proper yoke
Let f(x, y, z) = ... and A = (1, 1, −4).
(a) Specify the tangent plane to the level surface f(x, y, z) = 19 at point A.
(b) At what rate of change f′ v (A) does f increase or decrease in the direction (−6, 2, −3) away from the point A?
(c) In what limits does the directional derivative f′v(A) depending on the departure direction v away from A?
final saddleBOT
Let f(x, y, z) = ... and A = (1, 1, −4).
(a) Specify the tangent plane to the le...
final saddleBOT
@proper yoke Has your question been resolved?
final saddleBOT
@proper yoke Has your question been resolved?
soft zealotBOT
𝔸dωn𝓲²s
proper yoke
Hmm okay what does that mean do I put in A=(1,1,-4)?
drowsy epoch
I think the left is the same as mine
If you do the dot product with the gradient and x-a, y-b, z-c etc
And f(a,b) is my f(A)
I just didnt bother to write f(x_A,y_A,z_A) = f(A) every time
proper yoke
Okay so f(1,1,-4) • (x -1, y-1, z-(-4))?
drowsy epoch
It's the same as in yours but one dimension higher
proper yoke
Yea but I don’t know how to make that symbol
soft zealotBOT
𝔸dωn𝓲²s
drowsy epoch
It's your partial derivatives in column vector form
If you do the dot product you get the same what I wrote above
proper yoke
Okay w = fx(A)(x-1) + fy(A)(y-1) + fz(A)(z—4) + f(A)?
drowsy epoch
yes
proper yoke
Okay do I solve something out now?
drowsy epoch
f(A) = 19 btw
you nees the partial derivatives, plug A into them and thats it for a)
f_x(A) = f_x(1,1,-4) = ?
And the sams for the others
proper yoke
Wait I’m confused do I plug in 19 on all the f(A)s?
drowsy epoch
There is only one..
The others are again point A plugged in to the partial derivatives
drowsy epoch
f_x(A) = f_x(1,1,-4) = ?
And the sams for the others
I cant make it more obv
final saddleBOT
@proper yoke Has your question been resolved?
final saddleBOT
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gaunt condor
radius of the circle?
final saddleBOT
radius of the circle?
final saddleBOT
@gaunt condor Has your question been resolved?
gaunt condor
is that the full question
yes
gaunt condor
its wrong
nova coral
then you can apply the formula
gaunt condor
you cannot add 12+9
its not parallel
limber sundial
i found this on internet:https://www.tiktok.com/@rashmi0653/video/7306473214828399905
final saddleBOT
gleaming bluff
How do i find the area of a parabola can someone explain and give an example
gray acorn
How do i find the area of a parabola can someone explain and give an example
Are you familiar with integration
final saddleBOT
@gleaming bluff Has your question been resolved?
bright current
I know these types of questions are easy but I get confused
final saddleBOT
I know these types of questions are easy but I get confused
bright current
I found one of the points by plugging in 0
Aand I got (0,-1)
Not 0
-2
.close
final saddleBOT
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tranquil charm
how can i find uncertainty of Q when
final saddleBOT
how can i find uncertainty of Q when
tranquil charm
$Q=\int_{t_a}^{t_b}-k \left(\left(-12,07e^{-0,0106t}+16,34 \right)-T\right)dt$
soft zealotBOT
Slowaq
tranquil charm
i know boudaries of definite integral
k and T are constants
and i know uncertainty of T
final saddleBOT
@tranquil charm Has your question been resolved?
magic ether
can someone tell me what is a equivalence error in discrete math
final saddleBOT
can someone tell me what is a equivalence error in discrete math
magic ether
i asked for help in this problem earlier and the person corrected it and told me i need to add equivalence errors in each line
mental roost
he probably means:
soft zealotBOT
Martin
mental roost
this is the sign of an equivalence
meaning that two statements are equivalent to each other
one could argue that on your paper, you just have a list of statements
if you have a set of statements, you could do it like this:
statement 1
<=> statement 2
<=> statment 3
this would imply that all 3 statements are equivalent
as in, they mean the same thing
so it's pretty much just an equation but with statements
lyric lichen
what gives this equation no real numbers?
final saddleBOT
what gives this equation no real numbers?
proud plover
its domain is from -inf to inf
lyric lichen
Im not sure what that means
proud plover
the quadratic function has a domain of all real numbers
lyric lichen
why is it (-in,in)
proud plover
do u know what a quadratic looks like
lyric lichen
I don't know what you mean
lyric lichen
to find a domain don't I factor
proud plover
that is because there is a quadratic in the denominator
lyric lichen
okay
lyric lichen
making it a domanin
so not having the top makes it not a real number
therefore (-inf,inf) ??
