Ah yeah true. There's a much more clever sub
#help-13
upper abyss
south tundra
So you got (1 + u)^2 du, right?
queen veldt
yeah
slate lintel
do it again!
south tundra
Are you having trouble with integrating (1 + u)^2?
slate lintel
(or you can expand the square if you want)
queen veldt
The thing is I kinda get confused when to take out the integral
south tundra
You can either rewrite (1 + u)^2 as 1 + 2u + u^2 or immediately integrate it and get (1 + u)^3/3
queen veldt
yeah my question is mostly when do I know that I can already integrate
because substitution kinda confuses me on that
slate lintel
eh. just do the sub and you'll get a handle on when you can kinda skip it
the answer is "when the derivative of your substitution is equal to du" but that's hard to see without practice
upper abyss
It's the opposite of a derivative rule you have probably already accepted:
The derivative of sin(x + 1) is cos(x + 1). The +1 didn't do anything to change the process.
The derivative works around left/right translations. The integral does the same.
queen veldt
.close
solemn pawn
To get good at math do you just have to memorise the formulas and keep doing as many types of questions or is it better to understand the concept
slate lintel
depends on what you mean by good at math tbh
if you mean good at competition math, it's all practice, memorization, and tricks, less understanding
if you mean high school math, it's mostly practice
if you mean like undergrad math major, understanding is important and practice is good but it should be focused practice not mindless drills
solemn pawn
Like year 11 maths like polynomials further rates calculus and stuff
I feel like I always forget the topic a week after doing it and when the question changes a bit I can’t do it
tropic oxide
To get good at math do you just have to memorise the formulas and keep doing as ...
idt you should memorize formulas
bronze pivot
I feel like I always forget the topic a week after doing it and when the questio...
yeah but when you review it do you learn it faster than the first time?
solemn pawn
yeah but when you review it do you learn it faster than the first time?
A bit ye
tropic oxide
in fact i think you SHOULDNT memorize formulas, as a rule
formulas should be a thing that you can rederive for yourself if you forget them
ideally
muted bear
It is not considered memorizing if you understand the underlying reasoning
slate lintel
I think there are some benefits to memorizing certain formulas, like the pythagorean theorem for example
solemn pawn
I don’t understand the reasoning lol
slate lintel
but I find that memorization mostly comes with drills
solemn pawn
I just hope i recognise a problem and the formula and ways to solve it
muted bear
Which formula(e) are you having trouble with specifically
solemn pawn
Idk which formula solve which problem
tropic oxide
Idk which formula solve which problem
- you should try not to think of formulas in those terms
- when studying a formula you should not simply memorize/write down/note down just the equation, but also what stands for what
formulas are tools. if you understand why they work, there won't really be a question of which formulas "need to" be used
solemn pawn
So I just have to know what each formula does
And link it to what the question asking
tropic oxide
well
yes thats a better way to put it generally
can you share some problems youve found yourself struggling with?
solemn pawn
can you share some problems youve found yourself struggling with?
like some questions like this
solemn pawn
ye idk when some formulas and rules are applicable and stuff
tropic oxide
label all of its relevant measurements
height and base radius
volume obv since thats what we are given the rate of change of
also mark the angle
solemn pawn
ye but for this question i would never have known that the height and radius is the same
after seeing the solutions i can see that the triangle is isosceles and so the r and H are the same but without looking at the solutions i never wouldve kknown
tropic oxide
i would never have known that the height and radius is the same
again you need to draw the diagram
you cannot blind-reason your way into that
solemn pawn
also what does the dv/dt = dv/dh times dh/dt mean
tropic oxide
are you confused as to the literal meaning of this equation, or are you confused at where it comes from?
solemn pawn
literal meaning
tropic oxide
dV/dt is the rate of change of V (volume) with respect to t (time)
dV/dh is the rate of change of volume wrt height
solemn pawn
but why does dv/dt equal to dv/dh times dh/dt
slate lintel
because the dh's cancel
slate lintel
sure you could do that (that's effectively what you're doing with dV/dh * dh/dt)
slate lintel
if you have like $V = h^3$ and $h$ is a function of $t$
wraith daggerBOT
Hayley
slate lintel
then $\frac{\dd V}{\dd h} = 3h^2$
wraith daggerBOT
Hayley
solemn pawn
if you have like $V = h^3$ and $h$ is a function of $t$
where is the t tho
slate lintel
I guess you could write $V = h(t)^3$ then
wraith daggerBOT
Hayley
slate lintel
but that's kinda confusing and a pain when you have many variables and everything is a function of t
solemn pawn
how do you know if something is a function of smth else
slate lintel
based on the way the problem is set up
in this case we know that the height of the cone is changing
solemn pawn
for the differentiating with respect to time part why does dv/dt = (pi)h^2 times dh/dt and not just dv/dt = (pi)h^2
slate lintel
i mean that is just "why does the chain rule work"
Remember what a derivative means, it's the instantaneous change over time, so
if V is changing (pi)h^2 times as fast as h is changing,
and h is changing 3 times as fast as t is changing,
then V is changing (pi)h^2 * 3 times as fast as t is changing
as for why dV/dt doesn't equal (pi)h^2, well, why should it? That is an expression for dV/dh, the change in volume compared to the change in height of the cone
it's like... if a bike is going twice as fast as me, and a car is going 4 times as fast as a bike, then the car is going 2 * 4 = 8 times as fast as me
solemn pawn
ig that makes sense but for dv/dt it can alos be equal to dv/dt = dv/dr times dr/dt?
where r is radius
solemn pawn
if u wanted the rate radius is changing
slate lintel
this might help to convince you: let's say we had a formula for V expressed in terms of radius, let's say something simple like V = r^3. You can probably see that dV/dr = 3r^2; as the radius gets bigger, so does the volume.
