could I please get some help with this
#help-0
green solstice
lone heartBOT
could I please get some help with this
ionic oak
is there a particular part that you're stuck on?
mortal trellis
how old are you?
vale wigeon
@green solstice how old are you?
green solstice
<@331317947941257216> how old are you?
I am 13
vale wigeon
as you say.
fallen verge
13 year old with a 6 year old account...
green solstice
is there a particular part that you're stuck on?
I stuggle with multiplying above 10
vale wigeon
well she is 13 now so. nothing unkosher in the present
fallen verge
aight fair
vale wigeon
I stuggle with multiplying above 10
if you were asked to, say, multiply 20 * 6, could you do it
green solstice
yeah I started discord quite young
green solstice
if you were asked to, say, multiply 20 * 6, could you do it
yes because I can do 6 x 10 and then do it twice
but if its like 27
I get confused
green solstice
and it takes me a long time to figure it out
green solstice
I havent heard of it
green solstice
you're able to do 20 * 6 as 6 * 10 * 2, great
thanks
vale wigeon
shame, bc that's what is happening.
but then again, 21 groups of 6 is the same as 20 groups of 6 plus 1 group of 6 -- you might be able to get this even without it being phrased with the scary word "distributive law"
vale wigeon
21 * 6 = 20 * 6 + 1 * 6
do you understand this?
vale wigeon
yes that's what i said
green solstice
okay yeah I get it now
silk fox
Our prof just write it in the board
vale wigeon
@silk fox open your own channel
read #❓how-to-get-help for instructions on how to open your own channel
green solstice
@vale wigeon is there a fast way to figure out two double digit multiplication in your head?
like 53 x 27 for example
vale wigeon
two-digit by two-digit?
meh
i can't say i've ever needed that much in the way of mental math
green solstice
oh, well whats the best way you think to approach that question
mental or on paper
like in general
quasi sand
<@183668144404037632> is there a fast way to figure out two double digit multipl...
I think learning abacus may help you to figure out large number multiplication in you head
vale wigeon
"advanced" and "difficult" are both subjective
green solstice
I think learning abacus may help you to figure out large number multiplication i...
whats abacus
green solstice
"advanced" and "difficult" are both subjective
yeah I was kind of thinking that
it would probably be dificult for me but easy for you
quasi sand
whats abacus
It's a counting ancient tool.
vale wigeon
it's a matter of how much you have had to practice with it i guess
green solstice
It's a counting ancient tool.
this thing?
quasi sand
this thing?
Yep
fallen verge
the only method i can suggest is a "factor breakdown" method:
for example if have 28x15, you can break it down into (2x14)x(3x5)
you can rearrange it to be 14x3x2x5 which you can make to be (14x3)x(2x5)
this equals (42)x(10)=420
this does mean you have to know how to divide fast or know the factors of numbers
this is also unhelpful for prime numbers
green solstice
the only method i can suggest is a "factor breakdown" method:
for example if hav...
that sounds interesting
thank you
fallen verge
also abacus math is really cool, if you get super good at it, you look superhuman
green solstice
how does abacus work
fallen verge
you learn how to use an abacus, then your muscle memory kicks in and you can do the math with an imaginary abacus
green solstice
woah
fallen verge
some people can get some big numbers
but thats beside the point for now, start small and make your way up
lone heartBOT
@green solstice Has your question been resolved?
fast lichen
like 53 x 27 for example
in my head i do 53 * 10 * 2 + 53 * 10/2 + 53 * 2. basically doing smaller simpler calculations and adding them up
but doing mental math for large numbers isnt very useful. learn a method to do it by pen and paper and thats all you need really
alpine sable
lone heartBOT
alpine sable
i'm not sure how to even begin with this problem
fast lichen
figuring out the number of rows and columns for A can be a start
alpine sable
how?
fast lichen
first columns. you are multiplying with a 2x1 vector so for matrix multiplication to even be legal how many columns should A have?
alpine sable
2?
fast lichen
yes
and the 'output' is a 3x1 vector
av+bw is
so from that you can determine the rows of A
alpine sable
ye it would be 3 rows right?
alpine sable
2x2 multiplied 2x1 = 2x1
how do you calculate that
fast lichen
its just matrix multiplication
alpine sable
oh right nvm
alpine sable
ye
fast lichen
the b's have to match to be legal
you can go through giving the elements in the 3x2 matrix variable names and multiplying it with (a b) to solve for the values
or just revise in your textbook what matrix multiplication looks like
maybe that will give you an aha moment of what values it should be
fast lichen
wdym?
alpine sable
one sec, ill try it out to see if im crazy or if it works
edgy cliff
this thing?
