Meh
#help-39
leaden wadi
That's what W(t) would be and you would solve of the constant using t = 3 and W(3) = 2.5.
opaque iris
I guess you are saying I take the anti deriv of the two rates and subtract them to get W(t), then find the deriv of that twice?
That makes logical sense
But yeah sounds like it would be difficult
opaque iris
The collegeboard explanation says that difference of the derivatives of the two rates equals W’’
opaque iris
But anyways, **W'(t) = F(t)**.
Wym
leaden wadi
Is this studying for the AP test?
opaque iris
yes
leaden wadi
So you know that
L(x) = f(a) + f'(a)(x-a)?
Yea
leaden wadi
In this problem, f'(a) = F(t).
opaque iris
Yes
leaden wadi
And the anti-derivative of F(t) is not necessary to find because you are given f(a) = F^(-1)(t) by W(3) = F^(-1)(3) = 2.5.
Where ^-1 means the anti-derivative.
opaque iris
Oh so we’re supposed to approximate it with the value from part ‘a’?
leaden wadi
Yes.
So you can find the linearization without having to find the anti-derivative.
Which it looks like you did in part a).
opaque iris
So is that easier than trying to understand this then?
leaden wadi
At t = 8, W(t) has to take into account the water leakage. You can generate this equation.
W'(t) = F(t) - L(t)
And therefore W''(t) = F'(t) - L'(t)
leaden wadi
No, the independent variable in this problem is time, t.
opaque iris
W'(t) = F(t) - L(t)
So both these methods work?
leaden wadi
Should.
opaque iris
That and the approximation
leaden wadi
Yes.
opaque iris
W'(t) = F(t) - L(t)
That makes sense, so we never find the equation of W(t), but we don’t need to so yeah, makes sense
leaden wadi
Correct.
I suppose it's mostly about understanding the relationship between W(t) and the antiderivative of F(t).
opaque iris
Like it’s asking what it represents in terms of the question
after I get that I think I’m good to go then
leaden wadi
If F(t) and L(t) is the rate of change, then F'(t) and L'(t) would be the rate of change of the rate of change.
Which means how the rate of change is increase or decreasing.
opaque iris
I assume the collegeboard would accept some form of that answer
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chrome mesa
i have to prove "If a graph G is not connected, then its complement is". is this proof correct?
Assume G is not connected. Then G would contain more than once component. Also, there would exist two vertices, u and v in V(G) such that there is no (u, v)-path.
For there to be no (u, v)-path, u and v would have to be in different components, meaning there would be no edge between u and v. Therefore, in G complement, there would be an edge. Therefore, you could make a (u, v)-path where u ~ v.
tropic saddle
well ok that shows that there is a path between some u's and v's. but why should that show that the complement is connected
for example if u and v have an edge in G, then they dont have an edge in the complement. so why should they still be connected?
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chrome mesa
for a graph to be disconnected doesnt it mean there is no path between 2 vertices in the graph
so im just saying like in the complement they would have an edge which makes the graph connected
idk im confused about what you mean
chrome mesa
for example if u and v have an edge in G, then they dont have an edge in the com...
if u and v have an edge in G then wouldnt the graph be connected
like if you cant find 2 vertices in G that dont have an edge
tropic saddle
connected means that all pairs of vertices have a path
you can easily have a disconnected graph where some pairs still have a path
chrome mesa
what should i do instead then
tropic saddle
to begin just try some examples
chrome mesa
i can tell that its true by drawing examples but idk what to do with that
tropic saddle
understand why its true from the examples
well this is even more extreme, not just a path but even an edge
and then it immediately follows from the definition of complement of a graph
so if u,v dont have an edge in G, then they immediately have an edge in the complement
and what happens if u,v have an edge in G?
chrome mesa
they dont have one in the complement
tropic saddle
but do they still have a path?
tropic saddle
hint: that situation is also in your picture
chrome mesa
yeah
but if you look at it the other way
u and v have an edge in g complement but no path in g
tropic saddle
the complement isnt disconnected
chrome mesa
oh
tropic saddle
you need that G is disconnected
for such a vertex v to exist which is not connected to u and w
because there is at least one other connected component
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midnight haven
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midnight haven
I got to here but I’m not sure if I’m on the right track
Nor do I know what to do
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midnight haven
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sullen umbra
theres only 2 answers for this right>
sullen umbra
somehow the answer sheet is showing 4
midnight haven
theres only 2 answers for this right>
Add one on both sides
sullen umbra
huh
hard crystal
Depends on @sullen umbra Interval of θ
sullen umbra
Depends on <@1107824721405415526> Interval of θ
ok look
i dont even think its about the domain
2pi/3 gives -tanpi/3
hard crystal
I think it's asking for soln in the range [0,2 π)
sullen umbra
okay but
sullen umbra
theres only 2 answers for this right>
this becomes tanx=sqrt 3
does tan(2pi/3) result in sqrt 3?
