the red line
#help-13
livid hound
livid hound
can you rewrite waht yuo meant
slate pasture
a/3*sqrt(2)
livid hound
is incorrect
slate pasture
we get right triangle with 3 medians in the base right?
and all the medians are also lengths and bisectors, so we get a right angle triangle with 30 degree angle
so we have 3 sides. a/2, x and 2x
right?
livid hound
yeh...
stray ferry
Can someone explain me what is peano remainder in taylor series?
stray ferry
I think I understand LaGrange remainder but I cant undertsand what peano remainder is
boreal epoch
@stray ferry it's an error calculations that comes from the approximation of a function
boreal epoch
iirc they are completely different theorems
stray ferry
.close
dusty pasture
I don't seem to be able to find examples to prove the associative law, additive inverse, and distributive law...
boreal epoch
did you check them?
you are supposed to check till you find a sample that doesn't follow the rule
dusty pasture
I am meant to verify that these properties hold, not dispove tho
boreal epoch
it's the same thing
if you can't disprove them then they hold
if yo test and they don't hold you have disproven them
replace abc with Elements on your case
dusty pasture
.close
rugged beacon
cedar kilnBOT
cedar kilnBOT
✅
cedar kilnBOT
@rugged beacon Has your question been resolved?
rugged beacon
<@&286206848099549185>
blazing sphinx
:/
nimble veldt
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
making a sketch makes many things clearer.
nimble veldt
name everything what is given or asked.
nimble veldt
so i think I matches with T
I dont think so.
cedar kilnBOT
@rugged beacon Has your question been resolved?
torpid urchin
would someone be able to help me with this q
cedar kilnBOT
would someone be able to help me with this q
torpid urchin
pretty sure the e^-t^2 is not integrateable thus we have to use maclaurin series
and then integrate that im going to assume
but im struggling to be able to convert it
i am thinking maybe i can manipulate the e^x series and get something?
maybe could do something like this?
but even then i dont think i can integrate this
<@&286206848099549185> possibly i am thinking about this question wrong?
seems like im going in the wrong direction
torpid urchin
i need some help with integration
send the problem in a new channel
inland kraken
Ok mb
torpid urchin
👍
crimson sedge
would someone be able to help me with this q
Remember the taylor theorem?
torpid urchin
uh possible let me search quickly
may not know by name
oh like the series
yes
i have a feeling im not supposed to be doing something like this
since taylor series involves taking an nth derivative
crimson sedge
since taylor series involves taking an nth derivative
Well, that's what you have to do.
torpid urchin
yes
so is it possible that
since i have the integral
the nth derivative
is just the integrand?
crimson sedge
Well nope
torpid urchin
):
crimson sedge
The first derivative would be the integrand
torpid urchin
oh right
so maybe i can take the nth derivate of the integrand
and integrate the corresponding series?
crimson sedge
You don't need the nth derivative
torpid urchin
oh
crimson sedge
You only need M3
torpid urchin
because its asking for m3
torpid urchin
would m3 mean 3 terms or highest degree being 3?
which could be 4 terms
if there is a x^0
but i think im still going to have to create a series for this
crimson sedge
would m3 mean 3 terms or highest degree being 3?
I actually dont know
torpid urchin
i think its x^3
but that isnt really important
im going to have to convert it to a series still right?
torpid urchin
yeah since it is asking maclaurin
crimson sedge
As we want M3, you can put n = 4
Idk about this part cuz im not sure about the convention
torpid urchin
it wants the dominant term to be x^3
but wont we end up with all negative exponents
crimson sedge
but wont we end up with all negative exponents
Wdym
torpid urchin
since its e^-t^2
crimson sedge
How will that lead to negative exponents in the polynomial?
crimson sedge
Ah no, dont use this at all
crimson sedge
So it doesn't apply for it
crimson sedge
so is it possible i can integrate this series?