.close
final saddleBOT
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stark apex
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tulip coyote
Degrees mode - what do you get when you inverse tan that 1.144...?
stark apex
I was supposed to inverse it this whole time!?!?
wait how do i know when to inverse it ?
white night
use inverse tan function on your calculator
stark apex
ok
tulip coyote
wait how do i know when to inverse it ?
and because you want to get rid of the tan to get theta by itself, so applying the inverse tan gets rid of that for you
stark apex
ohhh
final saddleBOT
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plucky scaffold
final saddleBOT
plucky scaffold
i think 3 is wrong
which?
sturdy cypress
also 10 is wrong
kinda
if you start at 2 or 3, that's a different cycle from the other numbers
plucky scaffold
if you start at 2 or 3, that's a different cycle from the other numbers
agreed
final saddleBOT
@plucky scaffold Has your question been resolved?
unique estuary
final saddleBOT
ivory vessel
what was that? i didnt see his deleted msg
rare halo
what happens when u multply dem and num with the (1-root(3))
rare halo
what was that? i didnt see his deleted msg
he insta pinged helper and deleted
ivory vessel
unique estuary
rationalise the denominator by multiplying by the conjugate
i realise now my mistake isn't not knowing how to do it but in my working 😭
rare halo
oops
soft zealotBOT
_basudev
rare halo
now expand 
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wanton crypt
how do you find the missing length on a triangle with the hypotenuse and leg only
final saddleBOT
how do you find the missing length on a triangle with the hypotenuse and leg onl...
ivory vessel
right triangle, use Pythagorean
normal triangle, only when you also know the angle of two known sides
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tranquil pine
how would you differentiate this? We just learned about power rule, constant multiple rule, product rule, chain rule for powers of polynomials, sum and difference rule. I'm still very confused so I would appreciate any help on this question.
final saddleBOT
how would you differentiate this? We just learned about power rule, constant mul...
tranquil pine
bro I'm so cooked if I keep solving this question
tranquil pine
how would you differentiate this? We just learned about power rule, constant mul...
<@&286206848099549185>
final saddleBOT
@tranquil pine Has your question been resolved?
barren bay
I mean, if you haven't learned the quotient rule, you can rewrite the question as 1500(1 + 5t(t^2+30)^-1)
That way you can just use product rule and chain rule
tranquil pine
This is where I’m stuck
I kept going in circles like this. I don’t even know where I did wrong.
my brain is fried at this point lmao
barren bay
Lol, it's kinda awkward to type, gimme a second to look at this
Looks like you're right, just make sure to multiply by 1500 at the end still
If you want to check it in the future, the derivative of a fraction f(x)/g(x) is just (f'(x)g(x) - f(x)g'(x))/(g(x)^2)
tranquil pine
oh ok, thank you so much. We didn't learn about quotient rule yet so I'll keep that in mind.
barren bay
Yeah, I got a final derivative of 7500(30-t^2)/(t^2+30)^2 through both methods
tranquil pine
Yeah, I got a final derivative of 7500(30-t^2)/(t^2+30)^2 through both methods
ohhh, do you mind showing how you did that?
I haven't arrived at a final answer yet
barren bay
sure
your answer at the bottom right is correct, you just need to simplify and multiply by the 1500 from the original prompt
1500(f'(x)g(x) - f(x)g'(x))/g(x)^2
(7500(t^2 + 30) - 7500t(2t))/(t^2+30)^2
7500(t^2 + 30 - 2t^2)/(t^2 + 30)^2
7500(30 - t^2)/(t^2 + 30)^2
Jeez, that's kinda ugly to type lmao
tranquil pine
thanks a lot bro. It's a lot of work so I appreciate the help.
barren bay
Nah, I'm just surprised they didn't teach quotient before chain since it's just a formula
barren bay
Yikes, not even any proofs lol
tranquil pine
I mean this is just a summary of all the rules at the end so
proofs were shown in the beginning
anyways, thanks for the help. I'll close this
.close
final saddleBOT
barren bay
np
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tranquil pine
When we say the initial velocity is 3i + 4j
What does it actually mean
tranquil pine
Kindly represent through a graphing tool like desmos etc
mellow axle
you get a right triangle
x = 3, y = 4
so hypotnuse is 5
and use any inverse trig you like to get the angle
so arcsin(4/5)
so you have a vector having magnitude 5
and the angle of the vector is arcsin(4/5)
that's the velocity vector
you're going 5 units of distance per unit of time initially
and the direction of the distance is given by arcsin(4/5)
tranquil pine
Let's say if initial velocity is (1i + 1j)m/s
Then I would be going with 1 m/s in 45°
Right?
mellow axle
no
what is the magnitude of i+j
it's the sqaure root of 1^2 + 1^2
which is sqrt(2)
so you're going sqrt 2 m/s
in 45 degree = pi/4 radians
tranquil pine
so you're going sqrt 2 m/s
Ohh yeaahhhh
Correct correct, my bad
Cool, and why in some cases velocity and acceleration are at different angles when both are positive?
mellow axle
in general is accerlation and velocity always equal?
tranquil pine
in general is accerlation and velocity always equal?