hard crystal
this becomes tanx=sqrt 3
Wrong
hard crystal
tan²x =3
tan x = ±sqrt(3)
pearl pondBOT
midnight haven
Oh
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unkempt yacht
Conduct a Thomas Young's double slit experiment using a light source with a wavelength of 0,6 micrometers. The distance between the screen and the slits is 2m, and the distance between 2 slits is 3mm. Calculate the distance between the center bright band and the third bright band.
unkempt yacht
Yes this is a math server, but physics server was somewhat slow to respond
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dark condor
Yo what's up guys
pearl pondBOT
Yo what's up guys
dark condor
Can someone explain
This problem
The vertex angle is an isocles triangle 101.24 degrees. The base is 14.6. Find the permiter kf the triangle to nearest 10tu
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inland ivy
Aren’t the options simply wrong?
pearl pondBOT
Aren’t the options simply wrong?
inland ivy
This is what I did
The last term will give me a (2n-2) choose (n-2) somewhere in there
acoustic path
that line 2 is suspicious
inland ivy
$1+2x+3x^2+…+nx^{n-1}$
jolly parrotBOT
kheerii
inland ivy
After taking the x common
I’m not sure tbh
It looks good to me
Oh wait what am I doing lmfao
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flint drum
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flint drum
Question b and c
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sly dagger
brother u got that but zoomed in
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queen wharf
starting from the equation (A+G+C'+E)(A'+B+G)(B+C'+F+G) how do i get to that consensus theorem?
karmic dirge
queen wharf
np
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finite bridge
@gen question is not clear, so much clutter in that picture. Maybe write it down neatly
finite bridge
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orchid wagon
how do i do this pls
pearl pondBOT
how do i do this pls
vagrant dirge
Could you substitue 1 for n and equate the equation for the sequence to 2.75 and find b?
orchid wagon
hm
im not sure
i looked at the key answer and it says
a= -1/2
and b = 3
but idk how to readh it
vagrant dirge
Did you try the substitution?
pearl pondBOT
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random beacon
hey, i want a math expression that basically gives me an x and y position for each edge point for this pill kinda path
sin(u) for x transform
cos(u) for y transform
gives me path of a circle as you may know, is there a way to basically getting some sort of this path with math? thanks.
i don't mean to draw it, but once again, to move along a path like this
random beacon
like, moving along a pill-shaped path
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random beacon
maybe just a tiny help from <@&286206848099549185> ? thanks
random beacon
so officially it is called stadium shape, it's the 2d version of the capsule, let's not talk about the z distance there, the only thing im interested in is the x and y transform.
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gentle hatch
you good with singularity mathematics ?
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random beacon
you good with singularity mathematics ?
is it that complicated? 💀
random beacon
i kinda just wanna achieve the simplest pill looking shape path, it doesn't have to be exact lol
ive almost achieved it tho.
basically,
x: cos(u) * width
y: sin(u + a*sin(u*2))
where if i play around with a, it is somewhat giving me that kind of shape
ignore the trail and bloom effects, sorry for that
gentle hatch
the other way is using step functions, i don't know how to write it using Latex
random beacon
oh interesting, i don't mind that you don't know how to use latex, me neither, you may create a demo in geogebra/wolfram that would help me quite a lot lol thanks
vestal tapir
random beacon
<https://math.stackexchange.com/a/3135774>
that looks very promising, but how do i smoothly get the x and y coords for it?
random beacon
ive almost achieved it tho.
basically,
`x: cos(u) * width`
`y: sin(u + a*sin(u*2...
i mean as it's shown there, i kinda want the dot to go along this path
vestal tapir
good question, i don;t know
random beacon
i mean my solution i came up with is nowhere near perfect you know.. i don't even know what that "a" exactly does, it was more like a trial and error until it looks like that pill xd
using turbowarp to quickly experiment with it.
the problem with it is the wobbly motion around the long path..
random beacon
oh well, if you figure out anything, please ping me or dm me, the dms are open, i guess the help is gonna close now given that im going to sleep (1:23am nice time lol)
gn
thanks for all your help awesome people <3
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thorny crag
could someone help me find the sequence for {-1/1, 1/4, -1/9,...}
thorny crag
i'm having an issue finding the sequence for the denominator
sharp quest
notice that the terms are changing signs
and the denominators are squares
wicked totem
Can I convert this to tanh^-1(sinh t)?
pearl pondBOT
Can I convert this to tanh^-1(sinh t)?
pearl pondBOT
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dreamy wind
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mortal island
what happened here in part c?
pearl pondBOT
what happened here in part c?
pearl pondBOT
mortal island
.reopen
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✅
mortal island
actually, why > 5 and not < 5?
ok i got it
so like we need it to be > a so we can use < Var[X]/(a^2 n)?
