBOT
Can someone help me prove this
silent briar
This is logic
Blue is what needs to be proven
I can only use basic propertiws
Is that true?
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supple knot
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delicate phoenix
3x3
sonic smelt
What's your question?
delicate phoenix
What's 3x3
dense jay
unsure
delicate phoenix
6 right
sonic smelt
,w 3 * 3
woven radishBOT
sonic smelt
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lofty obsidian
How do i find the limit of (x approaching 0) for the equation: (x-1)/((x^2)(x+5)) ? I know the answer is negative infinity and got to the equation "((1/x) - (1/x^2))/(x+5)" but am not sure where to go from there.
open portal
$\frac{x-1}{x^3+5x^2}$
woven radishBOT
binibini
open portal
1 s
lofty obsidian
ok can u get me another person ToT
woven radishBOT
binibini
open portal
**binibini**
@lofty obsidian
left side -infinity , right side 1/5
but i m not sure solution
lofty obsidian
ok thank u
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visual basin
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reef carbon
I don't understand what I'm supposed to do here
devout snowBOT
I don't understand what I'm supposed to do here
reef carbon
what
hybrid snow
Use linearization (using the tangent line at x = 0)
reef carbon
i dont know what that is
hybrid snow
You don't know what a tangent line is?
reef carbon
"linearization"
hybrid snow
Use linearization (using the tangent line at x = 0)
I legit defined it for you
hybrid snow
Find the equation of the tangent line at x=0
Start with that
Let that line be L(x)
Then F(7) ≈ L(7)
supple pasture
Do you know about Taylor polynomials because that will give us better approximations
reef carbon
im honestly kinda confused on the first method you gave, can you like explain that
hybrid snow
Do you know what a tangent line is
reef carbon
yes
hybrid snow
,tex \linearization
woven radishBOT
Umbraleviathan
hybrid snow
x0 is where the line is tangent to
now ive explained it already so im just gonna run in circles again
L(x) is your tangent line. Linearization is using L(x) to approximate values around x0
so F(7) is approx L(7)
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cyan axle
I don’t know what I’m doing at this point
devout snowBOT
I don’t know what I’m doing at this point
candid timber
Try and graph both the functions.
cyan axle
?
cyan axle
….
cyan axle
vertical shift isnt inside the sqrt function
Is that just a rule?
I’ve had like nine of this stuff in the resources my prof gave me
None*
cyan axle
Yeah I haven’t even seen that before so I gotta watch a whole video on it
How do I do this?
I know that it wants me to find the Y value but why is there two?
The video connected to it isn’t even close to the problem
Like for the first one I just get -4 and -2
I legit tried bullshitting but can I get an explanation on why it flip and flops between the two expressions?
Oh shit I’m stupid
It’s the damn rule in the right
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shadow quest
Why is a double integral on a region D in the first quadrant which its value is negative is not possible
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Why is a double integral on a region D in the first quadrant which its value is ...
@shadow quest Has your question been resolved?
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@shadow quest Has your question been resolved?
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@shadow quest Has your question been resolved?
nova basin
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nova basin
so on the left i found the vertical asymptote and on the right i tried to "verify my conclusion using appropriate limit statements"
i wanted to know if its verified correctly and what does equation form mean
if anyone could help .-.
wait thats wrong 1 moment
im so confused
its not 0 its 1.5/0
which is undefined
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formal pecan
How can I check if function is piecewise smooth on an interval without going on Desmos to look at the graph?
midnight bane
piecewise smooth?
storm crater
I think he means smooth on intervals that cover the entire domain.
Possibly also contininous.
formal pecan
You mean continuous?
In order for f(x) to be piecewise smooth on an interval, it needs to be piecewise continuous.
midnight bane
so continuous and differentialable
formal pecan
Yes
If I was given a function, how can I decide if it's piecewise smooth or not without looking at the graph?
storm crater
I think he means smooth on intervals that cover the entire domain.
@formal pecan this?
midnight bane
make sure your functions that make up the piecewise are continuous and differentiable and check where they merge
almost no piecewise functions are differentiable though
storm crater
often smooth also refers to infinitely often differentiable.
