its fuzzy but i think independent events are events that do not influence eachother, as for the formulaic definition werent there multiple
#help-36
tired walrus
so you forgor.
sonic crystal
basically
tired walrus
do you not have any notes either?
P(A n B) = P(A) * P(B)
this is the definition of independence for the events A and B.
sonic crystal
oh
tired walrus
compute the left-hand side. separately from that, compute the right-hand side. check whether or not the two results are equal.
sonic crystal
well P(A) = 1/2 and P(B) = 1/3
tired walrus
ok, and what is P(A n B)? and most importantly show how you get the value.
bc there is a right way and a common-mistake wrong way.
sonic crystal
if they are independent then it is 1/2 * 1/3 = 1/6
tired walrus
that's IF they are independent
severe hawk
you said "if". You dont know that
tired walrus
you do not yet know that they are.
sonic crystal
so what should i do beforehand
tired walrus
you must find P(A n B) without assuming their independence.
first figure out what A n B means as an event.
for this you will need to use your brain, sorry
sonic crystal
P(AnB) refers to the probability of it occuring at the same time?
sonic crystal
P(AnB) refers to the probability of event A and event B occuring simultaneously
tired walrus
sure does.
but you need to
figure out what A n B means as an event.
like what does it mean for event A and event B to occur simultaneously?
sonic crystal
for it to happen at the same time? 
sonic crystal
but you need to
> figure out what A n B *means* as an event.
not sure
tired walrus
what dice rolls fall under event A?
sonic crystal
the numbers need to be even
tired walrus
list them.
sonic crystal
2,4,6
sonic crystal
if the dice rolls a 5 or 6
tired walrus
list them
sonic crystal
5,6
tired walrus
so then which rolls fall under both events at once?
sonic crystal
6
tired walrus
6 and only 6?
sonic crystal
yes
sonic crystal
1/6?
tired walrus
correct
tired walrus
that matches with P(A) times P(B).
so these events are independent.
"it"-overuse again, unfortunately.
sonic crystal
what would be the dependent definition?
tired walrus
two events are dependent if and only if they fail to be independent.
strange swan
final saddleBOT
strange swan
Is this right? Do I find the union of their domain? Because it is +
final tangle
you want the intersection of the individual domains, not union
strange swan
oh okay okay but how do i right the final answer in interval notation
final tangle
well first identify the intersection from what you drew
strange swan
should i still use the 'U'?
final tangle
only for the domain of the first root,
but for the intersection of the domains, no
$\cap$ for intersection
soft zealotBOT
ℝαμΩℕωⅤ
strange swan
oh why?
final tangle
inequalities don't work like that
the interval notation you have below is correct though
(-inf,-1] is representative of x<=-1, not x>=-1
strange swan
how does the inequalities work?
final saddleBOT
@strange swan Has your question been resolved?
hollow wolf
Every bounded sequence has convergent sub sequence
final saddleBOT
Every bounded sequence has convergent sub sequence
hollow wolf
Can anyone give me a perfect example for understanding this statment
desert mantle
what counts as a "perfect example"
worldly vale
Yeah the issue is any example.isnt going to he very enlightening, someone is just going to give you a bounded sequence and a convergent subsequence, so what? The power of the statement is that no matter what the bounded sequence is, there will be some convergent subsequence, even if we don't know what it is
hollow wolf
what counts as a "perfect example"
Any easy example so that i can understand
desert mantle
(-1)^n
hollow wolf
1/n...it is bounded sequence right?
desert mantle
every convergent sequence is bounded
hollow wolf
Because it's limit is 0
hollow wolf
(-1)^n
So in this example it is bounded by [-1,1]
So what will be convergent subsequence in it?
hollow wolf
wrong language but yes
Sorry. I am non English speaker
desert mantle
not bounded by (set)
hollow wolf
So what will be convergent subsequence in it?
Now please simple this thing
desert mantle
the constant sequence 1
desert mantle
yes
desert mantle
do you mean upper and lower bound?
hollow wolf
Yes
desert mantle
bounded means that |a_n| <= M. so you take care of both upper and lower bounds with a single number
desert mantle
if numbers are bigger than -47 and smaller than 93, then |a_n| <= 93
so you just need one number
no
the sequence 1/n is bounded by 1
it doesnt even include a constant subsequence
it itself is a converging subsequence
which converges to 0
lyric summit
the sequence (1/n) also has its subsequences, but they all converge to the same number 0, to which the sequence (1/n) converges
$a_{n}=\frac{1}n{}\\\text{examples:}\\a_{2k}=\frac{1}{2k}\longrightarrow 0\\a_{k^{2}}=\frac{1}{k^{2}}\longrightarrow 0$
soft zealotBOT
Joanna Angel
final saddleBOT
@hollow wolf Has your question been resolved?
mellow vale
hi
mellow vale
i got a question in discrete math
is {1} ⊆ {1, {2}}?
i thought yes but the answer key said no
AK said No, because {1} is a set and there are no sets as elements in {1, {2}}
but i thought
{1} is a set with element 1
and {1,{2}} is another set
hollow iron
is {1} ⊆ {1, {2}}?