.close
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coarse scroll
Find the roots of:
(y-2)(y-3)(y-4)(y-5) - 360 = 0
viscid sierra
what are we substituting here?
think about it
another hint: ||((y-2)(y-5))((y-3)(y-4))||
you should probably be able to substitute from here on
coarse scroll
So do I just expand them?
viscid sierra
what do you think?
sharp smelt
I'd probably substitute $y=e^{ix}$ , but that may not work
jolly parrotBOT
Why am. I here
coarse scroll
Im sure you dont need that
viscid sierra
I'd probably substitute $y=e^{ix}$ , but that may not work
how would that work
coarse scroll
This is a gcse level question
sharp smelt
how would that work
I was thinking you could after some simplification write it in the from cos(x)+isin(x) and the find x by equating the imaginary part to 0
viscid sierra
another hint: ||((y-2)(y-5))((y-3)(y-4))||
well yeah third and final hint: ||I gave extra parenthesis for a reason||
viscid sierra
I was thinking you could after some simplification write it in the from cos(x)+i...
oh well, haven't thought about it that way
coarse scroll
$(y^2-7y+10)(y^2-7y+12)=360$
jolly parrotBOT
GoodHood
coarse scroll
ok i got here
viscid sierra
notice something common in both the parenthsis?
coarse scroll
y^2-7y?
jolly parrotBOT
GoodHood
viscid sierra
solve for p
pearl pondBOT
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sonic sky
pearl pondBOT
sonic sky
Part ii I got wrong
limpid swallow
What is theta??
sonic sky
We don’t know it
limpid swallow
Part d you calculated theta
So
Tcos(26.07)=1200
Approx 2027
N
Not totally sure of the answer
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lyric helm
pearl pondBOT
lyric helm
could someone help me double check?
like for example 5 < x < 15
are the symbols right?
also if everything is wrong could u let me know how to use the symbols right?
tidal breach
looks good to me
lyric helm
looks good to me
oh wait what actually?
tidal breach
on the last one you can do x∈(15,+ ∞)U(- ∞,-10)
lyric helm
on the last one you can do x∈(15,+ ∞)U(- ∞,-10)
ohhh
lyric helm
you need the intersection?
no i don’t think so
tidal breach
what does the exercise say
lyric helm
graph the soluation set and then solve the system of inequalities
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quasi turtle
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quasi turtle
Do I think of this simple function as the u(x^n;i+1) as a mesh of the y axis? and the borel sigma algebra is the x axis?
plush bramble
What's u(x)
quasi turtle
an arbitary continous function, which I can say is measurable, which can be orchistrated as a linear combination of indicator functions called a simple function right (seriously is that the main idea??)
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smoky hinge
which statistical test should i use? i'm testing against an expected value of exactly 0 and i have observed values that are negative, 0 and positive. will post a sample of my data in the next message
EDIT: trying to reject null or otherwise prove my findings are 'relevant'
smoky hinge
0
0.063
0.026
-0.018
-0.07
-0.018
0.033
0.085
0.137
0.085
0.033
0.077
0.12
0.051
-0.021
0.129
0.051
0.086
0.119
0.033
0.062
-0.029
0.117
0.021
0.044
0.066
0.087
0.106
-0.002
0.014
0.028
0.041
0.053
0.064
0.074
0.082
0.089
0.094
0.098
0.101
0.103
additional information: the data above is the difference between a theoretical target and an observed number. the theoretical number is exactly y = 2^x - 1
i tried to google this and it looks like wilcoxon signed-rank test with one sample but i'm not at all sure if that is the right way to go
also never used that one before so i don't have the capability to judge whether i'm doing the right or the wrong thing
<@&286206848099549185> ? :/
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smoky hinge
be back in 10 minutes
back
i ran the test:
WilcoxonResult(statistic=array([51.]), pvalue=array([8.73837586e-07]))
but i also got:
Python\Lib\site-packages\scipy\stats_morestats.py:4088: UserWarning: Exact p-value calculation does not work if there are zeros. Switching to normal approximation.
warnings.warn("Exact p-value calculation does not work if there are "
pearl pondBOT
@smoky hinge Has your question been resolved?
smoky hinge
i generated some more values and deleted the leading zero which was apparently causing problems. i got:
WilcoxonResult(statistic=array([5503.5]), pvalue=array([1.49044709e-50]))
i still don't know whether i'm doing wrong things :/
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polar river
Can somene help me with this 2 questions
pearl pondBOT
Can somene help me with this 2 questions
polar river
lone shale
the mean is the numbers added up divided by the amount of numbers
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midnight haven
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midnight haven
how do i solve the mod inequality?
west sapphire
show the previous part so we can make sense of "hence"
sharp smelt
how do i solve the mod inequality?
consider multiple cases
vital crest
do i just send my problem
midnight haven
because -(2x - 3 ) = x
=> 3x = 3 x = 1
and 2x -3 = x
-x = -3
x = 3
midnight haven
do i just send my problem
not here
vital crest
where
midnight haven
a channel called help-32
vital crest
thx
sharp smelt
consider multiple cases
consider the case(s) when x is less than 0, 0<x<3/2 and x>3/2
and solve for each of them
midnight haven
consider the case(s) when x is less than 0, 0<x<3/2 and x>3/2
oh ok i think i got them
so i just had to use the values from the previous question
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wind birch
Need help with 6
pearl pondBOT
Need help with 6
wind birch
Don’t know how to graph that
A video explaining this type of equation would help
Or what type of equation that’s called cause idk
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wind birch
Sure fam
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wary zenith
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autumn narwhal
Start by coloring the top section red. Any coloring can be rotated so that the top section is red.
