fnnuy
#help-26
wraith heron
lyric lynx
try b = -1.4
lyric lynx
now that's just floating point arithmetic thing
i think you need to expand the thing inside limit using (1-x)^a but i don't really know calculus
found this using wolfram (i think this is taylor series)
so it becomes
sum from k=0 to inf of (-x^a)^k (x^b k)
i dont know what to do next
topaz sinewBOT
@plush flicker Has your question been resolved?
topaz sinewBOT
@plush flicker Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
keen spire
https://www.learncbse.in/ncert-solutions-for-class-10-maths-chapter-8-introduction-to-trigonometry/ should I do the problem no.6 with 1 or 2 triangles
topaz sinewBOT
https://www.learncbse.in/ncert-solutions-for-class-10-maths-chapter-8-introducti...
fluid belfry
can you just post a ss of it
keen spire
can you just post a ss of it
Ex 8.1 Class 10 Maths Question 6.
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.
this is the question
fluid belfry
do we have any diagram given
keen spire
yes
keen spire
do we have any diagram given
i cant post ss tho
keen spire
alas lag raha hai pc meh
keen spire
accha 😔
keen spire
kitna hi time lagega
can u not click open the link?
fluid belfry
can u not click open the link?
nhi, alas aa rha h
keen spire
mc
fluid belfry
can u not click open the link?
toh isme kya nhi smgh aaya?
keen spire
toh isme kya nhi smgh aaya?
NCERT does it with 2 triangles
tho, it has angle Q instead of B
so, why is that?
fluid belfry
abeey
ruko thoda, dinner pura krne do phle
ha
btao abhi
tumhe kaise pata ncert does it with 2 triangles?
@keen spire \
keen spire
tumhe kaise pata ncert does it with 2 triangles?
because I have the book? 🤣
fluid belfry
toh pic bhej de na bhen😭😭😭
fluid belfry
dhekho
kuch smgh nhi aa rha hai kehna kya chahti ho
bhalai isi mei hai ki pic bhej do seedhe
keen spire
bhalai isi mei hai ki pic bhej do seedhe
what do u not not understand
my question is, if I should use 1 or 2 triangles for this question?
keen spire
okay
keen spire
if instead of angle A & angle B
I had to do angle A & angle Q
would there be 2 triangles?
and why
fluid belfry
i mean its given that cos A=cos B
why is there even a need of second triangle
and would you even prove that with a second triangle
keen spire
why is there even a need of second triangle
idk, thats what im asking
topaz sinewBOT
fluid belfry
<@&268886789983436800>
craggy haven
,prune 20 --from 1175835986945654866 racism
fluid belfry
what is going on
mint raft
plug it back in?
topaz sinewBOT
topaz sinewBOT
Available help channel!
golden geode
Hello im currently making a shader for a project and i need to calculate the vertical angle between the triangle and the camera
what equation should i use ?
topaz sinewBOT
Hello im currently making a shader for a project and i need to calculate the ver...
icy sky
Which of adjacent, opposite, or hypotenuse do you have?
golden geode
i think i have adjacent and opposite
chilly walrus
use tan, then
waxen flame
if you're trying to program it, you should use the atan2 instead of arctan(vertical/horizontal)
basically you have to adjust for quadrants, and you can either work that out on your own or use someone else's working lol
waxen flame
whenever you feel like you've figured things out, you may close it at your discretion
golden geode
i think this works
atan2(sqrt(dist.x*dist.x + dist.z*dist.z), dist.y)
thanks
.close
limpid flame
topaz sinewBOT
wise garnet
Yep
limpid flame
.close
shut obsidian
Determine if $f: \mathcal P( \mathbb N) \rightarrow \mathcal P( \mathbb N), \quad S \mapsto S \cup {37}$ is injective, surjective or bijective.
topaz sinewBOT
Determine if $f: \mathcal P( \mathbb N) \rightarrow \mathcal P( \mathbb N), \qua...
shut obsidian
This is just like what we did before, @waxen flame and @chilly walrus, but now, it's with P(N)
This is not injective, right?
One set could include {37}
And the other not
And they'd be counted as the same
vale furnace
{1,37} and {1}
chilly walrus
f({1}) = f({1,37})
shut obsidian
Ah, just like I described, yeah
chilly walrus
mhm
shut obsidian
f({1}) = f({1,37})
What about its surjectivity though?
shut obsidian
{1,37} and {1}
Shouldn't it be {1, {37}} and {1}?
vale furnace
Shouldn't it be {1, {37}} and {1}?