Obviously no
mellow axle
so we shouldn't expect how they're represented to be equal as well
i can have a very small acceleration but a very high velocity
tranquil pine
i can have a very small acceleration but a very high velocity
But they should be at equal angles no?
mellow axle
nop, take for example in the real line
if i have an acceleration of 1
my veloctiry should be increasing right?
say my instantaneous velocity is -1 though
so im travelling to the left right now
but if i don't change my acceleration, i will slow down going left, stop completely, then begin travelling to the right
tranquil pine
Didn't get, plz explain
mellow axle
are you familiar with derivatives
tranquil pine
if i have a(x) = x then v(x) = x^2 right
No
mellow axle
x^2 /2
tranquil pine
If v(x) is x^2 then a(x) would be 2x
mellow axle
let's say that im initially going v(0) = -1
tranquil pine
let's say that im initially going v(0) = -1
How?
mellow axle
wdym how
soft zealotBOT
chebyshev's infinite pee norm
mellow axle
what is the acceleration and velocities at time x = 1/2?
tranquil pine
what is the acceleration and velocities at time x = 1/2?
V = -7/8
And a = 1/2?
mellow axle
yes
so the velocity is going in the negative direction
so it has angle -pi
on the real number line
and acceleration is going in the positive direction
so it has angle pi on the real nubmer line
tranquil pine
so the velocity is going in the negative direction
So i can say velocity is (-7/8)i + 0j
But how does it have -pi angle
It's +pi no?
tranquil pine
and acceleration is going in the positive direction
Yep so basically acceleration is (1/2)I +0j
So 0° with positive x axis
How +pi degree?
@mellow axle
tranquil pine
oh sorry
Oh thanks..
But because acceleration is positive, so as time passes
They both will have 0 degrees no?
@mellow axle last question
What exactly is unit vector
Like unit vector of 3i + 4j is 3/5i + 4/5j
But what does it mean
<@&286206848099549185>
final saddleBOT
@tranquil pine Has your question been resolved?
steep tendon
<@162769487765045248> last question
What exactly is unit vector
Like unit vector...
the hypotenuse is 1
the parallel vector from origin to the unit circle
tranquil pine
the hypotenuse is 1
Oooooooo
Big brain big brain
tranquil pine
nah thats just uh i know what it means
It makes sense tho...
gleaming bluff
how do i find the domain of $$f(x) = \frac{1}{\sqrt{4-2x-x^2}}$$
final saddleBOT
how do i find the domain of $$f(x) = \frac{1}{\sqrt{4-2x-x^2}}$$
soft zealotBOT
ghiolimer
gleaming bluff
idk where to start
spare glacier
Factor the denominator
The roots of that polynomial is part of the bounds of the domain
tranquil pine
The denominator can not be 0 and the stuff inside sqrt must be positive
Or in other words Domain can be a subset of 4-2x-x²>0
final saddleBOT
@gleaming bluff Has your question been resolved?
upper silo
this is a question on hypothesis testing
final saddleBOT
this is a question on hypothesis testing
upper silo
I have gotten to $\bar X $~$ N(65, \frac{9^2}{35})$
soft zealotBOT
sealpup321
upper silo
i cant put squiggly T-T
static plinth
what are you stuck on exactly?
upper silo
what are you stuck on exactly?
I dont know where to go from here I am doing 1.a.
upper silo
null is $\mu = 65$
soft zealotBOT
sealpup321
static plinth
yep
upper silo
alternative is $\mu < 65$
soft zealotBOT
sealpup321
static plinth
yep that’s correct
upper silo
great 🙂
static plinth
also by any chance, do you have to check the conditions or no
upper silo
what do you mean?
static plinth
to perform a one sample z test, we have to make sure that our sample is random and that the sample size is bigger than 30
upper silo
btw probably wont change much but we get access to smart calculators so you dont need to use the massive data table
upper silo
do i do $P(x <= 61.5)$?
soft zealotBOT
sealpup321
static plinth
on your calculator, do you have an option to do a one sample z test?
upper silo
because if so i got 0.065
static plinth
if you can calculate the probability of a normal distribution, you should be able to do that
upper silo
on your calculator, do you have an option to do a one sample z test?