That fixes the circle and allows us to not worry about rotations anymore.
wary zenith
ok
wary zenith
ok
autumn narwhal
Because we have more than one red section
wary zenith
ye
autumn narwhal
You have 5 sections left
You need to color 3 red, 1 green, 1 blue.
In how many ways can you do that?
autumn narwhal
No
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silk tinsel
How do you solve this? The possible answers are 200, 80, 15,2 and 3,2. One of them is correct and I know that 15,2 is definitely not it. So far I divided and got 5 + 3 x 5^102 but I am not sure how to go from there to reach one of the possible answers
west sapphire
that seems to have already been done: "So far I divided and got 5 + 3 x 5^102"
autumn narwhal
Ah okay, didn't notice
fickle falcon
exactly
autumn narwhal
The answer is definitely not one of those
west sapphire
the number is huge
autumn narwhal
Too small
west sapphire
does 15,2 mean 15 + 2/10?
silk tinsel
that makes no sense
Yeah but those are the options
west sapphire
or does the comma denote something else
silk tinsel
does 15,2 mean 15 + 2/10?
Yes it means 15 + 2/10
west sapphire
Yeah but those are the options
do you have a screenshot of the options? just in case there's some subtlety..
silk tinsel
there is definitely no subtlety
Either they expect people to calculate and go "none of the options are correct" or they just made it wrong
west sapphire
if there's a "none of the above" option then definitely that, otherwise yea the the person who wrote the question screwed it up
storm coral
are you absolutely sure that the possible options do not come with a worded statement?
silk tinsel
if there's a "none of the above" option then definitely that, otherwise yea the ...
there isn't one unfortunately lol
silk tinsel
are you absolutely sure that the possible options do not come with a worded stat...
they just come with "Calculate" and the problem I sent earlier
storm coral
then they're off by a great margin
thank you for your info
silk tinsel
yeah ofc
thanks for the help everyone even if all the options were wrong lol
.close
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autumn narwhal
The answer should be 20
Number of ways of coloring the 5 sections
5 options for blue, 4 options left for green,
The rest of the 3 sections must be red
wary zenith
ohk ty!
feral sedge
Find the polynomial of lowest degree (and lowest leading coefficient) that both 3x and 3(x-2) divide
You're thinking of greatest common factor
But no, it wouldn't be 1 even then
limpid lily
An LCM is the smallest number that's a multiple of both of them.
Like 3 and 7 have 21, which is a multiple of both of them.
1 isn't a multiple of both of them.
Do you know what a multiple of a number is?
OK, what is it?
Right, 10 is a multiple of both.
That's what a common multiple is.
Common because it works for both.
No.
10 is the common multiple.
2 isn't a multiple of both of them (it's not a multiple of 5).
Right.
OK, so one way to get the LCM is to list a lot of the multiples of both.
So, like 4 and 5, you have 4 giving 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.... You have 5 giving 5, 10, 15, 20, 25, 30, 35, 40....
Notice that both of them have 40 as a multiple.
So, 40 is a common multiple. It's a multiple common to both of them.
But it's not the smallest multiple.
It's not the smallest multiple that works for both of them.
20 is.
So, the least (smallest) common (works for both of them) multiple is 20.
Does that make sense?
OK, so here's a way to get the LCM with regular numbers that will help you with polynomials.
Do you know how to factorize a number?
OK, so factorize 4.
Right, so 2^2.
What about 5?
Why not?
OK, so we leave off the 1, and 5 factorizes to 5^1.
So, we get some prime numbers to whatever powers.
2 is a prime. 5 is a prime.
We take the highest power for each prime.
The highest power of 2 in both of the numbers is 2. The highest power of 5 in both of the numbers is 1.
So, we get the LCM as 2^2 * 5^1.
Which is 20.
Let's try with another example.
Find the LCM of 12 and 20 using factorization.
OK, keep factoring until you get primes (4 isn't a prime).
Right.
So, in prime powers, we have 12 = 2^2 * 3^1. What do we have for 20?
Almost, don't forget that the exponent on 5 is a 1.
So, we have three primes: 2^? * 3^? * 5^?.
Does it make sense that those are all the primes we found in both of the numbers?
OK, now what's the highest power of 2 we found in either of the numbers?
OK, what about 3?
What about 5?
OK, so we have the LCM as 2^2 * 3^1 * 5^1.
Does that make sense?
OK, now there's something called the GCF (greatest common factor).
It's like the LCM, except you take the smallest exponents rather than the biggest.
So, the smallest are 2^2 * 3^0 * 5^0.
Why do 3 and 5 have 0s? Because 20 was 2^2 * 5^1, which has no 3 power, so it counts as 3^0.
And 12 has no 5 power, so it counts as 5^0.
So, we do the same thing as the LCM, except we get the lowest exponents.
Does that make sense?
OK, now you have 3x and 3(x - 2).
With polynomials, we do the same thing. We factor them.
You can't really factor x because it's a first-degree polynomial. You also can't really factor x - 2.
So, the first one factors to 3^1 * x^1.