That is true
mellow vale
and it has the element 1
mellow vale
That is true
ig the answer key is wrong lol
hollow iron
{1} does not belong in {1, {2}}, but it is a subset of {1, {2}}
mellow vale
that is true yes
just threw me off
that the answer key said that
ig they made a mistake
alr thanks
final saddleBOT
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tranquil pine
What exactly is the benefit that is realised from the fact that the eigenfunctions of a Sturm-Liouville problem are complete with respect to mean convergence as compared to like being complete with respect to pointwise convergence 
final saddleBOT
What exactly is the benefit that is realised from the fact that the eigenfunctio...
tranquil pine
i just want some clarification on this
desert mantle
pointwise convergence isnt that strong
and I mean its always nice if the convergence fits with your topology
tranquil pine
pointwise convergence isnt that strong
ig because ur set of eigenfunctions are only continuous on 0 <= x <= 1?
oh wait i guess like
eigenfunctions that are complete with respect to mean convergence are complete for the set of functions that are square integrable on 0 <= x <= 1
and the set of square integrable functions is much bigger than the set of continuous functions
i assume
ok thanks
.close
snow solstice
can someone explain some machine learning formulas to me in an easy way
final saddleBOT
@snow solstice Has your question been resolved?
snow solstice
no
final saddleBOT
@snow solstice Has your question been resolved?
final saddleBOT
@snow solstice Has your question been resolved?
rustic sinew
can someone explain some machine learning formulas to me in an easy way
Does that help?
ionic hound
Im a little confused on this question
final saddleBOT
Im a little confused on this question
ionic hound
so at first I found cylinder volume, divided it by 2. Found sphere volume, and added that to the cylinder volume. I realized this was wrong as it wants how far the water rized
So then I found the volume before the sphere was dropped (cylinder volume divided by 2). Then found the volume after the sphere was added (sphere volume + original volume). Then bc it asks how far the water level raised, I did the volume of after the sphere was added, subtracted by the original volume. I get 26.1279
However, the answer key says 6.8cm which doesnt make sense
I was wondering if one of you could confirm
@spring depot
man
.close
light wren
Hey, im taking a look at this theorem in my notes , and in the proof there are some steps that are confusing me a fair bit, would anyone be able to explain them?
final saddleBOT
Hey, im taking a look at this theorem in my notes , and in the proof there are s...
light wren
so for y' = f(x,y)
what is the cause for introducing s in 3.5?
and where tf does y0 come into play in finding g(y)
worldly vale
what is the cause for introducing s in 3.5?
Its FTC in reverse
final saddleBOT
final saddleBOT
Available help channel!
amber junco
how would i Know the b in (a+b)^2 is a complex number
final saddleBOT
how would i Know the b in (a+b)^2 is a complex number
amber junco
i could do (s+1/2)^2 +7/4 but i need to rewrite in laplace form
amber junco
I need to rewrite (s^2+s+2) in the form (a+b)^2
tidal pumice
why?
timid gyro
Hello
final saddleBOT
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
Simplify into simplest radical form
Oh yeah I got it
I have one last one
I am on level 1
??
.close
dark bough
How do I find the reflections of points A,B,C in respect to the plane x+2y-3z=0? (plane acts like a mirror)
ABC are (1,0,0), (0,1,0) and (0,0,1)
final saddleBOT
How do I find the reflections of points A,B,C in respect to the plane x+2y-3z=0?...
fervent quiver
How would I do this?
final saddleBOT
How would I do this?
fervent quiver
I know that I can say that say one side is x
So second would be x + 9
area = (x) (x + 9)
Oh oops-
But idk what to do after I get x^2 + 9x
Should I convert it to vertex form?
Oh I forgot teh area existed
shut gazelle
You know the area
buoyant perch
Can anyone help me with this?
The task states
Show that the line h through the points P(0/12) and Q(13/4) is parallel to a tangent to the graph of f at a point (u/f(u) for 0<x<4
And idk what im supposed to do
nvm i had an idea
turns out
it was rigjht
forest flume
Need to find all the asymptotes of f(x) = x/lnx. x>0 and
x |= 1. First vertical: should i calculate the limit in 0? The horizontal: limx->+inf x/lnx [inf/inf] = lim x->+inf 1/1/x = +inf
So no horizontal
Lastly diagonal: a= lim x->inf x/lnx/x = 0
b also will be 0
That mean that diagonal is y=0?
final saddleBOT
Available help channel!
abstract moth
Let G be a group. is $H=\left{ g^{2} | g\in G \right}$ a subgroup of G?
