on a right triangle, the side that goes diagonally from the other two is the hypotenuse
#help-42
swift storm
alright thanks
btw
i didn't know that i had to use pythogoras
how would i know to use it?
keen grail
whenever you have two sides of a right triangle and you're asked to find the other you'd use the phythogoras theorem
swift storm
i mean i used the top triangle theorem to solve B)
and thought maybe i could do the same for a 😭
swift storm
whenever you have two sides of a right triangle and you're asked to find the oth...
alright thank you
swift storm
yes
keen grail
k
swift storm
ty man
keen grail
np
swift storm
.close
calm coralBOT
calm coralBOT
Available help channel!
floral turtle
yo
floral turtle
Can someone check if my answers are correct?
I'd really appreciate it
<@&286206848099549185>
If they're correct or not just @ me and I'll probably see the message later
It'll mean alot
calm coralBOT
@floral turtle Has your question been resolved?
floral turtle
I'm still here
floral turtle
.
calm coralBOT
@floral turtle Has your question been resolved?
hoary fjord
Can someone help me find the representation of the domain and range?
calm coralBOT
Can someone help me find the representation of the domain and range?
@hoary fjord Has your question been resolved?
compact totem
Where did I messed up
calm coralBOT
Where did I messed up
exotic falcon
message up
compact totem
im sorry?
compact totem
message up
do you mind explain wat you mean
ah wait i see...yeah sorry about that been doing math for bit. my brain is fried
i re look at my math...i wrote a plus when the answer show be with a minus
.close
calm coralBOT
calm coralBOT
Available help channel!
weary bane
calm coralBOT
weary bane
,rotate
potent lotusBOT
weary bane
q 7 i have found alpha which is 2 but i cant find what beta is
velvet osprey
$\frac{2}{\beta} + 2 + 2\beta = \frac{21}{2}$
potent lotusBOT
Ann
velvet osprey
use ^ for exponents.
like this: beta^2
but yes, $2 \beta^2 - \frac{17}{2} \beta + 2 = 0$.
potent lotusBOT
Ann
velvet osprey
now quadratic or something
yes, this is a quadratic equation in beta.
exotic hedge
b = (±(sqrt(13))/2
Is that correct
Or did I go wrong
Ob wait
I did go wrong
One sec
4b^2 - 17b + 4 = 0
I got this
weary bane
?
exotic hedge
wat
velvet osprey
why did i get an eigth or 2
show work.
weary bane
i didnt double does that change the result
exotic hedge
No
velvet osprey
8.5 * 2 is not 19
velvet osprey
??
exotic hedge
Wat
weary bane
-c/a
exotic hedge
Yea
exotic hedge
weary bane
ye thats not part of the first equation
weary bane
as you can see i still used the 8.5
exotic hedge
Ok wait
velvet osprey
as you can see i still used the 8.5
and then you still doubled it to 19 later on.
weary bane
and then you _still_ doubled it to 19 later on.
after
exotic hedge
weary bane
last line
exotic hedge
This is supposed to be -17
weary bane
gimme a sec
velvet osprey
that and you for whatever reason transmogrified the 19 back into 8.5 somehow.
you're making a right mess of your arithmetic here
exotic hedge
bruh
swift epoch
use split middle term method
weary bane
2*2 is not 8
velvet osprey
the denominator should be 2*2 aka 4. not 8
exotic hedge
Ye
swift epoch
it will make it more easy
weary bane
the denominator should be 2*2 aka 4. not 8
i just saw 8 and i wrote it
thanks guys
.close
calm coralBOT
calm coralBOT
Available help channel!
hybrid zephyr
calm coralBOT
cobalt galleon
im not sure how the hint is useful but this is my logic
we can we write it as (z^5-1)/z-1 = (z^2+az+1)(z^2+bz+1)
z^5-1/z-1=. (1+z+z^2+z^3+z^4)
now compare and find a,b values
hybrid zephyr
yeah that's what I did but I figured it would be best to use the hint so idk
.close
compact totem
i get its a formula but i dont understand how y got replaced with 10 or 20 replaced 270
inner zealot
i get its a formula but i dont understand how y got replaced with 10 or 20 repl...
10 and 20 are somewhat arbitrary. You can just as easily use 1 and 2 respectively to represent the decay from 2 grams to 1 gram. The only purpose is to determine the k constant.
compact totem
bless you kookie
so do i make assumptions ? im trying do this on my own and im so confused on where to start aside from pluging value you
so 80e^kt
then it be 80e^k1599
inner zealot
Once you find the k constant, you would then use 80 for the initial quantity with t equal to 9000 to find the remaining quantity after 9000 years.
compact totem
to cancel or resolve e it would be ln?
inner zealot
To find the remaining quantity or to find k?
compact totem
k
inner zealot
Yes, you would use ln() to get rid of the exponent.
compact totem
so it would be ln(80e^k(1599) ?
compact totem
it has to be a value of something? cant it be y = 80 e^1599k and you divide both side by 80 and do the ln?
inner zealot
That should be 80 e^-1599k. The negative sign is necessary to indicate exponential decay.
compact totem
I’m assuming this isn’t possible
inner zealot
That's a valid result. If you are trying to calculate k though, y would be half of 80, or just 40, which results in 40/80 = 1/2.
compact totem
so for calculation like this, what ever we start with for example 80, set y as half ?
because of half life
inner zealot
Yes, for determining the k constant.
