After graphing it is very clear
#help-27
quaint ice
dark dawn
seems a bit overpowered
potent marlin
Hey i need help with this
devout snowBOT
Hey i need help with this
potent marlin
How did we get x=0 and x= 4/3
This is from a yt video but she didnt explain it just wrote it
lofty niche
we have -3x^2+4x=0. firstly we factor out -x. this means that just one of the factors needs to be zero (see zero-product property). this means either -x=0 or 3x-4=0. therefore x=0 or x=4/3
potent marlin
Ohh we just solve it
lofty niche
yeah they are just solving h'(x)=0
potent marlin
Ok thx
muted lintel
can anyone help
muted lintel
i triedd
potent marlin
Bcaed
muted lintel
it’s says it wrong
potent marlin
This isnt even preschool lol
muted lintel
I’m british
muted lintel
its okk
devout snowBOT
Bcaed
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
@potent marlin Has your question been resolved?
Available help channel!
sturdy mirage
devout snowBOT
sturdy mirage
This is the question I'm on.
The video explanation says that I can rewrite the two (1-lambdas) as (lambda+1) and (2-lambda), but I'm not entirely sure how he reached that conclusion.
restive river
factor out -1 from (1-lambda)
sturdy mirage
factor out -1 from (1-lambda)
Where did the 3 come from though?
restive river
they factored (1-lambda)^2 -4
sturdy mirage
Where did the -4 come from?
sturdy mirage
So the 0 multiplier in the middle doesn't actually 0 it?
restive river
So the 0 multiplier in the middle doesn't actually 0 it?
its a typo
sturdy mirage
How is it a typo?
restive river
it should be 4(0 - (2-lambda))
sturdy mirage
Ah
Yeah that makes sense
The person that does these videos is not very good at them.
They just kind of assume you know every single thing they are talking about and don't actually explain what they're doing.
sturdy mirage
it should be 4(0 - (2-lambda))
It would look like this ?
restive river
,w char poly [[3,11,16],[0,4,0],[1,1,3]]
woven radishBOT
restive river
It would look like this ?
yes
sturdy mirage
Fair enough
sturdy mirage
or you could factor out (4-lambda) and get the roots by factoring
So it gives me complex roots?
woven radishBOT
sturdy mirage
sturdy mirage
Ah.
sturdy mirage
It also said I need to use the Gauss Jordan elimination method, which just looks like matrices stuff?
restive river
yeah, use row operations
sturdy mirage
The first eigenvalue
restive river
so you want to find the kernel of A-lambda I
fractions are fine, but can get messy
restive river
So I need to get it to 1 0 0, 0 1 0, 0 0 1?
no, it will never be invertible since lambda is an eigenvalue
sturdy mirage
no, it will never be invertible since lambda is an eigenvalue
What am I supposed to do with this then?
Do I do row operations until I only have 1s?
Or until the bottom row is 0?
restive river
yes
sturdy mirage
The book doesn't really tell me how to at all.
restive river
you want to row reduce it until you can take the kernel of it
sturdy mirage
you want to row reduce it until you can take the kernel of it
What is a kernel?
restive river
null space
sturdy mirage
So a bunch of 0s in the last row, or the last column?
restive river
yeah
sturdy mirage
It has been 8 years since I took Linear Algebra now
sturdy mirage
yeah
How would you personally eliminate this one? The book is so insanely bad at describing how to do this (it does not at all), that I have zero idea where to even start.
sturdy mirage
use a combination of these row operations
Would putting the 0 5 0 at the bottom be the best?
Oh never mind
restive river
yes, you can do that
sturdy mirage
use a combination of these row operations
I got the matrix to 1 1 4, 0 1 0, 0 0 0. Is that an acceptable form?
Or is it better to make it 1 0 4, 0 1 0, 0 0 0
restive river
Or is it better to make it 1 0 4, 0 1 0, 0 0 0
this makes it easier
restive river
huh?
restive river
yeah
but what do you mean by substitute -1
we have $\begin{bmatrix}1&0&4\0&1&0\0&0&0\end{bmatrix}\begin{bmatrix}x\y\z\end{bmatrix}=\begin{bmatrix}0\0\0\end{bmatrix}$
woven radishBOT
Toby
restive river
write the solution in terms of the free variable z
devout snowBOT
@sturdy mirage Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
jolly swan
what are intersection?
devout snowBOT
what are intersection?
jolly swan
Are two lines that cross but include the Cartesian plane?
devout snowBOT
@jolly swan Has your question been resolved?
weak cove
Are you asking what the intersection of two lines is?
jolly swan
Are you asking what the intersection of two lines is?
yes
weak cove
It is the point where they cross eachother (if they do)
jolly swan
It is the point where they cross eachother (if they do)
this is a intercept?
weak cove
there is only 1 line in that image
but the point you have selected
you could say that is where the line 'intercepts' the y-axis
or also you could say that is where the line 'intercepts' the x-axis
But, you don't have two lines in that
jolly swan
But, you don't have two lines in that
How do I calculate the angle of two lines?
zenith stump
can someone check if i did this correctly
devout snowBOT
can someone check if i did this correctly
sturdy mirage
This is the problem I am on and the solution I have come up with.
sturdy mirage
I know the solution is incomplete and that I need to solve for the 3 constants, I'm just not entirely sure how.