Suppose H is closed under the operation of G. Let $a\in H$ then $a=g^{2}$, $aa=g^{2}g^{2}=g^{4}$, thus $aa\notin H$ therefore H is not a subgroup of G.
final saddleBOT
Let G be a group. is $H=\left\{ g^{2} | g\in G \right\}$ a subgroup of G?
Suppo...
soft zealotBOT
marawrdr
abstract moth
is this correct?4
tulip coyote
(g^2)^2
royal gust
H contains all elements which are the squares of some other element
Naturally, g⁴ is a square of something. So, it's in H.
abstract moth
I know its not a subgroup so i have to show one of these
- Show that the identity is not in the set.
- Exhibit an element of the set whose inverse is not in the set.
- Exhibit two elements of the set whose product is not in the set.
I know 1 is a no go since the identity is in the set
2 follows from 1
so all i have to work with is coming up with two elements of the set whose product is not in the set
royal gust
Why do you think it's not a subgroup?
tulip coyote
(You may want to specify an actual group if you want a counterexample)
abstract moth
intuitively idk
it must not satisfy one of the conditions for a group
but its notclear which one
tulip coyote
(If G were commutative, you would have the result true, so there's that...)
abstract moth
It must not be associative since theres an identity and each element has an inverse
royal gust
Damn you really do have to grab a non-abelian group as a counter-example, huh? That's kinda ugly
final saddleBOT
@abstract moth Has your question been resolved?
tulip coyote
(You may want to specify an actual group if you want a counterexample)
See choosing specific counterexample of a group: they're using A_4 as their group, and the hint below is that you can find two squares such that the product of those squares is not itself a square
abstract moth
See choosing specific counterexample of a group: they're using A_4 as their grou...
So when they show that H is not a subgroup of a specific group, that means in general H will never be a subgroup
?
tulip coyote
So when they show that H is not a subgroup of a specific group, that means in ge...
Well it shows that it's not always gonna be the case that H will form a subgroup of a general group G (as above there are some exceptions, but it's not true for all groups G)
final saddleBOT
@abstract moth Has your question been resolved?
abstract moth
Well it shows that it's not always gonna be the case that H will form a subgroup...
I see, thats what confused me, its says let G be a group as if it was any arbitrary group, thats why it didnt even occur to me that i should find a specific group
i thought i was supposed to show that in general a subset of that type will never be a subgroup
tulip coyote
Yea it can be a bit confusing, whether their intention is that "there's at least one counterexample" and "it'll never work" 
At least for this one it was slightly clear that it's about a specific counterexample (in fact, you could think about the trivial group, where the subgroup is basically itself(!))
final saddleBOT
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Available help channel!
rancid idol
I typed out a question in #help-28. I need it to unlock to access it again, so just recycling channels. Sorry for the spam & ignore
final saddleBOT
I typed out a question in <#903486480985489478>. I need it to unlock to access i...
rancid idol
.close
mental roost
hey
mental roost
i am working on a simulation problem
i work in python
i have a list/array/vector
ordered = [0,1,2,...,N]
this means, this vector has N+1 entries
now i want to shuffle the entries of this vector around
but the problem gets difficult because:
-i want to not have 1-cycles, as in ordered[i]==i
if we for example have the array Arr=[0,2,1]
then Arr[1]=2, Arr[2]=1
BUT Arr[0]=0
i tried to solve this with minimal recursion, but that gets out of hand quickly
so i am looking for a mathematical way that is efficient
desert mantle
you could just generate a random permutation and reject it if it has a fixed point
mental roost
yeah that is what i tried
but that adds recursion
mental roost
when things get large, it makes it slower
but i think my problem lies somewhere else
i tried to make it more efficient but i think i made an oopsie
this is the unholy junk i wrote
mental roost
only 3?
if the array gets large, the amount of attempts should increase as well, no?
desert mantle
about a third of all permutations dont have a fixed point
mental roost
oh
desert mantle
no
mental roost
huh
desert mantle
in general it converges to about 37% of permutations have no fixed point
which really isnt that bad
molten ridge
hey
molten ridge
tired plume
Do you know how to solve an ODE of the form:
$\frac{dy}{dx}=f(x)g(y)$
soft zealotBOT
Max
tired plume
That's the easiest way IMO but there is another option
Have you seen how to solve ODEs of the form:
$\frac{dy}{dx}+f(x)y=g(x)$
soft zealotBOT
Max
tired plume
i know a little
What topic is this from?
molten ridge
what do you mean?
hazy panther
Am I cooked
tired plume
Wrong channel bro
tired plume
what do you mean?