since i can change the mean and standard deviation I can just change them to 0 and 1 respectively
static plinth
wait what?
upper silo
?
static plinth
can your calculator do a one sample z test or do you have to use normalcdf
upper silo
is that not how you do a sample test
static plinth
your calculator should have an option to do one
and all you have to do is just plug in the numbers and the hypotheses
static plinth
so what did you put in your calculator
upper silo
this is an online version of the calculator i am using
sorry i know its a bit of a hassle but Im unsure of what you mean
static plinth
sorry i know its a bit of a hassle but Im unsure of what you mean
i’m more so asking how did you get the 0.06
upper silo
i’m more so asking how did you get the 0.06
ohhhh I just found out that my calculator takes standard deviation not variance
so thats confusing
static plinth
i see
upper silo
thatll be why
static plinth
alright
final saddleBOT
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tranquil pine
Can someone explain to me the range of a matrix and how can I study a matrix with 1 unknown constant value
final saddleBOT
Can someone explain to me the range of a matrix and how can I study a matrix wit...
tranquil pine
Show that this matrix range is 3
vapid basalt
Show that this matrix range is 3
you need to show that all the column vectors are linearly independent
tranquil pine
you need to show that all the column vectors are linearly independent
If range = 3 means it's the the exact matrix right?
vapid basalt
If range = 3 means it's the the exact matrix right?
No this isn't the range lol
It's the rank
tranquil pine
It's the rank
Ye
vapid basalt
If range = 3 means it's the the exact matrix right?
Say you have a nxm matrix A. Rank(A) is just how many linearly independent column or row vectors you have.
vapid basalt
Rank is not the min(n, m)?
No
tranquil pine
Bruh I am really stupid sorry
vapid basalt
do you know what linear dependence is?
tranquil pine
No can you explain
vapid basalt
Bruh I am really stupid sorry
I think you're just missing the definition
tranquil pine
Can you tell me
vapid basalt
No can you explain
Okay two vectors are linearly independent when one is the scalar multiple of others.
tranquil pine
{ 1, 2, 3, 4}
Is this a vector?
vapid basalt
{ 1, 2, 3, 4}
Yes that's also a vector
tranquil pine
Yes that's also a vector
Ok so give me an example
vapid basalt
Okay two vectors are linearly independent when one is the scalar multiple of oth...
Do you understand what this means
tranquil pine
Of that definition
tranquil pine
Do you understand what this means
Can you give like 2 vectors
vapid basalt
Ok so give me an example
Say you have 2 vectors u,v. If there exist 2 numbers a,b not equal to 0 such that au+bv=0, then the vectors are linearly dependent. If not then they are linearly independent
tranquil pine
Say you have 2 vectors u,v. If there exist 2 numbers a,b not equal to 0 such tha...
Oh
I understand
vapid basalt
Geometrically, if the vectors are pointing in the exact same direction (they are on the same line), they're linearly dependent. If they don't, they're linearly independent
tranquil pine
Geometrically, if the vectors are pointing in the exact same direction (they are...
Got it
So coming back to the problem
vapid basalt
So coming back to the problem
imagine your matrix as 3 separate column vectors
tranquil pine
imagine your matrix as 3 separate column vectors
Yes
vapid basalt
Okay now you use the definition of linear independence to figure out how many of them are linearly dependent from each other
vapid basalt
Yep
tranquil pine
So now let's see
So I need to check the position one of the first vector with position one of the second
tranquil pine
So I need to check the position one of the first vector with position one of the...
?
vapid basalt
So I need to check the position one of the first vector with position one of the...
what do you mean by that
vapid basalt
No
You need to check if there are 3 numbers d,e,f which make the sum of these vectors 0
tranquil pine
You need to check if there are 3 numbers d,e,f which make the sum of these vecto...
Oh
Ok
vapid basalt
Ideally start with d,e and then f
tranquil pine
a - 1/ 2 e + b f + ck = 0
vapid basalt
a - 1/ 2 e + b f + ck = 0
Noooo
vapid basalt
{ a - 1 / 2, b , c}
This vector is u
vapid basalt
{c, a - 1/ 2, b}
This vector is v
vapid basalt
{ b, c, a - 1/2}
This vector is w
Try finding out if there are any numbers d,e such that du+ev=0
vapid basalt
Yes
tranquil pine
How do I find the constant after
tranquil pine
How do I find the constant after
Just by thinking of some numbers?
vapid basalt
How do I find the constant after
You need to construct a system of equations
tranquil pine
I will use the third vector
So I make the third
vapid basalt
So for vectors u,v and numbers d,e:
d(a-1/2)+ec=0
db+e(a-1/2)= 0
dc+eb=0
tranquil pine
So u took the first vector
And made the sum adding a
Constant
And = 0
Ok
So you check
The dependency
vapid basalt
Yeah you sum the multiples of their components and check if they can equal 0
vapid basalt
In this case you can immediately see that you simply can't multiply u with any number to get v or w and vice versa so therefore the matrix has full rank
But it's a good exercise
tranquil pine
I have to do that for every other vector (in my case the other vector have same components
tranquil pine
I have to do that for every other vector (in my case the other vector have same ...