算盘 in china
fast lichen
btw
alpine sable
ye
fast lichen
it literally is the definition of matrix multiplication
fast lichen
oh ok
errant dagger
lone heartBOT
lone heartBOT
@errant dagger Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
ionic oak
For what values of N does $\lim_{x\rightarrow\pi} \frac{d}{dx}(|\sin x |^{\frac{1}{N}x^2})$ exist?
ocean sealBOT
Quixz
ionic oak
I took a derivative, graphed it in desmos, and immediately got stuck
lone heartBOT
@ionic oak Has your question been resolved?
polar trout
lone heartBOT
polar trout
how is ln n > 1
edgy cliff
because n>3>e,and ln (e) = 1
gilded marten
can anyone help me with this
lone heartBOT
can anyone help me with this
gilded marten
simple geometry but i cant get no.8
languid bolt
In a parallelogram, such as this, the diagonals gets divided into 2 equal parts no?
by that i mean like...
For line DEB
DE = EB
cmiiw
gilded marten
yes
but the problem is, im trying to solve for the exact measurements for up and pl which is ul cut in half by trying to get x and y
so that means up and pl are of the same length
x=1, y=2 gives 5 for both up and pl
but y=7x-3 contradicts it
ionic oak
there are lots of x and y that satisfy x+2y = 3x+y
ionic oak
0,0
ionic oak
i think you should start by substituting y = 7x - 3 for the lengths of UP and PL
barren token
gilded marten
ahhh
ok
thats what we got, 1,2 and 0,0
but the other statement said y=7x-3
i think i got it
0.6 and 1.2?
ionic oak
sounds right to me 👍
clear juniper
"Given the equation (a-2)x-2y-1=0, find for what value of a represents a straight line:
a) parallel to the x axis
b) parallel to the y axis"
lone heartBOT
"Given the equation (a-2)x-2y-1=0, find for what value of *a* represents a strai...
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
4
lone heartBOT
Show your work, and if possible, explain where you are stuck.
clear juniper
i mean point a) was pretty easy i guess
a-2=0
a=2
b) is what i'm confused on
-2y=0
?
clear juniper
?
clear juniper
open your own channel
mortal flame
how
clear juniper
mortal flame
then what should i do now then*
ionic oak
"Given the equation (a-2)x-2y-1=0, find for what value of *a* represents a strai...
this is a bonkers question
whats the form of the equation for a line thats parallel to the y axis
its gotta be x = c or something like that right
the given equation distributes out to ax - 2x - 2y = 1 so i imagine you want to cancel out the y term... is it legal to put a = 2y/x?
clear juniper
no
ionic oak
why not
lone heartBOT
@clear juniper Has your question been resolved?
hallow vessel
lone heartBOT
hallow vessel
i know that the theorem is
if a <= b and b <= a, then a = b
but how do i use
like what are the steps in a proof for this
do i just count out the elements
and say that each one has a correlating value
0 -> 3
1 -> 4
2 -> 5
therefore mod(a) = mod(b)
?
lone heartBOT
@hallow vessel Has your question been resolved?
lone heartBOT
@hallow vessel Has your question been resolved?
lone heartBOT
@hallow vessel Has your question been resolved?
obtuse parrot
Hey guys
obtuse parrot
this is a small excerpt from a paper im reading
so the author takes the inverse Fourier transform of the top equation (equation 10)
but, the results of which in the next equation dont make sense
how does taking the fourier transform of u(k, t) somehow transform it into u(k, t+dt)?
this isnt a typo, because he goes on to take full advantage of it
and this "transformation" is critical to the paper but never explained
the final result works, meaning that it is correct, but i cant possibly fathom how
lone heartBOT
@obtuse parrot Has your question been resolved?
lone heartBOT
@obtuse parrot Has your question been resolved?
tender mirage
Out of curiosity, what is k is in this context?
obtuse parrot
wavenumbers, theyre precaculated in this context
tender mirage
Ah ok. I can't speak to the nitty-gritty, but the Fourier transform is a subset of Laplace and just converts from the time domain to the frequency domain. τ is actually just a constant (in general, maybe not here) https://en.wikipedia.org/wiki/Time_constant
Also, notice that the function on the left-hand side of the equation, u, has a "hat" in (10) but not in (11) - this denotes the Fourier transform of u, so to find u you just take the inverse. Applying the inverse Fourier to the left-hand side leaves you with just u. Applying it to the right-hand side translates the whole thing from the frequency domain into the time domain, so now you have to introduce time into the equation. I'm not sure why it's delta-time as opposed to just t here. But I think, from a quick google, the inverse of the right-hand side will be a convolution of of the two terms with respect to t.
Keeping in mind I learned the basics of this in a controls class 5 years ago :|
lone heartBOT
@obtuse parrot Has your question been resolved?
tender mirage
wrong place @alpine sable, you gotta take a channel in the available pool
lone heartBOT
lone heartBOT
Available help channel!
spare crane
trying to calculate further Information gain, already found out odor is the best classifier but now i need to find the next attribute for cases where odor is "okay" and somehow my information gain turns out to be -0.02 which ISNT nonnegative so it cant be the answer. what did i do wrong
lone heartBOT
trying to calculate further Information gain, already found out odor is the best...