That's a good question
torpid urchin
we learned it doesnt change the radius
we did examples where we integrate and derive series in order to find function representations of them
so i think it may be i integrate this?
crimson sedge
Actually this is where my knowledge hits the wall :p
crimson sedge
Yeah sure, if something goes wrong, hopefully you'd be able to fig it out or another helper helps u out
Or there's always taylor theorem
torpid urchin
did this but im not sure how this has any correlation to the second part
or if this is even right
.close
wide lintel
Hello I’m trying to figure out my error
cedar kilnBOT
Hello I’m trying to figure out my error
wide lintel
wide lintel
I thought only the highest order coefficient matters
uncut current
wide lintel
.close
crimson sedge
how do i differentia the equations in respect to dx/dt and dy/dt
green hornet
x is a function of t right? Simply differentiate no?
green hornet
Yep
green hornet
Yeah
crimson sedge
which is just 4 rigjt?
oh
well
thank you very much Jim
i hope you are having a great day with Pam
LMAo
I love the office btw!! great show
but thank you very much i wish you an awesome day
green hornet
i hope you are having a great day with Pam
crimson sedge
LMAO
green hornet
let's not discuss this here tho
haughty pendant
how do i get the integration of this?
cedar kilnBOT
how do i get the integration of this?
crimson sedge
how do i get the integration of this?
what is the derivative of $1 + \frac{1}{x}$?
dire geode
Use power rule
wraith daggerBOT
pulse
haughty pendant
ln x
dire geode
,tex .exp rules
wraith daggerBOT
riemann
wraith daggerBOT
pulse
haughty pendant
x^-1
-1x^-2
-1/x^2
crimson sedge
So do you see why you can use $u=1 + \frac{1}{x}$ and use u-sub to solve?
wraith daggerBOT
pulse
haughty pendant
i dont know how to do that
crimson sedge
ah
crimson sedge
i dont know how to do that
do you mind if i screenshare me solving this question to you
it's hard to explain u-sub over text for me lol
haughty pendant
idm
crimson sedge
cool
haughty pendant
but how do i know when to use u-sub or not
crimson sedge
ill show you
crimson sedge
but how do i know when to use u-sub or not
can i call you on discord in dms rq
haughty pendant
oh
lime saddle
My linear algebra book sometimes refers to vectors as oriented lengths which Ive heard is really unique- We're now onto "oriented areas" (area in a plan in G^3). Is there a more universal term for oriented area? When googling questions I have about them I'm not getting super high quality results so
cedar kilnBOT
My linear algebra book sometimes refers to vectors as oriented lengths which Ive...
@lime saddle Has your question been resolved?
Available help channel!
bronze briar
So i need to prove that if gcd(m,a) = 1 and gcd(m,b) = 1, then gcd (m, ab) = 1.
bronze briar
i split the proof into 2 cases: if m= 1: then it's clear to see that this lemma is true because gcd(1, any natural number) is 1
but if m is not 1 then i make use of the lemma that states if m|ab and gcd(m,b) =1, then m|c
so i say assume for contradiction that gcd(m,ab) != 1 and gcd(m,a) = 1. According to the lemma, since m != 1 and gcd(m,ab) != 1, then m must divide b. And since m != 1, then gcd(m,b) != 1. But we are given that gcd(m,b) = 1, and thus this is a contradiction.
Therefore, gcd(m,ab) must be 1
does this work?
leaden snow
Proof by contradiction doesn't work like that. You have a statement of the form p => q. The "opposite" (logical negation) of an implication is "p and (not q)". So in your case you have to assume that
- gcd(m, a) = 1 and gcd(m, b) = 1 and
- gcd(m, ab) != 1
and derive a contradiction from that.
So you should reword the first sentence of your proof "Assume for contradiction that gcd(m, a) = gcd(m, b) = 1 and gcd(m, ab) != 1. [...]"
Otherwise it looks fine, imo.
bronze briar
oh okay thank you so much
mighty drift
Otherwise it looks fine, imo.
You don't have m|b though
leaden snow
oh mateo is right
mighty drift
As I already said, look at a common divisor d instead
bronze briar
wait but if m|b and m != 1, and we have already assumed that gcd(m,b) = 1, isn't this a contradiction right here?
mighty drift
Yes but it's irrelevant since you start with m|b which is false
You have no reason at all to think that m|b
leaden snow
You have gcd(m, b) = 1 so m and b do not share any common factors, m | b is not possible
bronze briar
wait but if gcd(m,ab) is not 1 and gcd(m,a) is 1, then the lemma says m|b, right?
leaden snow
it only says that if you know that gcd(m, b) is not 1 iirc
mighty drift
The lemma first hypothesis is one of divisibility. Where it is found here ?
bronze briar
it only says that if you know that gcd(m, b) is not 1 iirc
the lemma i have is that m | ab and gcd(m,b) = 1, then m | a
leaden snow
whats c here?
bronze briar
a, my bad
and if m is not 1, then gcd(m,a) != 1.
