of course
#help-19
desert marlin
desert marlin
you can draw a nice picture
twin urchin
A level curve instead of a level surface
desert marlin
yes
twin urchin
So in the case of 2 variables
My r(t) is just my level curve
But in 3 variables
R(t) is a path on my level surface right?
desert marlin
I'm not entirely sure what you are asking me about since it isn;t clear what r(t) and R(t) are. This example I gave works as a proof in higher or lower dimensions is you just augment it correctly
twin urchin
lemme explain
r(t) is a vector valued function
Imagine we have a function of F(x,y) = K
essentially
imagine the horizontal trace of F(x,y) when z=k
now imagine if I were to find all the x and y values
that will lead to z=k
and were to plot those x/y values on thet xy plane
and then parametrize that path
desert marlin
r(t) is a vector valued function
from R^2 -> R?
twin urchin
Correct
and then parametrize that path with a vector valued function r(t) = <x(t),y(t)>
Therefore
F(r(t))=k
d/dt F(r(t)) = d/dt k = 0
Therefore
Lambda F dot r'(t) = 0
therefore Lambda F is orthogonal to r'(t)
and r'(t) is a tangent vector to r(t)
therefore Lambda F is Orthogonal to r(t)
aka the level curve
desert marlin
it is any path, not a specific path. the part where you are saying where z=k etc... and introducing the z is unnecessary and confusing. But any path along the level surface, F(x,y)=k, the rest of the proof follows from
but yes
twin urchin
got it
ty
wait
it should be a specific path
not any path
it should be the path such that F(r(t)) = k
desert marlin
r(t) is just a parametrization of a curve on your level surface
there are many such curves
twin urchin
Level surfaces are F(x,y,z) = K Level Curve = F(x,y) = k
desert marlin
okay yes I mean level curve then
desert marlin
imagine your level surface is a cross section of some sphere
twin urchin
I see what u are saying
desert marlin
okay
desert marlin
there are many paths along that circle
twin urchin
yes
desert marlin
and along all of them
twin urchin
its not specific
desert marlin
the value is still K
twin urchin
its technically all of them
desert marlin
technically any of them
twin urchin
Well if I am finding the gradient
at a specific point
the gradient is normal to the level curve of F(a,b) = k
at (a,b)
desert marlin
this was just a proof of why the gradient is normal to your level curve at any point
twin urchin
have a good day
odd edgeBOT
@twin urchin Has your question been resolved?
covert mortar
what is the probability of getting silvers diagonally in a 3x3 cube if the format from left to right and top to bottom is:
left/top: blue, silver, green
Middle: silver, white, red
Bottom: green, silver, blue
You are allowed to rearrange silver but only in its row
the answer is 1/27 apparently but I dont know how to find it out
stone mountain
Use favourable outcomes/ total number of possible outcomes
Firstly calculate the number of formations possible
Then the number of formations in which the sliver blocks are diagonally placed
covert mortar
so 27 total outcomes?
stone mountain
Nah
covert mortar
9 outcomes?
nopee
year 10 probability rn
would it be using a diagram?
like tree diagram or two-way table for example
<@&286206848099549185>
odd edgeBOT
@covert mortar Has your question been resolved?
stone mountain
9 outcomes?
Nah each row can have 6 different sets of formation like for first row it can be B S G , G S B , B G S , G B S , S G B , S B G . Likewise the other 2 rows have 6 different sets of formations too , so total number of formations will be 6×6×6 = 216
Now using this same way calculate the formations in which silvers are placed diagonally
stone mountain
Each row has only one silver
covert mortar
for one diagonal there would be 3 so then is it 3x3?
stone mountain
You have to place the silvers in such a way that they are diagonal
stone mountain
More formations are possible for this diagonal formation
Like in the first row if you exchange B and G you will get a new formation
covert mortar
OHH
stone mountain
For this , ignore the S and see the number of sets of formations possible for each row
covert mortar
2x2x2?
covert mortar
what if the S is on the other diagonal?
covert mortar
so would it be 8/216 or 16/216?
stone mountain
You will have to add those formations to these
covert mortar
so 8/216 + 8/216?
which is 2/27
would that be correct because the person who made the question said it was 1/27
but a lot of people got 2/27
stone mountain
Yeah I think so ,it's an error in the answer probably
1/27 will be only if you count the probability for one diagonal
For both it will be 2/27
As there can be 2 diagonals
covert mortar
yeah okay thank you so much
odd edgeBOT
Available help channel!
elder vault
odd edgeBOT
elder vault
I have couple questions about the equation
first, is it true?
second, is it able to consider it metaphorically? and how?
late pawn
well when your taking the absolute value of a+b, what if b is negative,
plug in 1 for a and -1 for b, see where that gets you
they cover some of the proofs better than I could
elder vault
well when your taking the absolute value of a+b, what if b is negative,
im trying to apply the mechanism of "forces" to explaining this equation
like two forces in real life
for these two forces n and s went for diffrent directions
late pawn
well forces have direction and magnitude so you can represent them as vectors right? if you think about the triangles that they show in the stackexchange as 2 vectors instead
elder vault
well forces have direction and magnitude so you can represent them as vectors r...