Like what are you currently studying?
tired plume
Because this could feature in like 3 different topics and so I don't know what hint to give you lmao
gritty minnow
final saddleBOT
gritty minnow
ornate knot
u can break them down into 2 fractions which makes it easier to solve
(3-18/x) / (x-6)
like this
final saddleBOT
@gritty minnow Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
remote crane
Hi 🙂
A statistics/R question. I'm trying to understand what and how does this function work. Can someone explain?
remote crane
For convenience:
This function returns the value of the__** inverse cumulative density function (cdf) of the binomial distribution**__ given a certain random variable q, number of trials (size), and probability of success on each trial (prob). And with the use of this function, we can find out the pth quantile of the binomial distribution.
Under this example, we are using the qbinorm function to get the 19th quantile of a binomial distribution with 30 trials with the prob of success to 0.6.
qbinom(.19, size=30, prob=.6)
I saw told that it some way it must return the inverse of binomial distribution, right? But tbh I don't see a connection there... Like, what does pth percentile has to do with the inverse?
If someone could provide some examples, that'd be awesome
@blissful condor, you may be interested in this 🙂
(please, let me know if you don't want to be pinged anymore; just thought statistics questions are of interest to you)
blissful condor
<@316739634405048331>, you may be interested in this 🙂
(please, let me know if ...
it’s okay, i am not a statshead but feel free to ping me. if you find anything that you think is interesting but not like a homework question, you can put it in #probability-statistics and people who are better at statistics than i am can comment on it and give good insight
remote crane
it’s okay, i am not a statshead but feel free to ping me. if you find anything t...
I'll probably get bullied there tho, since I don't have the foundation in stats yet 😦
anyway
blissful condor
I'll probably get bullied there tho, since I don't have the foundation in stats ...
you won’t get bullied for having no foundation, hopefully you don’t get that impression, we are all just here to talk about math and how much we like it
final saddleBOT
@remote crane Has your question been resolved?
final saddleBOT
@remote crane Has your question been resolved?
final saddleBOT
@remote crane Has your question been resolved?
final saddleBOT
@remote crane Has your question been resolved?
final saddleBOT
@remote crane Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
dense garnet
I'm reading about orthogonal projections and inner products, specifically in regards to least squares approximation, and suddenly I'm encountering this formula; $$\left\lVert u-v\right\rVert ^2=\left\lVert u\right\rVert ^2-\left\lVert v\right\rVert ^2.$$ Is this simply Pythagoras theorem? I know how to prove with a plus sign, but I don't know how to derive it when there's a minus sign. Any ideas?
final saddleBOT
I'm reading about orthogonal projections and inner products, specifically in reg...
soft zealotBOT
Philip
dense garnet
.close
unique talon
withou math jargon can any1 tell me what does interpolation mean
final saddleBOT
withou math jargon can any1 tell me what does interpolation mean
unique talon
i cant undertsnad
bold badge
it just means to estimate something
like find the value of something good enough for what ur working with
granite anvil
so what does extrapolate mean compared to that
bold badge
it's like taking the data u have to guess about data you don't hvae
interpolation is usually referring to guess about something within the bounds of ur data
extrapolation is that same idea but for a value outside of ur range of data that you have
unique talon
it just means to estimate something
aproxing shape of curve?
bold badge
hmmmmmmmmmmmm
well
i think in a sense, you could do something like that
but interpolate and extrapolate usually are terms used in stats when talking about trends and patterns and stuff
granite anvil
so say a line of best fit would be extrapolating?
bold badge
so say a line of best fit would be extrapolating?
yeah
I'd aruge it's both
tbh
argue*
unique talon
ok got u, is hroner method /synthetic divion can also be done by dividing polynomial with all non real rooots
@bold badge
last ques
plz
bold badge
I'm not sure so I can't say
unique talon
oh ohk np
bold badge
I haven't done polynomial divinsion since MS
and I'm now a junior in college sooo
lol
unique talon
ohh i see , nw , i will close her and ask sepratly , will get reply easily there
thanks
.close
verbal steppe
Consider the points A = (10, 4, −1), B = (12, 5, −3) and C = (6, 5, 9) and let L be the line through the points
A and B. Calculate the coordinates of the point P on the line L so that the triangle P CB becomes right-angled with angle π/2 at point P.
final saddleBOT
Consider the points A = (10, 4, −1), B = (12, 5, −3) and C = (6, 5, 9) and let L...
barren hound
right angled means dot product = 0, that probably helps
verbal steppe
Yeah i had a suspicion that was the case
however
This is what i think it should be like
I calculated the vector between the two points AB = L = B - A
But i need a vector from P to C and we don't know P?
So i'm not sure what to do
barren hound
if P is on the line L
then P is like (10 + x, 4 + x, -1 + x) or something
probably with more coefficients
verbal steppe
How did you come to that conclusion?
