send the question
#help-13
crimson sedge
ya
crimson sedge
c= 7-b
35 +40b =195
b=4
c= 3
crimson sedge
t = 0.18
0.75-0.52=0.23
e=0.23
crimson sedge
pls dont ditch me halfway bro ;-;
ima help finish this and ima go sleep
crimson sedge
lmao im sotired i cant do basic math
tired inlet
ima help finish this and ima go sleep
its alr u dont have to stray upfor me
crimson sedge
its 2am
crimson sedge
how many do u have left
tired inlet
THANKS FOR THE HELP AND DETERMINATION
tired inlet
how many do u have left
now i have to start over
lmao
its fine
u can. goto sleep
crimson sedge
gl and gn
plucky cedar
cedar kilnBOT
plucky cedar
can someone help me with that
toxic moat
hi
plucky cedar
hi
plucky cedar
oo
hybrid otter
3x + 21 = 63, 3x = 42, x = 42/3 = 14
plucky cedar
so in an isosceles triangle it works like hta
plucky cedar
ok that makes sense
plucky cedar
for some reason i dont think that was on the notes so i was confused
i thought u had to do some weird math
ty
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
sick sonnet
cedar kilnBOT
sick sonnet
Is the last rule in my book wrong?
For example this is wrong right, so the rule in the book is also wrong?
granite wyvern
What is g(x) and f(x)?
kind wedge
Well it looks like chain rule to me
granite wyvern
What you are doing is phi(x)=g(x)*f(x)
sick sonnet
Oh
sick sonnet
What is g(x) and f(x)?
Letβs say g(x) = 3x^2 and f(x) = 1-b
kind wedge
they have to be the same variable or f(x) is just a constant
you are doing f(x) not f(b)
sick sonnet
Ok so letβs say g(x) = 3x^2 and f(x) = 1-x
kind wedge
then phi(x) would be 3(1-x)^2
sick sonnet
Times -1 right
kind wedge
what?
kind wedge
wait what we aren't differentiating yet
sick sonnet
wait what we aren't differentiating yet
Oh ok
kind wedge
6(1-x) * -1
yea that looks right to me
sick sonnet
Ah i see
kind wedge
then phi(x) would be 3(1-x)^2
The rule is teaching you how to differentiate this function
kind wedge
if you have a function h(x) that can be composed of g(f(x)), then you can use the rule
to differentiate h(x)
sick sonnet
Ah
kind wedge
It's called the chain rule
sick sonnet
Thank you
kind wedge
np
sick sonnet
Have a nice day
kind wedge
you too
sick sonnet
.close
gilded wigeon
cedar kilnBOT
gilded wigeon
Hey, I'm looking at this solution and I don't see how his step proves it is injective.
I know injective means that there is AT MOST one element a in A that maps to an element b in B
How does proving f(a) = f(b) satisfy that requirement?
solid juniper
i think it's easier to imagine it as $a\neq b$ implies $f(a) \neq f(b)$
wraith daggerBOT
πππΆπππΆπ
toxic moat
if there exist some f(a) = f(b) where a != b
gilded wigeon
Oh, so he's doing the contrapositive?
toxic moat
then its not injective
toxic moat
**πππΆπππΆπ**
ok idk how u view that as easier i find this so confusing lol
solid juniper
Oh, so he's doing the contrapositive?
that's kinda semantic, depends on your definition of injective
solid juniper
ok idk how u view that as easier i find this so confusing lol
lol it just says
different inputs give different outputs
gilded wigeon
I got it, I appreciate you both chiming in here. Not my proudest moment
because I just realized this is literally how our book tells us to do the contrapositive proof of it.
toxic moat
yay
cedar kilnBOT
toxic moat
π
cedar kilnBOT
Available help channel!
fair sky
hey i have been looking at this for a while and honestly am so lost. Prof said something about using chain rule and difference law and im just confused on how to use them in this equation.
cedar kilnBOT
hey i have been looking at this for a while and honestly am so lost. Prof said s...
@fair sky Has your question been resolved?
cedar kilnBOT
@fair sky Has your question been resolved?
cedar kilnBOT
@fair sky Has your question been resolved?
cedar kilnBOT
@fair sky Has your question been resolved?
cedar kilnBOT
@fair sky Has your question been resolved?
cerulean star
yuck, what a science project
$h(x) = f(ax)g(bx)\left(f(x^2)+g(-x^{-2})\right)^{-1}$
wraith daggerBOT
Disorganized
cerulean star
let f(ax)g(bx) be one function. Then we can use the product rule between that and the latter instead of using quotient rule (which would be at least as complicated as two product rules)
I will do product rule in this order: (uv)' = uv' + u'v
$(ax)g(bx) \cdot -\left[f(x^2)+g(-x^{-2})\right]^{-2} \cdot \left[2x f(x^2) + 2x^{-3} \cdot g(-x^{-2})\right] + \
\left[f(ax)g(bx)\right]'\left[f(x^2)+g(-x^{-2})\right]^{-1}$
blech.
then we need to do product rule on (f(ax)g(bx))'.