I see
given Z are complex number
viral frost
This is the same.
elder vault
This is the same.
Do you mean i can consider Z1 and Z2 as two vectors
on the complex plane?
late pawn
whats the problem asking?
viral frost
Do you mean i can consider Z1 and Z2 as two vectors
Yes, you can.
You can consider them to be vectors with 2 dimensions.
elder vault
whats the problem asking?
I want to prove the equation by considering Z1,Z2 as vectors
late pawn
elder vault
im now having a confusion sit in my mind
IF two vectors, in a plane, was in the same quadrant then the two sides are equivalent, I suppose?
elder vault
im now having a confusion sit in my mind
IF two vectors, in a plane, was in the...
is it correct?
late pawn
well it shouldnt matter if they are in the same quadrent, as magnitude is magnitude no matter what
elder vault
well it shouldnt matter if they are in the same quadrent, as magnitude is magnit...
but if they aren't in the same quadrent then |the sum of vector A and vector B| would definitely be smaller than |vectorA| + |vectorB|
elder vault
that is when the right is bigger than the left
elder vault
I wonder when will the two sides be equivalent?
late pawn
they should only be equivalent when the vectors are pointing in the same direction
sorry its late for me
odd edgeBOT
@elder vault Has your question been resolved?
jade pagoda
is this valid?
If all F, then not L.
Therefore, If some not F, then some L.
south plume
proven summit
is this valid?
If all F, then not L.
Therefore, If some not F, then some L.
Maybe, may not be it's not certain
jade pagoda
Maybe, may not be it's not certain
right so it's invalid because some not F may not L
.close
cyan dragon
Can anyone like know a fast way to answer this
odd edgeBOT
Can anyone like know a fast way to answer this
cyan dragon
<@&286206848099549185> need welp
odd edgeBOT
@cyan dragon Has your question been resolved?
lament walrus
d?
cyan dragon
a, c
wind yew
isnt it b, since the only 2 numbers it doesnt cover are 0 and 1, any number in between can be gotten just by increasing n, just say any random number, if n is increased enough, it is in between them
cyan dragon
isnt it b, since the only 2 numbers it doesnt cover are 0 and 1, any number in b...
True but not finite, take c for example at n = 50 it becomes (1,0) = (0,1) or take n=200, (0,1) again
cyan dragon
Can anyone like know a fast way to answer this
Oh lol, you just have to see it in btw and it will solve immediately
.close
strong elbow
Thanks @cold urchin
odd edgeBOT
Thanks <@607479321350635520>
clever fjordBOT
Sam.
cold urchin
strong elbow
You helped me with a question last night and i read it this morning
odd edgeBOT
odd edgeBOT
Available help channel!
frozen ore
Isnt the solution for a) incorrect?
odd edgeBOT
Isnt the solution for a) incorrect?
frozen ore
The didnt multiplied 4/5 with 15
white basin
Isnt the solution for a) incorrect?
Yes their solution is wrong
frozen ore
So you were supposed to multiply 4/5 with 15?
white basin
Yes and get -12
odd edgeBOT
odd edgeBOT
Available help channel!
idle aspen
hi
mystic saffron
Can you?
idle aspen
yes
mystic saffron
Prove it
mystic saffron
It’s already asked
idle aspen
yes i m ready bro
mystic saffron
Just look in the help channels
idle aspen
just give me the question
mystic saffron
just give me the question
How can I check the convergence for $\int_{1}^{\infty} \frac{\sin(x)}{\sqrt{x}}, dx$
clever fjordBOT
Şêro
mystic saffron
?
idle aspen
IMPOSY
idle aspen
OK JUST WHAIT£
odd edgeBOT
@idle aspen Has your question been resolved?
thorny otter
What is meant here by “in the domain”
odd edgeBOT
What is meant here by “in the domain”
leaden widget
you know what a domain is right?
thorny otter
Yes
glass wedge
Just means a point in the domain of the functions
Not a point where one of them is not defined
thorny otter
But would a regular singular point be in the domain of a function ?
thorny otter
Not a point where one of them is not defined
Okay so by that a regular singular point would not be a part of the domain
glass wedge
I dont see what you mean
Of course a function is defined in a point
Is y=x defined in the point x0=2
leaden widget
i guess an element in the set of the domain is just the x part, the abscissa not a whole point (x,y), if that is the point (pun intended) you are trying to make
thorny otter
Let’s say, For a series solution about X=0 where we can prove x=0 is a regular singular point, would we exclude this point from the domain we are speaking about here ?