{1,{37}} is not a subset of N
shut obsidian
Oh
chilly walrus
${1} \cup {37} = {1, 37}$
thorny flameBOT
artemetra
vale furnace
is it surjective 
shut obsidian
Wait but what would the difference be if this was S -> S u {37} or S -> S u 37
chilly walrus
the last one is abuse of notation
shut obsidian
Oh, alright
chilly walrus
$\cup$ is union of \textbf{sets}
thorny flameBOT
artemetra
vale furnace
37 is not a set you union doesn’t make sense there
shut obsidian
is it surjective <a:thinkspin:586078649149554690>
Actually, no right?
Because we always need to throw a 37 in there
shut obsidian
So a counterexample would be {1} in P(N), right?
chilly walrus
yes
vale furnace
Right
shut obsidian
{1} is in P(N) but can't be reached by f
chilly walrus
also out of curiosity what course/book is this?
vale furnace
Looks like first year intro stuff
shut obsidian
also out of curiosity what course/book is this?
It's a course on linear algebra 1
chilly walrus
i see
vale furnace
shut obsidian
This is the beginning of it
So proofs, logic, set theory, ...
Only on page 30 of the lecture notes begins the real linear algebra part
vale furnace
I see
shut obsidian
Right
Now if we have [f: {S \in \mathcal P(\mathbb N) \mid S \text{ is finite}} \rightarrow \mathbb R, \quad S \mapsto |S| + \sqrt{|S|} + 1,] that would be injective, right?
vale furnace
Why?
chilly walrus
what about {1,2,3} and {1,2,4}?
shut obsidian
Oh, I was only looking at the magnitude of it
shut obsidian
what about {1,2,3} and {1,2,4}?
True, that'd give the same
shut obsidian
what about {1,2,3} and {1,2,4}?
This can't be surjective though, right?
How'd it reach pi or e, for example
chilly walrus
mhm
chilly walrus
eh, not really
i mean
this is essentially trying to map naturals to reals
which cannot be surjective because $|\bR| > |\bN|$
thorny flameBOT
artemetra
vale furnace
Eg 3/2 + sqrt(1/2)
chilly walrus
that too
in general anything that can't be expressed as $n+\sqrt{n}+1$, $n \in \bN$
thorny flameBOT
artemetra
topaz sinewBOT
chilly walrus
np
shut obsidian
.reopen
topaz sinewBOT
✅
vale furnace
shut obsidian
np
Btw, if we have a statement like
"If $g \circ f$ is injective, then $f$ is injective"
How would we determine if that is true or not?
Would you first try examples?
vale furnace
Sure to get intuition but you can prove this from definition
||let f(x) = f(y) then gf(x) = gf(y) but ..||
shut obsidian
||let f(x) = f(y) then gf(x) = gf(y) but ..||
Are you doing contraposition?
knotty ledge
They're assuming f(x) = f(y) and trying to conclude x = y
shut obsidian
They're assuming f(x) = f(y) and trying to conclude x = y
But that's not the direction of the statement?
knotty ledge
They're assuming f(x) = f(y) and trying to conclude x = y
You are trying to prove f is injective, that's what this is
You are going to use the fact that gf is injective along the way
shut obsidian
You are going to use the fact that gf is injective along the way
So it follows that $g(f(x)) = g(f(y))$. But then $x = y$.
So we are done?
shut obsidian
Sure to get intuition but you can prove this from definition
This is what you meant?
vale furnace
Yeah
shut obsidian
Need g be injective?
Say we have "If $g \circ f$ is surjective, then $g$ is surjective". That'd be true, right?
vale furnace
That’s true yes
vale furnace
Well recall the definition of surjective for g
shut obsidian
If $g: A \rightarrow B$, then $g$ surjective means $\forall b \in B: \exists x \in A: f(x) = b$.
vale furnace
Hint: ||the image of g circ f is a subset of the image of g||
shut obsidian
Hint: ||the image of g circ f is a subset of the image of g||
$\text{Im}(g \circ f) \subseteq \text{Im}(g)$, yeah
vale furnace
Let $f:A \mapsto B \ g: B \mapsto C$. if $g \circ f$ in surjective then $\forall c \in C, \exists a \in A, g \circ f(a) = c$ Now, $f(a) \in B$ so…$
Damn
shut obsidian
Let $f:A \mapsto B \ g: B \mapsto C$ if $g \circ f$ in surjective then $\forall c \in C, \exists a \in A, g \circ f(a) = c$ Now, $f(a) \in B$ so…$
thorny flameBOT
Pure
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vale furnace
Well idk mapsto was that thing
shut obsidian
**Pure**
Compile Error! Click the <:errors:504266556054962196> reaction for more...