(below has typos btw, look at the latest LaTeX below. It is correct.)
wraith daggerBOT
Disorganized
cerulean star
$(ax) \cdot g(bx) \cdot -\left[f(x^2)+g(-x^{-2})\right]^{-2} \cdot \left[2x f(x^2)' + 2x^{-3} \cdot g(-x^{-2})'\right] +
\left[a \cdot f(ax)' \cdot g(bx) + b \cdot f(ax) \cdot g(bx)'\right]\left[f(x^2)+g(-x^{-2})\right]^{-1}$
@fair sky
wraith daggerBOT
Disorganized
lament kelp
I would like a simple explanation on karnaugh map.
cedar kilnBOT
I would like a simple explanation on karnaugh map.
@lament kelp Has your question been resolved?
cedar kilnBOT
@lament kelp Has your question been resolved?
lament kelp
.close
marsh pilot
Just a simple question. How can rational function can be use in animation?
cedar kilnBOT
Just a simple question. How can rational function can be use in animation?
@marsh pilot Has your question been resolved?
bold hazel
cedar kilnBOT
bold hazel
checked this like two times now and it looks right to me
opal basin
maybe remove the brackets so it looks nicer
bold hazel
simplify it?
opal basin
yes
bold hazel
I don't think the homework program requires it, so I usually don't simplify it
modern compass
pretty sure the last term isn't 11x
modern compass
or the 2/11 should be affecting that term too, you're missing a parenthesis
bold hazel
ah sheit
ur right
ty
because I moved the 2/11 out of the integrand
I gotta parenthesis it but I didn't
thank the lort!!!!!
it's correct
.close
verbal night
Could I get help with this:
cedar kilnBOT
Could I get help with this:
verbal night
2^100 x 3^42= 4^n x 6^42 I need to figure out what n is
south tundra
You can rewrite the right hand side as 2^2n * (2 * 3)^42
So you have 2^100 * 3^42 = 2^(2n + 42) * 3^42, right?
south tundra
3^42 cancel out
So we're left with 2^100 = 2^(2n + 42)
And this means only one thing, 100 = 2n + 42
Can you solve for n from here?
heady salmon
what do they mean when they say "apply the Sin Squareroot method"
floral forge
just take the square root?
opal basin
sin^2(x) = (sin(x))^2
crimson sedge
I mean it goes to anything that can accept a square root
heady salmon
k ty
lean thunder
can this rule go for every other trig functions?
it's a notation not a rule
cedar kilnBOT
@heady salmon Has your question been resolved?
little oyster
cedar kilnBOT
little oyster
The answer key shows C, but I think its B, because the interval is defined between [a,b], and there are no extrema at cusps because they are not differentiable. Why am I wrong?
I can see why the answer might be A, if we assume that because at point a I could not definitively determine that mtan = 0, but C???
crystal raptor
absolute extrema don't have to be at differentiable points
little oyster
So local extrema must be differentiable but absolutes do not?
wintry prism
little oyster
I must have a mistaken understanding of extrema then. Is it not a maximum or minimum value along a function f(x) where when defined locally mtan = 0 and the given point is y>another point?
(greater or less than, respectively)
crystal raptor
if its a local extrema AND its differentiable at that point then thats true yes
really a local max is just a point where for some interval around that point all values of the function are lower than the max
if we happen to be in the case where that point is differentiable, then its tangent is zero etc
little oyster
yeah, so an absolute extrema is the highest or lowest y value where mtan = 0 over a given interval
crystal raptor
well like we just discusssed they may not be differentiable so there is no defined tangent line at that point
if thats what you mean by mtan
little oyster
So differentiability not required to define something as an extreme value then
thats my last question - sorry, just want to make sure I understand
crystal raptor
Correct
look at your graph, that point at the top is definitely bigger than anything else on the graph
but its not differentiable
absolute max but not diff
little oyster
thus where my confusion lay - under the impression that said point must be both 1. maximum/minimum and 2. differentiable
awesome, thanks sigma and slowbros
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
sonic lark
cedar kilnBOT
wraith daggerBOT
violet night
so our options are
454257
454281
454276
454247
from what I remember, perfect squares of an integer only ever end with 0,1,4,5,6 or 9
so A and D don't work
the number we square to get B will end with either 1 or 9
the number we square to get C will end in 4 or 6
crimson sedge
you literally have to test each answer lol
sonic lark
That's gon take long time
crimson sedge
How to get p and q for pq formula from an equation with 4 parts
crimson sedge
I have the equation 4xΒ² + xΒ³ - 2xΒ² + 5
crimson sedge
that's not a quadratic
Doesn't need to be one
cedar kilnBOT
crimson delta
for pq formula usually yes
cedar kilnBOT
Available help channel!