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nocturne hound
$\lim_{x \to \infty} \bigl(\frac{3x^2-6x}{4x-8} \bigr)$
devout snowBOT
$\lim_{x \to \infty} \bigl(\frac{3x^2-6x}{4x-8} \bigr)$
woven radishBOT
R(icky)
nocturne hound
How do I approach this
cosmic orchid
Isn't It infini since x squared to the infine will always grow bigger than 4x because it's derivate is superior to (4x)' so it's bigger growing infinity over a smaller one which leads to infinity ?
dark sable
How do I approach this
you know l'hopital's rule?
cosmic orchid
Of course you'll need to simplify and put all I said in evidence but just by being logic It seems good
nocturne hound
I get $\frac{3}{\frac{4}{x}}$
woven radishBOT
R(icky)
dark sable
lemme google
Yeah wrong application(I think)
nocturne hound
So if I sub in $\infty$ I will still get $\infty$
woven radishBOT
R(icky)
dark sable
**R(icky)**
Yeah
nocturne hound
Thanks
slate zephyr
So if I sub in $\infty$ I will still get $\infty$
consider the limit intuitively like Chetrit implied - since the numerator has an x^2 term, it will grow faster than the denominator, and ultimately the function will approach infinity
nocturne hound
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bold cypress
Do you guys have any tips on how to determine if an equation is a function or not without graphing it?
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Do you guys have any tips on how to determine if an equation is a function or no...
winter torrent
generally if you can put it into y = (stuff about x) form without branches like ± then it's a function
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wheat pawn
Do you guys have any tips on how to determine if an equation is a function or no...
if the same value of X can have more than one value of Y, it isnt
restive river
https://math.stackexchange.com/questions/1106170/proving-that-there-is-an-irrational-number-between-any-two-unequal-rational-numb Can someone explain to me how the irrational number is constructed in this proof.
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https://math.stackexchange.com/questions/1106170/proving-that-there-is-an-irrati...
silver fjord
You'd need the notion of a measure for that proof
Do you really want to go that far for that?
restive river
wdym by notion of measure?
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restive river
You'd need the notion of a measure for that proof
whats notion of meausre mean
supple knot
https://math.stackexchange.com/questions/1106170/proving-that-there-is-an-irrati...
Which part exactly don't you understand
restive river
Which part exactly don't you understand
how they constructed the irrational number
supple knot
how they constructed the irrational number
They explained that in detail
Which sentence or equation exactly don't you understand
restive river
They explained that in detail
dont know how they came to this conclusion
supple knot
dont know how they came to this conclusion
That's a number by construction
Do you know the axioms of real numbers
restive river
Do you know the axioms of real numbers
no
restive river
dont know how they came to this conclusion
did they have to divide by 2 here
supple knot
did they have to divide by 2 here
Why do you think they did that
What happens if there's no 2 in the denominator
restive river
its not in between
Also for proof by contradiction, do I still have to do it in an arbitrary way
or is an example okay
restive river
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vast violet
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vast violet
hi i am stuck
Like sure the addinf part i know
3x-38 there
But the when the = sign is there idk
😭
crude valley
what are you trying to do and what is your original problem
crude valley
honestly id multiply everything by x^2-4 for me personally that seems easier
quaint cove
Uhh, make the denominator x²-4 for every case and just focus on the above part
crude valley
you get (x+9)(x+2)=3(x-2)+44 right
quaint cove
Yup
crude valley
ye I did it the same way let me ping op @vast violet
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midnight sedge
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https://cdn.discordapp.com/attachments/1149351347032965132/1149351347171373076/7...
midnight sedge
how do i solve this?
i know that it involves force times sin of the angle
for horizontal force
but im not sure how to proceed
crude valley
isnt w=Tv
storm grotto
You have the force
you have the angle
how do you calculate F_y?
btw I answers your previous thread but you ignored it
midnight sedge
btw I answers your previous thread but you ignored it
i got on a bus home
didnt have service
midnight sedge
how do you calculate F_y?
im not sure thats what im confused on
storm grotto
You can get the vertical force by multiplying the force with sin(angle)
midnight sedge
is horizontal force force multiplied by cos(angle) then?