@spare crane Has your question been resolved?
spare crane
<@&286206848099549185>
lone heartBOT
@spare crane Has your question been resolved?
lone heartBOT
@spare crane Has your question been resolved?
spare crane
.close
icy plank
if sin(pi/7) = 0.434 what is sin(6pi/7)
lone heartBOT
if sin(pi/7) = 0.434 what is sin(6pi/7)
pseudo ice
What's pi - pi/7?
icy plank
.close
old mirage
lone heartBOT
old mirage
What're the bounds for this integral problem?
I messed up and had theta going from 0->2pi and r from 0->pi/2
But I'm thinking it should be theta from 0->pi and 0->1
lone heartBOT
@old mirage Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
am I correct that this cant be solved conventionally?
you need to use algebra right
like you can't simply do 3a+b / 3
you have to let PQ = xa + yb
then solve it that way
or is there a shorter way
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
.close
alpine sable
lone heartBOT
alpine sable
can you help me write the equation
olive oar
Apply transformations to a standard hyperbola
lone heartBOT
@grizzled shuttle Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Hello
clever nimbus
versed escarp
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
primal galleon
I'm struggling with the following integral:
$$\int_{-2}^1\left(\frac{1}{x}-3 e^{-x}+\sin (\pi x)\right) d x$$
ocean sealBOT
dgh
primal galleon
We've not been taught integration by parts for this problem. How do I solve it?
fierce prairie
We've not been taught integration by parts for this problem. How do I solve it?
Integration by parts is for functions being multiplied so that isn't needed
I would split the 3 terms into 3 integrals and solve each separately
1/x is just ln|x|
the other 2 are u-sub
primal galleon
$$\int_{-2}^1\left(\frac{1}{x}-3 e^{-x}+\sin (\pi x)\right) d x$$
$$=\int_{-2}^1\frac{1}{x}dx - \int_{-2}^1 3 e^{-x} dx + \int_{-2}^1 \sin(\pi x)dx$$
ocean sealBOT
dgh
primal galleon
Like this?
fierce prairie
Yeah
primal galleon
To compute the definite integral $\int_{-2}^1\left(\frac{1}{x}-3 e^{-x}+\sin (\pi x)\right) d x$, we can apply linearity and split it into three separate integrals: $\int \sin (\pi x) d x-3 \int e ^{-x} d x+\int \frac{1}{x} d x$.
\\
The first integral can be solved by substituting $u=\pi x$ and using the standard integral $\int \sin (u) d u=-\cos (u)$, which gives us $-\frac{\cos (\pi x)}{\pi}$.
\\
The second integral can be solved by substituting $u=-x$ and using the exponential rule $\int a ^u d u= \frac{ a ^u}{\ln ( a )}$, with $a = e$, which gives us $- e ^{-x}$.
\\
The third integral is a standard integral, which gives us $\ln (x)$.
\\
Plugging these solved integrals back in, we get $\int_{-2}^1\left(\frac{1}{x}-3 e^{-x}+\sin (\pi x)\right) d x=\boxed{-\frac{\cos (\pi x)}{\pi}+\ln (x)+3 e ^{-x}}$
ocean sealBOT
dgh
primal galleon
So now we just evaluate the definite integral between -2 and 1?
primal galleon
\begin{align*}
&\left(-\frac{\cos (\pi \cdot 1)}{\pi}+\ln (1)+3 e ^{-1}\right)\bigg|_{-2}^{1} = \
&\left(-\frac{\cos (\pi \cdot 1)}{\pi}+\ln (1)+3 e ^{-1}\right) - \left(-\frac{\cos (\pi \cdot (-2))}{\pi}+\ln (|-2|)+3 e ^{2}\right) \
=& \left(-\frac{\cos (\pi)}{\pi}+0+3 e ^{-1}\right) - \left(-\frac{\cos (-2\pi)}{\pi}+\ln (2)+3 e ^{2}\right) \
=& \left(\frac{1}{\pi}+3 e ^{-1}\right) - \left(\frac{1}{\pi}+\ln (2)+3 e ^{2}\right) \
\approx& \boxed{-21.12}
\end{align*}
ocean sealBOT
dgh
primal galleon
Btw, I was supposed to solve this without a calculator @fierce prairie
fierce prairie
primal galleon
cos(2π), cos(π) is fine…
fierce prairie
That can be left as well
primal galleon
I don't think they wanted the numerical answer
Leet me check
@fierce prairie It says the right answer is "Integral doesn't exist (divergent)"
Because of the 1/x?
fierce prairie
Hmm
fierce prairie
Because of the 1/x?
I think so
I honestly haven't seen one like this but symbolab is also saying it diverges
grave niche
The answer is 2/0 or 0 right?
lone heartBOT
The answer is 2/0 or 0 right?
remote heron
you should factor
grave niche
How did you get there
well because the Limit equals to 0/0 when you substitute 0 in for z we can do Hopetals rule
grave niche
Ya i guess the right move would be to Factor right?
finite flax
You have already covered LHospital's Rule?
remote heron
i see a common factor
wary stream
well because the Limit equals to 0/0 when you substitute 0 in for z we can do Ho...