Maybe I’m not phrasing my question correctly sorry
leaden widget
still confused by what exactly you are asking, but I do think they shouldn't be saying "for some point x_0 in the domain." the domain is not a set of points if they're talking about a single variable function. they should just say "for some x_0 in the domain" i guess
thorny otter
Let me try add more context
So here, we are asked to find two independent solutions which I find to be x and x^(1/3). But the Wronskian of these will be 0 for x=0. What I’m wondering is as I have proved that x=0 is a singular point, can I exclude from the domain we are looking in the wronskian
@leaden widget hope that makes more sense
Thus proving the solutions would be linearly independent
leaden widget
<@218476117101772801> hope that makes more sense
sorry I don't have a clue
thorny otter
No worries, I appreciate your time though!
odd edgeBOT
@thorny otter Has your question been resolved?
odd edgeBOT
@thorny otter Has your question been resolved?
odd edgeBOT
@thorny otter Has your question been resolved?
odd edgeBOT
thorny otter
.reopen
odd edgeBOT
✅
thorny otter
<@&286206848099549185> Could anyone confirm or have any input to my post above? Thanks!
tall veldt
x0 is just a point for which the wronskian is defined
thorny otter
Yes where x0 is part of the Domain of the function
would 0 be excluded from the domain of my ode though as X=0 is a singular point ?
tall veldt
If your f or g aren't differentiable at 0 then yes you would exclude it as you can't define the wronskian at 0
thorny otter
So the solutions I got from the above ODE by the series method were X and X^{1/3}, excuse my hand writing but here is a quick calculation for the wronskian, if it was for any X, then we would get a wronskian = 0 for X = 0 which would mean my solutions were not linearly independent, but I am trying to prove they are linearly independent. Which is why when the ODE is in its general form we get a singularity at X=0 due to P(x) and Q(x) being undefiend for this value of X
@tall veldt Due to the above, can I make the statement that the wronskain is !=0 for any X != 0, thus proving my solutions are linearly independent?
tall veldt
You only need to find one point that makes the wronskian non zero to conclude they are independent
That's what your theorem says
It does not say that if you find a point that makes the wronskian zero then the functions are dependent
thorny otter
oh wait, I may have tagged the wrong image
I beleive this proposition reflects what I am working with.
tall veldt
You want to use proposition 1
If you are trying to show they are independent
Prop 2 is not an if and only if, its just a test for dependence
thorny otter
But f and g are solutions to the ode that I am using in the wronskian
shouldnt I still be able to show independance by here by being able to say that for any point in the domain they are non zero
tall veldt
Okay but prop 2 will never tell you if two functions are independent
tall veldt
shouldnt I still be able to show independance by here by being able to say that ...
This would be using prop 1
tall veldt
You found a point that makes the wronskian non zero
(Infinitely many in fact but you only needed one)
thorny otter
that point just happen to be any point !=0
tall veldt
Yes
thorny otter
(Infinitely many in fact but you only needed one)
Yes!
So I am okay to label f and g as f(x) = x and g(x) = x^1/3 and say that their W(x) is !=0 for x=1, as a conclusion
tall veldt
Yeah
cursive bridge
how to solver log with zecimals? like log base3 0,(3)
royal herald
$\log_3 {0.3}$
clever fjordBOT
Stephen
royal herald
Wdym by solve @cursive bridge
tall veldt
0.333333.... ?
clever fjordBOT
pilot_raul
odd edgeBOT
@cursive bridge Has your question been resolved?
odd edgeBOT
@cursive bridge Has your question been resolved?
charred shadow
Hello
charred shadow
Can I assume that this is a valid contradiction?