upper bough
cedar kilnBOT
floral forge
what have you tried?
upper bough
.close
peak osprey
i need to find the X. i did the calculations and i'm not getting the right answer. Could you tell me if i transformed the equation in the right way
peak osprey
long arrow
peak osprey
A^-1 = 1 -2
0 1
peak osprey
2 -2
-1 3
peak osprey
i forgot to get rid of negative values :/
and now i'll get the correct answer thanks
β₯οΈ
.close
crimson sedge
Hi
main orbit
yes
modern compass
yes, just not in this channel. you should open your own.
see #βhow-to-get-help
crimson sedge
Can I?
modern compass
it says to type in the (available) rooms.
This one is occupied by Allalwii
crimson sedge
Can I ask my question
wraith daggerBOT
modern compass
yep, draw a picture
you have a house with side lengths 3m and 4m
then the rope is tied to the corner,
So the sheep can graze on a circle centered on the corner of the house
but it can't eat in the house
so you're looking for the area of the circle, minus what the sheep can't get to because of the house.
did you draw a picture?
post the picture when you're done
so what is the grazeable area you're trying to find?
you're trying to find the area the sheep can graze on yeah? Where is that in the drawing?
good
so the area the sheep can graze on in a fraction of a circle
yes a circle
so how much of the circle can the sheep graze on, since it can't go inside the house
yep
so find the area of the circle, and then multiply by 3/4
wraith daggerBOT
Kingo
gauss\:\begin{pmatrix}2&1&1&3-2k^2\\ \:4&3&4k-3&7-6k^2\\ \:1&0&-2k&1\\ \:k&1&-\left(k-4\right)&0\end{pmatrix}
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.57 gauss\:\begin{pmatrix}
2&1&1&3-2k^2\\ \:4&3&4k-3&7-6k^2\\ \:1&0&-2k&1\\ ...
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.
LaTeX Font Info: Calculating math sizes for size <14> on input line 57.
LaTeX Font Info: Trying to load font information for U+msa on input line 57.```
cedar kilnBOT
terse grail
gauss:\begin{pmatrix}2&1&1&3-2k^2\ :4&3&4k-3&7-6k^2\ :1&0&-2k&1\ :k&1&-\left(k-4\right)&0\end{pmatrix}
wraith daggerBOT
Kingo
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
terse grail
can someone help me reduce this matrix?
i need to find for which k values the system have
1 solution
no solution
or inf solutions
i tried to reduce but i feel like im wrong and stuck
cedar kilnBOT
Available help channel!
steel ember
Why is this not correct?
cedar kilnBOT
Why is this not correct?
solemn torrent
$2^x \cdot{64}$β $128^x$
wraith daggerBOT
Springsskateboard
crystal mason
If sets $A := {0,-1}$, and $B:= {-1, -2}$, what is $A\cdot B$?
wraith daggerBOT
Levens
solid juniper
so i'm not sure that's totally standardized notation, but it could mean ${ab:a\in A, b\in B}$
wraith daggerBOT
πππΆπππΆπ
solid juniper
wherever it's from should define it somewhere tho
crystal mason
So.. would it be {0,1,2}?
crystal mason
wherever it's from should define it somewhere tho
what do you mean by "it"
solid juniper
what A dot B means
solid juniper
oh cool
crystal mason
So.. would it be {0,1,2}?
would this be right for my example then?
solid juniper
So.. would it be {0,1,2}?
then yep π
crystal mason
yay
nice
another question..