Now suppose the radius isn't changing over time, it's static, so dr/dt = 0
Since the radius isn't changing neither is V (this should be clear) so we need dV/dt to equal 0 as well. But 3r^2 isn't zero! We need to multiply by dr/dt to make it make sense.
solemn pawn
so dv/dt = dv/dr times dr/dt where dv/dr = 3r^2 and dr/dt = 0
slate lintel
yep! so, 0 regardless of whatever the radius happens to be
solemn pawn
ok its getter more clear now pretty good explanation
my last question is how do u know what variables to pick
slate lintel
ty it's honestly a question that I've never had to explain so I liked thinking about it
slate lintel
my last question is how do u know what variables to pick
hmm what do you mean?
like in your cone example, how did we know to express volume in terms of height?
solemn pawn
actually nvm u already explained that
alright thanks for helping me understand better
have a good rest of ur day
slate lintel
ty! you as well
elfin otter
cedar kilnBOT
royal loom
just undo the transformation
take a point
(6, 24)
go backwards down the list
so it was vertically translated 3 units down
you want to undo that
so vertically translate it 3 units up
(6, 27) now
then undo the next step
it was horizontally translated 3 units to the left
you want to undo that
so.... continue
cedar kilnBOT
@elfin otter Has your question been resolved?
elfin otter
it was horizontally translated 3 units to the left
(9, 27)
(12, 64)
?
cedar kilnBOT
@elfin otter Has your question been resolved?
dusky peak
Think about the opposite
f=ae^(bx)
f'=abe^(bx)
Just chain rule
If we differentiate e^x we get e^x
That together with chain rule is enough
Then to integrate we kinda do in reverse
This does not always work nicely, but here it does
cedar kilnBOT
@crimson sedge Has your question been resolved?
lofty kraken
These scores are coded using the formula y=(x−15)/10.For the sample of 40 patients, Σy= 281 and Σy^2= 2551.
cosmic wren
cedar kilnBOT
cosmic wren
can someone help me find out what im doing wrong
did this question twice got the exact same answer twice
cedar kilnBOT
@cosmic wren Has your question been resolved?
cosmic wren
<@&286206848099549185>
cedar kilnBOT
@cosmic wren Has your question been resolved?
cosmic wren
.close
bronze pivot
How do I do number 1?
cedar kilnBOT
How do I do number 1?
next isle
I think it means, show that C1 and C2 both collide at the origin
bronze pivot
I think it means, show that C1 and C2 both collide at the origin
okay that is when P(0, any theta)
meaning r = 0
0 = costheta = 1 - sintheta
1 = costheta = sintheta
that's when theta = pi/4
but that's wrong
cos(pi/4) is not 0
and sin theta too
bronze pivot
r = cos(0) = 1
r = 1-sin(0) = 1
true
but
r is not 0
ok I guess I see it
but is it even algebraic when I say it like this
when theta = pi/2
0 = cospi/2 = 1 - sinpi/2
is that algebraic?
or is that just guessing
next isle
It’s more just from looking at the graph
bronze pivot
how do I do it algebraically then
next isle
Then proving with algebra
next isle
1 = costheta = sintheta
I think you were on to it here but got this line wrong
next isle
Why did you write that cos theta equals 1
next isle
Yeh
next isle
No worries
cedar kilnBOT
@bronze pivot Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
indigo crag
can anybody show me how to prove that the application k => 7k is a homomorphism?
indigo crag
as far as I understood an Homomorphism is a function that follow the group rules
so
its not very clear to me how should i proceed
i'd like to learn a method
the professor's notes r just a bunch of examples
crimson sedge
a homomorphism preserves the group operation https://en.wikipedia.org/wiki/Homomorphism#Definition
this
indigo crag
this
is it implicit that we're talking about (Z, +, 0)?
cause if it is, it make sense
crimson sedge
yes
crimson sedge
the natural way to form a group on Z is via addition
indigo crag
yh im sorry im new to this stuff
crimson sedge
the multiplicative inverse of integers (not 1,-1) is not an integer
which is why (Z, *, 1) is not a group
indigo crag
so basically i just have to prove that f(a) + f(b) = f(a+b). I also assume associativity and the existence of the identity element are taken for granted right?
crimson sedge
yes,
assume associativity and the existence of the identity element
we already know (Z, +, 0) is a group
we can also assume multiplication by 7 is distributive (via 'elementary' algebra)
indigo crag
is this an isomorphism as well?
crimson sedge
yes, thats right
crimson sedge
yup 
indigo crag
yup <:catthumbsup:614540188747563008>
if this was an isomorphism (and ik it isn't), it'd have been an automorphism as well right cause f maps from Z to Z which are the same group, right?
crimson sedge
yes, thats the definition of an automorphism
indigo crag
so here id have to show that e^a * e^b = e^(a+b)
it looks easy where's the catch lmao
wintry arrow
I need help with part a) This is a question from a mathematics of mechanics paper
cedar kilnBOT
I need help with part a) This is a question from a mathematics of mechanics pape...