Saying if alpha sup S is not the least upper bound for alpha S then sup S is not the least upper bound for S
because each element in alpha S is of some form alpha x
or should i make that more explicit in my proof?
odd edgeBOT
@charred shadow Has your question been resolved?
charred shadow
can anyone give me any guidance?
odd edgeBOT
@charred shadow Has your question been resolved?
ripe plinth
odd edgeBOT
ripe plinth
I want help with part b but I put part a for reference
in part a i found out k was = to 25/8
dim sandal
,rotate
clever fjordBOT
stiff pewter
In python what does a^b do?
odd edgeBOT
In python what does a^b do?
stiff pewter
Figured this was basic enough computation question
Google says bitewise exclusive or
lavish osprey
^ is a bitwise operator
honest violet
where do I even start
lavish osprey
it takes the binary representation of a and b and it runs an exclusive or operator on them
lavish osprey
where do I even start
#❓how-to-get-help , channel is occupied
stiff pewter
it takes the binary representation of a and b and it runs an exclusive or operat...
Got it cheers!
lavish osprey
yep np!
stiff pewter
.close
odd edgeBOT
lavish osprey
Got it cheers!
if you're ever interested in learning more about them, they're extremely fast operations! They also help with bit masking n' whatnot. For example you can have a function that returns all lowercase letters by bitwise OR'ing your 32 bit character with a binary value
super cool stuff
stiff pewter
if you're ever interested in learning more about them, they're extremely fast op...
I’m just 2 weeks into my python course at uni so I think we’ll get there eventually 😅
lavish osprey
I’m just 2 weeks into my python course at uni so I think we’ll get there eventua...
Have fun! super fun class
odd edgeBOT
Available help channel!
limber cloak
Let R, r ∈ ℝ with R > r > 0. Consider the circle with center (R, 0, 0) and radius r in the xz-plane, and rotate it around the z-axis. This results in the so-called torus T = {(x, y, z) ∈ ℝ³ : (R² − r² + z²)² + (x² + y²)² + 2(x² + y²)(z² − (R² + r²)) = 0}.
stone cipher
what's the question
limber cloak
I need to show that the equation is 0
By using the sphere coordinstes i guess. The are something like
Wsit
stone cipher
??
limber cloak
X=R+rcos(psi)*cos(theta)
Do i just brute force it by replacing c y and z
Bc that gets pretty complicated and maybe theres a trick
| (R + r * cos(ψ)) * cos(φ) |
| (R + r * cos(ψ)) * sin(φ) |
| r * sin(ψ) |
I have no idea how to format this
These sre the spherical coordinstes for s torus
Now if i wsnt to show that the above equation is 0 i could probably replace the x y and z by the spherical coordinates. That would get very ugly tho and i dont think that thats the best way
Well i guess im gonna try to brutefroce this.
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
find extrema of f=x^2 + y^2 + z^2 but 2xy + z^2 = 5
odd edgeBOT
find extrema of f=x^2 + y^2 + z^2 but 2xy + z^2 = 5
mystic saffron
my argument was that bc f was constant at the constraint, there are no extrema
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
stone cipher
my argument was that bc f was constant at the constraint, there are no extrema
doesn't sound right
it's not constant all along the constraint surely
i mean the way you're meant to do it is obviously gonna be
$x^2 + y^2 + z^2 = x^2 + y^2 + 5 - 2xy$
clever fjordBOT
Kaisheng21
stone cipher
and then this definitely has extrema
mystic saffron
So would extreme be (t,t,sqrt(5-2t^2))?
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
@mystic saffron Has your question been resolved?
green ledge
@mighty oasis probably better to ask this in physics discord
mighty oasis
<@713848660714192896> probably better to ask this in physics discord
okay thanks
odd edgeBOT
odd edgeBOT
Available help channel!
west zenith
Little brothers math homework
odd edgeBOT
Little brothers math homework
west zenith
<@&286206848099549185>
ionic heart
What's the issue
Surface area is basically sum of areas of all the faces in the figure
west zenith
Surface area is basically sum of areas of all the faces in the figure
ill ask him
he said that he needs the total surface area so that shpuld mean every face added up
ionic heart
If you have a cuboid, then surface area is the sum of the 4 rectangular faces and the 2 square faces
yeah
west zenith
i cant explain it cause i kind of forgot this
west zenith
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
only who is serious about math can come here
odd edgeBOT
only who is serious about math can come here
viral frost
Tried anything yet?
stone mountain
Use the formula of (a+b)²
olive ferry
Could someone help me with this question? I am familiar with the 'matrix' definition of positive semidefinite where for all vectors v, v^t M v >= 0 but i am not sure about the kernel function.
odd edgeBOT
Could someone help me with this question? I am familiar with the 'matrix' defini...
@olive ferry Has your question been resolved?
olive ferry
<@&286206848099549185>
odd edgeBOT
@olive ferry Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
How tf did that step happened????