But in the proof, since we assume that gcd(m, a) = 1 and gcd(m,b) is 1 and gcd(m,ab) is 1, then the lemma says that m must divide (either a or b)
leaden snow
how would you know m | ab in the first place though?
gcd(m, ab) != 1 does not imply m | ab
take m = 10, ab = 12 for example
bronze briar
yikes
mighty drift
The lemma first hypothesis is one of divisibility. Where it is found here ?
I am just invisible?
bronze briar
sorry, i just didn't know how to apply that
leaden snow
try playing around with mateo's approach
mighty drift
#help-19 message
Have I been invisible for the last 45 minutes ?
dire geode
https://discord.com/channels/268882317391429632/903463355619110912/1092558661764...
pretty much yes
mighty drift
I know
dire geode
who said that
mighty drift
I just want to make him realize reading is something he should pay more attention to
Cause that would have saved him 45 minutes then and there
bronze briar
i didn't mean to make you angry
dire geode
i feel a presence, but can't put my nose on it
bronze briar
i just wanted to try to go with the idea i initially had
see if it's possible
math does not all need be done using a certain method, i am open minded
mighty drift
math does not all need be done using a certain method, i am open minded
Yes. But that was clearly not working
mighty drift
i didn't mean to make you angry
No I'm not don't worry. It's not really losing my any time or anything. + I'm used to people being blind
bronze briar
i dont see why you feel the need to insult me
mighty drift
But like 3 layers of blind kind of blind
bronze briar
kinda unnecessary
mighty drift
Would you prefer "oblivious to clearly visible and useful remarks laying in plain sight"
Or "didn't see a message in a discussion meant to be read"
Arguably I use the word blind a bit undeservingly yes, but it's not like you only missed it once...
Sorry if that sounds rude
But I struggle to stand people who can't be helped because everytime you tell them something important, they read past it and just keep going
bronze briar
forcing someone to use your method of solving is pretty arrogant though. As i said, there's more than one way of doing things in math, that's the beauty of mathematics
i mean you don't have to help me, and certainly dont have to insult me
mighty drift
One sec
bronze briar
i mean im sorry that i read past your message, but i didn't need to be berated for it
mighty drift
#help-19 message
Here I am, pointing to a flaw in the proof, and offering a fix that keeps basically all of the previous reasoning untouched
But yes, I am "forcing you to use my method"
cedar kilnBOT
@bronze briar Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
fringe tree
cedar kilnBOT
split jetty
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
granite knoll
replace "f(x)" with y, then solve for x
static fern
or you could think about it intuitively and try to undo the operations one at a time
cedar kilnBOT
cedar kilnBOT
Available help channel!
maiden stirrup
halp.
Question is: solve for the inverse
1.f(x)=2/3x-4
So far I've got
4+y=2/3x
= 3(4+y)= 2/x
I cant figure out how to move the 2 over to the other side.
I tried breaking 2/x into 2/1(1/x) then moving '2/1' over to the other side to get 3/2(4+y) = 1/x but then im stumped
humble karma
If $\frac{a}{b}=\frac{c}{d}$, then $\frac{b}{a} = \frac{d}{c}$. You can actually see this if you multiply both sides by x and then divide both sides by (3/2(4+y)).
wraith daggerBOT
Azyrashacorki
humble karma
(Also we're supposing here that a,b,c,d are non zero.)
leaden snow
is the x in the denominator? (you should parenthesize correctly)
maiden stirrup
idk tbh
leaden snow
You're almost there
$$4 + y = \frac{2}{3x} \iff x(4+y) = \frac{2}{3}$$
Can you figure out the next step?
wraith daggerBOT
nvx
leaden snow
if its $f(x) = \frac{2}{3}x - 4$ it should be easier.
wraith daggerBOT
nvx
maiden stirrup
i agree it would be
leaden snow
if we assume the x is in the denominator, did you see what i did in the previous step?
maiden stirrup
but I had a previous question like this
leaden snow
yeah usually if it isnt in parentheses, the x should be in the numerator
maiden stirrup
Im assuming that one reads as (1/2)x and the former reads 2/3x
leaden snow
2/3x = (2/3)x, usually, but a bunch of people mess that up
2/(3x) would be the correct notation if x should be in the denominator
maiden stirrup
or who ever wrote it made a mistake
maiden stirrup
**Azyrashacorki**
I don't get how this applies
I'll try messing around with it on paper
I really need a pen tablet D:
leaden snow
they just flipped both fractions on both sides
maiden stirrup
yeah, but idk how that will get me any closer to the answer
leaden snow
you can get this by cross multiplying too
maiden stirrup
I just cant figure out how to isolate x to one side without turning it into a fraction
leaden snow
well can you see the step i took in the image i sent?