Do it's easier
So*
Here
But in a hard cases do I need to that for every vector?
vapid basalt
But in a hard cases do I need to that for every vector?
well to prove it you need to show that they're all linearly (in)dependent
but if you know that u,v are linearly dependent and w is linearly independent, then you know that both u and v are linearly independent from w
vapid basalt
watch this series andyou will understand immediately what i mean
tranquil pine
After I look
vapid basalt
After I look
best if u look through the series at least up to ch 4
tranquil pine
Ok
clever epoch
can anyone help me with this 3. Given the quadratic and linear equations below, determine the point(s) of intersection
using 2 different algebraic methods. Hint: remember systems of linear equations from
grade 10)
i. X
2
– 2x + 3y + 6 = 0
ii. 2x + 3y + 6 = 0
final saddleBOT
can anyone help me with this 3. Given the quadratic and linear equations below, ...
warm wraith
Have you tried anything?
clever epoch
yes
i tried to subsitute them
to equal each other
and i ended up with x^2 - 4x + 0
but im prtty sure that is not the right answer
warm wraith
Are you able to send a picture of your work?
warm wraith
Ah thanks
Well, i don‘t see an issue with doing it this way, did you go all the way through with that method?
clever epoch
i think so i again i got to x^2 - 4x
warm wraith
Also, i think you put a + instead of an =
clever epoch
after thee 6?
warm wraith
After x^2-4x
clever epoch
oh yeah
i dont know if that answer would be right because guath math gave me different answer but i want to understand it
also how would i get the coordinates from x^2-4x
warm wraith
You get the x coordinate from x^2-4x=0
clever epoch
what would it tbe
warm wraith
I don‘t know, solve for x
clever epoch
ok one sec
i just factored out x
im not sure if that would work but my x coordinate is there now
warm wraith
Hm? What are the possibles values of x if you know x(x-4) = 0. there are 2
clever epoch
0 and 4?
warm wraith
Correct. So your x coordinate is either 0 or 4. You‘re gonna have to try them afterwards. But now you can use this to find the possible y coordinates
clever epoch
ok so i would plug both into the equation i found?
warm wraith
What do you mean by "equation I found"?
warm wraith
Well, you know X, and you want to find Y. Do you know of any equations in this problem that connect X and Y together?
warm wraith
No, because in this the y cancel out, so there‘s no point. But if you pick one that the question gives you, you‘ll be fine
clever epoch
ok
let me do it ill send a photo in a second
so far i got this
before i go any further im just wondering if the steps are good so far
warm wraith
So, you picked equation I and plugged 0 for X?
clever epoch
yes
warm wraith
Then you‘re on the right track
clever epoch
ok ill finish it and send
i got y=2
for that equation so my first intercept would be
(0,2) right?
warm wraith
You had 3y = 0 and you found y=2?
clever epoch
sorry i miss wrote it
it is 3y=-6
because there was a +6
iso i moved it over and divided it by 3
warm wraith
And -6/3 is?
warm wraith
:p
warm wraith
Okay, so one potential intersection is (0, -2). Now you had another X point so you have to try that one as well
warm wraith
Great, so you have 2 potential intersections now. Last thing to do is plug them in the equation that you haven‘t used to make sure they work
warm wraith
Well, you have 2 points, which do work in the first equation, the one with x^2. but you need to check i. The other
warm wraith
but they both = 0
Nice! Well then you‘ve found the 2 points
warm wraith
Yeah it‘s possible. When you think about it, you have a parabola and a line
So it‘s very possible that the line cuts the parabola in 2 places
clever epoch
ok thank you sm
can i give you like a vouch or somethingg this is my first ttime using the server
warm wraith
I don‘t think this server has a reputation bot or somwthing like that, but thanks I appreciate it :)
final saddleBOT
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Available help channel!
jaunty anchor
I have a coding problem. I am looking to find the coordinates of an area in a grid. Currently I am doing something like this:
glad kraken
Corner1 = 10, 0, 10 (x, y, z)
Corner2 = 20, 0, 20
Area = Corner2 - Corner1
BlocksPerArea = 10
Block = Area / BlocksPerArea
This means that Block = 1, 0, 1
and when block is multiplied (1, 2, 3, 4, etc up to 10) I recieve a number of 1, 0, 1 | 2, 0, 2 | 3, 0, 3 etc... However I need to get the numbers of 1, 0, 1 | 1, 0, 2 | 1, 0, 3 | etc...