But if you did this way, you don't get 2/0, I don't think. I'm doing it mentally but pretty sure it's not 2/0
finite flax
Ya know, factoring, actually, I agree that's all you need
remote heron
you have to do something special since its complex right
wary stream
I agree with factoring too but you did LHospital's wrong
finite flax
Zeros won't hurt you after you factor out common factor in top and bottom
finite flax
Ooh...top will be odd power of z though
Does that matter?
I think the limit is same from LHS and RHS anyway
grave niche
Welp i guess i over complicated myself lol, thanks guys
remote heron
or youd need the limit to be the same approaching from any path
finite flax
well there is no lhs and rhs
...of 0. What z approaches
remote heron
right but isnt z complex
im just assuming
so theres no lhs or rhs of 0, theres a region surrounding it
finite flax
so theres no lhs or rhs of 0, theres a region surrounding it
How do you mean if it's not complex?
remote heron
is it not complex?
remote heron
well then why did they use z 
finite flax
This is like a Monty Python sketch now
finite flax
DOES THIS SHOP HAVE ANY CHEESE AT ALL???
finite flax
$\lim_{x \to 0} \frac{z+1}{z^2 - 1}$
remote heron
$\lim_{z\to0}\frac{z+1}{(z+1)(z-1)}$
ocean sealBOT
jan Niku
remote heron
ocean sealBOT
Disorganized
finite flax
Oh, yep: then @remote heron
1/(z-1)
So LHsopital doesn't need to come into this
@grave niche
finite flax
Well it technically can.... right?
Sure it can, but usually when you ask a teacher or a student if you are expected to use LH, they arent
remote heron
its a sin to use the hospital rule where you dont have to
finite flax
We had to learn how to prove LH before we could use it
grave niche
So LH is basically a cheat code?
grave niche
im pretty sure in order to use LH you need to get 0/0 or ♾️ /♾️ in a limit right
remote heron
analysis can kill
tired nexus
How would I graph this?
lone heartBOT
How would I graph this?
tired nexus
this is in general form
lone heartBOT
@tired nexus Has your question been resolved?
real cipher
place y alone
in ur case
y = 3x - 9
now put any value of x in your equation u would get the value of y and then plot in the graph
for e.g
if x=2
y = 3*2 - 9 = -3
(x,y) = (2,-3)
similary follow this process 2 or three times
lone heartBOT
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Available help channel!
orchid forge
lone heartBOT
orchid forge
Im confused on how to integrate this
I got until here but then when i integrate this it just gives me 1 which isnt the answer
vale wigeon
$\int u^{-1} \dd{u} = \ln|u| + C$ though
ocean sealBOT
Ann
vale wigeon
so where are you getting just 1 from
coral thorn
power rule cannot be used when exponent is -1
digital galleon
orchid forge
power rule cannot be used when exponent is -1
Oh
Wait what
But what happens to the numerator then?
limpid turret
where?
left trellis
But what happens to the numerator then?
the numerator is just 1 if you rewrite it
$u^{-a}=\frac{1}{u^a}$
ocean sealBOT
ℕαv
lone heartBOT
@orchid forge Has your question been resolved?
orchid forge
Oh shit yeah thx
lone heartBOT
Available help channel!
agile grove
What is the application of the unit circle in the real world, and what is the reasoning behind the specific unit of 1? Also are we limited to just the 2 special triangle cases where they are labelled on the unit circle. Or can we use any value for the angles and thus find the proper lengths of its sides and it stuff? I know its good for trigonometric rations.
limpid turret
Real-world application is always subjective to someone's skill-set
unit circle is used for trigonometry
So you're asking what the real-world applications to trig are, which is a heckin' lot
If by 2 triangle cases you mean 45-45 and 30-60, then no
Those are just the easiest to memorize
We use 1 because it's literally a "unit". It makes the math easiest
If it was anything besides 1, we'd have to divide or multiply to account for the non-unit ratio
Or can we use any value for the angles and thus find the proper lengths of its sides and it stuff
I don't know what you mean by this
lone heartBOT
@agile grove Has your question been resolved?
thick beacon
lone heartBOT
thick beacon
how do I even start doing this question ?
I know how to differentiate it, but how do I form that equation
?
thick beacon
Just differentiate and chuck everything into that equation
?
I kinda understand but can you like show me how to do it ?
winter light
Compute first and second derivative of the y they give you above, and substitute those into the diff. eq. and check whether you reach an identity or not
limpid spade
real chads solve the diff equation first
remote tapir
real chads solve the diff equation first
Integratiosns?