Oh
vale furnace
Let $f:A \to B \ g: B \to C$ if $g \circ f$ in surjective then $\forall c \in C, \exists a \in A, g \circ f(a) = c$ Now, $f(a) \in B$ so…
thorny flameBOT
Pure
vale furnace
That’s better
vale furnace
Correct
shut obsidian
Thanks!
shut obsidian
No
vale furnace
Okay let’s see
Let S, T be disjoint countable (ie. there exist infections f: S to N and g: T to N) Prove S U T in countable.
shut obsidian
Okay let’s see
Wait, there are some more of these: \ "If $g \circ f$ is surjective and $g$ is injective, then $f$ is surjective". This is false, right?
Oh, wait nvm
That's like one we had before
But stronger this time
vale furnace
What do you think
let A = {0} B = {1,2} C = {3,4}
Can you come up with a counter example
shut obsidian
It doesn't seem like there is a counterexample, atleast not for algebraic functions
vale furnace
let A = {0} B = {1,2} C = {3,4}
Ignore this
shut obsidian
Let g(f(x)) = x^3, surjective.
Let g(x) = x, injective.
Let f(x) = x^3, surjective
It doesn't seem like we can change around stuff to make f not surjective
vale furnace
It’s true lol I misread
Thought it said gf injective
Try proving it with definition
shut obsidian
$g \circ f$ surjective $\implies \forall c: \exists x: g(f(x)) = c$. \ $g$ injective $\implies$ $g(a) = g(a') \implies a = a'$.
shut obsidian
You have proved that this means g is surjective
So g is bijective
We need to show g o f with g bijective means f is surjective
vale furnace
Sure.
Because g is surjective for every c in C there must be a b in B such that g(b) = c.
Now, we have gf(a) = g(b)
And so by surjectivity of g it follows that …
shut obsidian
Sure.
Because g is surjective for every c in C there must be a b in B such that ...
For some f(a) = b, yes
shut obsidian
f(a) = b
vale furnace
Yes and so f is surjective
shut obsidian
From injectivity of g sorry
We need f surjective
"If $g \circ f$ is surjective and $g$ is injective, then $f$ is surjective".
vale furnace
Yes f is surjective
shut obsidian
shut obsidian
Yes f is surjective
Oh
vale furnace
For all b in B, there exists an a in A such that g(f(a)) = g(b) which means f(a) = b
shut obsidian
For all b in B, there exists an a in A such that g(f(a)) = g(b) which means f(a)...
= b, why = g(b)
vale furnace
Follows from surjectivity of g
shut obsidian
Sure.
Because g is surjective for every c in C there must be a b in B such that ...
How did you get g(f(a)) = g(b)
g(b) = c, sure
vale furnace
since for all c there’s some a such that g(f(a)) = c. Also for all c in C there’s some b such that g(b) = c
Or more simply if b in B then g(b) in C. Since g o f is a surjective map from A to C it must be the case that we have some a with f o g(a) = g(b) for every b
atomic robin
What angle should the point be so that the shape has the largest perimeter?
atomic robin
The point is on a semi circle with a radius of 1
torpid matrix
The point is on a semi circle with a radius of 1
what is the perimeter of the shape you are forming, in equation form?
atomic robin
Well the equation for the perimeter is 2a+2b
$$a=cosx$$
$$b=\sqrt{sin^2x+(1-cosx)^2}$$
thorny flameBOT
N1x1T4
torpid matrix
From your drawing, it looks more like it should be 4a + 2b
assuming a only goes to the dotted like of course (which is easier to get)?
also how did you get b here?