If you were to determine the third-life and were given a third-life time of t years, it would be ln(1/3)/t). Note how I changed 1/2 to 1/3.
But we generally only use half-life so it's always ln( 1/2)/t.
compact totem
im trying understand the general relationship of y and ce inregarding to the equation y = C e^kt because i know it can be used for more then just half life
inner zealot
im trying understand the general relationship of y and ce inregarding to the equ...
Yeah, anytime you assume exponential growth or decay, you can use that formula. + for growth and - for decay.
compact totem
bless you kookiemon if i ever discovery a cool organic molecule ill remember to name it after you as a reminder who help me through cal II
.close
calm coralBOT
calm coralBOT
Available help channel!
vestal kite
I am trying to understand the proof from proofwiki of the inclusion exclusion principle but this step where they talk about the expansion...how did they come up with the formula for those intersections? Why are there only 2 sums (with interval indexes)..does anyone have a more in depth way of explaining this step?
calm coralBOT
I am trying to understand the proof from proofwiki of the inclusion exclusion pr...
@vestal kite Has your question been resolved?
calm coralBOT
@vestal kite Has your question been resolved?
vague bison
I am trying to understand the proof from proofwiki of the inclusion exclusion pr...
Why are there only 2 sums ← to allow grouping of the general term in each one of those "2 sums", according to the number of subsets chosen from the collection
,,{A_1, A_2, \dots, A_{r+1}}
potent lotusBOT
vin100
vague bison
inside this
,,f\underbrace{\qty(\bigcap_{i\in \bigstar} A_i)}_{\text{big parentheses}}
potent lotusBOT
vin100
vague bison
there $\bigstar \in {I, J}$
potent lotusBOT
vin100
vague bison
how did they come up with the formula for those intersections?
- logically: induction hypothesis
- practically: inductive thinking = observation from small cases = a general problem-solving strategy
calm coralBOT
calm coralBOT
Available help channel!
dusky veldt
Could someone help me understand the du substitution here?
calm coralBOT
Could someone help me understand the du substitution here?
dusky veldt
I understand the -sinx disappears here? Because you sub du into it
swift dragon
$\dd x=\frac{\dd u}{-\sin(x)}$
potent lotusBOT
Bonk
swift dragon
plugging that in cancels out the sin(x)
$\int\cos(x)^5\sin(x)\dd x=\int u^5\sin(x)\frac{\dd u}{-\sin(x)}=-\int u^5\dd u$
potent lotusBOT
Bonk
dusky veldt
$\dd x=\frac{\dd u}{-\sin(x)}$
Is this a formula?
swift dragon
Is this a formula?
no?
its literally given at the top of the screenshot you wrote
just rewritten
it depends on your choice of u of course
swift dragon
$\dv{u}{x}=-\sin(x)\\dd u=-\sin(x)\dd x\\dd x=\frac{\dd u}{-\sin(x)}$
potent lotusBOT
Bonk
dusky veldt
I can just set du equal to one of them and they go away?
swift dragon
I can just set du equal to one of them and they go away?
if you choose the correct u, then yeah
usually
it depends on your integral of course
it will not work for every integral
dusky veldt
Is there something I can read about when it is correct and isn't?
swift dragon
wdym?
swift dragon
and du = cos^5(x)
you cant choose du
you choose u
and then you get a du/dx
if u=sin(x), then du=cos(x)dx
dusky veldt
ahhhh
I see now
I thought we arbitrarily chose du here
but we took the derivative of U
this is all makes sense now
thank you
.close
calm coralBOT
calm coralBOT
Available help channel!
floral turtle
Can someone lmk if my answers are correct?
calm coralBOT
Can someone lmk if my answers are correct?
calm coralBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
calm coralBOT
@floral turtle Has your question been resolved?
calm coralBOT
@floral turtle Has your question been resolved?
floral turtle
<@&286206848099549185>
ivory lion
<@&286206848099549185>
i checked the first page, looks fine, didnt check the computation but the work looks to be right
though side note, not sure if you learned complementary counting yet
for #2, it would be easier for first count the total number of ways to order all of the digits, and subtract the opposite of what youre looking for
maybe thats not part of the lesson yet
calm coralBOT
@floral turtle Has your question been resolved?
floral turtle
maybe thats not part of the lesson yet
Yea I haven't learned that yet
But as long as it's right
Ty for checking
glossy haven
whats the answer to this? i got 153 but its wrong
calm coralBOT
whats the answer to this? i got 153 but its wrong
@glossy haven Has your question been resolved?
calm coralBOT
@glossy haven Has your question been resolved?