Let $A \subseteq \mathbb{R}$ be a nonempty set bounded below and $a \in \mathbb{R}$ chosen arbitrarily. Show that $a = \text{inf}A$ if and only if
$$
a = \text{sup}{c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }
$$
is satisfied.\
\
How can I approach this?
wraith daggerBOT
Levens
solid juniper
what definition of sup and inf do you have?
cedar kilnBOT
@crystal mason Has your question been resolved?
crystal mason
what definition of sup and inf do you have?
well, infimum and supremum
crystal mason
Supremum is the least upper bound and infimum ist the greatest lower bound
crystal mason
or screenshot or something
its in german
solid juniper
that's ok i just want to be able to reference it
and i think i'll be able to follow enough
crystal mason
they dont really define "inf" and "sup" in the question itself - i just know the definition from lectures
solid juniper
oh ok
crystal mason
ill send u the original uesiton anyway if u want
solid juniper
well there usually multiple ways to do questions like this
crystal mason
ill send u the original uesiton anyway if u want
solid juniper
one is show $a\leq \text{sup}{c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }$ and $a\geq \text{sup}{c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }$
wraith daggerBOT
πππΆπππΆπ
solid juniper
another option is $a< \text{sup}{c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }$ and $a> \text{sup}{c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }$ both lead to contradictions
wraith daggerBOT
πππΆπππΆπ
crystal mason
**πππΆπππΆπ**
i think this one seems better
solid juniper
ok π
crystal mason
im gonna try and do it myself first
solid juniper
sure thing, lmk if you need any help
crystal mason
sure thing, lmk if you need any help
lol nvm idk how to start
solid juniper
lol ok so i'd guess proving $a\geq \text{sup}{c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }$ is easier than the other thing
wraith daggerBOT
πππΆπππΆπ
solid juniper
because a >= sup{...} just means a is an upper bound for {...}
crystal mason
true true
solid juniper
oh also to recall some details we're assuming a=inf A here
crystal mason
yes
wait i think i change my mind.. a>sup{...} and a<sup{...} and then contradiction would be more comprehendable to prove no?
solid juniper
i think both would be ok but you can try that if it sounds easier
crystal mason
oh also to recall some details we're assuming a=inf A here
okay.. all we know about A is that its a set of real numbers that is bounded below
and a in words would be.. the lowest upper bound of other real numbers, where all those real numbers are smaller than the ones in A
wait wait
crimson sluice
crystal mason
clash royale
crystal mason
and a in words would be.. the lowest upper bound of other real numbers, where al...
so we have to show that a is the infimum of A if and only if that thing i replied to is true
with the approach of showing "a>= sup{...}" and "a<= sup{...}"
solid juniper
i think we're really just trying to prove inf(A) = sup{...}
crystal mason
yeah
solid juniper
adding the a and the iff part seems like it's just a slightly convoluted way to say that
crystal mason
yeah the iff part is just how the question was phrased, so I wanted to like link the question to my comprehension
solid juniper
i think we're really just trying to prove inf(A) = sup{...}
if it was translated right i think it's just this
crystal mason
in the german question it also has the iff thing
crystal mason
yep
solid juniper
ok, want to try $a\geq \text{sup}{c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }$?
wraith daggerBOT
πππΆπππΆπ
solid juniper
actually i think it might be easier to show $a< \text{sup}{c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }$ is false
wraith daggerBOT
πππΆπππΆπ
solid juniper
which is the same thing
so if we assume that
it says a is not an upper bound for S
so that means there exists...?
(you fill in the blank lol)
crystal mason
it means that there exists an s in S that is s>a
solid juniper
yep
let's call ${c \in \mathbb{R} \ | \ x > c \ \text{for all} \ x \in A }$ $S$ lol
instead of {...}
crystal mason
haha okay
wraith daggerBOT
πππΆπππΆπ
solid juniper
it means that there exists an s in S that is s>a
so what can you say about s?
crystal mason
we know that s is a real number that's smaller than all elements in A
which then contradicts
what we said before
so a<sup(S) is not true
nice
solid juniper
sup(S) but yep π
solid juniper
so this one might be a little trickier, but i'd start with inf(A) > sup(S) means sup(S) isn't a lower bound for A
crystal mason
ok
solid juniper
getting anywhere?
crystal mason
im still writing down the first part formally
solid juniper
oh ok
crystal mason
it says a is not an upper bound for S
wait how can supremums have upper bounds or bounds in general
like
do we know that sup(S) is in A?
crystal mason
right right
solid juniper
i changed it to S
crystal mason
so this one might be a little trickier, but i'd start with inf(A) > sup(S) means...
so if sup(S) isnt a lower bound for A, then that means there exists .. actually im not quite sure
uh
solid juniper
b in A such that b < sup(S)
cedar kilnBOT
@crystal mason Has your question been resolved?