Bro am doing it right now
Partial fraction
limpid spade
what
remote tapir
ITS CONFUSING
lone heartBOT
@thick beacon Has your question been resolved?
thick beacon
Thats it
I don’t know how to further differentiate and I tried to figure out a way to make it form the equation given but so far I don’t really know
cyan storm
dont take e^2x in common before differentiating again
in second last step itself you get two functions in addition both are similar to the original function so just differentiate them separately and then add together
cyan storm
i can understand your frustration from the fact that you are doing it by assuming the functions being multiplied first
then differentiate individually and then apply the product rule
lone heartBOT
@thick beacon Has your question been resolved?
vapid smelt
It would be of great help if someone could explain how the last step came to be. Appreciate it.
The question is:
marsh rapids
,w d/dx arctan(ax+b)
ocean sealBOT
limpid turret
marsh rapids
So if you adapt it you can find such antiderivatives
untold forge
but it's 3/4
vapid smelt
,w d/dx arctan(ax+b)
ummm, what?
marsh rapids
,w integrate 1/((x+a)^2 + b)
ocean sealBOT
limpid turret
You can do this, slowly, with a lot of u-substitution
vapid smelt
<:hmmCat:831508801646755850> but it's 3/4
it added 3/4 to change the limit from 0 to pi/4 to 0 to 1
limpid turret
,w derivative 1/(x^2+1)
ocean sealBOT
vapid smelt
xd
vapid smelt
You can do this, slowly, with a lot of u-substitution
ohh
limpid turret
,w derivative arctan(x)
vapid smelt
i guess that was what it was intended for since its worth 6 marks
ocean sealBOT
limpid turret
This is the key thing you need to know
after a butt-load of u-subs, you can get here and solve your integral
vapid smelt
xd. Alright thanks, i'll try
noble ginkgo
hello
vale sapphire
acoustic mirage
Seems like a tough problem
noble ginkgo
thanks for offering
but it seems like the answer was hidden in plain sight
all i did was watch a 2 minute video and i understood lmaoo
lone heartBOT
@noble ginkgo Has your question been resolved?
acoustic mirage
so this was the ques
can we simply cancel out the term which is present inside the mod and the denominator ?
acoustic mirage
Well not directly
why not ?
as the modulus function makes everything +ve , so why can't we just cancel it out
?
wind cloak
Yeah but the inside of the absolute value is negative
So you'll get 4(2 - x)
Then you can cancel if you wish
You actually can lol
acoustic mirage
i already got the ans 😁
i'm wasn't able to figure out how to solve the mod fucntion thingy
acoustic mirage
Then you can cancel if you wish
if i cancel it i get 16, not -16
wind cloak
So you'll get 4(2 - x)
.
acoustic mirage
So you'll get 4(2 - x)
how do u know that we will get 4(2-x) and not 4(x-2) ?
wind cloak
Because the term inside the absolute value is negative
So we multiply it with -1 to make it positive
acoustic mirage
Because the term inside the absolute value is negative
how do we know that its negative ?
by putting x = 2-h ?
acoustic mirage
is there any other way ?
acoustic mirage
ok
wind cloak
Then you see for yourself that it's negative
keen plinth
the root of 4x - 8 is 2
wind cloak
If you put 1.99999 in the absolute value term
acoustic mirage
ah yes as 4*(number less than 2) < 8
wind cloak
Yes
acoustic mirage
so it must be negative on the left
how did you come to that conclusion ?
ocean sealBOT
acoustic mirage
but it also extending in the positive side ?
how would i be able to plot such a graph so fast ?
wind cloak
but it also extending in the positive side ?
You're interested in a number slightly smaller than 2
Not greater than
acoustic mirage
have you plotted linear graphs before in your life
yea 💀
keen plinth
so it's literally just an upward sloping straight line passing through 2
acoustic mirage
You're interested in a number slightly smaller than 2
oh ok so i would plug in the values of x which are less than 2
wind cloak
Yes
acoustic mirage
so is 4x-8 = 0 ?
quasi sand
You're interested in a number slightly smaller than 2
Why so?. Since for 2- you move from right to left , that means you should foucs on greater number , right? Or am I wrong?
wind cloak
2- is approaching from the left
quasi sand
2- is approaching from the left
Okie sorry.
acoustic mirage
so is 4x-8 = 0 ?
.?
acoustic mirage
when you said plot a graph, 4x-8 would be equal to 0 right ?
keen plinth
i said plot a graph to see that it's negative on the left
it should be a 1 second thing you do in your head to check how to evaluate the absolute value
acoustic mirage
it should be a 1 second thing you do in your head to check how to evaluate the a...
i'm dumb 
keen plinth
well now you know
acoustic mirage
i said plot a graph to see that it's negative on the left
but for plotting a graph we need something in the right hand side right ?