atomic robin
here is a better image
atomic robin
no problemo so the question is at what angle is the sum of these green lines at it's maximum
atomic robin
yes
torpid matrix
okay sure, so the top one is definitely $2\cos(x)$
thorny flameBOT
atomic robin
I made a function like so:
$$P(x)=2cosx+2\sqrt{sin^2x+(1-cosx)^2}$$
thorny flameBOT
N1x1T4
torpid matrix
okay sure I agree with that
so now we need to maximize it
$P(x)=2\cos(x)+2\sqrt{\sin^2(x)+(1-\cos(x))^2}$
thorny flameBOT
torpid matrix
the inside of the square root should simplify down to $2-2\cos(x)$
thorny flameBOT
torpid matrix
then its just finding critical points to check the max
atomic robin
And for clearance I opened it up a little bit:
$$P(x)=2cosx+2\sqrt{sin^2x+1-2cos+cos^2x}$$
$$P(x)=2cos+2\sqrt{sin^2x+cos^2x+1-2cosx}$$
$$P(x)=2cosx+2\sqrt{1+1-2cosx}$$
$$P(x)=2cosx+2\sqrt{2-2cosx}$$
thorny flameBOT
N1x1T4
torpid matrix
$P(x)=2\cos(x)+2\sqrt{2-2\cos(x)}$
thorny flameBOT
torpid matrix
yes, then you need to take the derivative to find critical points
atomic robin
I got something like this for now:
$$P'(x)=-2sinx+\frac{1}{\sqrt{2-2cosx}} \cdot 2sinx$$
thorny flameBOT
N1x1T4
atomic robin
$$P'(x)=\frac{2sinx-2sinx\sqrt{2-2cosx}}{\sqrt{2-2cosx}}$$
$$P'(x)=\frac{2sinx(1-\sqrt{2-2cosx)}}{\sqrt{2-2cosx}}$$
thorny flameBOT
N1x1T4
atomic robin
the nominator roots now
so
$$\begin{cases}
2sinx=0 \
1-\sqrt{2-2cosx}=0 \end{cases}$$
thorny flameBOT
N1x1T4
atomic robin
the first one is just:
$$ x=\pi n$$
torpid matrix
should be $\pi n$
thorny flameBOT
atomic robin
ah yes true
thorny flameBOT
N1x1T4
atomic robin
the other one:
$$1-\sqrt{2-2cosx}=0$$
$$\sqrt{2-2cosx}=1$$
$$2-2cosx=1$$
$$-2cosx=-1$$
$$cosx=\frac{1}{2}$$
$$x=\pm \frac{\pi}{3}+2\pi n$$
thorny flameBOT
N1x1T4
torpid matrix
yeah that looks right to be
so the only solutions we care about out of these are $0, \frac{\pi}{3}$
thorny flameBOT
atomic robin
yes so we chuck both of them into the original P(x) function
torpid matrix
yes
atomic robin
$$\begin{cases}
P(0)=2cos0+2\sqrt{2-2cos0} \
P(\frac{\pi}{3})=2cos \frac{\pi}{3} + 2\sqrt{2-2 cos \frac{\pi}{3}}
\end{cases}$$
$$\begin{cases}
P(0)=2+2\sqrt{2-2} \
P(\frac{\pi}{3})=1 + 2\sqrt{2-1}
\end{cases}$$
$$\begin{cases}
P(0)=2 \
P(\frac{\pi}{3})=3
\end{cases}$$
torpid matrix
this is not right
atomic robin
what did i do wrong, there seems to be a problem
thorny flameBOT
N1x1T4
atomic robin
I found it
tender girder
topaz sinewBOT
drifting briar
this domain has to be right, right?
the domain is right yes
for the first question
you just need to remember that sin(sin^-1(x))=x
and that cos(sin^-1(x))=sqrt(1-x^2)
tender girder
so if it was arccos or arctan, the values would be different right?
drifting briar
do you mean for the 2nd question?
tender girder
this stuff is very complicated
I mean for the first question, I know the domain is based off of the inside portion, in this case arcsin
drifting briar
so if it was arccos or arctan, the values would be different right?
if it was arccos in parentheses the domain would still be the same
tender girder
but if I was calculating tan(arccos(x)), sin(arccos(x)) would not be x?
and cos(arccos(x)) would not be sqrt 1 - x^2?
drifting briar
and cos(arccos(x)) would not be sqrt 1 - x^2?
cos(arccos(x)) is also just x
they cancel each other out
drifting briar
and for tan(arrcos(x)) just remember that tan = sin/cos
drifting briar
so sin(arccos(x)) is sqrt 1 - x^2?
yes
i forgot how to prove that one tbh but you can probably use euler's identity in order to prove it
tender girder
so I need to use tan = sin/cos to solve this?
drifting briar
yea
tender girder
that's awesome!!!!
drifting briar
:)
tender girder
thank you so much Jill
drifting briar
yw
tender girder
.close
hazy pumice
that's kind of funny
usually they will at least tell you what they want you to prove
I think that ? is supposed to be PC
junior stratus
I have a silly question. Consider the complex square root $f(z)=z^{1/2}$. Suppose we are on the branch $\arg z\in(\pi,3\pi]$. Then if I input a positive real number, I should get a negative real number. Let $r>0$. Then $f(re^{2\pi i})=(re^{2\pi i})^{1/2}=(r\cdot1)^{1/2}=-r^{1/2}$, where $r^{1/2}>0$. What would be incorrect about factoring another $1$ in $(r\cdot 1)$, i.e. $(r\cdot 1\cdot 1)$ and then end up with $r^{1/2}$ instead?
topaz sinewBOT
I have a silly question. Consider the complex square root $f(z)=z^{1/2}$. Suppos...
calm plover
topaz sinewBOT
topaz sinewBOT
@calm plover Has your question been resolved?
keen venture
Yeah basically. It will still be 4 cases. But they're all easy solves
analog linden
Does this mean you can cover all possibilities with 210 games
topaz sinewBOT
Does this mean you can cover all possibilities with 210 games
bitter hemlock
Does this mean you can cover all possibilities with 210 games
no one's going to know what you're trying to ask if you don't provide the full context of your question, right now this is just a bunch of random numbers
calm plover
Yeah basically. It will still be 4 cases. But they're all easy solves
(sorry that it's unrelated)
Thank you!
analog linden
no one's going to know what you're trying to ask if you don't provide the full c...