crystal mason
b in A such that b < sup(S)
idk how to continueπ
solid juniper
b < sup(S) means there exists s in S such that b < s
crystal mason
ah ahhh ok ok hold on
umbral sand
<@&286206848099549185> what is 8/2*(2+2)
cedar kilnBOT
<@&286206848099549185> what is 8/2*(2+2)
solid juniper
yay thanks layla
yep ^-^
solid juniper
<@&286206848099549185> what is 8/2*(2+2)
silly question lol
umbral sand
silly question lol
me and a friend having a discussing
gleaming cloud
Let me guess. One of you thinks it's 1 and the other thinks it's 16?
umbral sand
Let me guess. One of you thinks it's 1 and the other thinks it's 16?
yes
so what is it
umbral sand
tf
solid juniper
look it's whatever you want it to be because it's ambiguous notation
solid juniper
if you agree to parse it as 8/(2*(2+2)) then it's 1 and if you agree to parse it as (8/2)*(2+2) then it's 16
zenith sail
The year is 2100. Society has collapsed into oblivion. There are wars being fought over water. Nothing is the same, except that people are still posting intentionally ambiguous mathematical expressions on social media to create arguments and generate engagement. Will it ever end?
solid juniper
.-.
conventions for how expressions are parsed are made up
clearly, you and your friend don't have the same conventions for that ambiguous expression
like the universe doesn't have a built in pemdas rule
umbral sand
like the universe doesn't have a built in pemdas rule
if it wasnt it would still be 16
zenith sail
so im right
In any language, there are ways to communicate clearly. It is no different for mathematical notation. Whoever wrote that expression intentionally decided not to communicate clearly. There is no one clear answer. It's ambiguous.
That's the entire reason people post expressions like that on social media. It gets people arguing and commenting
umbral sand
In any language, there are ways to communicate clearly. It is no different for m...
but... im right tho
zenith sail
See how well it works?
fluid ruin
hey chingy chongys
solid juniper
can both of you try to actually read and understand what has been said?
because none of it says either of you are right
fluid ruin
8 divided by 2(2+2)
umbral sand
because none of it says either of you are right
but...... no
cedar kilnBOT
@umbral sand Has your question been resolved?
round totem
How do you do question b.)
cedar kilnBOT
How do you do question b.)
steep oasis
how do i do small maths problems fast
cedar kilnBOT
how do i do small maths problems fast
steep oasis
like 586 divided by 6
ig i could do like 6x100 thats 600 then how many multiples of 6 are needed to make 600 then minus that by 100
but is thre a shortcut
mighty drift
600-14 / 6 = 100-(2+1/3) = 97 + 2/3
cedar kilnBOT
@steep oasis Has your question been resolved?
runic oxide
i was wondering what i got wrong here
cedar kilnBOT
i was wondering what i got wrong here
modern compass
i was wondering what i got wrong here
isosceles triangles have two sides with the same length
modern compass
MNP?
MN is 6
MP is 9.2
NP is 8.1
runic oxide
ohh i see
i forgot the add them
alright thats pretty much all i needed
thanks
.close
pliant latch
How do I factor 49 in order to be able to do partial fraction decomposition
violet night
How do I factor 49 in order to be able to do partial fraction decomposition
do polynomial divison
try like x+1 and x+2 etc
pliant latch
oh
digital whale
is this the correct approach to this laplace transform question?
cedar kilnBOT
is this the correct approach to this laplace transform question?
@digital whale Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
open swallow
for 101 uh I understand how to find the intersection of the two now Im just not sure how to find the r for it
open swallow
since I have 2 equations how do i solve for the r in this case
solemn torrent
equate
open swallow
?
open swallow
right so I know I can do
yeah but once I have those I need to get the r values for it
open swallow
so I know my points in this case is 3Ο/4 and 7Ο/4
oh wait it
doesnt matter which equation I sub it into ?
solemn torrent
yeah it doesnβt
solemn torrent
np
open swallow
.close
distant kelp
bro
solemn torrent
you got $\frac{(1-sinΞΈ)(1-sinΞΈ)}{(1-sin^2ΞΈ)}$
look at the denominator
1-sin^2 is
(1+sin)(1-sin)
wraith daggerBOT
Springsskateboard
wraith daggerBOT
Springsskateboard
solemn torrent
see anything u can cancel
solemn torrent
yeah
distant kelp
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
bold hazel
how would you integrate this? $ \int x^2 \frac{1}{1+x^2}$
cedar kilnBOT
how would you integrate this? $ \int x^2 \frac{1}{1+x^2}$
runic garnet
Looks like it, any other way u can send the problem
warm jolt
There is a bit of a trick to this one
bold hazel
can it be done with IBP?