L: (10, 4, -1) + t( 2, 1, -2) @barren hound Is this what you mean?
barren hound
yeah
so if you've got a point P on L then you know that P can be described by (10 + 2t, 4 + t, -1 - 2t)
and then you can just figure out what t is so that PCB is right angled
verbal steppe
(x, y, z) = (5, 8, 11) + t(3, 14, 12)
With this equation no matter the t it will always be on the line however
@barren hound
barren hound
i don't understand what those numbers are coming frmo
verbal steppe
Yeah
barren hound
so P = (10 + 2t, ... )
verbal steppe
what about the condition that it has to be pi/2 ?
final saddleBOT
@verbal steppe Has your question been resolved?
verbal steppe
@barren hound 
barren hound
PC = C-P = (6-x, 5-y, 9-z) ?
hi yes this is what i mean
so now you have PC and you have PB
or you can get PB at least
and you know that if angle CPB is a right angle then those two have a dot product of 0
verbal steppe
So we take the vector PC and PB and the dot product of those should be = 0?
so PB = B - P = (12-x, 5-y, -3-z)
What now?
opal plinth
What's wrong? You have PB and PC so do their dot product
opal plinth
Yeah, now solve for x,y,z
verbal steppe
x = 12 and 6
y = 5
z = -3 and 9
verbal steppe
(12-x)(6-x) + (5-y)(5-y) + (-3-z)(9-z) = 0
opal plinth
Yes, now there's one more thing you know about x,y,z
verbal steppe
(12-(10+2t))(6-(10+2t)) + (5-(4+t))(5-(4+t)) + (-3-(-1-2t))(9-(-1-2t)) = 0
(12-10-2t)(6-10-2t) + (5-4-t)(5-4-t) + (-3+1+2t)(9+1+2t) = 0
(2-2t)(-4-2t) + (1-t)(1-t) + (-2+2t)(10+2t) = 0
opal plinth
Continue
verbal steppe
yeah i'm doing it on paper getting rough
One sec
i got t to be 1, -3
,w (12-(10+2t))(6-(10+2t)) + (5-(4+t))(5-(4+t)) + (-3-(-1-2t))(9-(-1-2t)) = 0
soft zealotBOT
opal plinth
opal plinth
Yes, though usually when you get two solutions one is degenerate
verbal steppe
if t = 1 i get that P = B
opal plinth
Right
verbal steppe
So it has to be -3?
opal plinth
To have a triangle PBC, yes
verbal steppe
That makes sense because otherwise we dont get the triangle, only a straight line
Let me insert -3 and see what i get
P = (4,1,5)
opal plinth
You can use Pythagoras if you want to confirm that this makes a right triangle
verbal steppe
I'm aware on how pythagoras works but i'm not sure how to apply it in this context
Or rather apply Pythagoras on points in a 3d envir
opal plinth
Pythagoras only deals with distances, it doesn't matter how many dimensions you work with
By distances I mean triangle side lengths
opal plinth
Yeah
verbal steppe
So i use Pythagoras to calculate the length of each side of the triangle and then utilize trigonometry to see if they create a pi/2 angle?
opal plinth
Is this Pythagoras?
opal plinth
... is that not how you calculate the length of each side?
verbal steppe
Yes
opal plinth
So what do you use Pythagoras for
verbal steppe
To find the length of each side in a triangle
opal plinth
You just said this is how you do that, and that it's not Pythagoras
verbal steppe
a^2+b^2 = c^2
okay i'm very sleep
Forget what i just said
If lhs = rhs = a pi/2 exists
:)
🙂
opal plinth
Ok that's not trigonometry though, no need to say pi/2 or whatever
If a^2+b^2 = c^2 then the triangle with sides a,b,c is a right triangle
verbal steppe
Yes
I just completely forgot about that and thought that Pythagoras was used for only calculating the length of a side in a triangle
opal plinth
Ok so you actually use Pythagoras multiple times
opal plinth
Once for the triangle at the end, but also this is actually Pythagoras
(or a generalization)
verbal steppe
Aah that makes sense
opal plinth
FYI, in software, when you want to know if a 2D point (x,y) is inside a circle with center (z,w) and radius r, you just do (x-z)^2 + (y-w)^2 < r^2
Similarly for a 3D point inside a sphere, there's just one more term on the left
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Available help channel!
tranquil pine
final saddleBOT
vital crag
Integration by parts
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
ok yea thanks
final saddleBOT
forest flume
.close
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Available help channel!
normal juniper
can someone please help me with c?
final saddleBOT
can someone please help me with c?
versed shuttle
can someone please help me with c?
take a look at subquestion a again
normal juniper
🤔
versed shuttle
it's given that a + b is itself a root
normal juniper
right
but how can I use that
oh wait
A/2 is a root?