midnight sedge
what do i do with vertical force now tho
storm grotto
if you divide that with gravity you can get the mass
midnight sedge
u mean the weight?
storm grotto
weight sorry
midnight sedge
how do i get gravity tho
storm grotto
add a () on numerator
midnight sedge
im getting 1.23
its not right tho
is there anything we could have missed?
in the process
like a diff way to calculate gravity maybe
storm grotto
yea
Its been a serious long time I did physics
but yea I think so lol
since we just calculated one side
midnight sedge
still not working lol
midnight sedge
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pine patrol
Would this be correct?
devout snowBOT
Would this be correct?
pine patrol
I thought it was positive 6 but it was wrong
near stone
we dont help in quizzes
pine patrol
It isn't a quiz there is multiple attempts
livid carbon
Would this be correct?
Are you aware of the general form of the equation of a circle centred at a point (h,k) with radius r?
livid carbon
State it
livid carbon
r^2
pine patrol
Oh so it would be negative cuz of the formula
livid carbon
Wdym?
livid carbon
"it" what?
rancid dune
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rancid dune
I'm starting to graph sin and cos functions and instead of help with the specific question I'd appreciate it if someone could go more into depth of how I find the numbers to graph onto the graph
it was phrased a little confusing and was super exhausted when it was gone over
stark shuttle
What kind of transformations do you see?
autumn sparrow
You dont need to know that besides the transformations and the period of the sine function
stark shuttle
Translations even perhaps
rancid dune
3pi/2 i believe is shifting it to the left 3pi/2
autumn sparrow
Yes
autumn sparrow
Well wait, lemme explain why that's the answer
autumn sparrow
The period (the length of the interval which repeats forever) of the sine function is 2pi
so you can say that sin(x) = sin(x +- 2npi) where n is an integer
Thus you can use that identity to say that sin(x + 3pi/2) = sin(x - pi/2) which is that the graph D represents
rancid dune
i dont understand how we go from sin(x) = sin(x +- 2npi) to sin(x + 3pi/2) = sin(x - pi/2) could u elaborate on that
it just looks like u removed n from the 2nd equation and only changed the left
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rancid dune
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hexed solar
Pedro Henrique has low grades in Portuguese. The last test of the year will have 56 questions. To be approved and move on to the following year, Pedro Henrique's performance in this test must be, at least,
8/5
. What is the smallest number of questions he must get right on this test to pass?
devout snowBOT
Pedro Henrique has low grades in Portuguese. The last test of the year will have...
hexed solar
how do i solve this?
unique kelp
he needs to get 8 out of every 5 questions correct?
hexed solar
hexed solar
he needs to get 8 out of every 5 questions correct?
It's his minimum performance
unique kelp
can I see the question?
hexed solar
can I see the question?
unique kelp
ok so they wrote 5/8 and you wrote 8/5
hexed solar
Ah, sorry, I tried to translate the question
main gull
Pedro Henrique has low grades in Portuguese. The last test of the year will have...
You do not need to close your previous channel if no one helps you
devout snowBOT
Helpers are just people volunteering their time to help you. Be polite.
hexed solar
You do not need to close your previous channel if no one helps you
the other one didn't close?
main gull
Yes it did, you deleted your message there which made it close
unique kelp
Ah, sorry, I tried to translate the question
so he needs to get 5 8ths of the questions correct, yes?
hexed solar
so he needs to get 5 8ths of the questions correct, yes?
yes
unique kelp
can you write that out mathematically?
hexed solar
5/8 mathematically?
unique kelp
5 8ths of 56
hexed solar
5 8ths of 56
I don't know how to do this mathematically
unique kelp
generally when we say some fraction of some number it means the fraction and the number multiplied together
for example, 1 half of 4 = (1/2)*4 = 2
hexed solar
then it would be: 56/1*5/8
unique kelp
yeah
hexed solar
56/1*5/8=280/8=35?
unique kelp
looks good!
rancid dune
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grizzled roost
For which t values in [0,2pi) does this guy converge in C?
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For which t values in [0,2pi) does this guy converge in C?
@grizzled roost Has your question been resolved?
grizzled roost
<@&286206848099549185>
supple knot
Did you try ratio test