maiden stirrup
x(4+y)=2/3 ?
leaden snow
$$4 + y = \frac{2}{3x} \iff x(4+y) = \frac{2}{3}$$
wraith daggerBOT
nvx
leaden snow
the left is what you had right
maiden stirrup
yeah
leaden snow
then we can multiply by x on both sides
so we get x out of the denominator
to isolate the x, what would you do now?
maiden stirrup
mm so then you would have
x = (2/3) / [1/(4+y)] // 3/2(4+y) ?
therefore x=3/2(4+y)?
maiden stirrup
also did i write that correctly? I meant (3/2)(4+y)
leaden snow
you would divide by (4+y) right?
maiden stirrup
because you said tha a/b = c/d == b/a = d/c
leaden snow
nah someone else said that
maiden stirrup
I went:
x(4+y) = 2/3
= x = (2/3) / (4+y)
= x = (2/3)* [1/(4+y)]
leaden snow
$$x(4+y) = \frac{2}{3}$$
Divide by $4+y$ on both sides:
$$x = \frac{2}{3(4+y)}$$
maiden stirrup
oh yeah so it should be 2/3(4+y)
wraith daggerBOT
nvx
leaden snow
no
maiden stirrup
if you divide 2/3 by (4+y) shouldnt it be 2/3 ÷ (4+y)?
leaden snow
yes
but you can directly write it in the denominator, same effect as a division
$\frac{\frac{2}{3}}{4+y} = \frac{2}{3(4+y)}$
wraith daggerBOT
nvx
maiden stirrup
OHHH I see what i did wrong
for some reason I thought (4+y) = 1/(4+y) but its actually (4+y) = (4+y)/1 so if you flip them then you get (2/3)*[1/(4+y)] = 2/[3(4+y)]
tysm
leaden snow
correct
maiden stirrup
leaden snow
can you state domain & range?
leaden snow
alright so in the process of getting from f to f inverse we divided by y+4 right
maiden stirrup
yeah
leaden snow
can you see how this could be a problem?
maiden stirrup
because if you divide y by y then y disappears
leaden snow
mhm but thats not illegal here. we still have it on the other side
maiden stirrup
but in this case, y would turn into x when graphing the inverse so it should be okay right?
maiden stirrup
yeah thats how i was gonna get my first point
so {DER|x>(-3)}
because you cant divide by 0 and in this case you also cant divide by negatives?
by > i mean x must be equal to or greater than
idk the alt code for "greater than or equal to"
maiden stirrup
mm why is that
I thought that goes into the realm of imaginary numbers
since this is only real numbers i thought negatives would be excluded
or am I misunderstanding?
this is a line isnt it? not a quadratic
leaden snow
imaginary numbers only come up once you take the square root of a negative
maiden stirrup
ahhhh
leaden snow
but we're not concerned with square roots here
maiden stirrup
i didnt realize this was a line until now
but then why would -4 not be okay? wouldnt that just mean y=0
so when x=-4, y=0
leaden snow
$\frac{2}{3(4 - 4)} = \frac{2}{0}$ this is undefined
wraith daggerBOT
nvx
maiden stirrup
but then how would you find when y=0
maiden stirrup
if its infinite, it would cross both axis' at some point though?
leaden snow
,w plot 2/(3(4+x))
wraith daggerBOT
leaden snow
no, since we had x in the denominator i cant be a line
unless you wanted the inverse of $f(x) = \frac{2}{3} x - 4$
wraith daggerBOT
nvx
maiden stirrup
this makes so much more sense now
is there a guide on the syntax for this:
$f(x) = \frac{2}{3} x - 4$
wraith daggerBOT
nvx
leaden snow
or do you mean a guide for the available syntax?
its called LaTeX if you want to research it
maiden stirrup
yeah, like a library for available commands
leaden snow
maiden stirrup
tysm
leaden snow
np!
hollow garnet
cedar kilnBOT
hollow garnet
Hi I dont understand what the alteranting thing in the begenning is for
If its asking for ratio/root test and not alternating series test
leaden snow
note in both ratio & root test you take the absolute value of your a_k, so the (-1)^k term will vanish anyway
$\abs{(-1)^{k+1} \cdot a_k} = \abs{a_k}$
wraith daggerBOT
nvx
cedar kilnBOT
@hollow garnet Has your question been resolved?
hollow garnet
$\abs{(-1)^{k+1} \cdot a_k} = \abs{a_k}$
So it doesnt really matter that the alternating thing is there?