We have to do quadratic approximation
nimble blaze
$H(x) = (1-x)^{-1} = \red{-}(x-1)^{-1}$
clever fjordBOT
ℝαμΩℕωⅤ
mystic saffron
you'd get something equivalent
I got the answer as 1-x+x^2
The correct answer given is 1+x+x^2
nimble blaze
show your work
mystic saffron
nimble blaze
your derivative is wrong
mystic saffron
your derivative is wrong
I know
nimble blaze
you didn't apply chain rule
mystic saffron
you didn't apply chain rule
I know
I used the exact same thing and I got the answers for (a), (b) and (c)
Correct answers
Why here then?
mystic saffron
nimble blaze
,rcw
clever fjordBOT
mystic saffron
nimble blaze
,rcw
clever fjordBOT
nimble blaze
show your thought process for differentiating
$$(1-x)^{-1}$$
clever fjordBOT
ℝαμΩℕωⅤ
nimble blaze
you didn't apply chain rule
to which you replied "i know"
that's why you're getting the wrong result
mystic saffron
Using chain rule is should be
(1-x)^-2
nimble blaze
yes
mystic saffron
that's why you're getting the wrong result
But why apply chain rule here
And not in a b and c
nimble blaze
chain rule isn't optional
mystic saffron
Exactly
Wait I think I got my mistake
It's FUCKING (1+x)
It's K
OMG
WHAT AM IDIOT I AM
The chain rule derivative of of both of them should be 1
AHHHHH
THAT EHY I DID WRONG STUFF AND GOT THE RIGHT ANSWER
I am right right?
odd edgeBOT
@mystic saffron Has your question been resolved?
remote token
odd edgeBOT
remote token
No additional context given.
glass wedge
How can there be no context
Where is this from
Is it an assignment
A problem in a textbook
remote token
Where is this from
Reddit.
glass wedge
This is like me posting "2 4 7 1" and saying theres no context
remote token
But I assume it is some sort of pattern.
glass wedge
Its unsolvable without context
Its not a pascal triange esque thing i guess because its not a triangle
remote token
It’s just a pattern I have to find, no?
From the top and up probably, since the numbers generally get bigger add they approach the top.
glass wedge
not really since you have a 1/6 in the bottom and 2nd to top
sick sigil
odd edgeBOT
sick sigil
Where did this term appear from?
So context; the video is about partial antiderivatives
glass wedge
integration by parts of 2te^tdt
hard field
Where did this term appear from?
the rhs of the equation above simplifies to that,
sick sigil
Uhhh
But isn’t the right hand side still on the right hand side??
To me it looks that way
hard field
yes
sick sigil
Like if i look at the line above
sick sigil
But doesn’t the - / (-2)e^t become the +2e^t on the line below??
leaden widget
honestly it's mostly confusing because whoever was writing that work did a sub of t = cos x (commonly known as u-sub) and then doing integration by parts at almost same time without writing much work
hard field
But doesn’t the - / (-2)e^t become the +2e^t on the line below??
yes
then they evaluate it on the same line
they have just wrote it in a confusing way
leaden widget
try to rewrite it and write down more of the intermediate steps, i hope this isnt your teacher working stuff on the board cause then they are doing a great job presenting it in a confusing way
sick sigil
If they wrote it in a confusing way could you write What happens between
The line above the one i marked
I was gonna write the equation out but then i remembered that im on my phone😝
leaden widget
so youre familiar with integration by parts right?
or sometimes it's written with f(x), g(x) instead of u, v
sick sigil
uhhhh i am not familiar with that
Like what I’ve learned is
Imma use ”/” for integral btw
/f(x)*g(x) dx = F(x)*g(x) - /F(x)*g’(x) dx
Where F is the antiderivative of f
So it does kind of look the same But..
leaden widget
well if you are not familiar with integration by parts then go watch a lecture on it, not going to teach you that in a chat tbh
glass wedge
/f(x)*g(x) dx = F(x)*g(x) - /F(x)*g’(x) dx
this is integration by parts
sick sigil
But the integration by parts video that our teacher made is literally the thing i wrote :p
That’s why im confused with the thing you sent
glass wedge
its the same thing
leaden widget
here is version with f(x) and g(x) since thats what your teacher is using
sick sigil
Ah Yeah exactly
But the issue is that I just don’t see where the term came from because to me that term is on the right hand side and then out of nowhere it’s moved to the left while still staying on the right
leaden widget
well it also doesn't help they wrote the f(t) and g(t) backwards i think
sick sigil
No it indeed does not
I think the idea is that they want to make it easier BUT its literally the opposite
clever fjordBOT
Soosh
sick sigil
And now i understand What the other person meant
leaden widget
ok, well can you follow along for a sec, ill work it through step by step
sick sigil
Is he not just doing the right hand side only on that line for no reason at all😭
leaden widget
so you see now we have
$\int-2te^t,dt =\int f(t)g'(t)$
sick sigil
and yes i will🥺❤️❤️
clever fjordBOT
Soosh
leaden widget
right?