y-x=0
like this sort of a thing
keen plinth
is anything stopping you from plotting the graph of the function f(x) = 4x - 8
like it's just to determine the sign of the values inside the absolute value
you don't need to get caught up on this
acoustic mirage
i haven't been taught to do this
i am from somewhere where we are taught trigo without graphs 💀
acoustic mirage
like it's just to determine the sign of the values inside the absolute value
ig i will just stick with the 2-h method 💀
keen plinth
sure
arctic dirge
lone heartBOT
muted furnace
here's how I'd do it
- find angle MOA
- OAM
also reminder that the whole shape is a regular octagon as mentioned in the question
weary void
lone heartBOT
weary void
how would you approach
v(t) = e^(-s)
I know that s(0) = 0
meaning
v(0) = e^(-0)
v(0) =1
echo socket
v(t) = e^(-s)
Differentiate both sides of that with respect to t and get a(t) = e^(-s) * ds/dt
weary void
ok
echo socket
Hm, we still need s(t) though
I suppose we need to solve the differential equation then
ds/dt = e^(-s)
weary void
ye
echo socket
e^s ds = dt
e^s = t + C
You can solve for C by plugging in t = 0 and S = 0, yielding C = 1
So you end up with s(t) = ln(1 + t)
The rest is solving for value t such that the second time derivative of s is equal to -4
weary void
ok so then you get derivative of s(t) as v(t) as 1/(1+t) right
then derive that again for a(t)?
echo socket
Yes
weary void
what is the derivative of 1/(1+t) then
nvm got it
what is the differential equation?
weary void
@echo socket e^s ds = dt
e^s = t + C
HOW DID you get that pleae
please
could you please @ me when your back
lone heartBOT
@weary void Has your question been resolved?
weary void
oh
so you integrate e^s ds to get e^s
and integral of dt is t + c
ok i think i get it
thank you btw
errant dagger
lone heartBOT
ocean hawk
what class is it for? calculus?
errant dagger
what class is it for? calculus?
yup
ocean hawk
so I don't know if this is the best way to solve it
but you're looking to find a substitution $u = x^n$ for some $n$.
ocean sealBOT
cwatson
ocean hawk
take the derivative of that, which gives you "du = ?? dx", where the question marks you can fill in
jolly widget
so I don't know if this is the best way to solve it
definitely not, one could just compute the integral directly without substitution...
ocean hawk
you also know that 7u^2 du should equal 28x^11 dx. so you can combine the 2 equations
ocean hawk
~~definitely not, one could just compute the integral directly without substitut...
true but they're looking for the substitution itself. it can be done in your head but I'm trying to explain how I went about it
lone heartBOT
@errant dagger Has your question been resolved?
errant dagger
true but they're looking for the substitution itself. it can be done in your hea...
i expanded it and equated it and i got it 🙂
u = x^n was perfect starting idea ty
i was very lost
.sloe
.close
dark ibex
Is this wrong?
lone heartBOT
Is this wrong?
dark ibex
i dont understand where the cos(x) in the denominator came from.
marsh rapids
They factored out sec x = 1/ cos x
dark ibex
both the sec(x) ?
marsh rapids
You don't factor something there's only one of
languid bolt
can I say
log_x (0) = -∞
for x > 1
and
log_x (0) = ∞
for x < 1
languid bolt
or not
median oar
The limit of something doesn’t have to be defined at that point
It is entirely possible that the limit of a function is not equal to the function at that point
languid bolt
The limit of something doesn’t have to be defined at that point
What does this mean sorry?
median oar
Consider the function f(x) = 1 for x<0 and x>0
And f(x) = 0 at x=0
The limit as x->0 of f(x) = 1
Even though f(0) = 0
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
@alpine sable Has your question been resolved?
torpid mirage
Put the above expression under the sum, and use the linearity of summation to split sums and get constant outside
in the end it ends up being a sum of k over k which is easy to do
torpid mirage
thanks bro
he probably won't follow it from the first time since it's all words so I will keep an eye for questions
pseudo lily
oh ok
torpid mirage
Just wanna show him how to do it rather than giving the answer
pseudo lily
yes that is the way
ocean sealBOT
Mohamed Mohsen
torpid mirage
you can plug that expression in here $\sum_{k=1}^{n}f(a+k \times \frac{b-a}{n}) \times \frac{b-a}{n}$
tell me if you follow up to this point
ocean sealBOT
Mohamed Mohsen
lone heartBOT
@alpine sable Has your question been resolved?
prisma lantern
Hey, does the least squares methods still give a valid answer even if ker(A) != {0}
prisma lantern
Cause I know there's no unique solution, but I wonder if it still gives you something
lone heartBOT
@prisma lantern Has your question been resolved?
tacit arch
Hey, does the least squares methods still give a valid answer even if ker(A) != ...
What is A
lone heartBOT
prisma lantern
.reopen
lone heartBOT
✅
tacit arch
and how does A relate to least squares?
prisma lantern
Well if you have a system of linear equations
like Ax = b
and b isn't in the image of A, i.e. there is no solution for Ax = b
then you can find a vector x* thats the closest it possible can come to solving Ax = b
heady pollen
riemann, i just got the tex preamble
are you the one who made that? i saw your name and profile picture there
prisma lantern
And I know that if ker(A) has more than just 0
alpine sable
Hey, does the least squares methods still give a valid answer even if ker(A) != ...