warm jolt
To start with, rewrite it with x^2 m the numerator just to help you see the trick better
You donβt need ibp for this
warm jolt
try to see what is missing between the numerator and denominator and see if you can find out how to βaccommodateβ that
warm jolt
Exactly thatβs whatβs missing
How can you make a +1 appear in the numerator without changing the equation?
warm jolt
It had to do with adding 0
bold hazel
and subtract another 1
warm jolt
Yes!
warm jolt
You got it π
bold hazel
ok so
hm
interesting
you just got rid of the x^2
crazy
I see what happened now
seems like black magic
warm jolt
Yep π
warm jolt
0 is the root of all black magic
warm jolt
Can you show me what you have now?
warm jolt
Close but you forgot about the first fraction, it isnβt 0
warm jolt
And donβt forget your dxβs π
bold hazel
the caffeine is wearing off
warm jolt
And you are right about the second fraction just being an inverse trig identity
warm jolt
Assuming you know the identity for the second it should be trivial
crimson sedge
Go complex 
bold hazel
I googled trig identities
crimson sedge
Just kidding, although I think I have something for this
warm jolt
I already helped them solve it pretty muchβ¦
bold hazel
where should I look for trig identities
crimson sedge
Oh nice
bold hazel
like as a reference
this page I found... I don't think it's a complete list or something
warm jolt
where should I look for trig identities
Iβll just let you know which one it is; itβs the inverse tan aka arctan identity
crimson sedge
A brain teaser would be thinking of the integral of lnx/(1+x^2)
warm jolt
Memorization π
crimson sedge
U can derive most of them
warm jolt
Have you learned about them in class yet?
crimson sedge
I don't really remember any of them except something like sin(a+b) because that's kinda hard to derive
bold hazel
equivalents basically
warm jolt
If by equivalents you mean identities then yes
crimson sedge
For that u r just dividing the cos^2x+sin^2x=1 by cos^2x
warm jolt
Yes, though we are looking at inverse trig identities related to integration in our case
warm jolt
Best way to look it up is something like inverse trig derivatives or integrals
Such as this
warm jolt
Oh sorry that one has some weird stuff lol
bold hazel
so there should be like a table of derivatives
for inverse trig functions
or rather, their equivalents
and what inverse trig function they integrate to
warm jolt
You can look at this then note that integration is basically going in the opposite direction
(+ C)
manic acorn
I dont have any of these memorized
warm jolt
Those arenβt really what we are looking at; we are technically looking at inverse trig derivatives but going backwards with integration
warm jolt
Notice how we donβt have an inverse trig getting integrated, just some rational function
bold hazel
right
so derivative of arctan
would be the rational function?
so just going in reverse basically?
oh, okay, that makes sense
warm jolt
would be the rational function?
Yes derivative of arctanx = 1/(1+x^2) so integrating the RHS gives the LHS + C
bold hazel
we know that d/dx(arctanx) = [...]
so we can just assume the integral then
equivalence
warm jolt
This image doesnβt have the equation we are using
warm jolt
Ah
warm jolt
Precisely
bold hazel
ok, cool, it would just bother me if I didn't know how to refer back to this
XD
or how to remember what's what
warm jolt
Just keep in mind that integration is trying to go the opposite direction of derivatives (with an extra constant thrown in since it was eaten up when taking the derivative)
You can technically also look at it as integrating both sides, then having the integral and derivative cancel out with a + C remaining
bold hazel
hm, ok
bold hazel
all good
is that an f on the left?
or integral sign
oh, I think I see the meaning here
pretty much going in reverse
warm jolt
Just an integral sign canceling out the derivative and leaving a +c
radiant charm
i need help on how she got this
cedar kilnBOT
i need help on how she got this
runic garnet
Got what?
crimson sedge
It's written she multiplied the equation by 15 on both side
radiant charm
how did she get 5x+6=3x-6 from the question above it
radiant charm
It's written she multiplied the equation by 15 on both side
i donβt understand
crimson sedge
Let's say you have a = b
Then 15 * a = 15 * b right?