sick sigil
Sure
leaden widget
ok now we integrate g' to get g, and its just $g=e^t$
clever fjordBOT
Soosh
sick sigil
Yes
leaden widget
so now using the integration by parts we can rewrite the integral with the formula:
$\int f(t)g'(t) = f(t)g(t) -\int g(t)f'(t)$
clever fjordBOT
Soosh
leaden widget
the left side is just what we start with so we get:
oh and f' = -2dt since we are just getting the differential of f = -2t
so we have
$\int -2te^t,dt= (-2t)(e^t) - \int (e^t)(-2,dt)$
clever fjordBOT
Soosh
leaden widget
i wrote each of the quantities in parenthesis we are substituting for clarity
sick sigil
Thank you🥹
leaden widget
plz check my work that i am not making mistakes \ following so far?
sick sigil
I do not believe so
leaden widget
ok so now we pretty much get what the underlined part in red is in your original question, your teacher just skipped various steps like multiplying the negative sign, didnt even show work for integrating g' and taking derivative of f on the side, which is just horrible way to teach partial derivatives for the first time to someone
sick sigil
But i will definitely put more time into this to get a better understanding
With that said
Partial functions
Anti derivatives
Integrals
leaden widget
$\int -2te^t,dt = -2te^t +2\int e^t,dt$
clever fjordBOT
Soosh
leaden widget
so see we got exactly this
sick sigil
Are these different words that mean the same thing or am i in the wrong there?
leaden widget
kind of...
well computing the anti derivative is defined as the basically the reverse operation of computing the derivative
computing integrals is defined as calculating the area under a curve using riemann sums
it TURNS OUT AFTER defining them in this way that basically you CAN use antiderivatives to calculate integrals and they are basically equivalent, but this is not obvious at first since you start defining them in completely different ways
the idea that integrals are essentially equivalent to antiderivatives is what is being said in the fundamental theorems of calculus
'
sick sigil
Got it. That’s one of the things that really confused me as well during the lectures
Thank you so much for the help
Wish you the best of days!!❤️❤️
leaden widget
thanks, you as well : )
sick sigil
.close
leaden widget
!done
odd edgeBOT
If you are done with this channel, please mark your problem as solved by typing .close
Available help channel!
supple crater
odd edgeBOT
cold sage
are you trying to solve it?
supple crater
Yes
supple crater
Now it is 9*2^x-4^x=8
Now what
I get it
No i didnt get it
Guide me further
.close
naive yarrow
hi i need help with integral stuff
odd edgeBOT
hi i need help with integral stuff
mystic saffron
Sorry
golden vale
what about 0^0?
1
naive yarrow
zenith tartan
its undefined too
zenith tartan
!da2a
odd edgeBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
summer cradle
0^0 = 1
naive yarrow
The integralgraph, the tangent in P(-2,f(-2)) and the y axis makes a group of points and i need to calculate the exact area of it
so i need to calculate the area highlighted here... so its area under graph from x=-2 to x=0, but its also only from y=1 and up till the graph hits the yaxis in (0,26.56)
waittttt
the tangent
so its a triangle
i made wrong depiction of area i think
forest sky
generally if you have an area that's bounded above by f(x) and below by g(x), then the total area is given by integral of (f(x) - g(x))
naive yarrow
yeeee
i think i read task wrong
lemme try plot the graph again
so the tangent in point (-2,f(-2)) is x+3 so i think the area i need to calculate is the one below the blue line?? or the one above?
so this area
where the blue line is tangent line
and the green is integral curve
where f(x) is integral curve and g(x) is tangent?
i think thats correct
if anyone can confirm?? 😦
xdxdxd
who emoted
🤓
seems correct ill just hope it is and pray
.close
odd edgeBOT
odd edgeBOT
Available help channel!
unkempt ice
hello. ive been stuck here for a while because im not sure with my answer. this was sort of not properly discussed by my prof. is this a function or not? why?
desert vector
yes y is a function of x
because for every value of x there is exactly one value of y
unkempt ice
so my answer is correct? :DD
craggy leaf
odd edgeBOT
craggy leaf
can someone help me on this please?