so I sub it back into the original equation
versed shuttle
try it out :)
normal juniper
ok so far im on -A^3 + 24A = 0
-A(A^2 - 24) = 0
so A^2 = 24
so A = 2sqrt(6)
does that track
versed shuttle
ok that's correct but i'd just like to let you know that that's technically not the only possible value of A in our case
versed shuttle
yes
floral hazel
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floral hazel
hey i have a controls problem, im not sure if you'll be able to help but all i need to do is lable this correctly and im having trouble
there are a couple that i'm pretty sure are correct like signal 1 is the reference speed
final saddleBOT
@floral hazel Has your question been resolved?
floral hazel
no it hasnt......
marsh horizon
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marsh horizon
,rotate
soft zealotBOT
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@marsh horizon Has your question been resolved?
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prisma lantern
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prisma lantern
Find dA/dt, but I'm using the formula A=1/4πD^2
neon slate
sounds good
prisma lantern
But I get 157
neon slate
so what did you get for dA/dt?
neon slate
is it multiple choice?
prisma lantern
Yeah
neon slate
!original
final saddleBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
neon slate
oh i see your problem, dD/dt is given in terms of inches \ minute, while the width of the patch is given in feet
prisma lantern
Ohh
neon slate
so you'll need to convert the 20 feet to inches
prisma lantern
Oh ok ok
neon slate
since answers are in inches
prisma lantern
Thank you
neon slate
other than that, your logic is sound
prisma lantern
Alright, thank you bro!
neon slate
careful with those units, theyll get you on the AP test 😄
prisma lantern
I know, I'm nervous about that exam
neon slate
well you seem to be getting things fine
just remind yourself to double check when the problem involves units, it isnt that many of them
prisma lantern
Truee, luckily
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heady wing
I need help.
final saddleBOT
I need help.
heady wing
well fractions
so basically
u gotta find felles nevner
im from Norway
And im struggling with it
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amber junco
how is x^5y^2 a potential
final saddleBOT
how is x^5y^2 a potential
formal trail
if you take the gradient of x⁵y² it gives you the given vector field
amber junco
.close
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amber junco
.reopen
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amber junco
@formal trail I dont get it do i need to compute the partial derivatieves f(x,y,z)?
also i dont know how to do it with this intergral with dx and dy
normally i just got this to deal with
how do i get the vector field out of that intergral?
ooh
wait
nvm
.close
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amber junco
.reopen
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amber junco
@formal trail one last thing. How can i see that the vector field is conservative
how can i see that this vector field is conservative
formal trail
a vector field is conservative if a potential function exists (i.e. $f$ exists such that $\grad f = \vb{F}$. you can alternatively use the fact that $\curl (\grad f) = \vb{0}$ since that means $\vb{F}$ is conservative if $\curl \vb{F} = \vb{0}$
soft zealotBOT
cloud
formal trail
if you don't know that yet, you can also just try and find a potential function and see if it works or not
formal trail
yes
formal trail
gradient is an operator that takes a scalar function and returns a vector field. so F is the vector field you already have, and f is a potential function of F if $\grad f = \vb{F}$
soft zealotBOT
cloud
amber junco
@formal trail my gradiant is 20x^3y^2 +2x^5
formal trail
gradient of what?
amber junco
how can i see that this vector field is conservative
of this
formal trail
you can't take the gradient of a vector field
you're trying to find a potential function f whose gradient is the vector field you already have
amber junco
**cloud**
oh but how would i want to proof it would be conservative then by doing this
formal trail
you need to find a potential function f, and take the gradient of f, and if that gradient is your original vector field F, then F is conservative
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fallow sky
Is this logic correct
final saddleBOT
Is this logic correct
final tangle
,rotate
soft zealotBOT
final tangle
are you integrating $\frac{6}{x^2}$ or $-\frac{6}{x^2}$
soft zealotBOT
ℝαμΩℕωⅤ
final tangle
then yes
final tangle
missing the dx
fallow sky
If I added dx, would it be good?
final tangle
application of power rule is fine
fallow sky
What about when I move x to bottom
final tangle
don't forget the constant of integration
fallow sky
+C?
final tangle
that's the application of the negative exponent law, which you also applied at the start, is also fine
supple atlas
pls
supple atlas
ty
Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks. Create a system of equations that can be used to find the number of CDs she sold last week, and the number of CDs she sold this week. Then use your equations to solve for each.