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
do they mean maximum speed? feels like they mean maximum speed
wintry arrow
I don't think so since this was an official exam from 2019 and if there were any errors they would've been fixed by now
.close
marsh pond
cedar kilnBOT
halcyon marlin
no, av=0 only when a=0
neon moon
Can you find an non-trivial solution in single-vector case? 🙂
neon moon
No you may not 🙂
neon moon
Can you find an non-trivial solution in single-vector case? 🙂
This definition concerns about every component of every vector in the set.
marsh pond
set D is
-0.5
for both rows
if you multiply the first vector by -0.5 (scalar)
you get second vector
so therefor it's linearly dependent
but for the other vector sets I can't do that
halcyon marlin
i dont think a lot of people use that definition
tropic oxide
just because you cannot do it does not a priori mean it can't be done
i for example can tell you for sure that set C is LD when you marked it as LI
neon moon
I think you may wanna revise on the definition more. When there are more than 2 vectors, "common factors" is not the only possibility for linear-dependence.
halcyon marlin
definition jimmy is more closely related to solving systems of linear equations
which i think you are familiar with
neon moon
Can you find an non-trivial solution in single-vector case? 🙂
And the def here says nothing about you can just go by only looking at "common factors" on each row.
cedar kilnBOT
@marsh pond Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
supple frost
need some help on angles and parallel lines
cedar kilnBOT
need some help on angles and parallel lines
cedar kilnBOT
supple frost
thank you
cedar kilnBOT
Available help channel!
royal nexus
Im confused on how the limit is not DNE? its not defined since there is a hole?
south tundra
$\lim_{x\to3}g(x)$, according to the graph, should be equal to $1$
wraith daggerBOT
alonelybean
royal nexus
but why? theres two values for 3 would that not make it defined for 3?
south tundra
g(x) is defined for x = 3 as well
Graphically $\lim_{x\to{a}}f(x) = L$ means that the closer a point is to $x = a$ the closer its $y$-coordinates gets to $L$
wraith daggerBOT
alonelybean
south tundra
But it does not mean $f(a) = L$
wraith daggerBOT
alonelybean
south tundra
Limit at a point is different than the function evaluated at that same point
south tundra
Im confused on how the limit is not DNE? its not defined since there is a hole?
Here the function g does not "have two values" for x = 3
If you are talking about the empty dot at (3, 1)
Then it just means that the graph does not cross that point
Without the empty dot it would look like it did
And the black dot is an actual part of the graph
royal nexus
so the black dot has a different representation for the graph but has nothing to do when limit x-->3 ?
south tundra
Yes, the black dot is the point (3, g(3))
And the dot helping you with finding limits will most of the times be the hollow dot
royal nexus
got it so can i assume that the black dot is true when its asking to find the value of 'g(3)'
south tundra
Yes
cinder venture
How do I do this?
cedar kilnBOT
How do I do this?
sonic wing
Write in sequence notation.
Term 1 is a(1)
Term 2 is a(2)
term n is a(n)=f(n)
for example, you can have a(n)=2^n
a(1)=2
a(2)=4
etc
cinder venture
I mean for c specifically
I do not understand it @sonic wing
I can see the trend
But I do not know how to show how I got it
sonic wing
What is the trend in C?
Ah, to show how you got it?
I dont know any formal method to find a sequence if that is what you are asking.
But the sequences in the example are simple, so just by intuition you can find the trend, then write the function
cedar kilnBOT
@cinder venture Has your question been resolved?
cinder venture
Ah, to show how you got it?
Yes
I can see it increases by 1 in the numerator
And goes up as powers of 2 in the denominator
Anyway
Dyk how to do the b part?
sonic wing
Well, a term is p/q ,
write the next using p and q
from a(n) to a(n+1) the numerator increases 1 and the denominator is multiplied by 2
cinder venture
Why?
sonic wing
Well, the first term is 7/8
the next is 8/16
if you take p/q as a term, you can write it as ter 1 for example, to understand better.
so that p=7 and q=8
if the next term is 8/16 you will have what in terms of p and q?
cinder venture
so that p=7 and q=8
if the next term is 8/16 you will have what in terms of p an...
p+1/2p
sonic wing
(p+1)/2q yeah
sonic wing
yep
zealous crag
I have been reconnected to the internet, so let's try this again! I am looking for assistance with at least one (any letter is fine, but preferably (a), (d), or (e)). I have already solved for the homogenous solution for all of these, but am stuck trying to solve for the nonhomogeneous solution using undetermined coefficients. I am mainly not sure how to modify the standard guess to solve the problem. I will attach my work momentarily - thank you!
zealous crag
My work so far.
dawn junco
My work so far.
you forgot to add the coefficients of your DE when trying to find P
(looking at equation a))
zealous crag
that would've been helpful, wouldn't it? 🥴
wait which coefficient maybe i am thinking the wrong thing.
dawn junco
u'' + 9u' + 20u = ...
when doing your undetermined coefficients you just added u_p'' + u_p' + u_p
@zealous crag
zealous crag
ok, one moment then.
zealous crag
u'' + **9**u' + **20**u = ...