this is a optimization problem for calc 1
i was just having a difficult time
on uhm understanding the C point, and how i could use it to find the greatest arrea
any help would be much appreciated! thanks in advancce
livid storm
!status
odd edgeBOT
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,
livid storm
You know how to find the sides in function of C? (x and y)
Its on the image
even
A(x,y) = x*y
craggy leaf
ye.
livid storm
You can turn A(x,y) into a one variable function
craggy leaf
ooooh thats write thats write
so like y= -2/3x+17/3
right?
and i can plug that into another formula?
livid storm
where did the 17 come from
livid storm
why -2/3?
livid storm
good
livid storm
and i can plug that into another formula?
yes
craggy leaf
can i plug it into the formula for a area of a rectangle?
livid storm
yes
wind yew
just plug it in x*y
craggy leaf
hmm..... but honestly
ye i was thinking of doing that at first
but what was tripping me up
was like how do i know if its like the max
wind yew
do you know how to find the max/min of a square function
livid storm
was like how do i know if its like the max
You have the area in function of x
a single variable function
You know how to maximize / minimize these
craggy leaf
hmm......
wind yew
you already have the function for the area, after substituting y
then you get a square function for the area
in terms of x
after you get that function, do you know how to find the min or max of it?
craggy leaf
i found the derivaitve of the function that was in terms of x
and made it =0
and found x
livid storm
good
livid storm
Write A(x) instead of A
Write A'(x), then write A'(x) = 0
It's not clear what you did on step 3
I know you did that, but assume your reader doesn't
craggy leaf
oooo okay okay i fixed that
thanks
and then i can plug x back into the equation?
to find y?
livid storm
Yes
craggy leaf
hmm.. but like
how do i know thats the max value?
cuz i did the derivative twice
and the second derivative was a -
OH
that means its the max
ooooo okay okay
i think i got it
livid storm
Yeah
odd edgeBOT
odd edgeBOT
Available help channel!
vital rivet
I need quick help understanding what this question means when it says units. Does it mean what the x and y are (minutes, calories) or does it mean the parts of the calculation for the constant rate?
vital rivet
I'm just a little lost as to what it means tbh. I understand the rest of it. Does it mean the ratio between changes?
wind yew
rate of change is like speed to distance, meaning that you go x meters for y seconds, the unit would be m/s
so if you lose calories for a certain amount of minutes the unit for the ratio would be?
vital rivet
m/c (minutes/calories) correct?
wind yew
you dont burn minutes but calories, the thing that changes is above, and the thing that causes the change is below
so you dont say i burn 5 minutes for every calorie, but you say...
vital rivet
Ok yeah, makes sense. I got it mixed up a bit cause you have your x as the dependent and the y and the independent and I have it the other way around.
This was how I got it lol
So yeah it would be
c/m or calories over minutes since you burn so many calories per minute.
wind yew
yep
vital rivet
Awesome thanks for the help with that. I was just missing that cause we barely focused on that in class so I forgot about worrying about what the full unit is.
.close
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
i need help with my ixl problem
odd edgeBOT
i need help with my ixl problem
median cedar
how we suppose to help if u don't post the question 🤦♂️
cold sage
how so?
cold sage
you trying to send an image?
median cedar
do you have a stable internet
median cedar
type out the question then
mystic saffron
ok
Emily tried to evaluate an expression. Here is her work:
24+(11+13)–(1+5)÷23
24+24–6÷23 Step 1
16+24–6÷23 Step 2
16+24–33 Step 3
16+24–9 Step 4
40–9 Step 5
31 Step 6
Is Emily's work correct?
thats the question
then the asnwers are like
idk the answers
..
median cedar
in step two how did 24+24 change into 16+24
mystic saffron
uh idk
worthy raptor
How did -6÷23 turn into -33
mystic saffron
IDK BRO ITS IXL
worthy raptor
so it isnt correct??
Id hope not
cold sage
emily was high when they wrote that
mystic saffron
bru its ixl this shit is ass
cold sage
probably say theyre wrong and why
raw palm
idk how emily survived till now tbh
raw palm
young sedge
odd edgeBOT
young sedge
how do i find the equation of the asymptote
dense sonnet
what value does f(x) never touch/reach
stone cipher
do you know what an asymptote is
young sedge
i know what a vertical and horizontal asymptote is
young sedge
ik you find the va by setting the denominator equal to 0 and ha by comparing the degree of the num with the denom
young sedge
no
stone cipher
horizontal asymptote at y = 5
horizontal asymptotes at y = pi/2, y = -pi/2
horizontal asymptote at y = 1
vertical asymptote at x = -3
vertical asymptote at x = 2
young sedge
looks like it's 0
stone cipher
no asymptotes
stone cipher
looks like it's 0
right
stone cipher
oh, you have to prove it?