I am not really sure how to go about this thanks
@jaunty anchor Has your question been resolved?
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orchid hill
Am I correct in saying the following
final saddleBOT
Am I correct in saying the following
orchid hill
For any $n$-tuple of natural number $v=(v_1 \ldots v_n)$ it can be mapped to the natural numbers via the mapping $$\prod^{n}_{i=1}p^{v_i}_n$$ where $p_n$ is the $n^{\text{th}}$ prime number. So $p_1 = 2, p_2 = 3$. This is true the via "unique factorization theorem".
soft zealotBOT
Br;an
orchid hill
this for a formal logic course, im trying to write it more formally but i think i might have might have left some parts ambigious i.e. i dont know if this a mapping or it actualyl does work to being with
mellow axle
are you claiming that this mapping is a bijection?
or are you just saying you can make this map
orchid hill
hmm just a map with no restrictions
i think it would have to be injective
tho
but then i would have to show that?
my objective was to prove that all n-tuples can be mapped to the naturals numbers
mellow axle
well if you're writing a proof for something then yeah you generally want to prove your claims
orchid hill
as in there exists a map $f : X \to \mathbb{N}$
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Br;an
orchid hill
where X is any n-tuple of natural numbers
i think thats equilvnent to what i want to prove
mellow axle
if there's no conditions that f need to satisfy there are many maps that can take an n-tuple to a natural number
orchid hill
so if i can demonstrate one of them exists does that also mean my orignial statment is true (the statement being "that all n-tuples can be mapped to the naturals numbers")
mellow axle
yeah
orchid hill
based
mellow axle
and i think you using the prime decomposition is overthinking it
mellow axle
just take $f:\mathbb N^n \rightarrow \mathbb N,f(x) = 1$
soft zealotBOT
chebyshev's infinite pee norm
orchid hill
ohhh okay
my orginal statement was flawed then
actually i was trying to show that the set of all n-tuples for some specific is countable
hence why i said there exist a map from that (the n-tuples for a specific n) the naturals?
mellow axle
n-tuples for some specific is countable
do you mean for some specific set is countable?
orchid hill
all sets of sets of n-tuples? so like all 2-tuples are countable and all 3-tuples are countable indivdiually
not all at once
but
with one proof
mellow axle
ok well
orchid hill
if that makes sense
mellow axle
first of all
to show a set is countable, you need a bijection with N
not just any random mapping
second of all
probably induction
orchid hill
huh, oh right cause i could just map the same element if were not injective
mellow axle
**chebyshev's infinite pee norm**
yes
that or just show the product of countable sets is countable
orchid hill
product of a countable sets as in cartesian prodcut?
mellow axle
yea
bleak bone
2+2=5?
tranquil pine
Please don't troll
tight quail
.close
graceful lantern
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tired glen
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tired glen
i need to find CD and area of the quadrangle
im kind of stuck, the only thing i was able to find was BD which is root of 189 and AC which is root of 37
AD is 12 AB is 3 BC is 4 and there are only 2 of these angles given
nothing else
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tired glen
<@&286206848099549185>
iron coyote
im kind of stuck, the only thing i was able to find was BD which is root of 189 ...
how did you get to these values?
tired glen
how did you get to these values?
from the law of cosines
tired glen
<@&286206848099549185>
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sturdy cloak
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sturdy cloak
how is this 0?
2k+1 is odd
which means u will be at an odd step
but that would have taken u even steps to get to that odd step
zenith pollen
I'd post the original example but it seems like you're moving on a number line so you'll only hit even numbers at even timesteps
sturdy cloak
I'd post the original example but it seems like you're moving on a number line s...
x1 is the first step
x2k+1 is odd step
ie 3 5 7 9 etc
to go from 1 to an odd step
u need to have taken an even number of steps
or bets
by the example
sturdy cloak
do you want it to be X2k instead of X2k+1
yh so my point is that it should only = 0 when the number of steps is odd
ie
yes
if thats 2k
than 2k - 1 ( the first step)
is an odd number of steps
however
going by this
we can only return after an even number of steps
hence
that probability would be 0
do u see my point?
zenith pollen
but like clearly it alternates between nonzero and 0
sturdy cloak
but like clearly it alternates between nonzero and 0
yh
zenith pollen
idk what X is yet
zenith pollen
example 3.3 I think
sturdy cloak
sry]
sturdy cloak
example 3.3 I think
zenith pollen
oh ok
sturdy cloak
oh ok
heres the next part
but this doesnt make sense
2k bets havent happened
in facts 2k-1 bets have happened no?