What does the second one factor to?
Right.
So, what's the LCM?
No, remember what we did before.
We list all the prime factors. Like 3^1 * x^1 and 3^1 * (x - 2)^1.
Then we take the highest exponents.
So, what are the three prime factors and the highest exponents on each?
No. What are the three prime factors?
It's the same general idea.
A polynomial is a prime if it can't be factored any further.
Like if you have x^2 - 1, that factors into (x - 1)(x + 1).
So, x^2 - 1 isn't prime.
But x - 1 and x + 1 are.
Also, 4x - 2 can be factored into 2(2x - 1).
So, 4x - 2 isn't prime, but 2x - 1 is.
Does that make sense?
OK, so we have 3^1 * x^1 and 3^1 * (x - 2)^1 from what you said before.
Everything there with an exponent is a prime.
What are all the primes you have there?
OK, list them.
Right.
What's the highest exponent on 3?
What's the highest exponent on x?
Right.
The LCM is where you take the highest power of each prime.
What about x - 2?
So, we have 3^1 x^1 (x - 2)^1 as the LCM.
No.
What did I say was the LCM just now?
Right, but that wasn't what I said the LCM was.
Yes.
You take the three primes.
You find the highest exponent for each prime.
Then, you write that out.
So, 3, x, x - 2 are the primes.
3^1, x^1, and (x - 2)^1 are the highest exponents on each.
Then you multiply those together.
3^1 * x^1 * (x - 2)^1.
That's the LCM.
Do you have any questions about how I got that?
Right.
You can if you want to or you can leave it factored. Did your teacher tell you which they wanted?
OK, then I'd leave it factored because it makes it easier to see your answer is correct.
No problem.
Why?
You too.
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waxen smelt
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waxen smelt
I need to determine if the series is convergant or divergent
so can someone plase review my method?
S_2 = 1/2 + 1/4 > 1/4 + 1/4
S_3 = 1/2 + 1/4 + 1/6 > 1/6 + 1/6 + 1/6
s_n = 1/2 + 1/4 +..+1/n > 1/n + 1/n + 1/n..
ember cloak
so can someone plase review my method?
If you showed it.
waxen smelt
If you showed it.
yea i sorry i was typing it out
west sapphire
the idea looks fine, what can you conclude
ember cloak
So you just showed that the infinite sum is bigger than or egal to 1?
waxen smelt
So you just showed that the infinite sum is bigger than or egal to 1?
yea i just realised that
west sapphire
in particular, write a formula for that 1/n + 1/n + 1/n ...
how many 1/n's is that
waxen smelt
it just becomes n/n = 1
west sapphire
no, careful, there aren't n of them
waxen smelt
i think the right hand side has to be some series that diverges
west sapphire
yea
this idea is right but you'll have to do a bit more work to show that S_n actually diverges
you're giving up too much when you say S_n > 1/n + 1/n + 1/n ...
some of those terms can be given higher bounds than 1/n
pearl pondBOT
@waxen smelt Has your question been resolved?
wary dragon
havent done calc 2 in a long time but like test for big values of n and see what u get
do the numbers keep getting smaller?
waxen smelt
havent done calc 2 in a long time but like test for big values of n and see what...
i tied it uptil 40 and it was getting bigger
waxen smelt
yea but like their sum get sbigger
waxen smelt
how do i prove it
@west sapphire i looked at the solution and it was fairly straightforward
then took 1/2 outside the sigma sign and then proved 1/n is divergant
which makes sense
thankyou so much
west sapphire
nice
west sapphire
do you have some other method in your mind?
i thought you were trying to prove it from scratch, not using the fact that the 1/n series diverges
what you were doing is similar to how you prove that the 1/n series diverges
waxen smelt
i think its called the p series test or smth
yea we havent covered it yet
wary dragon
search it up
waxen smelt
what you were doing is similar to how you prove that the 1/n series diverges
aaah
thankyou so much guys
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fresh silo
pearl pondBOT
fresh silo
i need help for this
pearl pondBOT
i need help for this
west notch
rewrite it using trig identity
fresh silo
sin²x/cos²x
west notch
No
terse cedar
sin²=1-cos²
west notch
sec^2(x) = 1 + tan^2(x)
terse cedar
$\int \tan ^2(x) \dd x \ =\int \frac{\sin ^2 (x)}{\cos ^2(x)}\dd x \= \int \frac{1-\cos ^2 (x)}{\cos ^2 (x)} \dd x\ =\int \frac{1}{\cos ^2 (x)}-1 \dd x$
jolly parrotBOT
Adam Chebil
west notch
$\int tan^2(x) \dd x = \int (sec^2(x) - 1) \dd x$
jolly parrotBOT
Panda
rough python
"Let T_A, T_B, and T_C: R^3 --> R^3 be three linear transformations with standard matrices respectively" [image 1].
Exactly one of these transformations is invertible. Call this transformation T and solve for T^-1 [image 2]".
rough python
So I found out that C is the invertible one, and I attempted to find the inverse of C....