Maybe I am missing something but I'm not sure where this fits into the undetermined coefficients - are you saying I forgot these particular values or just the ones that I should have solved for?
dawn junco
nah
the thing is
your particular solution should be a solution to the differential equation we have right
so you should have u_p'' + 9u_p' + 20u_p = 2e^(-4t)
dawn junco
here you wrote u_p'' + u_p' + u_p = ...
zealous crag
Yes!
✨oh✨
Okay lol sorry thank you i just wasn't processing what you meant.
Okay one moment lol.
If I'm not mistaken, I would get 0=2, yes?
And from here I'd modify the particular solution guess?
zealous crag
maybe it was the choice of r i used?
I mean the problem states that the "standard" guess will fail, and in my work it did.
Because 0≠2, at least it didn't last i checked. 😅
dawn junco
lemme actually try and do it
zealous crag
I appreciate your help, thank you!
dawn junco
uh yeah I don't see how you get 0=2
zealous crag
Damn what did I do😭
zealous crag
16-36+20?
zealous crag
it happens, we're forgetting coefficients all over the place tonight 🥴
dawn junco
ah yeah the guess is bad indeed
learned something today
the idea is e^(-4t) is already a part of the general solution
so it can't be a guess for the particular sol
so we do the usual trick of multiplying by t
zealous crag
Good ol' t.
I think I'm getting the hang of this.
I'm guessing that the method to find the modified guesses is just "mess around and see what works."
dawn junco
yes
but yeah in the pdf I posted there's more examples
for example if you had multiple roots in the characteristic equations of your DE
then you'd go add even higher powers of t for the particular sol
zealous crag
Got it, got it.
Well i think I've got it from here. If another issue arises I shall be back. Thank you, again, for your help!
One of these days I will not forget the coefficients... 🙏🕺
.close
hushed glacier
2j * 16j^-5 = 32j^-6?
cedar kilnBOT
2j * 16j^-5 = 32j^-6?
hushed glacier
i mean, i know its not, but it says so on a book that im reading
so is there an explanation to this or something
cedar kilnBOT
@hushed glacier Has your question been resolved?
hushed glacier
can you give the screenshot
crimson sedge
2j * 16j^-5 = 32j^-6?
What is your question?
hushed glacier
look
2j * 16j^-5 is actually 32j^-4
not 32j^-6
as said on the book
i would say it was a mistake from the author but he does it more than once
is there any situation where 2j * 16j^-5 = 32j^-6?
well, its not a fraction
hushed glacier
hushed glacier
😭😭😭😭😭😭😭
crimson sedge
It's all good
hushed glacier
these small words
hushed glacier
It's all good
at least i learned right 😭
crimson sedge
Yeah that is crappy resolution
cedar kilnBOT
cedar kilnBOT
Available help channel!
turbid isle
Can someone explain how they came up with that eqn
cedar kilnBOT
Can someone explain how they came up with that eqn
cedar kilnBOT
@turbid isle Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
small bison
can someone give sol for (3)?
cedar kilnBOT
can someone give sol for (3)?
dire geode
can someone give sol for (3)?
Do your own work. The server doesn't give answers
cedar kilnBOT
@small bison Has your question been resolved?
bronze pivot
$2\int_{\pi/6}^{\pi/2} \frac{\cos^4 (\theta)}{\sin^2 \theta}$
bronze pivot
pls help I got stuck 😦
rose swan
what did you try?
bronze pivot
what did you try?
I was doing this one
but I got stuck in this step
I tried power reduction
but I got nowhere
there must be a better way
bronze pivot
try rewriting the integrand as something squared
?
rose swan
you keep changing the problem. which one is it?
wraith daggerBOT
casiofx991exz
bronze pivot
this one
bronze pivot
I was doing this one
so I'm doing this
bronze pivot
**casiofx991exz**
then I got here
bronze pivot
**casiofx991exz**
but now I'm stuck here
idk how to proceed
I tried power reduction
but got nowhere
bronze pivot
you keep changing the problem. which one is it?
so how do i proceed from
rose swan
i gave you some hints already, but maybe there's other ways to do it
i just worked it out with one method
but try rewriting as (x/y)^2
bronze pivot
try rewriting the integrand as something squared
isn't this already something squared
ok
rose swan
and apply an identity at the top
bronze pivot
and apply an identity at the top
$2\int_{\pi/6}^{\pi/2} (\frac{\cos^2 (\theta)}{\sin \theta})^2$
wraith daggerBOT
casiofx991exz
bronze pivot
then power reduction maybe at the top
so
$2\int_{\pi/6}^{\pi/2} (\frac{ \frac{1}{2}(1+cos2 \theta}{\sin \theta})^2$
wraith daggerBOT
casiofx991exz
rose swan
i'm not sure if your identity is going to make things easier
bronze pivot
$2\int_{\pi/6}^{\pi/2} (\frac{1-\sin^2 \theta}{\sin \theta})^2$
casiofx991exz
rose swan
yep
bronze pivot
$2\int_{\pi/6}^{\pi/2} (\frac{1}{\sin \theta} - \sin \theta)^2
casiofx991exz
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rose swan
good, and now expand
bronze pivot
$2\int_{\pi/6}^{\pi/2} \csc^2 \theta - 2 - \sin^2 \theta$
casiofx991exz
tropic oxide
all of these are missing the dθ
bronze pivot
yeah yeah yeah
rose swan
yeah, i didn't really bother to mention it lol
rose swan
but yeah, trig integrals can take a while
bronze pivot
but yeah, trig integrals can take a while
how did you see this though
like how did you think of what to do
rose swan
just experience
bronze pivot
😦
bronze pivot
just experience
what were you thinking when you saw cos^4/sin^2
rose swan
pythagorean identity
bronze pivot
i hope i dont get this in the test
bronze pivot
that's how it usually goes lol
lol
cedar kilnBOT
@bronze pivot Has your question been resolved?