glossy haven
<@&286206848099549185>
twin ruin
absolute amount of mammels in both woodlands are equals to 146 <=> deviding by two, because both have the same amount of mammels -> 73
not quite sure if its that easy or if i just misjudged anything haha
calm coralBOT
@glossy haven Has your question been resolved?
glossy haven
absolute amount of mammels in both woodlands are equals to 146 <=> deviding by t...
they both turned out to be wrong
a new one came up
calm coralBOT
@glossy haven Has your question been resolved?
white pebble
whats the answer to this? i got 153 but its wrong
All the points are a woodland so anything above 18 doesn't make sense here
try to find 2 woodlands which have the same amount of birds(y) and two woodlands which have the same amount of mammals(x), and that both of the pairs share a woodland in common
calm coralBOT
@glossy haven Has your question been resolved?
slim knoll
It looks like each mark plots out the number of Mammals (X) and the Number of Bird (Y) Species
coral moss
Can i use the derivative test to know if the series is decreasing for alternating series
swift laurel
id you have a sequence a_n and a function f(x) such that f(n) = a_n for all n, then if you can show that f(x) is decreasing that would also show that a_n is decreasing
and you can show f(x) is decreasing with a derivative
coral moss
With a derivative that has opposite sign right
swift laurel
a function is decreasing if its derivative is negative
calm coralBOT
calm coralBOT
Available help channel!
open goblet
I know that I can solve this with rational root theorem but I wonder why I can't do this
glacial coyote
I know that I can solve this with rational root theorem but I wonder why I can't...
you're trying to simplify?
open goblet
you're trying to simplify?
finding roots
glacial coyote
by using the quadratic formula you've assumed that $x^2 - 2x + 16 = 0$
potent lotusBOT
Deftioon
glacial coyote
when that might not be the case
crisp minnow
calm coralBOT
topaz raft
whats ur question
velvet osprey
so far so good
crisp minnow
crisp minnow
i didnt?
velvet osprey
but more importantly how did 1/u^2 happen
you should have had $\frac23 \int_4^{23} u^2 \dd{u}$ yes?
potent lotusBOT
Ann
velvet osprey
yes so
redo the integral
and do not forget to actually integrate
$\int_a^b f(x) \dd{x}$ generally does not equal $f(b)-f(a)$. a function is generally not the same as its own antiderivative, with a single exception
potent lotusBOT
Ann
calm coralBOT
@crisp minnow Has your question been resolved?
quick karma
calm coralBOT
quick karma
umm any1?
desert nymph
give it a bit of time. you've got a pretty difficult question so I imagine the amount of people who can help is small 😛
quick karma
oh ic
remote mural
just plug in 1?
remote mural
?
quick karma
g1 is a + b
is the ans coming out to be 0
could you check?
for any value of x, I get g(x) = 0, f(x) = x(x+1)(2x+1)(3x^2+3x-1)/30
so ax+b = 0 for any val of x
so a=b=0
can anyone verify this?
<@&286206848099549185>
calm coralBOT
@quick karma Has your question been resolved?
quick karma
g**(**1**)**
welp
calm coralBOT
@quick karma Has your question been resolved?
remote mural
Integral Equation. Why is there extra y inside integral? How do I do this
calm coralBOT
Integral Equation. Why is there extra y inside integral? How do I do this
@remote mural Has your question been resolved?
calm coralBOT
@remote mural Has your question been resolved?
potent smelt
I have no idea why there are two ys in that integral, seems weird, like it might be a typo
remote mural
I'm thinking the same
potent smelt
So this is a Fredholm integral equation of the second kind. The general form is
[
\phi(x) = f(x) + \lambda \int_a^b K(x, t) \phi(t) , \dd{t}
]
For this equation we have $f(x) = x^3 - x^2 + x \mathrm{e}^{x} + 1$, $\lambda = -1$, and $K(x, t) = \mathrm{e}^{t}$.
potent lotusBOT
OmnipotentEntity
potent smelt
Here are the steps to solve: https://en.wikipedia.org/wiki/Liouville–Neumann_series
Note, that if y is squared in the integrand, this method does not work, and probably does not have a solution.
calm coralBOT
calm coralBOT
Available help channel!
elder mesa
Where is my mistake???
calm coralBOT
Where is my mistake???
elder mesa
Well you good for x4
yes, but check x3
x3 correct is 1
I get 3
sorry about blurry
elder mesa
really?
glad parrot
Where is my mistake???
You change 2 into -2 last matrix for no reason
glad parrot
Yw
spark adder
Two persons, S and A, will arrive to some park at some random time between 1PM and 2PM, and will wait for 15 min. What is the Probability that S and A will meet each other, given that S will arrive before 1:30PM and A will arrive after 1:30PM?
calm coralBOT
Two persons, S and A, will arrive to some park at some random time between 1PM a...