Which got me:
$$ T^{-1} =\begin{bmatrix}-1 & 4 & 3 \2 & -3 & -2 \-2 & 2 & 1 \end{bmatrix} $$
jolly parrotBOT
HqppyFeet
rough python
However, I noticed that when I tried to multiply this with C, I'm not getting the identity matrix I_3.
...Perhaps I should show my row manipulation process and you could troubleshoot if I made any errors?
frank goblet
you did a typo
in the last picture
the bottom left matrix
at the bottom left
should be -2
not +2
your inverse matrix is correct
rough python
frank goblet
yeah haha
pearl pondBOT
rough python
.reopen
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elfin fulcrum
can you help me calculate mew? or is the mew 0?
pearl pondBOT
can you help me calculate mew? or is the mew 0?
grave thistle
Mew?
trail bough
pearl pondBOT
trail bough
2s 2m
so
1?
somethings telling me that logic may not be right can anyone guide
me
!status
pearl pondBOT
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
what is plotted?
west sapphire
i mean is that displacement vs time
trail bough
yes
west sapphire
so what's the derivative of that graph when the displacement is -2 meters?
trail bough
i dont know
i dont know how to find the derivative
is it like negative one
ping: @west sapphire
west sapphire
derivative = slope, right?
west sapphire
yea so what's the slope at the points where the displacement is -2?
trail bough
2/-2
west sapphire
you don't have to do any calculation, just look at the graph
nova mortar
pearl pondBOT
nova mortar
how did they go from that to that?
pearl pondBOT
how did they go from that to that?
unique ibex
how did they go from that to that?
They multiplied both sides by x
pearl pondBOT
@nova mortar Has your question been resolved?
unkempt yacht
Apply an AC voltage to an RLC circuit connected sequentially with fixed frequency and RMS voltage.
The RMS voltages measured on each component R, L and C are 40V, 80V and 50V respectively. Replace the capacitor C with another capacitor C' = 0,5C.
Calculate the RMS voltage on the resistor then.
sharp smelt
!status
pearl pondBOT
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
do you know the formula for Voltage in AC?
How the coltage across each component is related to one another?
*voltage
unkempt yacht
do you know the formula for Voltage in AC?
$U\sqrt2\cos{(\omega t+\phi)}$
jolly parrotBOT
FungusDesu
unkempt yacht
How the coltage across each component is related to one another?
hmm, I = Ur/R = Ul/Zl = Uc/Zc?
sharp smelt
The phase difference between the voltage across C and L is π , and that between R and L and R and C is π/2(This is just the magnitude)
*between C and L
unkempt yacht
yup, that i know well
sharp smelt
Can you use that here?
unkempt yacht
the problem is that no I or omega or anything sufficient is given here
sharp smelt
assume an inductance of L, capacitance of C and angular frequency (w) and then find the relationship between R, Xc and XL to solve it
unkempt yacht
Can you use that here?
dont think it would help much though
sharp smelt
so Xc is now doubled thus shouldn't the voltage across it double too? Either that or I'm applying DC concepts here
unkempt yacht
so Xc is now doubled thus shouldn't the voltage across it double too? Either tha...
dont think so
I also changes so it wouldnt depend on Xc alone?
sharp smelt
I also changes so it wouldnt depend on Xc alone?
oh, right sorry
pearl pondBOT
@unkempt yacht Has your question been resolved?
waxen talon
pearl pondBOT
pearl pondBOT
@waxen talon Has your question been resolved?
worldly glacier
is this right and is there a non life hating way to solve this q
worldly glacier
btw
,w simplify \frac{1}{1-x^5} * \frac{1}{1-x} * \frac{1}{1-x} * \frac{1-x^3}{1-x} * \frac{1-x^5}{1-x} * \frac{1-x^2}{1-x}
jolly parrotBOT
acoustic path
to start, do you know what the series expansion of 1/(1 - x) is ?
worldly glacier
to start, do you know what the series expansion of 1/(1 - x) is ?
I mean we did tis remeber
I just fully solved it
you remember me
acoustic path
that is not a good way of writing the answer
worldly glacier
I just 💀 wanna end it all bc of this formula
worldly glacier
that is not a good way of writing the answer
is it the answer tho 😭
acoustic path
it might be but that's not much of a "closed form"
worldly glacier
,w simplify $\frac{\frac{-5(-1)^n n!}{(x-1)^{n}} - \frac{9(-1)^n n!}{(x-1)^{n+2}} - \frac{6(-1)^nn!}{(x-1)^{n+3}}}{n!} $
jolly parrotBOT
acoustic path
ideally your answer should not have an x term in it
acoustic path
to start, do you know what the series expansion of 1/(1 - x) is ?
this again
worldly glacier
to start, do you know what the series expansion of 1/(1 - x) is ?
yeah
acoustic path
what is it?
jolly parrotBOT
nosqldb
acoustic path
uh..
worldly glacier
having it in that form doesn't help for this problem
$\sum_{k=0}^{\infty} x^k$
or sm like this
acoustic path
nice that's right
worldly glacier
ye
jolly parrotBOT
nosqldb
acoustic path
so let's consider the following
worldly glacier
so let's consider the following
yes
I mean I did consider that to be fair
to get the generating functoin
acoustic path
what happens when we differentiate both sides?
worldly glacier
what happens when we differentiate both sides?
nx^{n-1}
acoustic path
ye
acoustic path
,w simplify \frac{1}{1-x^5} * \frac{1}{1-x} * \frac{1}{1-x} * \frac{1-x^3}{1-x} ...
using the repeated differentiation process, we can get a simple closed form for the individual coefficients of this gf for any n value
worldly glacier
using the repeated differentiation process, we can get a simple closed form for ...