It's kind of like testing you to know that the tests have absolute value?
fluid oasis
Yo what is 2 x 4?
leaden snow
It's kind of like testing you to know that the tests have absolute value?
@hollow garnet could be, yes
odd sierra
cedar kilnBOT
odd sierra
ignore the points i put in the graph
so i complete the square then what im stufk here
f(x)=(x+2)^2 + 2 is what i got
so what am i supposed to do with that in this problem X d
NVM
.close
chrome scroll
i need help with understanding how to do pigeonhole principle problems
chrome scroll
five vowels. How many strings of six lowercase letters of the English alphabet contain
• exactly one vowel?
• exactly two vowels?
• at least one vowel?
• at least two vowels?```this is my problem
i am using chatgpt and i think the way theyre doing it is wrong
i was using it bc i wanted to know how to do this
but i think its wrong bc the math is incorrect
idek if theyre solving the problem right
this was the feedback i got for the first bullet
6×5×215=1,791,840,000
thts the answer they gave
bright bridge
i am using chatgpt and i think the way theyre doing it is wrong
why
chrome scroll
i keep getting a different answer
chrome scroll
why
their math is incorrect
i tried correcting it many times
and it said it was incorrect
but it would still gice me a wrong answer back
bc if you do tht in a calculator, its wrong
i also dont know if theyre using the right formula to do the problem
sick mirage
hey
chrome scroll
hello
sick mirage
you typed a lot and nobody can see the original problem now
chrome scroll
i am sorry, ill paste it again
five vowels. How many strings of six lowercase letters of the English alphabet contain
• exactly one vowel?
• exactly two vowels?
• at least one vowel?
• at least two vowels?```but for this problem - the first 1 you have 1 slot that's a vowel so it's 5 possibilities for that spot 5 choose 1
chrome scroll
feedback given :6×5×21^5=1,791,840,000
sick mirage
then for the remaining 5 spots you have 21 possibilities since repeats are allowed
chrome scroll
i corrected the typo, but yeah this is still wrong
sick mirage
5(21^5) I believe for that one
does that method help a bit? I find that drawing lines of spots and then how many choices are possible for each one helps with these
chrome scroll
tht helps so much
sick mirage
yeah for the second it's gonna be similar
chrome scroll
but heres the thing.. when i did my math
i got a different answer than chatgpt.. my answer was 122,523,030 when i did 5 * 21^5 * 6
sick mirage
wanna know a secret?
chrome scroll
yes
sick mirage
chat gpt is wrong a lot with combinatorics problems 🙂
chrome scroll
o.o ya
sick mirage
it's funny too because it should excel there but it just doesn't
chrome scroll
its my first day using it
sick mirage
yeah it's POSSIBLE for it to be helpful, but strangely unlikely with combinatorics
chrome scroll
im just worried about getting anything wrong bc i cant afford to do bad on any assignments i have or else ill be kicked out of the major forever
and when i have my final, i want to make sure i have something to study
thts why im using chatgpt and wanting to come her eto make sure im not making any mistakes ig, this is a new chapter too so idk if im doing it right. i'll do the second problem now
sick mirage
yeah coming here and making sure you got the formulas down is your best bet!
this problem you gotta have product rule mastered!
you can do it
chrome scroll
._. oh the product rule?
im guessing tht would be 6 * 2 * 21^ 2
i did 2 because 5/2 is 2 r 1
?
wait
im going to draw a picture
sick mirage
I think you might be getting permutation/combination formula confused with it
chrome scroll
like you did..
sick mirage
ok sounds good
chrome scroll
ok so the math i tried to do is
10621^4
?no wait i think its 25 * 6 * 21^4? @sick mirage
chrome scroll
?no wait i think its 25 * 6 * 21^4? <@731008127889047654>
yeah i meant this
sick mirage
ok true try to work that out
chrome scroll
why are we not multiplying by 6 though in your answer?
sick mirage
which option has 6 choices ?
ohhh for each spot no you're just doing the amount of choices PER spot
does that make sense?
chrome scroll
wait so why did we count the 6 for the first question?
sick mirage
like I said before I think you're confusing it with the perms/combs formulas
chrome scroll
i dont know want berms and combs formulas are tbh >.< ..
chrome scroll
i thought you were because of the 6
sick mirage
you might be getting into that next
ahh the numbers underneath have nothing to do with the product rule multiplications
chrome scroll
so for the first question i only to 5 * 21^5 then
chrome scroll
oki, tht makes sense
sick mirage
does it make sense that you're just multiplying the choices you have for each spot with eachother?
chrome scroll
yes
now im stuck on my 3rd and 4th question
ill fix the other one you told me to fix
five vowels. How many strings of six lowercase letters of the English alphabet contain
• at least one vowel?