vapid sphinx
need solve of c
cedar kilnBOT
need solve of c
dire geode
need solve of c
Solve for cosine then take the reciprocal
vapid sphinx
Solve for cosine then take the reciprocal
sorry. I didn't get it.
cedar kilnBOT
@vapid sphinx Has your question been resolved?
slate lintel
sorry. I didn't get it.
take the original equation and solve it for $\cos\theta$
wraith daggerBOT
Hayley
vapid sphinx
take the original equation and solve it for $\cos\theta$
Then what? 😐
slate lintel
as riemann said, take the reciprocal
actually hmm that doesn't seem like it'll work right away
vapid sphinx
actually hmm that doesn't seem like it'll work right away
I also think so.
neon moon
Add up two equations (the given one and (b)), what will you get then? 🙂
weary vessel
Add up two equations (the given one and (b)), what will you get then? 🙂
You end up with the same equation
weary vessel
actually hmm that doesn't seem like it'll work right away
It will not work out because it is wrong
No matter how you try :|
vapid sphinx
Found different result
Show me what have you found?
slate lintel
I substituted 60° in both
does that satisfy the original eqn though?
vapid sphinx
This solution is valid. I think so....
weary vessel
I thought we were trying to prove a formula that is always correct
Not specifically for this exercise
vapid sphinx
I thought we were trying to prove a formula that is always correct
At first I was also thinking that 🥲
weary vessel
So basically this formula works only for the angles which satisfy the original equation
Among those angles, pi/8
Which you found
Smart!
Just one thing
For generalization purpose
Like you wrote, it looks like the original equation is valid only for pi/8
Therefore, question c's formula is valid for pi/8 only
Since cosine and sine are periodic with period = 2 pi
We can generalize to:
And if you plug the whole (pi/8 + 2 pi K) into sin(2x) = 2 . sin(x) . cos(x)
You will still always get the result!
cedar kilnBOT
@vapid sphinx Has your question been resolved?
calm hedge
cedar kilnBOT
calm hedge
so it's asking for the average rate of change from interval 0,1200
so i was thinking
(1200-0)/(5-x)
the last value is x
because i dont know what the cardiac output is when workload is 1200
is this the correct pathway
for the answer
calm hedge
(1200-0)/(5-x)
using the formula f(a)-f(b)/a-b
gritty galleon
I think u can get a better avg if u Calc the rate of change per square (slope) and take the AM of that (also u might be better off estimating the function based on it shape since u need to find the derivative for part b)
calm hedge
am?
calm hedge
I think u can get a better avg if u Calc the rate of change per square (slope) a...
ok
so for interval 0 to 300
how do i know what the y value is when x value is 300
is there any way to tell
cause i need the y to calculate the slope right?
also our class hasnt learned derivatives but ig we could do that
i dont understand how we use derivatives here tho
gritty galleon
Yeah..it's given 5 (from the graph)
gritty galleon
Hmm..Well then u might as well go ur way
gritty galleon
I was thinking of approximating the y values
gritty galleon
Looking...
cedar kilnBOT
@calm hedge Has your question been resolved?
crisp flint
Why \frac{\sqrt{9}}{3} \neq \sqrt{3}
cedar kilnBOT
Why \frac{\sqrt{9}}{3} \neq \sqrt{3}
gritty galleon
Missing $ signs around the tex
crisp flint
But \sqrt{18} = \sqrt{3} \ast \sqrt{54}
gritty galleon
Missing $ signs around the tex
...
crisp flint
I dont that emoji in keyboard
gritty galleon
Kk
gritty galleon
But \sqrt{18} = \sqrt{3} \ast \sqrt{54}
Untrue
gritty galleon
Why \frac{\sqrt{9}}{3} \neq \sqrt{3}
Since accord to order of operations u have indices first so u have to do the square root first, which makes the expressions 3/3 which is 1, which is not equal to sqrt(3)
grave inlet
differentiate cardiac utput withr espect to workload than integrate it with limits 0 to 1200
crisp flint
But \frac{\sqrt{9} \ast {9}}{3} = \sqrt{18}
tropic oxide
,calc sqrt(9)*9/3
wraith daggerBOT
Result:
9
,calc sqrt(18)
wraith daggerBOT
Result:
4.2426406871193
no.
grave inlet
differentiate cardiac utput withr espect to workload than integrate it with limi...
.
its calculus
grave inlet
120?
because using calculus the average will be delta x by delta y
delta x is 1200
delta y is 10
tropic oxide
@grave inlet if you want to follow up with @calm hedge on this problem it is better to go to #calculus or other thematically appropriate channel instead of clogging up this channel which has somebody else's question now
grave inlet
hmm
cedar kilnBOT
@crisp flint Has your question been resolved?
gritty galleon
differentiate cardiac utput withr espect to workload than integrate it with limi...