I'm an idiot
I just had to plug in x = 0
$\frac{\frac{-5(-1)^n n!}{(-1)^{n}} - \frac{9(-1)^n n!}{(-1)^{n+2}} - \frac{6(-1)^nn!}{(-1)^{n+3}}}{n!}$
jolly parrotBOT
nosqldb
worldly glacier
,w simplify $\frac{\frac{-5(-1)^n n!}{(-1)^{n}} - \frac{9(-1)^n n!}{(-1)^{n+2}} - \frac{6(-1)^nn!}{(-1)^{n+3}}}{n!}
jolly parrotBOT
Requested by nosqldb
worldly glacier
,w simplify \frac{\frac{-5(-1)^n n!}{(-1)^{n}} - \frac{9(-1)^n n!}{(-1)^{n+2}} - \frac{6(-1)^nn!}{(-1)^{n+3}}}{n!}
jolly parrotBOT
worldly glacier
nvm
I'm so confused
@acoustic path
literally if I do the nth derivative of f
and plug in 0
and divide by n!
shouldn't I get the coef
acoustic path
to my knowledge you are not supposed to plug in 0
acoustic path
ye
to illustrate this point,
can you come up with a closed form for the nth coefficient of this function right here?
worldly glacier
to illustrate this point,
can you come up with a closed form for the nth coeffi...
yeah I mean
I would use the same technique tho
of f^(n)(0)/n!
basically ur clearning all the terms with variables
and ur left with the constant of x^n multiplied by n!
then divide by n!
so you jsut get a_n
acoustic path
that idea's right although something seems to be amiss
and imo it slightly overcomplicates things
worldly glacier
I mean I have my generating function
acoustic path
because if you can write a sum of a series, then you immediately have the coefficients already
worldly glacier
I just need the coefficient
acoustic path
**nosqldb**
the coefficients are right here
worldly glacier
because if you can write a sum of a series, then you immediately have the coeffi...
I converted the sum of series
INTO the fraction representation
idk why I'm converting it again
acoustic path
to illustrate this point,
can you come up with a closed form for the nth coeffi...
@worldly glacier the main idea here is that the coefficients of x^n in the sum are the components of the closed form answer your are looking for
pearl pondBOT
@worldly glacier Has your question been resolved?
kind finch
Question 13
pearl pondBOT
Question 13
kind finch
How do i start?
I tried rewriting the equations in as u and v = in terms of x and y but that got me nowhere
cold swift
kind finch
Yeah
kind finch
I did with v and I could get an equation for that but with u i couldnt
But is rewriting the equations the right thing to do?
cloud zephyr
consider the use of words in the textbook, i think it requires you to do "example 3" instead if "Ex14.8 question 3"?
not sure though 🤔
kind finch
consider the use of words in the textbook, i think it requires you to do "exampl...
Ohhhh that must be it
Thank you
.close
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distant plinth
Let 0<=x<=4. Find the maximum value of x^3(4-x). (No calculus)
distant plinth
I've been stuck for a while
pearl pondBOT
I've been stuck for a while
distant plinth
I'm assuming I should use AM-GM because that was taught in the lesson
gritty quarry
distant plinth
and 4-x is always non-neg for the range
I tried x+x+x+(4-x)>=4* fourthroot(x^3(4-x)) but that gave me the max as 16
rain inlet
i had a question do you read this as the power set of the set containting A?
distant plinth
what
jolly parrotBOT
damianxxz
sharp smelt
Let 0<=x<=4. Find the maximum value of x^3(4-x). (No calculus)
can you try finding the vertex perhaps
distant plinth
im not sure what you mean
sharp smelt
i had a question do you read this as the power set of the set containting A?
!occupied
pearl pondBOT
i had a question do you read this as the power set of the set containting A?
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
distant plinth
can you try finding the vertex perhaps
how?
sharp smelt
hmm, no calculus, right?
distant plinth
also why did AM-GM not work
distant plinth
hmm, no calculus, right?
yea
pearl pondBOT
@distant plinth Has your question been resolved?
granite kiln
Is this available
distant plinth
Wdym
acoustic path
Let 0<=x<=4. Find the maximum value of x^3(4-x). (No calculus)
after writing this as 4x^3 - x^4,
you want to be able to manipulate this expression in a way that effectively sets you up to apply am-gm
hint: ||when performing your manipulation, think about how you can to make that pesky x^4 term disappear||
pearl pondBOT
@distant plinth Has your question been resolved?
distant plinth
after writing this as 4x^3 - x^4,
you want to be able to manipulate this expres...