That's what she did with a = left part and b = right part of the equation
radiant charm
she wants it done a certain way tho
something like 15/3x1 to get 5x
but iβm not sure if thatβs correct
crimson sedge
I guess you need to get rid of the fractions
You have 3 and 5 as denominators so the least common multiple is (5*3=)15
So if you multiply by 15 you get rid of all the fractions
radiant charm
.close
cedar kilnBOT
cedar kilnBOT
@crimson sedge Has your question been resolved?
dire geode
just pick any x that's not 1 or 2 and calculate the corresponding y using your equation
silver fern
solemn torrent
wassup
cedar kilnBOT
@solemn torrent Has your question been resolved?
solemn torrent
<@&286206848099549185>
neon moon
how do I find the derivative of x^x^x^x^xβ¦.^x
Let y = that crazy expression, then $y = x^y$. <= Do you see why? And with this new formula do you know how to proceed?
wraith daggerBOT
jimmy1234
solemn torrent
so
If we let y =x^x^x^...,
y=x^y
y=e^[ylnx]
dy/dx=x^y [lnx(dy/dx)+y/x]
dy/dx=[(x^y)(y/x)]/[1-(x^y)(lnx)]
solemn torrent
Let y = that crazy expression, then $y = x^y$. <= Do you see why? And with this ...
is that right?
<@&286206848099549185>
solid juniper
i donβt see why y = x^y π
crimson sedge
Let y = that crazy expression, then $y = x^y$. <= Do you see why? And with this ...
But aren't you adding an extra x with you saying that?
hollow minnow
Is there a finite or infinite number of x
solemn torrent
infinite
solid juniper
howβs that a function
warm bone
howβs that a function
I think it is, but it's not very interesting?
solemn torrent
πΉ
solid juniper
if you view at as the limit of a sequence of functions, it doesnβt converge to anything even pointwise?
solemn torrent
oh no
solid juniper
I think it is, but it's not very interesting?
oops meant to reply to this
solemn torrent
limits again
solemn torrent
oops meant to reply to this
okay phew
warm bone
if you view at as the limit of a sequence of functions, it doesnβt converge to a...
1 is a fixed point
But I don't know how to handle the function anywhere except that
So I suppose I'm not going to solve this either
warm bone
Let y = that crazy expression, then $y = x^y$. <= Do you see why? And with this ...
This doesn't really help I think..
crimson sedge
Where did u get this from my guy you don't even know limits yet π@solemn torrent
crimson sedge
Oh damn
solemn torrent
the hint was to use implicit differentiation
crimson sedge
the hint was to use implicit differentiation
Yeah I mean
solid juniper
1 is a fixed point
iβm not sure it even converges anywhere else lol
crimson sedge
I think you have to see some pattern here
solemn torrent
wait itβs x^x^x^xβ¦. infinitely
warm bone
iβm not sure it even converges anywhere else lol
Literature says yes but I'm definitely not solving this myself
solid juniper
wait itβs x^x^x^xβ¦. infinitely
itβs probably not supposed to be
solemn torrent
,w derivative of x^x^xβ¦.
wraith daggerBOT
Requested by Springsskateboard#8145
solemn torrent
:(
YouTube
letβs go
bruh thereβs no vids on it either
this sucks
WAIT I FOUND A VID
crimson sedge
https://youtu.be/i_l1lz26C2M
Oh wow so it is what that guy said?
warm bone
Just checking but for x^x^... for x=2, if it diverges, it diverges at infinity right?
By that I mean, it doesn't 'not exist'
Wait never mind, this article says it all
Damn, literature is OP
solid juniper
something i just read says it converges on [1/e^e, e^(1/e)]
solemn torrent
a bit of the vid
solid juniper
and nowhere else
solemn torrent
itβs what that red guy said
wait itβs not red guy
JIMMY*
@neon moon <33 thx bro
solemn torrent
When your best friend wolfie fails u π
sigh
crimson sedge
You really called the guy "red guy"π
warm bone
Ah so it's an implicit function derivative as well?
The derivative is defined in the same domain I suppose
I didn't look through the vid
But that is what I assume
warm bone
something i just read says it converges on [1/e^e, e^(1/e)]
This is the domain by the way.
for > the right value, you get +infty everywhere.
For < left value, it's weird (DNE anywhere I think)
solid juniper
yea it oscillates or something on the left
warm bone
it oscillates from left value to 1 too, but the odd/even powers agree
warm bone
You can see the oscillation by low powers on desmos
warm bone
https://www.maa.org/programs/maa-awards/writing-awards/exponentials-reiterated-0
Yeah I read this
dire geode
18 pages of fun
solid juniper
now i want to ask someone to differentiate 1/(xxxxβ¦)
will they realize itβs the 0 function everywhere >1 it converges or will they try to use derivative rules?
dire geode
That only converges for x=1
solid juniper
now i want to ask someone to differentiate 1/(xxxxβ¦)
this?
dire geode
Yes
solid juniper
why doesnβt it converge to 0 when |x|>1?
dire geode
Oh I mean nonzero
warm bone
why doesnβt it converge to 0 when |x|>1?
Why does it converge for x < 1?