since X1 is the initial state
zenith pollen
yea there's some weird consideration for if you're doing it after or before a bet
that changes things from even to odd
sturdy cloak
yea there's some weird consideration for if you're doing it after or before a be...
the way they do it only works if we define X0 instead of X1
zenith pollen
here it's before where usually I'd write it as after I think
calling the first step 1 instead of 0 is also a convention so it's annoying to sort which is which lol
before first bet means even number of wins/losses
sturdy cloak
oh i see
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sturdy cloak
really annoying haha
sry quic question
how is the expectation equal to this?
same question as op
zenith pollen
each visit is +1 to N_0
sturdy cloak
ye
sturdy cloak
summed over any time
but isnt by definition the expectation the sum of each likehood of on outcome multiplied by its respective outcome?
but here we r just adding probabilities
zenith pollen
each time is like 1*P(x=0) + 0*P(x!=0)
sturdy cloak
each time is like 1*P(x=0) + 0\*P(x!=0)
oh yh cuz the possible outcomes r only 0 and 1
yh kl makes sense
thanks
tranquil pine
how am i supposed to solve w/o a function?
final saddleBOT
how am i supposed to solve w/o a function?
tranquil pine
tranquil pine
this is the question sorry
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tranquil pine
.close
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umbral shuttle
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umbral shuttle
am i correct with everything here?
please let me kno
it looks right to me just need someone to verify
<@&286206848099549185>
hallow wasp
is that a minus or an equals?
If its an equals then yes that is correct
but unholy levels of inefficient
hallow wasp
eh solve using matrices, yeah ig u did it the right way
hallow wasp
y = -2
meant in main problem
i know y = -2
if its an equals
because we have
2x +7y = 4
2x +6y = 6
subtract bottom from top
for y = -2
solved
teacher doing u guys dirty if theyre not allowing that
umbral shuttle
meant in main problem
ohh yeah equals
umbral shuttle
teacher doing u guys dirty if theyre not allowing that
well i think they are i'm just following a help vid they sent me
same problem basically with diff numbers
hallow wasp
yeah I recommend seeking the best way first
hallow wasp
because it goes from this to literally 3 lines
umbral shuttle
because we have
2x +7y = 4
2x +6y = 6
is this way easier
hallow wasp
yes just like in algebra 2 you can cancel out things in a system of equations
you multiply out the matrix for
[2x +7y] = [4]
[2x +6y] = [6]
and then just "subtract bottom row from top row"
you know its an option when one of the variables is cancellable
like 2x = 2x
umbral shuttle
damn i see what u mean
hallow wasp
hell even if it was like
umbral shuttle
way easier
hallow wasp
[4x +7y] = [4]
[2x +6y] = [6]
umbral shuttle
you know its an option when one of the variables is cancellable
yeahh
hallow wasp
u can say "subtract 2x the bottom row from top row"
umbral shuttle
wow ok
hallow wasp
thatll give u some constant*y = something
solve for y
if u need x then u can just plug in for y and isolate x
bol on future questions 👍
umbral shuttle
like i had a similar one i just did 20 mins ago and it was so much
had to solve for x and y tho
umbral shuttle
bol on future questions 👍
ty for that man
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zealous yoke
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Jaxx
stray rose
does this make sense
then distribute r and use the identities that x=rcost and y=rsint
stray rose
yeah
stray rose
in the future find ways to group r together with sin and cos
that way you can use the identities
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raw sundial
.close
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solemn hornet
help
solemn hornet
I need help figure out what to put into this simlarity I have been on it for forever
.
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smoky bane
Wait what’s the correct path of multiplying?
If I have
3x + 3
Times 5x + 2
——————————-
Would I do 3 times 2 and then 3x times 2 and then 5x times 3 or 3x times 5x next?
final saddleBOT
Wait what’s the correct path of multiplying?