@spark adder Has your question been resolved?
fickle wigeon
You can try drawing a graph
tough prism
^
fickle wigeon
Something like this
spark adder
So the square is that one hour that I understand but the 2 lines
The each persons 15 mins?
fickle wigeon
So the square is that one hour that I understand but the 2 lines
The two lines are basically separated by 15 units in the y axis
so anywhere in between they can meet
spark adder
Thanks
fickle wigeon
Your question is a subset of what I’ve previously done, it had no requirements for them to come after/before a certain time
which is just the area between the two lines I’ve drawn
dapper bramble
What's this notation called again/its definition?
calm coralBOT
What's this notation called again/its definition?
deep violet
?
graceful wagon
Huh
dapper bramble
Also a basis
graceful wagon
Oh I think it changes basis
Prob from B to C
I’ve never seen this notation so not sure
dapper bramble
Found it in my script now.
Didn't know what to sift through with. Thanks
(yes it is change of Basis btw)
.close
calm coralBOT
calm coralBOT
Available help channel!
small crag
for part c, ive found that M has coordinates of [(Qx+Px)/2, (Qy+Py)/2] but i dont know what do with it next?
small crag
.close
calm coralBOT
calm coralBOT
Available help channel!
whole steeple
Is it possble to find the angle alpha?
calm coralBOT
Is it possble to find the angle alpha?
pliant coral
Is it possble to find the angle alpha?
Is there a right angle between the 6 and 8 sides?
whole steeple
Nah thats the catch
pliant coral
Then yeah idts, you need at least 3 things from any triangle before you can apply trig stuff
whole steeple
Yh my math teacher gave me this
She said if you cannot solve it then make it a right angle
But thats too easy
velvet osprey
there is not enough info
wraith geode
Is it possble to find the angle alpha?
Yea
wraith geode
Nah thats the catch
Wait really
calm coralBOT
@whole steeple Has your question been resolved?
teal drift
!occupied
calm coralBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
Available help channel!
white edge
here is my problem (Calculus II)
calm coralBOT
here is my problem (Calculus II)
white edge
I found an answer I believe to be true based on an integration table provided by my professor, but does not match wolfram alpha's answer. I will send screenshots shortly.
this is my work (everything in the square is related to the problem)
this is the integration identity I used to reach my answer
where u=9x^2, u=3x, du=3, a^2=2, a=sqrt(2)
this is the answer WolframAlpha got (the difference is the three in my answer is missing)
in the right side of my work, I try to show why I have a three outside of my integral
please ask me questions and let me know where I went wrong, thank you
holy smokes I just figured it out
stone root
The problem is you are not integrating with respect to d(9u)
white edge
d(9u)?
stone root
But with respect to u. It's okay to multiply and divide by 9 to get 9x² both inside and outside the root but in your formula the integration is with respect to the variable u
stone root
d(9u)?
The formula is u² and du
You have used 9x² and dx. It's not matching because it is not d(9x).
white edge
you're saying I am using dx as the du for 9x^2? Am I understanding that right?
considering u, u=sqrt(9x^2) which equals 3x
derivative (or du) of 3x = 3dx, which I apply to my problem
checking my new answer, and it appears to match WolframAlpha's work
stone root
u=3x → du/dx = 3 → dx/du=⅓ mmm
white edge
I'm not sure what mmm stands for
to get my du in the integral, I multiply 1/3 outside of the integral and put a 3 inside (technically this is 3 x 1/3 which equals my original equation)
stone root
Mmm stands for thinking
white edge
ah ok xd
stone root
I did what you did
white edge
did you get the right answer?
fickle musk
Did you also express x² in terms of u
stone root
I got your answer
white edge
where I went wrong was I forgot to apply 3x in the denominator instead of x - this cancels out the 3 in the numerator, hence leaving you with WolframAlpha's answer
white edge
Did you also express x² in terms of u
I express 3x in terms of u
stone root
That's it
white edge
9x^2 in terms of u^2
white edge
That's it
least embarrassing facepalm mistake I made this semester
.<
though with all this in mind, this problem does appear to certify that the variable u in these integration formulas can represent a coefficient with x that isn't 1 without error
stone root
9x² in terms of u² is u² innit?
fickle musk
9x² in terms of u² is u² innit?
Yes
white edge
in this circumstance, yes
although I did manage to figure out the mistake on my own, I nonetheless appreciate the assistance 👍
.close
calm coralBOT
fickle musk
Please not here
stone root
Yes, it is crucial to undo the change of variables
calm coralBOT
Available help channel!
zenith spear
could someone tell me where i went wrong in my process?
calm coralBOT
could someone tell me where i went wrong in my process?
untold compass
could someone tell me where i went wrong in my process?
the h/r stuff works for a cone, but here that formula for cap volume has r constant the whole time
zenith spear
ohh i see
untold compass
so skip that part and take r as a constant, h as a variable to derive
zenith spear
in that case would i just plug r in then derive with respect to t?
untold compass
yea that works
zenith spear
sorry this is a silly question but how would i derive it? is it just product rule? i know dr/dt is 0 but when i derived i still had r
would i get the right answer by just plugging values in or did i do something horribly wrong
calm coralBOT
Available help channel!