• at least two vowels?```at least one means you need 1 vowel or more
sick mirage
yep
sick mirage
it means that one spot will have 5 choices
and how many choices for the others? (it could be a vowel or a consonant)
sick mirage
sorry kinda not understanding
chrome scroll
youre saying only one slot will have 5 and the rest will be 21
sick mirage
one will have 5 yep
but the others could have how many choices?
they could be either a vowel or a consonant so :
26
make sense ?
chrome scroll
:/ no..
you got 26 by adding 5 vowels and 21 consonants
but why would you add them
sick mirage
because it could be either of them now...
you know that one spot only has 5 choices
but the others could be any of the lowercase letters
chrome scroll
.. o
i still dont get it but ill just do the math for both of them
i have one last problem
Show that in a group of 10 people (where any two
people are either friends or enemies), there are either three mutual friends or four mutual
enemies, and there are either three mutual enemies or four mutual friends.```tis is my last problem
chrome scroll
😄 omg ty, tht actually cleared it up a lot
sick mirage
for product rule, definitely just draw out the spots and think of how many possibilities for each
hmm I think that one is where you're gonna need permutations because the order matters
chrome scroll
```
Show that in a group of 10 people (where any two
people are either friends o...
for this ?
sick mirage
yeah
chrome scroll
ill look up permulations
sick mirage
ok yeah try also permutations with inclusion/exclusion
I may have to check my notes for this one
but I'm wracked with these linear algebra problems rn oi vey
cedar kilnBOT
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radiant topaz
Are you here to help me ?
Ofcourse
cedar kilnBOT
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radiant topaz
That's good beekybeaks
chrome scroll
lol ty
) Show that in a group of 10 people (where any two
people are either friends or enemies), there are either three mutual friends or four mutual
enemies, and there are either three mutual enemies or four mutual friends.
this is wht im having trouble with
radiant topaz
Ok lets see
chrome scroll
btw do you know stuff about half adders
radiant topaz
What are you supposed to do
radiant topaz
btw do you know stuff about half adders
No maybe you can give context
radiant topaz
Ah then I can't help with that
chrome scroll
oki
o.o
actually im going to study something for a different class i have
i didnt think my question would have took this long but ill be on later today
srry for wasting your time
but tysm
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nocturne flax
Hey this is the problem I'm working on and my calculations.. I'm not sure what to do next. please help
cedar kilnBOT
Hey this is the problem I'm working on and my calculations.. I'm not sure what t...
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nocturne flax
Hey this is the problem I'm working on and my calculations.. I'm not sure what t...
<@&286206848099549185>
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livid hound
erase that last line because square roots don't work like that
once you have the expression for area in terms of r,
differentiate
to determine locations of stationary points/local extrema
cedar kilnBOT
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nocturne flax
erase that last line because square roots don't work like that
what am I supposed to do instead? I can't remember
nocturne flax
once you have the expression for area in terms of r,
differentiate
yes tyy
frozen valve
crimson sedge
please close if not
sudden grail
cedar kilnBOT
sudden grail
What's wrong with my first blank
green hornet
they've asked to make coefficient of x as 1
unkempt steeple
Let m be an integer, let X_m = {p = n^2 + m^2 | n is a natural numbers} be the set of primes of the form n^2 + m^2. Prove that the Dirichlet density of X_m is 0 for each fixed m.
cedar kilnBOT
Let m be an integer, let X_m = {p = n^2 + m^2 | n is a natural numbers} be the s...