See "No linear dependence": https://en.wikipedia.org/wiki/Ordinary_least_squares#Classical_linear_regression_model
alpine sable
riemann, i just got the tex preamble
are you the one who made that? i saw your n...
riemann came up with the idea and organised everything, snow made it possible
heady pollen
crazy
prisma lantern
Hey so @alpine sable I'm not so good with statistics, whats the notation here?
Is it probablility that rank(X) = n is 1?
alpine sable
yup
prisma lantern
Cool
lone heartBOT
@prisma lantern Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
violet ore
I don't understand their formula for the second derivative (in blue)
violet ore
I understand that are are differentiating with respect to x but dx/dy is in terms of t
so we must do something.. but I don't get why they do that
lone heartBOT
@violet ore Has your question been resolved?
vapid shuttle
so we must do something.. but I don't get why they do that
it's an application of the chain rule
violet ore
Yes but I don't see how to derive it
if I have a parameterized curve x = f(t), y = g(t) then I accept dy/dx = [dy/dt]/[dx/dt] but the second derivative I just don't see
So they're doing (d/dx)[dy/dx] = [(dy/dt)/(dx/dt)] but how do they reduce ?
lone heartBOT
@violet ore Has your question been resolved?
lone heartBOT
high wolf
am trying to develop a working understanding of the integral test, comparison test, and p series...this was a question and answer on my study guide but I'm having trouble following
high wolf
Can someone help me understand from the first step. I think they applied u substitution firstly but I'm lost on what they did afterwards..
lone heartBOT
@high wolf Has your question been resolved?
high wolf
Is it not via u substitution?
So that turned into integral of 14/u^3? But how did he get -7/u^3 from that?
Can we start from the beginning? So we have the original function given to us, and we must apply substitution on 2+ root x. Shouldn't that give us instead 7/(root x)*u^3?
Sorry, these sorts of functions are tricky for me to understand
we multiply root x by u^3?
What do we need to multiply u by?
ok.
Any advice?
ocean sealBOT
Azka Aska
high wolf
Is the above for u = 2+ root x?
terse rampart
thien
high wolf
So this is the process, correct?:
How exactly did it become -7/u^2 though...?
Alright, I'm fixing to solve it.
Still not sure how, but it's fine. Somehow, we get -7/(u^2)...then we plug our u back in and get this: now how do we apply this integral test?
How about this. What are they doing in these few steps?
^
How are the getting 7/9 though?
What is going on?
Wait how do you get 1?
We have b there not 1?
ocean sealBOT
Azka Aska
high wolf
Wouldn't it be -7/9 though?
Aren't we meant to subtract upper bound from lower bound?
Okay, you're right. Sorry. So here we were doing integral test. But remind me, why do we set 7/9 less then infiniy?
What do I do with that information though?
How can I use it to determine if there’s convergence or divergence?
How do I know that this integral converges though?
What does this mean? That it’s finite?
Does it have to do with the 7/9?
How do we know it’s not infinite?
Now I’m understanding. But what about the other function?
The /7/(2+ root(b))^2?
This makes it of sense. May I ask more questions?
^
Give me one moment I am heading back to my computer to get the questions
high wolf
Still not sure how, but it's fine. Somehow, we get -7/(u^2)...then we plug our u...
I gave up here.
Im at the point where I have 14 * integral of 1/(u^3)du
I'm confused on the next step to integrate
yes
like, add one to exponent and multiply
Can you visualize the steps for me? Functions like these are weird to me.
high wolf
**Azka Aska**
Like how you did here
ocean sealBOT
Azka Aska
high wolf
Like this?
Got it. I can understand it. My other question is related to another problem:
im doing it now..let me try and see
So does this also converge?
does it not go to 0 like the problem before?
oh wait!
Is it because it's a fraction and this isn't a fraction?
so it won't go to 0 in this case?
As long as b is in the denominator or a variable is in the denominator..?
when we plug infinity in, it goes to 0?
But when it isn't in denominator it goes to infinity?
How does it depend? Can you explain a little further. 😄
high wolf
Okay, are you still available?
Can we go over some more of these types of problems? They're called integral tests?
do these involve p-series as well?
Can we do this?
Okay, working on it rn
Does the process look right?
🙂
And it converges because -1/ln(inf)) goes to infinity because infinity in the denominator as b goes to infinity?
like you said before?
Got it. Are you familiar with the comparison tests?
high wolf
Can we do a problem? I'm not good at comparison tests at all
Can we do this?
No problem!
I sent friend request. 🙂
shell widget
@high wolf Still need help?
high wolf
<@415124030408884245> Still need help?
Yes. Can we work on comparison tests?
shell widget
As n approaches infinity, what do you think the numerator acts like?