river stump
calm coralBOT
velvet osprey
the x coordinates of P and Q can be figured out
river stump
difference of squares right
velvet osprey
nope
they are the vertices of their respective parabolas
their x coords are -b/2 and d/2
river stump
oh alright alright
river stump
difference of squares right
i meant completing the square not difference my fault
velvet osprey
well you can complete the square ig but i don't think it'll help you that much
river stump
yeah that would just be the same thing for x coords anyways right
velvet osprey
well it would give you the same result i wrote
river stump
i tried isolating for e and c in each equation and subbed then into 2(e-c) = bd
velvet osprey
that ought to do it
velvet osprey
i tried isolating for e and c in each equation and subbed then into 2(e-c) = bd
very likely to do no good
river stump
yeah that didnt work
calm coralBOT
💔
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
calm coralBOT
calm coralBOT
Available help channel!
round kraken
calm coralBOT
lone compass
Okay
Draw it out
Get the essence
and play with it
maybe use someg eometry
replace log with something that makes more sense to u
replace 1/k with a spatial analogy
Metric spaces
Basically
Imagine a ruler that shrinks and grows
and u r also shrinking and growing
how would u measure things?
calm coralBOT
@round kraken Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
ornate star
Problème pour une question
calm coralBOT
Problème pour une question
ornate star
I have a question
runic fjord
Alright
runic fjord
,rotate
potent lotusBOT
runic fjord
I'm gonna be honest bro, I can't really read that at all
also, I'm not sure what the problem says either, do you mind translating it?
runic fjord
What is the question? Like what is the goal here?
runic fjord
Sure I see that
ornate star
runic fjord
this looks fine to me so far
calm coralBOT
calm coralBOT
Available help channel!
ocean relic
I've been stuck on this question for a while , any hint for it?
elder pawn
contradiction probably
thats the same way that we prove there are infinitely many primes
manic hawk
I'm not sure I could use dancing numbers to create new dancing numbers
A nondancing number is precisely a number n where n^2+1 is prime
So we need that n^2+1 is prime infinitely many times
calm coralBOT
calm coralBOT
Available help channel!
blissful zephyr
calm coralBOT
nocturne heron
what does that sigma thing mean?
the letter sigma ?
blissful zephyr
yeah i mean I know that it's a sum
but what are a and b
are they like all combinations up to p-1?
coral anchor
i beleive that's writing 2 sums in a single one
nocturne heron
but what are a and b
a and b are discrete variables
blissful zephyr
i beleive that's writing 2 sums in a single one
so
how do i understand this
is a and b like all pair 1, 2 ; 1, 3 ; 1, 4 ; 1, 5 ; .... 1, p-2 ; 1, p-1 ; 2, 3 ; 2, 4 ; 2, 5 ; ... 2, p-2 ; 2, p-1 ; 3, 4 ....
nocturne heron
the $(\frac{a}{p})$ is for Legendre symbol?
potent lotusBOT
tm
nocturne heron
oh okay
blissful zephyr
is a and b like all pair 1, 2 ; 1, 3 ; 1, 4 ; 1, 5 ; .... 1, p-2 ; 1, p-1 ; 2, 3...
are they this?
nocturne heron
do you know how to rewrite this sum?
coral anchor
is a and b like all pair 1, 2 ; 1, 3 ; 1, 4 ; 1, 5 ; .... 1, p-2 ; 1, p-1 ; 2, 3...
yes, b can go upto (p-1), for some chosen value of b, a can be from 0 to b-1
like (a,b) can be (0,1), (0,2), (1,2), (0,3), (1,3), (2,3),....
blissful zephyr
like (a,b) can be (0,1), (0,2), (1,2), (0,3), (1,3), (2,3),....
yeaah thanks
!close
.close
pliant spruce
I know I need to use synthetic division but wth do i do with i
pliant spruce
eternal shard
you can also just substitute z = x²
pliant spruce
the teacher wants us to do it this why
nocturne heron
I know I need to use synthetic division but wth do i do with i
you know that f(i)=0
pliant spruce
way *
pliant spruce
you know that f(i)=0
so instead of i I could put 0 ?
nocturne heron
Personally, I would do the Euclidean division of f(x) by (x-i)
Because is f(i)=0, f(x) can be rewritten as f(x)=(x-i) *P(x) with P(x) a grade 3 polynomial
And with the euclidean division of f(x) by (x-i) you can find the polynomial P(x)
pliant spruce
And with the euclidean division of f(x) by (x-i) you can find the polynomial P(x...
dude this is beyond cancer
I did it the synthetic way and it just doesn't make sense
ill send a pic
nocturne heron
dude this is beyond cancer
😭 I didn’t try
pliant spruce
🤣
nocturne heron
i found $f(x)=(x-i)(x^3+ix^2 +25x+25i)$
potent lotusBOT
tm
pliant spruce
Is the first screenshot I sent right though I didn't solve for x yet
nocturne heron
what is this method ?