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cunning jay
I have been trying this question for the whole day but keep getting a negative answer for the radius
cunning jay
i used the hint to devise a method for solving it
i approximated the volume that a single molecule sweeps to be a sphere. Every time the molecule collides with another, it would be at the edge of this sphere
so if i take 2r-a
i get the diameter of the smaller sphere
which is that of the bromine
a is the mean free path (distance before a collision)
and r is the radius of the sphere of volume that each molecule takes
as per the hint
i used the ideal gas law to find the volume per molecule
then to find the radius of bromine i did the following:
the radius is negative
when i put this into the website it of course registered as being wrong
im not sure on how to proceed from here
(btw the value of , a, the mean free path was calculated before hand)
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dawn cosmos
To estimate u I have a function $Q\left(\mu \right)=\sum _{i=1}^n\left(Y_i-\mu \right)^2+\lambda \mu ^2$ that I have minimized. The point estimator for this is $\mu =\frac{n\overline{\left{Y\right}}}{n+\lambda }$. I have shown that estimator is unbiased to estimate u. I calculated the MSE to be $\left(\frac{n}{n+\lambda }\right)^2\cdot \frac{\sigma ^2}{n}+\left(\frac{n}{n+\lambda }\mu -\mu \right)^2$. I need to show that for some lambda $\left(\frac{n}{n+\lambda }\right)^2\cdot \frac{\sigma ^2}{n}+\left(\frac{n}{n+\lambda }\mu -\mu \right)^2:<\frac{\sigma ^2}{n}$. Wouldn't lambda necessarily require knowing the values of sigma and mu?
wraith daggerBOT
catnwaffles
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dawn cosmos
<@&286206848099549185>
boreal epoch
damn
violet rapids
@dawn cosmos feel free to use the advanced channels if you do not find success here
dawn cosmos
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cedar kilnBOT
crimson sedge
,w 1+1
wraith daggerBOT
crimson sedge
,w 151x + 200 = x + 500
wraith daggerBOT
crimson sedge
Assuming you did the simple arithmetic correct, then you you should be good
Alright
,rotate
wraith daggerBOT
crimson sedge
Also you don't need to put 1 before x since 1 * x = x
Wait
What are you trying to solve
Well
VZ and YZ
Those two are equal so you set them equal
You did that
,w 81x = x+160
wraith daggerBOT
wraith daggerBOT
cedar kilnBOT
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pale badger
cedar kilnBOT
pale badger
can someone explain (c) to me
tropic oxide
you can make a graph of y=f(x) to help you
pale badger
still dont really get it
warm ridge
first, substitute -3 for x and show that f(-3) = 0
pale badger
first, substitute -3 for x and show that f(-3) = 0
no for (c)
warm ridge
ah ok
you can use part b to help you
you already found the max and min points, so now f(x) will have 1 solution only when the min point of f(x) + a is >= 0
and also when the max point of f(x) + a is >= 0
pale badger
but they use ’>’ ?
warm ridge
ah sorry, if you use >= then you will have 2 solutions
vale dove
cedar kilnBOT
lyric narwhal
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
warm ridge
try to think of a series where only the odd terms are there
so that you can use the information given
lyric narwhal
it will create another gp with r^2 as it's common ratio
lyric narwhal
think about how many terms there will be
lyric narwhal
first, see what kind of GP the odd indices create
vale dove
Gp?
lyric narwhal
say your original AP is $a, ar, ar^2,...,ar^{2n-1}$
wraith daggerBOT
kheerii
vale dove
Yeah?
lyric narwhal
so, the odd ordered terms are $a, ar^2, ar^4,...,$
wraith daggerBOT
kheerii
vale dove
n-1?
lyric narwhal
why
lucid shell
Hi I dont get this question at all
cedar kilnBOT
Hi I dont get this question at all
cinder urchin
do you know set theory??
lucid shell
Yea, but having power sets of a set be equivalent to a normal set is foreign to me
idk even know how to start
cinder urchin
Yea, but having power sets of a set be equivalent to a normal set is foreign to ...
both are power sets
lucid shell
wdym
cinder urchin
the set whose power set is being taken must also be the subset of the superset
in this case (X U Y)xY is subset of Xx(X U Y)
cinder urchin
in this case (X U Y)xY is subset of Xx(X U Y)
so you can start from here
and then just consider some arbitrary element to further do the ques
lucid shell
in this case (X U Y)xY is subset of Xx(X U Y)
is it not (X U Y)xY is subset of P(Xx(X U Y))
cuz the first power set is of the entire expression
cinder urchin
cuz the first power set is of the entire expression
no bro
just match the brackets
lucid shell
oh shit mb
cinder urchin
np
cinder urchin
yeah
crimson sedge
how we get this?
cedar kilnBOT
how we get this?
crimson sedge
green color
that is a partial fraction
simply i don't know how to make a partial fraction from a factored polynomial
anyone?