Can someone help help me solve this using linar systems its been a minute and this is my practice question totaly forgotten how it worka
works
clear hearth
What have you done so far
clear hearth
So you absolutely can not remember anything?
supple atlas
well i can start the question
clear hearth
How would you?
supple atlas
she sold total of 110 cds
clear hearth
Yes
supple atlas
idk bro
clear hearth
Okay
supple atlas
lowkey
clear hearth
So let the no of CDs she sold this week be x
supple atlas
lemme get my calc
clear hearth
They say she sold 6 MORE than 3 TIMEs the no of (CDs she sold this week)
clear hearth
lemme get my calc
Need not my brother
clear hearth
They say she sold 6 MORE than 3 TIMEs the no of (CDs she sold this week)
What do you infer from this? Can you make a relation?
supple atlas
6 x 6 x 6?
supple atlas
alr
clear hearth
Say John had y apples
supple atlas
ok
clear hearth
Laurence had 3 more than 2 times the no of apples than John
clear hearth
How many apples does Laurence have?
supple atlas
pretty please
clear hearth
can you show me how it looks solved and ill do the next question
I'm supposed to help you get the answer and not give answers
You're here to learn bro
😭
You could try
clear hearth
Laurence had 3 more than 2 times the no of apples than John
John has y apples so according to this statement, Laurence had 3+2y apples, does that make sense
supple atlas
not really
clear hearth
If Laurence had 3 MORE than 2 TIMES the no of apples than John
Laurence should have 2y+3 apples
Or 3+2y
Same thing
vagrant tundra
@supple atlas is this from khan academy algebra 1?
clear hearth
I was helping you to make equations
supple atlas
this guy has 2 apples
aint the formula
i want to kknow how to do it
not make the question
😭
clear hearth
Ok tell me this, you understood how to frame relations now right?
You understand the above examples right?
They're not related to your question at all they were just to help you frame relations
supple atlas
ok so for my question where do i start
idle dune
May I also provide an explanation?
supple atlas
Ms. Kitts works at a music store. Last week she sold 6 more than 3 times the number of CDs that she sold this week. Ms. Kitts sold a total of 110 CDs over the 2 weeks. Create a system of equations that can be used to find the number of CDs she sold last week, and the number of CDs she sold this week. Then use your equations to solve for each.
please
clear hearth
Assume Mrs Kitts sold x CDs this week
supple atlas
yes
clear hearth
So according to the question, she sold 6 MORE than 3 TIMES the number of CDs than THIS WEEK
idle dune
Let y be number of CDs sold last week
idle dune
So according to the question, she sold 6 MORE than 3 TIMES the number of CDs tha...
Then equate y=3x+6
And total CDs sold in both weeks add upto 110
supple atlas
okok
idle dune
Basically the question is teaching you the method of substitution of solving linear equations in 2 variables
You substituted the value of y from one relation in the other relation
clear hearth
It's important to know how to form relations
idle dune
Always remember a correct question will always have two meaningful relations to solve 2 variables
supple atlas
can you show me how its written i have the question and all that but in the formula i don’t understand substitution
idle dune
See what does substitution here mean?
It means we are using the obtained value of y (from one equation in terms of x) in another equation involving both x and y
Are you following?
final saddleBOT
@supple atlas Has your question been resolved?
supple atlas
sorry bro thanks
candid dome
who can help
final saddleBOT
final saddleBOT
Available help channel!
naive shoal
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https://cdn.discordapp.com/attachments/903463351789694986/1199716419185684580/PX...
naive shoal
Last 2 times my ticket got cloed without an answer so lets try this again...
But can someone explain each of the different types of angles and how they relate (not just ones in here but all types I would find) and bow they relate?
i want to know the anme all of types of angles that can be related and like how you can get there degress based on that other one its releted to
static fractal
unless you have parallel lines, these angles generally don't relate to each other at all
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@naive shoal Has your question been resolved?
naive shoal
unless you have parallel lines, these angles generally don't relate to each othe...
is there specific names for them though? in my assignment im suppost to and i remeber there being like 5 dif names or something like that
final saddleBOT
is there specific names for them though? in my assignment im suppost to and i re...
static fractal
corresponding will be on the same side of the transversal
so 1 and 3 are transverse in Q6, for example
eh, let me find something
naive shoal
https://study.com/skill/learn/how-to-identify-corresponding-and-alternate-angles...
okay 1 sec i may have another question about this so dont close the chat
final saddleBOT
@naive shoal Has your question been resolved?
static fractal
you need to react with ❌ or the channel will close
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amber junco
how do i use polar coordinates here?
final saddleBOT
how do i use polar coordinates here?
vital crag
how do i use polar coordinates here?
Transform x and y to their r and theta formulas
amber junco
Transform x and y to their r and theta formulas
should i intergrate theta first or r?
and can i factor them out of the intergral of r?
vital crag
Depends on D
vital crag
You're missing dA
amber junco
can you give me a hint how to proceed further? @vital crag
amber junco
You're missing dA
okay but besides that
vital crag
And you're missing your limits in theta and r
vital crag
Just do it
vital crag
Don't even know what you're asking for
vital crag
Just do it
.
amber junco
how long are you online @vital crag ?
vital crag
Stop pinging me
amber junco
@vital crag im stuck
vital crag
Stop pinging me
.