nocturne heron
i don’t know this method
pliant spruce
Dude I am about to crashout on my teacher
pliant spruce
dude I fucking love this guy I found the one video going over this https://youtu.be/o6vJa2ZquuI?si=FVMjPe6q4psRCLwp
fuckin suck this dude off anyways thanks tm
.close
calm coralBOT
calm coralBOT
Available help channel!
rough blade
how to integrate $\int \frac{1}{(e^t + 1)^n}dt$
calm coralBOT
how to integrate $\int \frac{1}{(e^t + 1)^n}dt$
potent igloo
potent lotusBOT
<rajel />
rough blade
<:helpparens:371658456215584789>
?
rough blade
oh ok
sweet stag
what did you try?
rough blade
was thinking of $\int (e^t + 1)^{-n} dt$
potent lotusBOT
<rajel />
sweet stag
and?
rough blade
and then to use a rule for that
sweet stag
no
primal smelt
sweet stag
whats the context of such question, what exercice is it coming from? @rough blade
rough blade
whats the context of such question, what exercice is it coming from? <@124324313...
we are given that $f(x) = \frac{1}{e^x + 1}$ and $f'(x) = f(x)^2 - f(x)$
$$I_n = \int f(x)^n dt $$
sweet stag
okey and?
potent lotusBOT
<rajel />
sweet stag
send full picture of the problem
rough blade
french ?
sweet stag
just do I_(n+1) - I_n
rough blade
just do I_(n+1) - I_n
thats what im trying
but gotta calculate I_(n+1) first
and to do that i need to integrate
the function i sent earlier
sweet stag
do integration by part for I_(n+1) to write it in terms of I_n & then see what might happen
rough blade
do integration by part for I_(n+1) to write it in terms of I_n & then see what m...
for the integration by part should i chose du = 1
and v = 1/(e^x+1)^n
@sweet stag
sweet stag
mhmmm, ok dont do that yet
use f'(x) = f²(x) - f(x)
multiply it by $f^{n-1}(x)$ on both sides to get what you need first then apply IBP
sweet stag
@rough blade
$I_{n+1} - I_n = \int_0^\alpha f'(x) f^{n-1}(x) dx$ $$= \frac{f^n(\alpha) - f^n (0)}{n}$$
calm coralBOT
potent lotusBOT
Goëtia
calm coralBOT
Available help channel!
pseudo cedar
Hi everyone, I need help finding ways to disprove some theory I'm working on. My reasoning is explained as best as I can in the images, if something isn't clear please ask and I'll answer best way possible.
pseudo cedar
Someone adviced me to translate what is explained there to Lean language which is meant to check consistency on math theorems. I started learning it but it'll take me a great while to get used to it, so in the mean time I figured I could keep asking out for help
desert nymph
from the second paragraph you have never explained what TI_n is
doesn't make sense either
pseudo cedar
Its any number > 0
I use two instances of it in the equation to keep track of it, is the number you multiply 6 with to check for potential twin prime location, Twin Index that would be
I'm very sorry for the notations, I'm a programmer and it's the first time I do this
desert nymph
two instances of what? just two instances of any integer?
pseudo cedar
Yeah
Greater than 0 ofc
On the right side of the equation, for TIx > 0, you can find solution for all composite numbers which aren't divisible by 2 or 3, that is, numbers which are of the form 6n± 1
desert nymph
"6 TI_2 +/- 1" is not necessarily a prime
pseudo cedar
It doesn't need to be
desert nymph
there is no justification for, even if those two are prime, that they can compose any other number
this is just idek what
pseudo cedar
If you try to find product of any primes greater than 3 you will only get 6n± 1 by definition. All other residues of division by 6 imply that the number is either divisible by 2 or 3
desert nymph
they are not, though
pseudo cedar
At the end of the paragraph it says " (6*TI1 ± 1) can also be any product of primes greater than 3. This will guarantee that all cases of potential TI’s are covered by the equation"
Even so, is it wrong to constrain an equation so that only certain values are stored in the variable?
As in, it would be very helpful if there was a way to constrain TI_2 only to valid TI's which have been proven by the equation. We should be talking about a function here then i suppose. The invalid TI's are those of the form TI mod(p)=p//6 where p is a prime greater than 3. How could I write this?
calm coralBOT
@pseudo cedar Has your question been resolved?
calm coralBOT
@pseudo cedar Has your question been resolved?
pseudo cedar
.close
calm coralBOT
calm coralBOT
Available help channel!
winter plinth
How do I answer this
calm coralBOT
How do I answer this
pure kayak
quaint sphinx
How do I answer this
drag the three vertices of the triangle to locations on the graph such that the enclosed region represents the deadweight loss
winter plinth
What’s the answer
quaint sphinx
do you know what deadweight loss is
winter plinth
No clue
quaint sphinx
your course should have some sort of textbook
winter plinth
It’s for my brother
winter plinth
your course should have some sort of textbook
Do you know how to solve it
spark cloud
How do I answer this
Yes. Deadweight loss is defined as the area directly under the intersection point of the supply and demand curve. Does that help?
winter plinth
Yes. Deadweight loss is defined as the area directly under the intersection poin...