Like how simplified? @crimson sedge
well from this table I need to read the partial fraction
cedar kilnBOT
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cedar kilnBOT
cedar kilnBOT
Available help channel!
simple crest
Hey! How do I calculate angle BDC considering that BD is a bisector?
snow zodiac
!status
cedar kilnBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
gray blade
Is it given that ABC is a right angle?
opaque root
snow zodiac
Bro don't say the answer
livid hound
what type of bisector
simple crest
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
1
I think i figured something out
snow zodiac
1
Start by looking at the 138° angle and the angle BCD, you can see that there are on ONE line
snow zodiac
and what did you get?
simple crest
42
snow zodiac
And angle B is?
snow zodiac
Is alright
simple crest
92
snow zodiac
Yes
simple crest
yeah now its easy
snow zodiac
And you know what a bisector is right?
simple crest
yes
snow zodiac
Nice now you can solve the problem easily
snow zodiac
Nice
crimson sedge
Hey! How do I calculate angle BDC considering that BD is a bisector?
Is the B angle is 90°
cedar kilnBOT
cedar kilnBOT
Available help channel!
fossil night
Hey
I had to make a proof for the squeeze theorem, and I did that :
fossil night
("soient" and "si" (before the blue-green line) mean "if")
the sentence just after the blue-green line translates to "then, when n tends to infinity"
I believe i took shortcuts (especially when jumping from the suites to the limits) but i'm not sure if I did so...
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muted bear
dusk finch
cedar kilnBOT
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slender wasp
cedar kilnBOT
slender wasp
Any help?
slender wasp
Better?
violet rapids
slender wasp
it is 1
slender wasp
how tho
violet rapids
8/28 = 4/14 = 2/7
wraith daggerBOT
slender wasp
oh shit
violet rapids
so
cedar kilnBOT
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Available help channel!
whole pecan
Two quadrilaterals are similar. The sides of the first quadrilateral are 12 m, 21 m, 15 m and 27 m, and the perimeter of the second is 50 m larger than the first. Find the sides of the other quadrilateral. Answer. The second quadrilateral
whole pecan
how?
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crude scroll
Why is $\sum_{i=0}^{n} c(n,k)= n!$?
cedar kilnBOT
Why is $\sum_{i=0}^{n} c(n,k)= n!$?
wraith daggerBOT
KN
crude scroll
Where c(n,k) is Stirling numbers first kind
tropic oxide
(x)_n = sum c(n,k) x^k right
crude scroll
right
tropic oxide
what does x=1 give
crude scroll
c(n,k)?
ok, well I want to see this more intuitively. I know that c(n,k) counts the number of permutation of [n] with exactly k cycles
Im not very familiar with that formula tbh
I guess interpreting it as distributing n people to k tables and then arranging it makes more sense
For example, making a simple case like c(4,1) c(4,2) c(4,3) c(4,4) and looking at all the cases.
tropic oxide
... ok sorry got distracted by a chess game
soft jay
Wouldn’t this just be 70g? Just tryna figure out why it’s 5 marks
green hornet
Wouldn’t this just be 70g? Just tryna figure out why it’s 5 marks
No
You forgot about vertical components of the applied forces
soft jay
Ah so I need to find the resultant force then?
green hornet
sum of all forces in each direction = 0
soft jay
Would this be correct ?
cedar kilnBOT
Would this be correct ?
slow thicket
Would this be correct ?
your work is so disorganized
soft jay
Ty
slow thicket
is this physics or math
slow thicket
math or mechanics
soft jay
Mechanics
slow thicket
okay yeah so you need to learn to not do what that is
keep everything in symbols until you isolate for your answer
soft jay
Yeah lol
slow thicket
also why did you calculate values you dont need
soft jay
Just for future q’s
slow thicket
there is way too much on that paper and it is very hard to follow along
soft jay
Because it asks for horizontal acceleration next
slow thicket
leave it for the next questions
soft jay
Normal has to be positive?
slow thicket
Also that
soft jay
Okay so if we say N is the positive direction
soft jay
Would that not be it’s vertical component?
slow thicket
yes
soft jay
When you say check the signs do you mean I have set which direction will be positive incorrectly?
slow thicket
that does not matter
As long as you are consistent you can choose any direction to be positive
I meant the normal was supposed to be positive
And I didn’t see a -mg in there
soft jay
Yeah that was supposed to be the 673sin(270)
I’m gonna try add them all up and set it equal to zero
Make them all positive
slow thicket
Yep