Same question for denominator
high wolf
As n approaches infinity, what do you think the numerator acts like?
wouldn't it also be infinity?
high wolf
Yes but I'm not asking that
Then I do not know.
shell widget
3nsqrt(n) or 3n^(1.5)
Or even n^(1.5) will work
The denominator acts like n^2
So as n approaches infinity, the series acts like $\sum_{n=1}^{\infty} \frac{n^{1.5}}{n^2} = \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}}$
ocean sealBOT
Sup?
shell widget
So you can use the limit comparison test with this series
shell widget
@high wolf From the original series
3nsqrt(n) + 1 acts like 3nsqrt(n) = 3n n^(0.5) = 3n^(1.5)
n^2 + 4 acts like n^2
So your series acts like 3n^(1.5) / n^2 = 3/n^(0.5) = 3/sqrt(n)
you can get rid of the 3, doesn't matter, so the series you are interested in is 1/sqrt(n)
high wolf
<@415124030408884245> From the original series
Are you still available?
lone heartBOT
@high wolf Has your question been resolved?
charred valley
yo whats up with the coefficent for x =3
lone heartBOT
yo whats up with the coefficent for x =3
hidden heart
if the planes are parallel dont they have the same normal?
charred valley
yeah thats what i did
hidden heart
so your plane should be 3x -3y + 2z = something not 6
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
Please simplify
alpine sable
simplify this plese
raven dagger
What is the coefficient of x² ?
alpine sable
uhh
alpine sable
What is the coefficient of x² ?
1
subtle birch
You need to simplify or solve for x?
alpine sable
You need to simplify or solve for x?
simplify
subtle birch
Take Lcm in denominator
raven dagger
Do you need to like factories it ?
raven dagger
No rizz so i call it factories
lone heartBOT
@alpine sable Has your question been resolved?
ornate imp
how do I know that the force at right end will be W-A or A-W
I'm solving other subject, but I thought this is simple maths
marsh rapids
The force needed to make it stable ?
ornate imp
yes
vapid shuttle
because if not then the thingy will tip
marsh rapids
Including rotation?
ornate imp
yes rotation too
marsh rapids
Yes exactly. Unless A = W/2 you can't have a force on the right end that won't lead to nonzero torque
And keep it vertically stationary
ornate imp
if I say we have to check the direction of rotation after finding reaction at right side
it's not actual force but we are just considering it
marsh rapids
Then you also look at the sum of torques
ornate imp
what if I write this. is this right
marsh rapids
Is the sum of forces 0 ?
marsh rapids
what zero
This is supposed to be a Galilean referential, in which the 3 laws of Newtonian mechanics apply. What does the first one say ?
Conclude
ornate imp
can I talk in terms of shear force or moment if you know those things
this is not mathematics, but I was trying to make it a simple question which would come under mathematics
marsh rapids
This is supposed to be a Galilean referential, in which the 3 laws of Newtonian ...
It becomes math when you apply the principles and laws that turn your system into a bunch of equations
ornate imp
we are taking a section of a body, I drew only the section, and then we are finding the force at right side (from where we have cut the section)
it's fine anyway. close channel if I don't reply
marsh rapids
what if I write this. is this right
You want the resulting force to be 0
So A+x - W = 0
lone heartBOT
@ornate imp Has your question been resolved?
ornate imp
.close
ember isle
This may be a silly question, but I'm still confused with this kind of notations, I know this is the second derivative but why it's not written dy^2/dx^2 ?
earnest saddle
just notation
median oar
earnest saddle
$\frac{d^2y}{dx^2}=\frac{d(\frac{dy}{dx})}{dx}$
ocean sealBOT
Pro_Hecker
earnest saddle
we just write (dx)^2 as dx^2 for convienience
ember isle
ok thanks, after all it boils down to notation
median oar
ok thanks, after all it boils down to notation
Having y² also seems to imply we are differentiating the function y²
Rather than differentiating the function y, twice
wind cloak
In the end it's just quirky Leibnitz notation
It looks like youre just multiplying the differential operators
ember isle
Having y² also seems to imply we are differentiating the function y²
thinking about it that makes sense
.close
noble hornet
Wassup guys
lone heartBOT
Wassup guys
wind canyon
yo
noble hornet
it doesnt seem like people are very keen to help over here
wind canyon
Wassup guys
pls respect the language
raven dagger
it doesnt seem like people are very keen to help over here
Did you send the question?
hollow frost
what are you struggling with?
earnest saddle
Am i meant to enter with a humurous math joke?
No
quasi sand
.close
lone heartBOT
lone heartBOT
Available help channel!
sweet hemlock
Whats the reason for r1 and r2? Because i know it equals 40 and r1 and r2 =20 but whats the reason
earnest saddle
is RS angle bisector?
sweet hemlock
Whats that?
median oar
The dots suggest that it is I think
sweet hemlock
Yes
earnest saddle
what do you need then?
sweet hemlock
The reason for r1 and r2
earnest saddle
what is statement?
earnest saddle
for what
a) <PRQ = 40
b)r1=20and r2=20
c)both a and b