I told him to predict the function using its shape and values, I didnt know how to use calculus to find f(x) since neither derivative nor integral is known (+ the gys not taught calculus)
gritty galleon
because using calculus the average will be delta x by delta y
oh u found the derivative at a given x..I should've thought of that 💀 i was thinking of finding the general derivative and then evaluating
grave inlet
oh u found the derivative at a given x..I should've thought of that 💀 i was thi...
yea
you can find the general tho
but its timetaking
youll have to make 3-4 equation at x+h intervals
gritty galleon
true (timetaking part)
gritty galleon
youll have to make 3-4 equation at x+h intervals
wait wdym?
grave inlet
I told him to predict the function using its shape and values, I didnt know how ...
its actually a general formula before you study calculus remeber average velocity
gritty galleon
its actually a general formula before you study calculus remeber average velocit...
u+v/2? or total displacement/total time
grave inlet
wait wdym?
so basically what u do is take a unkown function and put in values of it as it chnages the height at very small intervals
that would give a small oeice of fx
grave inlet
x-speed, y-time?
you can take any tbh but geeraly x is for time
gritty galleon
so basically what u do is take a unkown function and put in values of it as it c...
oh k...I had a similar problem where the function graph looked logarithamic and i had various f(x) values. i was pretty confused what to do, asked around and they said its not really possible to get an accurate f(x) and rate of change or area orsmthing
grave inlet
hmm
gritty galleon
you can take any tbh but geeraly x is for time
Ah k
cedar kilnBOT
@crisp flint Has your question been resolved?
stiff stratus
@crisp flint Whats your question
crisp flint
Why \frac{\sqrt{9}}{3} \neq \sqrt{3}
stiff stratus
Why $\frac{\sqrt{9}}{3} \neq \sqrt{3}$
wraith daggerBOT
Gilgamesh
stiff stratus
Because $\sqrt{9} = 3$
wraith daggerBOT
Gilgamesh
stiff stratus
Ok? @crisp flint
crisp flint
But \sqrt{18} = \sqrt{3} \ast \sqrt{54} so it doesnt match
stiff stratus
But $\sqrt{18} \neq \sqrt{3} \ast \sqrt{54}$ so it doesnt match
Nah
And dont use \ast for • instead use \cdot
$\cdot \neq \ast$
stiff stratus
@crisp flint its not equal
crisp flint
?
stiff stratus
$\sqrt{18} = \sqrt{9} \cdot \sqrt{2} = 3 \cdot \sqrt{2}$
crisp flint
It is just \sqrt{18}^0.5 for \sqrt{3}
wraith daggerBOT
Gilgamesh
stiff stratus
It is just \sqrt{18}^0.5 for \sqrt{3}
Nah
crisp flint
Yeah so if it is \frac{\sqrt{9}}{3} then it should be \sqrt{3}
stiff stratus
$\sqrt{18} ^{0,5} = \sqrt[4]{18}$
wraith daggerBOT
Gilgamesh
stiff stratus
Yeah so if it is \frac{\sqrt{9}}{3} then it should be \sqrt{3}
No its wrong
Use your calc
crisp flint
$\log_2{9}^2 = \sqrt{9} \neq 3$
stiff stratus
$\log_2{9}^2 = \sqrt{9} \neq 3$
No
wraith daggerBOT
아리스킨충∪
crisp flint
So \sqrt{9} \neq 3
tropic oxide
log_2(9^2) is not equal to sqrt(9).
stiff stratus
log_2(9^2) is not equal to sqrt(9).
👍
tropic oxide
sqrt(9) is 9^0.5
log_2(9^2) is not equal to 9^0.5
log_2(x^2) is not equal to x^0.5 generally
cedar kilnBOT
@crisp flint Has your question been resolved?
wraith daggerBOT
umbraleviathan
cosmic steppe
How tf did you get to that conclusion
stiff stratus
How tf did you get to that conclusion
😂 thx
$\log_2(9^2) \ \log_2((3^2)^2) \ \log_2(3^4) \ 4 \cdot \log_2(3)$
wraith daggerBOT
Gilgamesh
dull shard
cedar kilnBOT
dull shard
what does the answer mean
if it was a positive correlation but with e instead of log values would an exponential decay curve still be used?
cedar kilnBOT
@dull shard Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
dry cargo
hello someone can teach me this integrals?
cedar kilnBOT
hello someone can teach me this integrals?
granite knoll
did you find the derivative first?
dry cargo
did you find the derivative first?
Yea it's dy/dx = 6(1-6x)(x-3x²)²
iron saffron
Yea it's dy/dx = 6(1-6x)(x-3x²)²
So, if you know that's the derivative, and he is asking to integrate the other one
you should be able to solve that just by looking y
He is asking you something like this.
y = 2x^2
What's y'?
y' = 4x
Knowing this, what the integrate of 2x?