This is for a lottery. There are 45 numbers to pick from. You need 6 matching to win, but you can choose up to 20 your odds of matching 6 when choosing up to 20 OUT OF 45 are 210.14 now if you plays 210 games can you cover all possibilities
bitter hemlock
what do you mean by cover all possibilities?
so are you asking are you guaranteed to win if you play 210 times?
if you flip a coin, the odds to get heads are 1/2, are you guaranteed to get heads if you flip it twice? no
analog linden
We’ll kind of
So you can’t actually cover all possibilities
But the odds are stating you will win right?
bitter hemlock
what do you mean by cover all possibilities?
you haven't answered my question ^
analog linden
Like cover all possibilities I ment a gauranteed win
Cover all possible different outcome
bitter hemlock
there is no guaranteed win if each individual event is independent
so if each game has a 1/210 chance to win that means your chance to win each game is 0.00476190476
each game you have a 0.99523809523 chance to lose
if you play 210 games your chance to lose all 210 games in a row is 0.99523809523 raised to the 210 power (0.99523809523)^210
that means you have a 0.36700179506 or 36% chance to lose ALL Games with those odds, i.e. you have a 68% chance to win at least one of 210 games with those given odds
analog linden
so if each game has a 1/210 chance to win that means your chance to win each gam...
They will not be played one after the other they will be played all at once. 210 seperate games in the same ENTRY
not week after week
analog linden
there is no guaranteed win if each individual event is independent
Each individual event is not independent
analog linden
With 210 games? While chosing 20 numbers in each game
Out of 45 numbers??
If you can do this and give me the 300 I will pay you.
If you can find the smallest amount of games to win wether it’s 210-300 I will pay you for them
What country are you in
Im@sorry what np hardness
I could even run simulations aswell to make sure it works
So can you do this or ? Like I said I am seriously happy to pay you
Why would you say it’s suboptimal if it’s a guaranteed win and you don’t even know the prize amount either
What do you mean disjoint subsets of 20 if you only entered 1 entry a week then your chances are one 210 every week which is bad
topaz sinewBOT
@analog linden Has your question been resolved?
tight rivet
What was I suppose to do
topaz sinewBOT
What was I suppose to do
sonic dawn
adding everything together is not taking the average
the 2nd one is just wrong and you have to evaluate the inner inverse first
tight rivet
adding everything together is not taking the average
the 2nd one is just wrong a...
So f-1 first =4 and then =3?
sonic dawn
yes
tight rivet
Bruhh wtf I thought that was if there was no -1
sonic dawn
what
i mean you always resolve the innermost expression anyway
tight rivet
Like I thought it was suppose to say fof instead if it wanted me to do it like that
Like first f(0)= 4 and f(4)=3
tight rivet
adding everything together is not taking the average
the 2nd one is just wrong a...
So how was I supposed to do 15
sonic dawn
take the average rate of change
you added the value and did nothing with it
something something rise/run
topaz sinewBOT
topaz sinewBOT
Available help channel!
river berry
Hi
river berry
.close
topaz sinewBOT
charred burrow
I would like to know if I solved this correctly
topaz sinewBOT
I would like to know if I solved this correctly
charred burrow
Quite confused about the 0.25 and A
shut spindle
cunning yarrow
thorny flameBOT
topaz sinewBOT
@charred burrow Has your question been resolved?
alpine estuary
the setup is correct, but A is way too high
alpine estuary
what kind of calc do you have?
alpine estuary
yeah
charred burrow
Ti-84
alpine estuary
can you create a function equal to e^(-x^2), and calculate using the function?
alpine estuary
just type it into your calculator and you should get the answer. don't forget to close the parenthesis before multiplying by 0.5
charred burrow
I got 0.8862
alpine estuary
that's correct
neon iron
I have a question
topaz sinewBOT
I have a question
fluid belfry
I have a question
ask
neon iron
Number of years after the start of 1967
thorny flameBOT
jan Niku
lone pier
So 1966 - 1967 = t
neon iron
How do I put the times in place of t
neon iron
So 1966 - 1967 = t
What about the plus 1
lone pier
t+1
neon iron
So the exponent is 0?
lone pier
yep
fluid belfry
I was struggling on what the +1 is
its just with the exponent
lone pier
Not getting that last bit.
fluid belfry
u just equate the function to the price and solve for t
fluid belfry
oh mb i was telling for the second one
cinder rapids
if you're done do .close
lone pier
Unclear - no confirmation of any form.
lone pier
Do you have away to do them now, or need a little more?
lone pier
What is "a"? There' no formula.
lone pier
Seems you have two points, but 3 constants to solve for.
lone pier
Maybe there is a simpler formular for "constant exponential growth"?
neon iron
idk what that is
lone pier
googling ...