Thank you I’ll try that
vale turtle
pearl pondBOT
vale turtle
I'm checking for one one many one
So here i split it into
X>=0 2×4^x
X<0 4^x+1/4^x
I can see both function are increasing
So it will be above x axis
Y>2
pearl pondBOT
@vale turtle Has your question been resolved?
pearl pondBOT
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spark parcel
pearl pondBOT
spark parcel
so in the answer key of a
they replaced cos (4pie/25 t) by 1 for high and -1 for low
why
nvm i got it
thanks ren :))
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fleet blaze
I don't know if this is the right channel but. I need an equations that equals 18 for my 18th birthday cake. Any idea is welcomed, just I don't want it to be too simple or too complex. (Like 1 integral is fine.)
pseudo oxide
take like a function that has a difference of 18 b/w two values
and then differentiate it
then use integrals to come up with a fancy equation and stuff
if you want a complex-looking integral it has to be really weird so
pearl pondBOT
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pearl pondBOT
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fleet blaze
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mellow pine
I need help on this problem - I have no clue where to start
pearl pondBOT
I need help on this problem - I have no clue where to start
mellow pine
pearl pondBOT
mellow pine
I know how to project a vector A onto a plane described by vectors B and C
but I don't even have a vector to project in this case? What do I do???
west sapphire
the vector will be the "input" to the multiplication by P
i.e. given a vector v, the new vector Pv will be the projected version
you need to find the matrix P that makes this happen
mellow pine
the vector will be the "input" to the multiplication by P
i.e. given a vector v,...
I'm still lost, sorry 😭
mellow pine
the vector will be the "input" to the multiplication by P
i.e. given a vector v,...
we don't have a vector v though!
they didn't give us any
west sapphire
you need to find a matrix P that takes an arbitrary vector v and projects it to a vector Pv which is in the indicated plane
the same P will work for any v
west sapphire
i never remember formulas so i have to derive stuff like this from scratch haha
do you have a formula for the projection if you knew the vector v?
mellow pine
you need to find a matrix P that takes an *arbitrary* vector v and projects it t...
just to reiterate, given our OWN matrix which we create, it takes ANY vector V, and it creates the subspace S
mellow pine
do you have a formula for the projection if you knew the vector v?
if I wanted to project vector v into the plane described by the two vectors
west sapphire
just to reiterate, given our OWN matrix which we create, it takes ANY vector V, ...
well the subspace exists regardless of our efforts
our matrix which we created will do the job of taking any vector v and projecting it to a new vector called Pv which is in S
mellow pine
then I would do vector v - projection of v onto normal of plane
west sapphire
then I would do vector v - projection of v onto normal of plane
yea good so far
mellow pine
well the subspace exists regardless of our efforts
our matrix which we created w...
OHHHHH I see
west sapphire
normal of plane you can get by the cross product of those two vectors yea?
mellow pine
i never remember formulas so i have to derive stuff like this from scratch haha
yeah I hope to eventually get knowledge like this
where even like 5 years pass
I am still know the concepts well enough to derive formulas
west sapphire
where even like 5 years pass
yea this is why i don't memorize, i just remember geometrically what it looks lke
then work out the formula from that
everyone's brain works differently tho
mellow pine
yea this is why i don't memorize, i just remember geometrically what it looks lk...
unfortunately my class doesn't do that!!!
they just give formulas, and sometimes no formulas at all
west sapphire
unfortunately my class doesn't do that!!!
well your description was a pretty good geometric summary!
west sapphire
from that you could draw a picture and work out what gets dot producted with what etc
mellow pine
well the subspace exists regardless of our efforts
our matrix which we created w...
also just to confirm, this new vector Pv is in the form of (a, b, c) right
west sapphire
yea, it'll still be a 3-dimensional vector even though it's constrained to the two dimensional plane S
mellow pine
from that you could draw a picture and work out what gets dot producted with wha...
lemme think
lemme get paper
mellow pine
from that you could draw a picture and work out what gets dot producted with wha...
I am still confused - for the dot product, we dot product the Normal Vector with vector K
west sapphire
what's K here
mellow pine
where K is the vector getting projected onto the plane described by the Normal Vector
mellow pine
well the subspace exists regardless of our efforts
our matrix which we created w...
oh I hsould use "any vector v"
west sapphire
haha
mellow pine
ah ok so K is your input vector?
lets call it v my bad
NewV = OldV - Projection of V into plane
west sapphire
yea so you need to do something like:
v - (v.n)n
where n is a unit vector normal to the plane
west sapphire
dot product of v with n
west sapphire
yep
mellow pine
yea so you need to do something like:
v - (v.n)n
where n is a unit vector normal...
this makes sense, yes
wait I thought it was
v - v dot product n divided by magnitude of n^2 times vector n
ohh same thing
cuz n is UNIT vector
got it
bro i'm sorry i'm lokey slow
💀
west sapphire
now you can find a matrix A such that
Av = (v.n)n
that's the harder part
and certainly you know a matrix B such that Bv = v
so
if your P was B - A
then you would have:
Pv = (B - A)v = Bv - Av = v - (v.n)n