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lilac oxide
hey could someone help with this problem please
final saddleBOT
hey could someone help with this problem please
lilac oxide
<@&286206848099549185>
versed crater
What have you tried
lilac oxide
What have you tried
i think that if 2 vectors arent parallel they span a plane, i think these 2 are right
versed crater
If 2 vectors aren’t parallel then yes they span a plane
But what’s that got to do with this question?
Let’s start with the first one
How can you know if x lies in the plane spanned by u and v?
lilac oxide
is it that each on of the numbers in the x vector are between the same numbers on u and v?
versed crater
What do you mean by that
lilac oxide
the first number in the x vector (1) is between or equal to the first numbers of the u and v vectors (0 and 1)
and each of the numbers fit, so i would guess that the first one is correct?
scarlet sequoia
I see what you mean, but this type of reasoning would be easier if you wrote x as a linear combination of v and w already
You've very much almost found it, just need to formalize it
lilac oxide
im not sure what you mean, i looked through the question and found every thing to be true which i dont think is right aswell
scarlet sequoia
im not sure what you mean, i looked through the question and found every thing t...
Well it's impossible for all of them to be true
Since u and v are not colinear, they span a plane
If u,v and w together spanned a plane
Then w is immediately in the plane spanned by u and v
So it's a linear combination of u and v
So answers 3 and 5 are already incompatible...
lilac oxide
mm ok. so i think 3 is wrong 5 is right
scarlet sequoia
Just remember
"c is in the plane spanned by a and b" exactly means "c is a linear combination of a and b"
(Meaning c = xa + yb)
So let's check answer 4
lilac oxide
so what i said earlier was wrong, it doesnt mean that the numbers are in between?
scarlet sequoia
so what i said earlier was wrong, it doesnt mean that the numbers are in between...
The justification is not completely valid no
There is a step in between
And that is showing that x = av + bw
So, if a and b exist, what are they?
lilac oxide
uhhh
scarlet sequoia
Focus on the 2nd and 3rd coordinates
lilac oxide
not sure
scarlet sequoia
Your remark that x's coordinates were "in between" those of v's and w's was practically on the spot...
But "in between" as in what more precisely?
lilac oxide
1/2?
lilac oxide
is a and b both 1/2?
lilac oxide
it does
scarlet sequoia
It does what?
lilac oxide
the equation works
i mean
is there something else im suppose to conclude?
that they are a linear combination?
scarlet sequoia
Just remember
.
scarlet sequoia
Pretty much if you wanna be sure.
If a and b don’t exist, then x cannot be in the plane spanned by such and such
lilac oxide
also if 3 is right does that mean 2 is right? or are they different things?
scarlet sequoia
Yes
lilac oxide
ok
scarlet sequoia
If w is in the plane of u and v, then u,v and w make a plane
lilac oxide
so i unchecked the first one, and have the 3 middle ones checked, you think thats right?
scarlet sequoia
so i unchecked the first one, and have the 3 middle ones checked, you think that...
x is indeed not spanned by u and v
Because if x = au + bv, we would need a = 1/2 and b = 1, which doesn't work...
So 1 is wrong
For 2 I suggest you try the same thing
Find a and b such that w = au + bv
lilac oxide
i dont think it works
scarlet sequoia
Aye so if no a and b exist, what can we say?
lilac oxide
its wrong
lilac oxide
also if 3 is right does that mean 2 is right? or are they different things?
so i was wrong to say this?
they are different things
scarlet sequoia
No, what you said here was right.
3 and 2 are indeed equivalent statements
lilac oxide
but we found 3 to be correct but 2 to be incorrect?
scarlet sequoia
When did we say 3 was correct?
lilac oxide
yes? or is 3 wrong since 2 is
scarlet sequoia
We said 2 and 3 were equivalent
scarlet sequoia
Sounds good to me
lilac oxide
alright thank you
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@lilac oxide Has your question been resolved?
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Available help channel!
normal jasper
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normal jasper
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normal jasper
Oh i learn about that
but how do i do foil
there’s only 1 of them
1 polynomial
vital crag
but how do i do foil
x^2 = x * x
final saddleBOT
@normal jasper Has your question been resolved?
normal jasper
Oh
soft zealotBOT
dr. matlab plot
vital crag
https://www.cuemath.com/foil-formula/
Follow this
vital crag
Follow this
.
final saddleBOT
@normal jasper Has your question been resolved?
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@normal jasper Has your question been resolved?
soft zealotBOT
woods
halcyon fog
I got this wrong and want to know where I got off track my teacher said formulas and everything is correct