Wikipedia says f(x) = a(1+r)^x - does this match the classes you have, maybe?
lone pier
All good.
neon iron
Wikipedia says f(x) = a(1+r)^x - does this match the classes you have, maybe?
how do i know when to use this one or the other one?
lone pier
You don't. "constant exponential growth" is a term from your examples - You need to work out what it means to the guy who wrote these. From the coursework, or maybe it's a standard term?
My turn to say "sry" 🙂
Close when done?
lone pier
"rate"?
lone pier
Which formula do you thinks you want to use?
lone pier
Where did you get that one?
Check the same place to se if they give you one for "constant exponential growth".
neon iron
thats the one i use for exponential equations
anyways it doesnt matter
i just want to know how to solve
its rly late for me
lone pier
p(1981) = 3,014
p(1988) = 4,287
two points, need a p(t) that you can solve for the constants
neon iron
isnt the b supose to be the rate?
lone pier
I have no clue what they call "b". We can call it "rate" if you like.
lone pier
so two points, three constants - in general you can't solve it.
There is another piece of information that you need.
My guess is that your book, or this test paper - has a definition of "constant exponential growth" That makes one constant go away.
lone pier
With y = ab^x + c - we can fit an infinite number of expnential curves through 2 any points.
neon iron
topaz sinewBOT
neon iron
potent nova
Find the area of all the squares in terms of the length of the smaller square
Then find the minimum of it
potent nova
only the black squares are the same size
neon iron
oh
potent nova
so you have to find the side length of the larger square in terms of the side length of the smaller square
neon iron
uh
potent nova
Find the length of the diagonal of one smaller square
thorny flameBOT
Shubh
thorny flameBOT
Shubh
potent nova
@neon iron
thorny flameBOT
Shubh
thorny flameBOT
cyan mesa
Sub sqrt(2) into the equation and you get 12
What do you exactly mean?
cyan mesa
It should be sqrt(2) (10)
potent nova
why?
thorny flameBOT
cyan mesa
There
cyan mesa
Well yeah it should be sqrt(2) times 10
cyan mesa
,w simplify y = 4x^2+(60-2xsqrt(2))^2
Oh you plugged 6 instead of 60
That’s where the problem is
thorny flameBOT
potent nova
Alg
cyan mesa
That’s some weird ass notation
potent nova
,calc 2^(1/8)
thorny flameBOT
Result:
1.0905077326653
Yea, at first I thought it was tetration
cyan mesa
Is p log(2) the same as log p base 2
thorny flameBOT
Shubh
cyan mesa
Ah
potent nova
,w N[log(2^p)=8]
thorny flameBOT
potent nova
I get some weird stuff that's not matching the solution
cyan mesa
Yeah I don’t see how it would be 2^(1/8)
potent nova
Yeah I don’t see how it would be 2^(1/8)
What could be the possibility of what the question actually meant?
cyan mesa
Oh I found it
cyan mesa
The base is p not 10
plog(2) means log(2) base p
log(2) base p = 8
2 = p^8
2^(1/8) = p
The rest should be easy
potent nova
Bruh wth?
neon iron
wth
cyan mesa
log(2) base p = 8
2 = p^8
2^(1/8) = p
@neon iron
neon iron
Sub sqrt(2) into the equation and you get 12
the last answer is 1/3 bro
thorny flameBOT
neon iron
bruh
cyan mesa
1200
cyan mesa
Check this out
cyan mesa
Aka 1200
potent nova
cyan mesa
potent nova
Oh my bad I used 6 again
cyan mesa
cyan mesa
base is p
potent nova
Bruh
potent nova
That could make more sense
Why would they write it like that?
@neon iron is it normal this way?
potent nova
Or they have an insane log constant that equals this
thorny flameBOT
Shubh
neon iron
????
potent nova
@neon iron get it?
topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
idk
wide bane
topaz sinewBOT
wide bane
Don't know where to start with questin B
acoustic tangle
Just choose a value for c so that f(0) = 1 where f(t) = c * e^(e^t)
potent nova
topaz sinewBOT
potent nova
,rotate
thorny flameBOT
potent nova
Have I done a mistake anywhere?