stone cipher
i mean the easiest way to do it is definitely with the graph but ok ok ok
so essentially what is an asymptote in words, well
young sedge
this isnt like x+2/x-2 this is with an exponent subtracting something
which is why i dont know what to do
stone cipher
a horizontal asymptote at infinity is when, as x gets closer and closer to infinity, the function gets closer and closer to something
arbitrarily close
and similarly a horizontal asymptote at -infinity is when, as x gets closer and closer to -infinity, more and more left, the function gets closer and closer to something
so in this case there's a horizontal asymptote at 0
as x -> -infinity
so you want to show that e^(x-4) gets arbitrarily close to 0 as x goes to -infinity
but it's like
it just does
like, e^x when x is really large and negative is just really close to 0
young sedge
okay well what if we had 5^(x-2) for example
stone cipher
right so basically all exponential things will get closer and closer to 0 in the same way
it's just like
young sedge
it just is 0
stone cipher
you can sorta see a pattern
young sedge
well i understand that it's a shift
stone cipher
i mean i can prove that e^x goes to 0 as x goes to -inf if you want
if you're not satisfied
young sedge
well this is pre-calc but am i supposed to find the asymptote just by looking at the graph?
stone cipher
yes
young sedge
what if my asymptote was fractional
stone cipher
at this level you're just supposed to go 'yeah the graph basically looks like that'
'it's gotta be true'
and not worry too much about proving it
stone cipher
what if my asymptote was fractional
wdym
young sedge
it just looks like its really close to 0
hm okay i guess im asking if there's a way to find the asymptote the same way we would do with (x+3)/(x-1)
like do we flip anything or invert anything
with e^(x-4)
stone cipher
not exactly
you just sorta go
'e^x goes to 0 when x is negative and very large'
'so e^(x-4) does as well'
young sedge
damn i just have to hope im right i guess?
stone cipher
yeah i mean
you gotta trust the graph ig lol idk
i mean again i can just prove that e^x goes to 0 when x is very large and negative, if that would help?
young sedge
is that within pre-calc
stone cipher
sooorta not really
like it's pretty obvious
one way to think about it is
to go 1 unit left with e^x
you have to divide by e
young sedge
someone told me pre-calc is just doing things and calc is explaining why those things are true
stone cipher
so to go to -infinity then you have to keep dividing by e over and over and over
so the thing will always get very small
and close to 0
stone cipher
someone told me pre-calc is just doing things and calc is explaining why those t...
yeah that sounds about right
young sedge
and close to 0
so it just gets infinitely smaller but never 0
stone cipher
yes
torpid ginkgo
odd edgeBOT
torpid ginkgo
But the values of x
stone cipher
like, Z should be less than 1 right
torpid ginkgo
Like I graphed it in demos where z = 2
stone cipher
ok ok
odd edgeBOT
torpid ginkgo
.reopen
odd edgeBOT
✅
odd edgeBOT
odd edgeBOT
Available help channel!
placid fulcrum
odd edgeBOT
placid fulcrum
honestly have like no idea how to do it
ik the formula but idk what half life means
forest sky
a half-life is the time period it takes for half of the element to decay
placid fulcrum
is full life just 2 times it?
placid fulcrum
is the formula Q(t)=Qo(r)^t/T?
cs im not sure how to find the rate with the information given
forest sky
use the fact that by the definition of the half-life, at
t = the half-life, Q = 1/2 * initial mass
odd edgeBOT
@placid fulcrum Has your question been resolved?
empty arrow
2^(1-x)>0
2^1/2^x>0 *(2^x)
2^1>2^x
1>x
which part of this is wrong?? why is this wrong?
cold sage
did you say 0*2^x=2^x?
cold sage
,ti
clever fjordBOT
The current time for aldrnari_ is 02:50 AM (GMT) on Sat, 11/11/2023.
cold sage
standard
odd edgeBOT
@empty arrow Has your question been resolved?
elder inlet
I need help with simple Harmonic motion.
Here's the problem
y=-0.25 cos(1.5t - Pi/3)
i figured out how to do problems where their's usually nothing after t. but now their's this - pi/3 thing after t and i'm lost.
nocturne belfry
its a translated problem
you might try something like... x=1.5t - pi/3
then solve y = -0.5 cos(x)
"solve"
its still not really clear to me exactly what the problem is
so maybe this wont help
i guess yea what do you mean solve 
whats the problem?
elder inlet
the exercise wants me to find the amp, period and frequency of the motion than sketch it.