He doesn't want you to use any method to solve the integral
beside the observation
dry cargo
He doesn't want you to use any method to solve the integral
i should express it ?
iron saffron
You can (must) use words to explain why you reach to your conclusion
granite knoll
well, you need to solve it. but you can solve it using what you found for dy/dx
slate lintel
look up the fundamental theorem of calculus
cedar kilnBOT
@dry cargo Has your question been resolved?
static pine
How exactly do we find out the angle given the value of the function?
inland ocean
$tan(2\phi) = tan(\frac{3\pi}{4})$
wraith daggerBOT
coldtee
brave aspen
With regard to important values of tangent, you can memorize them or recall that
Sin(x)/cos(x) = tan(x) and go off that
slate lintel
it should be noted that that's not the only angle that satisfies that equation
for example, $tan(-\frac\pi4) = -1$
wraith daggerBOT
Hayley
cedar kilnBOT
@static pine Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
feral egret
How do I find the diameter of a circle with only the area of a circle
tropic oxide
do you know how to do the reverse?
i.e. how to find the area of a circle using its diameter?
feral egret
I know the formula to find the area
wraith daggerBOT
itszme
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
tropic oxide
bad
tropic oxide
I know the formula to find the area
ok then state it
feral egret
Oki
tropic oxide
let me restate itzme's question then
what is the radius's relationship to the diameter?
feral egret
Radius is half the diameter
No I have the area
I’m trying to find the diameter
The area is 59.726
That’s it
Just the area
wraith daggerBOT
itszme
wraith daggerBOT
itszme
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
feral egret
The variable is being multiplied
So divide
But it’s a exponent
Is there anything different???
Oh wait
I get it
Thank you
Your like my teacher 🤣
Have a good one
nimble lily
how can i find the distribution of change in depression for the subjects receiving each of the three treatments.
nimble lily
to make a segmented graph but i need help starting it
granite knoll
a segmented graph?
nimble lily
yes
granite knoll
can you show an example?
nimble lily
of a segmented graph?
granite knoll
yes
nimble lily
nimble lily
mm
granite knoll
but you have "two-way" data so a mosaic plot is probably more appropriate
stark bronze
I'm not sure how to approach this
cedar kilnBOT
I'm not sure how to approach this
stark bronze
I want to get rid of the denominator right?
finite raven
Work on the numerator
finite raven
I want to get rid of the denominator right?
right
stark bronze
[\frac{\frac{1}{x} - \frac{x}{x}}{x-1}]
wraith daggerBOT
dopediscorduser
stark bronze
.close
surreal cave
I am trying to find a formula for:\$n!+n(n-1)!+n(n-1)(n-2)!+\ldots+(n-k)!\prod_{i=0}^{k}(n-i)$
I tried doing this myself but ended up getting $\sum_{k=0}^{m}(n-k)!\prod_{i=0}^{k-1}(n-i)$ but this obivously wasn't the right approach as WolframAlpha gave the closed form of this sum/product as $(m+1)\Gamma(n+1)$ which is not at all what I'm looking for, I would really appreciate any help!
surreal cave
(https://www.wolframalpha.com/input?i=Sum[(n-k)!Prod[(n-i)%2C{i%2C0%2Ck-1}]%2C{k%2C0%2Cm}]) Wolfram link in case it helps ;-;
wraith daggerBOT
XxMrFancyu2xX
crimson delta
each term is just n!
so what do you expect as closed form except (number of terms)*n!
cedar kilnBOT
cedar kilnBOT
Available help channel!
smoky idol
Hello! I wanted to try this classic integral $\newline \int_{-\infty}^{\infty} e^{-x^2}dx \newline$ Now I know you can do that using polar coordinates and Jacobian transforms, but I wanted to know if there was any other way to do it. Mainly, using Feynman's technique. I have been trying for a bit, but I can't find a suitable way to introduce a parameter. Is there actually a way to solve this integral using Feynman's?
wraith daggerBOT
imtyp0
smoky idol
i tried that, and maybe I just suck but that didn't work out too well
I got $I'(t) = \int_{-\infty}^{\infty} -x^2 \cdot e^{-tx^2} dx$
wraith daggerBOT
imtyp0
tropic oxide
hm
smoky idol
and there's not much I can do there
smoky idol
It would be interesting to get a 2x multiplied with the e^{whatever} but I don't see how you'd do that
plus considering the answer is sqrt(pi), how would you even get a pi with e^{something} 🤔
tropic oxide
found this from some googling
but i do not really see how this could have been arrived at
smoky idol
yeah that's weird. They start with a seemingly random integral
Maybe introducing a trig function? Like sin(tx)e^{-x^2}
we might get something cyclic when differentiating twice and be able to make a differential equation?
tropic oxide
dunno doesn't look like itll help
dire geode
we might get something cyclic when differentiating twice and be able to make a d...
try it and share your work here
cedar kilnBOT
@smoky idol Has your question been resolved?
smoky idol
try it and share your work here
will do one moment
smoky idol
try it and share your work here
Something like that?
dire geode
that looks okay so far
smoky idol
not sure how I'd solve the diff eq though because we know nothing about its form?
surreal cave
isn't the solution for that diff eq. just sin(x)+cos(x)?
smoky idol
constants where
surreal cave
smh
surreal cave
$c_1\sin(x)+c_2\cos(x)$
wraith daggerBOT
XxMrFancyu2xX
velvet radish
Hi guys
smoky idol
then what info should we use to figure out the constants?
velvet radish
Where is the chat
surreal cave
Hi guys
Hello Supremite, welcome to the Math server, please visit #discussion or #chill to talk or #❓how-to-get-help to ask a question! 
smoky idol
Can we use $I(0) = 0$?
wraith daggerBOT
imtyp0
dire geode
Something like that?