The solutions I get don't look as nice as the answers
lean meteor
potent nova
Have I made a mistake here?
thorny flameBOT
potent nova
Or here?
thorny flameBOT
potent nova
Or here?
<@&286206848099549185>
I'm just asking to check my work, as it is not lining up with the answers provided
topaz sinewBOT
@potent nova Has your question been resolved?
potent nova
<@&286206848099549185>
pastel salmon
i have verified it, all is ok
topaz sinewBOT
@potent nova Has your question been resolved?
misty forge
how do i show that it satisfies the logistic equation?
topaz sinewBOT
how do i show that it satisfies the logistic equation?
strange whale
you plug the function inside the equation
if you were asked "is x=4 a solution to the equation 2x^2 + 4x - 3 = 0 ?" what would you do ?
it's very similar here
@misty forge
misty forge
im very confused how do i plug it in and do i plug in what yprime/y =?
strange whale
well you compute y' first for the function you're given
and then you can get y'/y
and check that this thing equals k(1-y/M)
misty forge
can u give some tips on how to get the derivative because i have never seen a equation like this
strange whale
lookup the derivative of tanh if you don't remember
it's not like I remember it myself 
cyan mesa
how do i show that it satisfies the logistic equation?
You could just take the log of y(t)
And differentiate that
I tried it and it works with a couple of steps
Also I don’t suggest using the exp form of tanh
Actually maybe just differentiating then dividing the derivative by y and simplifying to required form could be easier
misty forge
okay thank you i got that one
i have one more question
im also stuck on this problem
not sure how to get started
and do it
@prisma shore
topaz sinewBOT
@misty forge Has your question been resolved?
misty forge
<@&286206848099549185>
timber schooner
topaz sinewBOT
timber schooner
.close
topaz sinewBOT
Available help channel!
frozen axle
topaz sinewBOT
frozen axle
@cold wagon
topaz sinewBOT
@frozen axle Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
wind marsh
topaz sinewBOT
wind marsh
ive done a
but i dont understand how to do b and c
nvm i did b
i dont get c tho
nvm i did it
ig im a genius
<@&286206848099549185> how do i do d
topaz sinewBOT
@wind marsh Has your question been resolved?
tacit sundial
topaz sinewBOT
tacit sundial
How is this equal to ln (0)
polar narwhal
How is this equal to ln (0)
Because the natural logarithm of zero is undefined
vale furnace
you can rationalise the expression
tacit sundial
No I get that
polar narwhal
Alr
tacit sundial
But -inf+inf =0??
vale furnace
should get something like $\frac{-1}{a - \sqrt{a^2 + 1}}$
thorny flameBOT
Pure
vale furnace
should be pretty clear why this is 0
shrewd lance
why not?
vale furnace
yes
tacit sundial
Hmm alright then
Is it because it’s indeterminate
Form
Well I think so
Make sense ty
topaz sinewBOT
Available help channel!
tender girder
topaz sinewBOT
tender girder
I don't get it
I think I need to find the cos value, which is 30 degrees, so x is 10 degrees or pi/18?
except I don't think the x= values it gave me like equals what I got, they equal like 130 degrees and 230 degrees?
narrow cradle
Let $\alpha$ be a known angle and we want to find the angle $\theta$ which satisfies
$
cos \alpha = cos \theta$
This is given by $\theta=2n\pi \pm \alpha$
thorny flameBOT
diaas_(yt)
narrow cradle
Now it is given that $cos(3x)=\frac{\sqrt 3}2$
thorny flameBOT
diaas_(yt)
narrow cradle
$cos(3x)=cos(\frac\pi6)$
thorny flameBOT
diaas_(yt)
narrow cradle
Using the formula I gave you
narrow cradle
That should be the answer
Just replace n with k, and you can use the compound angle identities to represent $\frac23n\pi -\frac\pi{18}$ in the form asked in the question
thorny flameBOT
diaas_(yt)
tender girder
Thank you sorry I was afk
topaz sinewBOT
Available help channel!
elfin slate
Alright, from here I got stuck…
topaz sinewBOT
@elfin slate Has your question been resolved?
topaz sinewBOT
@elfin slate Has your question been resolved?
placid latch
I need solutions to these questions
topaz sinewBOT
I need solutions to these questions
bitter hemlock
!status
topaz sinewBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
you might want to ask more specific questions rather than posting your whole homework assignment
!occupied
topaz sinewBOT
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).
ivory gyro
placid latch
you might want to ask more specific questions rather than posting your whole hom...
Okay
topaz sinewBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
Help plssss
placid latch
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
Status!