If I have
3x + 3
Ti...
robust mulch
you do all of those
the order doesnt matter, just make sure you combine like terms in the end
smoky bane
Oh ok
smoky bane
Thx
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sage kindle
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sage kindle
I don’t know what i did
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magic ether
y''+2y'+2y=0 y(0)=0 y'(0)=pi
is c1=0 and c2=pi?
final saddleBOT
y''+2y'+2y=0 y(0)=0 y'(0)=pi
is c1=0 and c2=pi?
scarlet sequoia
what are c1 and c2? need more context
magic ether
what are c1 and c2? need more context
scarlet sequoia
so plug in y(0) = 0 you indeed get that -c1 = 0 so c1 = 0
and then compute y'
y'(t) = c2e^(-t)(cos(t)-sin(t))
but now that y'(0) = pi, it means -c2 = pi...
so c2 = -pi
magic ether
wait let me see where i messed up
ok i havent
so basically
pi=-1(c1·1+c2·0)+1(-c1·0+c2·1)
pi=-1·c1+c2·1
pi=-c1+c2
pi=0+c2
pi=c2
@scarlet sequoia
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scarlet sequoia
y'(t) = c2e^(-t)(cos(t)-sin(t))
this is y'
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peak sorrel
Determine the dimension of the column space of matrix A
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Determine the dimension of the column space of matrix A
peak sorrel
Don't know if my calculations are right
urban maple
,w rref {{1,-4,-3,-4},{3,4,-9,4},{-7,-7,21,-7},{5,-4,-15,-4}}
soft zealotBOT
urban maple
Seems like there may have been some issues in your row reduction
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bold jungle
In geometry, what does it mean when senθ = 0,60 and cosθ = 0,80? I need the degrees to solve a certain exercise but im not sure what this means
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In geometry, what does it mean when senθ = 0,60 and cosθ = 0,80? I need the degr...
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bold jungle
Im not quite sure, i know the hyp is 5, so in this case would i just like, cosθ = adj/5,
and then adj = 5 . 0,8?
iron coyote
yep
iron coyote
inverse cosine i suppose
bold jungle
That sounds very disturbing so ill just stick with what the exercise asked me, thank you for helping tho
iron coyote
np 
bold jungle
(how do i close this channel again?)
iron coyote
type “.close”
bold jungle
.close
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faint locust
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https://discord.com/channels/268882317391429632/1195800467880558672/122883242248...
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glossy pewter
Hello
I'm trying to write a bot to play nim perfectly. I'm using multiple heaps with a restriction of only taking 1 or 2 tokens at a time under normal play.
If I do it without a limit my code works perfectly fine however I'm struggling to impose the limit correctly.
I'm following this part on the wiki page, they call it the subtraction game: https://en.wikipedia.org/wiki/Nim#The_subtraction_game
As far as I can tell all I need to do is:
I think that sums up my issue, I'm really not sure what goes wrong. Any help would be appreciated
final saddleBOT
Hello
I'm trying to write a bot to play nim perfectly. I'm using multiple heaps ...
@glossy pewter Has your question been resolved?
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@glossy pewter Has your question been resolved?
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@glossy pewter Has your question been resolved?
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@glossy pewter Has your question been resolved?
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@glossy pewter Has your question been resolved?
junior token
Hello
I'm trying to write a bot to play nim perfectly. I'm using multiple heaps ...
How have you implemented this strategy?
junior token
Hello
I'm trying to write a bot to play nim perfectly. I'm using multiple heaps ...
If you send your code, maybe you could work out what goes wrong
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restive copper
wondering if correct
final saddleBOT
wondering if correct
primal sierra
i don't think either are correct
restive copper
i don't think either are correct
how should they be worked?
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marsh shuttle
hii, this is 8th grade math, don't come for me, but i need help. The first one asks for the green area, and the 2nd one asks for the green area perimeter (has options), could someone help?
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hii, this is 8th grade math, don't come for me, but i need help. The first one a...
glossy pewter
You just need to break it into parts.
The end caps are semi circles so put together they are just a circles area. The inside bit is a square - circle
So if you can work out the area/perimiter of a circle and square you got it 🙂
pearl wraith
what is diracdelta(0) is it 1 or infinity
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what is diracdelta(0) is it 1 or infinity
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weary oar
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weary oar
Just use implicit differentiation right
versed crater
Just go for it yeah
final tangle
yeh and a crapton of product and chain rule
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long sequoia
help me
late pumice
Okay let's see
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Flux Fissionist
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novel walrus
how is the divisor 1200 when the cost is $1.80
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how is the divisor 1200 when the cost is $1.80
sterile pollen
the bottle is 1.2 L, and that costs 1.80
dividing it by the size of the bottle you get the price per L
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supple jolt
well how would you find x
novel walrus
by dividing
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novel walrus
.reopen
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✅
novel walrus
@supple jolt by dividing right
supple jolt
yeah
set up fractions
simply draw a fraction line between the first and second equation
soft zealotBOT
Oogy Boogy
novel walrus
ok
how about this one
i divided 54 by $8.10 which gave me 0.15
and then divided 1000 by 1300 which gave me $13
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novel walrus
540 g = 8.10 dollars
1 kg = x dollars
1KG - 13.00
long wraith
pliant shore
warm ether