Not really is there a way you could show me the answer
spark cloud
Move the triangle to this same spot. That is how you answer the question.
winter plinth
This is what I’m getting but it says I’m wrong
spark cloud
No. It is bounded by tax revenue, and the area under the intersection point.
winter plinth
No. It is bounded by tax revenue, and the area under the intersection point.
So how do I make it right. I’m helping my older brother with this because he’s busy and so I know nothing about this
spark cloud
That's fine. You don't even have to know anything about Deadweight Loss to understand its location. Like I said before, take a look at where it is shaded in the photo I sent, and place it in that exact same spot in your question. You can also reorient the photo, if it confuses you that much. Most supply and demand curves are graphed horizontally, but that's not the case in your problem, so just flip the photo I sent.
winter plinth
Never mind I figured it out thanks
spark cloud
Okay, good to know.
calm coralBOT
@winter plinth Has your question been resolved?
signal light
how did they get to this factorisation
calm coralBOT
how did they get to this factorisation
manic vault
how did they get to this factorisation
Because that is how ti works?
Think of it like $4x^2-6xy+2y^2=0$
potent lotusBOT
mathisfun
warm warren
Well you typed it way faster than me
manic vault
We thus have $4x^2-8xy+2xy+2y^2=0$
potent lotusBOT
mathisfun
signal light
whats that process called again
signal light
**mathisfun**
does this factorisation work?, which terms should we be groupiong
manic vault
does this factorisation work?, which terms should we be groupiong
Yes
Ah wait
Not the right factorization
$2x^2-3xy+y^2$
potent lotusBOT
mathisfun
signal light
divide by 2 everything?
manic vault
Yeye
calm coralBOT
calm coralBOT
Available help channel!
signal light
calm coralBOT
signal light
is this simplification true?
if so, how is it true. Should it not be sin4θ
solutions had error
.close
prime rapids
calm coralBOT
prime rapids
hi, can someone help check it for me ?
plain bone
,w integrate (2x^3 - x^2 - 19x + 18)/(x^2 - 9) from x=1 to x=2
potent lotusBOT
plain bone
✅
calm coralBOT
calm coralBOT
Available help channel!
prime topaz
Hi, I don't get how the teacher went from the first to second step
pearl iron
Hi, I don't get how the teacher went from the first to second step
looks like they did it incorrectly
after you let u = -x^2 + 3x - 2, du = -2x + 3
it turns into integral of -1/2sqrt(u) du
which is -sqrt(u)
and it's also a definite integral
so that is just not right at all
calm coralBOT
pearl iron
i don't think that was your teacher
but yw
the second part of your integral looks right
calm coralBOT
Available help channel!
remote mural
i have no idea how to do problem 2.11
calm coralBOT
i have no idea how to do problem 2.11
pearl iron
what book is this
junior hamlet
what book is this
aops volume 1 i think
junior hamlet
what book volume 1
only one
remote mural
what book volume 1
art of problem solving
i dont understand the proof tho
z1 and z2 are different numbers
junior hamlet
which part
remote mural
how tf do we take it as one
remote mural
we arent adding z1 and z2
i know
they are two different numbers tho - how can we treat that as one?
junior hamlet
wdym
by treat as one
oh you mean
let z=z1+z2i?
they're expressing it in complex form a+bi
like z1 is real part and z2 is the coefficient of the imaginary part
remote mural
let z=z1+z2i?
I understand, but z1 and z2 are two different numbers and yet they are both evaluated to z
and i dont understand that part
junior hamlet
I understand, but z1 and z2 are two different numbers and yet they are both eval...
we're js simplyfying it
like say
c=x+y
pearl iron
z = a + bi
w = c + di
where a, b, c, d ∈ℝ
z + w = (a + bi) + (c + di) = (a + c) + (b + d)i
conj(z + w) = (a + c) - (b + d)i
= a - bi + c - di
= conj(z) + conj(w)
remote mural
(x+y)(x+y)
Yes
remote mural
z = a + bi
w = c + di
where a, b, c, d ∈ℝ
z + w = (a + bi) + (c + di) = (a + c)...
ohh
so say z = 4 + 5i and w = 3 + 6i
Wait
oh
i get it now
thanks
.close
calm coralBOT
remote mural
.reopen
calm coralBOT
✅
pearl iron
z1 and z2 is not equal to z
they're completely different variables
but the naming just relates them to z conceptually
remote mural
they're completely different variables
thats why i was confused
remote mural
z1 and z2 are like a and b
thats why i was confused, cause they were basically saying the two expressions were the same when they simplified it
they fucking jumped steps
junior hamlet
wdym
remote mural
I really cant explain it
junior hamlet
they're js saying z=a+bi
remote mural
they're js saying z=a+bi
Mhm
junior hamlet
and w=c+di
remote mural
yes i get that
junior hamlet
yeah
remote mural
I understood it in the first place
junior hamlet
alright
remote mural
z = a + bi
w = c + di
where a, b, c, d ∈ℝ
z + w = (a + bi) + (c + di) = (a + c)...