!status
topaz sinewBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
topaz sinewBOT
@placid latch Has your question been resolved?
topaz sinewBOT
@placid latch Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
proven narwhal
topaz sinewBOT
timber current
mellow venture
,w integral of x^2e^x^2
thorny flameBOT
mellow venture
Yeah
golden mesa
,w integrate (2x^2+1)e^(x^2)
thorny flameBOT
golden mesa
mm
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
I tried u substituting here but it didn’t work
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
<@&286206848099549185>
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
<@&286206848099549185>
pastel salmon
$\int_{}^{}\left( 2x^{2}+1 \right)e^{x^{2}}dx=\int_{}^{}2x^{2}e^{x^{2}}dx+\int_{}^{}1\cdot e^{x^{2}}dx=\\\\int_{}^{}2x^{2}e^{x^{2}}dx+xe^{x^{2}}-\int_{}^{}x\cdot 2xe^{x^{2}}dx=xe^{x^{2}}+C$
thorny flameBOT
Joanna Angel
pastel salmon
this trick is called eating your own tail, if it involves certain integrations by parts 🙂
topaz sinewBOT
@proven narwhal Has your question been resolved?
proven narwhal
this trick is called eating your own tail, if it involves certain integrations b...
where did this X come from?
pastel salmon
integraiton by parts
i deliberatley wrote number 1
to make you notice, that it was integraiton by parts
topaz sinewBOT
@proven narwhal Has your question been resolved?
dark plank
topaz sinewBOT
dark plank
Ugh
cursive thorn
Dont rewrite it!
answer is still correct, but for the other side
@dark plank
If one side is x, then the other could be 3 + x
topaz sinewBOT
@dark plank Has your question been resolved?
dawn shadow
Hi
dawn shadow
Im trying to optimize an assignmentproblem with Gurobi.
strange whale
is it really that much of a problem to use two loops here ?
the long part is solving the constraint problem, not defining it
@dawn shadow
dawn shadow
<@659407302217957387>
Well this loop gets executed 108mil times, and I have like 8 of them.
It takes hours to finish the loops
strange whale
ah ok
so what's your constraint problem actually ?
and what does x_vt mean here ?
dawn shadow
so what's your constraint problem actually ?
I have to assign 145k volunteers to 750 tasks, with every task having a certain volunteer-demand. The objective is to assign as many volunteers as possible.
x_vt is a huge array with volunteer indexes and task indexes, and it contains of 0's and 1's.
strange whale
aren't most entries 0 in x_vt ?
dawn shadow
Yes, there is max one 1 in a row, since a volunteer can only do 1 task
A volunteer can only do 1 task, but a task can be done by multiple volunteers
strange whale
so a volunteer can only demand one task ?
dawn shadow
A volunteer can have 0 tasks or 1 task
strange whale
or can they demand multiple tasks, and in the end they only do one
dawn shadow
A volunteer can be suitable to do 100's of tasks, but at the end he can only do 0 or 1
strange whale
ah ok
strange whale
A volunteer can be suitable to do 100's of tasks, but at the end he can only do ...
so that's what x_vt represents then ?
suitability of volunteers for each task ?
dawn shadow
No x_vt is the actual assignment.
So x_vt[1][2] = 1, means that volunteer 1 is assigned to task 2
strange whale
ah ok ok it's the assignment
ah yeah so 1 task max per volunteer, that's what this code represents, got it
strange whale
well in this formulation of the problem you're using (145k * 750 binary variables), you can't really escape writing the constraint like that
seems like you can make your row with one call in gurobi though
dawn shadow
well in this formulation of the problem you're using (145k * 750 binary variabl...
Maybe I should try to think on not making a square
dawn shadow
https://www.gurobi.com/documentation/10.0/refman/cpp_lex_addterms.html#cppmethod...
Ill have a look at this. Thank you.
I know from in advance that a volunteer can only do certain tasks, so maybe there is no point making the full matrix 750 wide
But then it requires more preprocessing aswell
strange whale
Ill have a look at this. Thank you.
I know from in advance that a volunteer can...
yeah if you can have a sparse matrix instead it should go much quicker
that's what I was thinking about
dawn shadow
Im not sure how to accomplish that yet but I will definitly have a look.
strange whale
yeah if you can have a sparse matrix instead it should go much quicker
but that will only help for the suitability constraints
you can't escape the "every volunteer can only do max 1 task" one
yeah try addTerms first
no, I just searched in the docs
like I know what gurobi is
never used this solver in particular
dawn shadow
The goal was to solve it with a local search but random swaps and random inserts wont work out. So thats why I was thinking about opimizing with fixating variables
The Hungarian algorithm is very fast but its nearly impossible to embed these constraints in them
strange whale
so you're trying to maximize the number of completed tasks I suppose