use I'(t)
wraith daggerBOT
imtyp0
wraith daggerBOT
imtyp0
smoky idol
but, now I can't seem to find a good value to input for t
the only "good" ones would be pi/2 +2npi, but that would cancel out the cost, and the C_2 at the same time
even worse, I run into a contradiction
$y'(\pi/2) = 0 \newline 0 = C_2cos(\pi/2) - sin(\pi/2) \newline 0 = 0 - 1$
wraith daggerBOT
imtyp0
smoky idol
furthermore, even if we did find a C_2, I don't see how we would get the sqrt(pi) with just regular trig functions
dire geode
I'(0) is simpler than I'(pi/2)
smoky idol
I(0) = I?
oh bruh
it simplifies to I = C_2
thanks captain obvious
(not you riemann, just to be clear)
smoky idol
I'(0) is simpler than I'(pi/2)
I don't see how you want to use I'(0) then
dire geode
**imtyp0**
plug it in here
smoky idol
I did
You mean using that I'(0) = I?
Because if so @dire geode ,
$y' = C_2cost - sint \newline I = C_2cos(0) + sin(0) \newline I = C_2$
wraith daggerBOT
imtyp0
smoky idol
and like, we already know that the result of I is a constant
dire geode
dire geode
Maybe introducing a trig function? Like sin(tx)e^{-x^2}
try sin(tx) instead of just sin(t)
smoky idol
*agressive erasing intensifies*
oh
that just might do it
@dire geode what would my t input be to cancel out the sin(tx) then?
dire geode
not sure what you mean. just show your work
smoky idol
not sure what you mean. just show your work
I didn‘t do the integral of cos(tx)e^(-x^2) because 1) I have no clue how to do it, and 2) I don‘t think there‘s anything to input for t to have I(t=something) = I
dire geode
Something like that?
you do similar process here except you pick up an x term that comes from chain rule
$\frac{d}{dt} \sin(tx) = ?,\ \frac{d}{dt} \cos(tx) = ?$
wraith daggerBOT
rie.mann
smoky idol
xcos(tx) and -xsin(tx)?
dire geode
I didn‘t do the integral of cos(tx)e^(-x^2) because 1) I have no clue how to do ...
use that in your integration by parts
smoky idol
use that in your integration by parts
Yeah I don't think it's working :/
dire geode
Yeah I don't think it's working :/
And why not
dire geode
Just show your work again
smoky idol
Just show your work again
Let me know if it‘s not clear enough
dire geode
i see. yea that doesn't work
smoky idol
i see. yea that doesn't work
So, should we try more stuff or is it just not possible by Feynman's?
And if it's not possible, could you suggest an integral to do with Feynman's? Because I want to practice it.
dire geode
So, should we try more stuff or is it just not possible by Feynman's?
probably just google it
should get more results if you call it by its original name
smoky idol
should get more results if you call it by its original name
I always saw it called Feynman's technique. I thought the Leibniz rule was you could swap the derivative and integral signs under some conditions.
And yeah alright thanks a lot for sticking with me till the end even though we weren't successful
.close
crimson sedge
how did we get to this answer
cedar kilnBOT
how did we get to this answer
cosmic steppe
,rotate CC's
wraith daggerBOT
cosmic steppe
I mean
crimson sedge
i dont really understand
cosmic steppe
It's a shit proof
Do you know vectors
That's the only real way to prove why that's so
crimson sedge
no
cosmic steppe
This is so
Is going to be hard to understand for you
So if you really wanna know, just tell me
crimson sedge
i'd like to try to understand
cosmic steppe
Okay well basically every line, in any vector space (1D, 2D, 3D, 4D, etc) has a directional vector
Think of this as the slope
If we have the equation of a line, y, it's slope is going to be y' = m
Now regarding 2D space, your slope is always going to be m. You can represent this as <1, m> (or m/1 = m)
Vectors are read as <change in x, change in y, etc>
Now a neat thing about vectors is that if we have a vector A and a vector B, if they're orthogonal (perpendicular in direction), then the "dot product" of A and B is 0.
From the law of cosines, we can get that:
A • B = |A| |B| cos(θ)
The vertical bars in this case represent the magnitude of A and B. If you wanna read further, google "vector dot product"
Because cos(90°) = 0, A • B = 0 if and only if A is orthogonal to B
Dot products in 2D is given by this formula:
<x1, y1> • <x2, y2> = (x1 • x2) + (y1 • y2)
So <-m, 1> will always be orthogonal to <1, m>
Since:
<1, m> • <-m, 1> = (1 • -m) + (m • 1)
= -m + m
= 0
if <1,m> can be represented as m, then <-m, 1> can be represented as -1/m
cosmic steppe
Okay well basically every line, in any vector space (1D, 2D, 3D, 4D, etc) has a ...
Read from here @crimson sedge
crimson sedge
Okay
hmm. im sorry to say that i dont quite understand. could you let me know what knowledge i need to understand vectors? please let me know
im sorry for wasting that time 😭
so, there's no other way to prove this?
nvm i think i found something
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
open nacelle
If 3f(c) = 3, what's f(c)
crimson sedge
If 3f(c) = 3, what's f(c)
f(c)=1
crimson sedge
Use the definition of the function to solve for c
Answer is 10?
I'll show you my work
open nacelle
Sure send it