So
that symbol means
a b c and d are rational
pearl iron
ℝis real numbers
pearl iron
it includes ℚ (irrational) and ℤ (rational)
junior hamlet
∈=belongs to
pearl iron
and it's a subset of ℂ (complex)
junior hamlet
so their coefficients have to be the same
remote mural
Ok
junior hamlet
i
remote mural
school aint taught me shit yet
remote mural
wait nvm
remote mural
aops went over it
junior hamlet
yea
remote mural
its fucking 11:30 im too tired to think lmao
junior hamlet
its fucking 11:30 im too tired to think lmao
real 😔
remote mural
thanks
calm coralBOT
@remote mural Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
pastel heart
calm coralBOT
velvet osprey
try just the 3rd or 1st quartile?
exotic cosmos
has to do with the quantile definition that’s being used right
pastel heart
i guess
let me check so more examples that quantiles have been used
here is another example, where racetimes is the data set
clearly first quartile is 21 and third quartile is 35
no
its correct like that
exotic cosmos
here is another example, where racetimes is the data set
oh its R
yeah then what i told is right
it’s not using the nearest rank algorithm
it’s something like this:
(k-1)/(n-1) = 0.75
n = 11
so k = 7.5
so they take the average of the 7th and 8th element to get 23.5
calm coralBOT
calm coralBOT
Available help channel!
blazing coyote
Trying to find the inverse path here
calm coralBOT
Trying to find the inverse path here
blazing coyote
I'm thinking $f(t)= ( -(1-t),(1-t))$
potent lotusBOT
What a wonderful world !
blazing coyote
Would this be fine?
Thanks
one more question
this time on product path
I would first want to re-parametrize g so that it's domain is either [a,0] or [1,b]
$f(t)= (2-t, (2-t)^2)$. where $f:[1,2] \to \R^2$
potent lotusBOT
What a wonderful world !
blazing coyote
[
h(t) =
\begin{cases}
(-t, t^2) & 0 \leq t \leq 1 \
((2-t), (2-t)^2) & 1 \leq t \leq 2
\end{cases}
]
oops
potent lotusBOT
What a wonderful world !
blazing coyote
I think this works
calm coralBOT
Available help channel!
magic zodiac
I'm creating a polynomial java method that has multiple functions, but primarily the one I'm having trouble with understanding is the polynomial multiplication method in which two inputs are given in ascending order (constants first), and returned in the same format but the result being the expanded and simplified array. Below is my code:
magic zodiac
The strategy im using to create the aforementioned multiplication method is firstly, creating an ArrayList that appends all the expanded values (the raw multiplied values without adding like terms), and then recognizing the pattern of the two polynomials. I've determined that when you multiply certain polynomial lengths you end up getting a pretty predictable sequence of numbers which represent the occurrence of similar powered variables
both of these methods are correct upon testing, but the main issue I'm having is applying the logic. for the arrays {1,2,3} and {1,5,3} I'm getting the output [1,7,16,8,1] which is almost correct aside from the second last and last integers
I've determined that this is because the function does not recognize when it has already counted an integer and instead sequentially processes each integer 1 by 1, leaving room for the same variable integers to be counted multiple times. This isn't a problem early on with the 1,7,16 but it becomes a problem when values are not as organized as the program accounts for
I'm trying to figure out a way around this, is there a way to even tell java to backtrack if a number has already been processed?
I apologize in advance to anyone who takes a look at my code as it is not the neatest 😅
calm coralBOT
@magic zodiac Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
deep violet
calm coralBOT
deep violet
Help is needed!
If a circle exists inside a bigger circle as shown such that the inner circle passes through the centre of the larger one and the inner circle (smaller circle) is tangent to the larger circle at B, prove that DE = EB where D is a point on the outer circle and E the point of intersection of the line segment which contains both the points D and B and the smaller/inner circle.
velvet osprey
won't this then just make the small circle exactly half as big as the bigger one
deep violet
In terms of radius, yes.
velvet osprey
a circle's size is specified by nothing but its radius
deep violet
Ye
velvet osprey
what i mean is that AB will be the small circle's diameter
deep violet
But that can also mean area.
velvet osprey
like the circles are internally tangent at B so BA and BC are both perp to their common tangent at B
and thus BA and BC coincide as straight lines
deep violet
like the circles are internally tangent at B so BA and BC are both perp to their...
Nahh
💀
velvet osprey
wdym, "nahh"
deep violet
Nah = no
velvet osprey
no shit sherlock
do you mean like
A) "You are wrong outright."
B) "I agree with your assertion but not your proof thereof."
C) "I agree with your assertion and proof thereof, but you have violated an unstated restriction on proof methods."
D) "My disagreement does not fit into any of the above categories."