Doesn't it osciilate?
dire geode
Diverges for 0<x<1
solid juniper
i didnβt say it does
solid juniper
it only oscillates in [-1,0)
solid juniper
mine is on point every day
cedar kilnBOT
@solemn torrent Has your question been resolved?
solid juniper
another good one might be ln(xxxβ¦)
i think it just converges for x=1
by good one i mean umm
warning about β¦βs in functions
brisk ferry
Does a pyramid base have to be square?
grave cloud
Does a pyramid base have to be square?
i guess yes...?
i have never seen other shape before
brisk ferry
can't it be a rectangle?
undone halo
Does a pyramid base have to be square?
what pyramid?
solid juniper
i donβt think the naming conventions there are steadfast
undone halo
if youre talking about the pyramids such as the pyramids of giza, they are square
solid juniper
pyramid could mean square pyramid, or not
undone halo
4 sides dies are also pyramids but they have a triangle base
solemn torrent
Does a pyramid base have to be square?
doesnβt necessarily mean square base
solemn torrent
i have never seen other shape before
there are rectangular pyramids
got pentagonal
hexagonal
idk what gonal
livid hound
pyramid could have any polygon base
solemn torrent
pyramid could have any polygon base
RAMONOV
the fastest latex typer
along with Ann of course
brisk ferry
ok ye thx
late urchin
Someone might help me with flow rate calculations? I just need to understand it i have the answers already
mental trail
Someone might help me with flow rate calculations? I just need to understand it ...
bruh it's the second time I tell you to get your own help channel. #βhow-to-get-help
late urchin
Wym i aaw this the first time
Oh i send my message before u told me to diffrent channels
cedar kilnBOT
@brisk ferry Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
broken locust
hey
broken locust
im practicing relational algebra
a bit lost, would really appreciate explanations
i don't need the answers id just be happy to understand what's going on π
cedar kilnBOT
@broken locust Has your question been resolved?
cedar kilnBOT
@broken locust Has your question been resolved?
cedar kilnBOT
@broken locust Has your question been resolved?
lament kelp
How do I do a kanaugh map for half adder and full. With the bits C carry and sum. And I want the function in sp-form.
cedar kilnBOT
How do I do a kanaugh map for half adder and full. With the bits C carry and sum...
@lament kelp Has your question been resolved?
cedar kilnBOT
@lament kelp Has your question been resolved?
crimson sedge
hi
fierce sorrel
You mean eruption?
fierce sorrel
If you want to know the speed or rate of flow of the lava, try dividing the volume by time taken in seconds
cedar kilnBOT
@crimson sedge Has your question been resolved?
wild spear
how do i go through this question?
cedar kilnBOT
how do i go through this question?
wild spear
the question can be factorised to $(x^2-7x+1)^3=0\implies x^2-7x+1=0$, but i dont know how to simplify $a^{2^{2023}}+\frac{1}{a^{2^{2023}}}$.
wraith daggerBOT
nichoals
cedar kilnBOT
@wild spear Has your question been resolved?
wild spear
<@&286206848099549185>
wild spear
<@&286206848099549185>
cedar kilnBOT
@wild spear Has your question been resolved?
wild spear
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
jagged yacht
cedar kilnBOT
jagged yacht
The motivation for the solution is the following
I don't understand how if a_k = a_k+1 = ... mod phi(n)
then a_k+1 = a_k+2 = ... (mod n)
phi is the euler totient function
cedar kilnBOT
@jagged yacht Has your question been resolved?
cedar kilnBOT
@jagged yacht Has your question been resolved?
solid juniper
I don't understand how if a_k = a_k+1 = ... mod phi(n)
in general, if gcd(a,n) = 1 and b = c mod phi(n), then a^b = a^c mod n
it follows from eulerβs theorem
because if a = b mod phi(n) then a^b = a^(d*phi(n) + c) for some integer d
and a^(d*phi(n) + c) = a^(d*phi(n))*a^c = a^c mod n
jagged yacht
a^(d*phi(n)) = 1 mod n
right?
solid juniper
yep
jagged yacht
thank you so much!
solid juniper
np ^-^
jagged yacht
you seem pretty good at this, can I dm you to ask some questions later?
solid juniper
iβm not good at this but i guess π΅βπ«
jagged yacht
yes you are this is question is from an olympiad
hahaha
i'll close this, thank you!
solid juniper
if you want me to help on olympiad problems, prepare for disappointment
that was just reading the beginning of a solution loll
cedar kilnBOT
solid juniper
youβre overestimating me T_T
cedar kilnBOT
Available help channel!
maiden garnet
cedar kilnBOT