This is the matrix I have, I'm just not sure how to do row reductions on it to get constant values.
devout snowBOT
@sturdy mirage Has your question been resolved?
crisp fossil
first of all, x(0), so t=0
so all your e^rt become 1
then you get a normal matrice [-3, 1, 3][0, -4, 0][1, 3, 1] times [c1, c2, c3] = [1, 4, 0] which is trivial to solve
@sturdy mirage ty for doing all the work bc I do not remember how to do systems of differential equations, but I can scoop up the glory for this problem regardless :D /j
devout snowBOT
@sturdy mirage Has your question been resolved?
sturdy mirage
then you get a normal matrice [-3, 1, 3][0, -4, 0][1, 3, 1] times [c1, c2, c3] =...
Trivial as in only the trivial solution?
crisp fossil
Trivial as in this is a simple system of equations, it’s poor notation on my part
sturdy mirage
Trivial as in this is a simple system of equations, it’s poor notation on my par...
It's the first problem of the chapter, I would hope it's a little easy lol
Do I still do the row reduction?
frosty cradle
yes, unless you wanted to invert the matrix and multiply that by [1, 4, 0]
sturdy mirage
yes, unless you wanted to invert the matrix and multiply that by [1, 4, 0]
I got this
Ignore the e's
devout snowBOT
@sturdy mirage Has your question been resolved?
devout snowBOT
@sturdy mirage Has your question been resolved?
slate bramble
How do I find the range to the double integral in the uv-plane?
devout snowBOT
How do I find the range to the double integral in the uv-plane?
@slate bramble Has your question been resolved?
devout snowBOT
@slate bramble Has your question been resolved?
devout snowBOT
@slate bramble Has your question been resolved?
devout snowBOT
@slate bramble Has your question been resolved?
slate bramble
.close
deep vortex
Given that [\lambda \mapsto \Bigl(\frac b a_1 - \frac{a_2\lambda}{a_1}, \lambda\Bigr),] my book says that when plugging in $\lambda = a_1$, we get $(-a_2, a_1)$.
devout snowBOT
Given that \[\lambda \mapsto \Bigl(\frac b a_1 - \frac{a_2\lambda}{a_1}, \lambda...
devout snowBOT
deep vortex
(Posted this in #linear-algebra)
devout snowBOT
Available help channel!
warped tartan
I need help for letter b
devout snowBOT
I need help for letter b
devout snowBOT
warped tartan
.reopen
devout snowBOT
✅
warped tartan
@rancid verge sorry continue your sentence..
rancid verge
What?
warped tartan
.close
hardy ruin
devout snowBOT
devout snowBOT
@hardy ruin Has your question been resolved?
devout snowBOT
Available help channel!
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
winter patrol
do you know the relation between slopes of perpendicular lines?
wdym by "it"
gradient of what
you really need to be specific here
no
wrong phrasing / words omitted results in the wrong result
there are two lines here
the product of gradients of two perpendicular lines
(excluding horizontal/vertical)
is -1
yeh, as horizontal lines have a gradient of 0, slope of vertical is undefined, so that property doesn't apply there
to find the slope of the perpendicular line,
you can take the negative reciprocal of the given line
slope is pretty much same as gradient
yes
that can be simplified though
yes
well now you have the slope/gradient and a point
and there's a formula that pretty much tells how to get the equation of a line from that
the point-slope/gradient formula
no
look up point slope formula
actually seeing as you're given the y-intercept
you can just use
slope/gradient intercept form directly
yeh
rapid mauve
There is a question with a total of 9 points. The Mean score was 4.48 with a standard deviation of 3.19.
I calculated that at least 7.8% of students got 9/9. I also calculated that at least 4.3% of students got at or below -1/9 as a score, and that at least 4.1% of students got 10/9. Even though neither of those makes sense
How can I correctly calculate how many students got 9/9 if the score can only go from 0 to 9?
devout snowBOT
There is a question with a total of 9 points. The Mean score was 4.48 with a sta...
devout snowBOT
@rapid mauve Has your question been resolved?
hasty moat
screw probability
supple knot
screw probability
don't interrupt help channels
hasty moat
yeah im gonna help the dude chill
some light banter first
@rapid mauve
you alive?
muted stump
I wanna learn fraction decomposition integration, got a few basics down. I am solving a few of my past papers and I wanna learn how to integrate sqrts since there are a few of those in my papers
devout snowBOT
I wanna learn fraction decomposition integration, got a few basics down. I am so...
rapid mauve
yeah im gonna help the dude chill
I am really confused by your response.
hasty moat
I am really confused by your response.
not gonna explain it if you already got it and the channel was dead
hasty moat
I wanna learn fraction decomposition integration, got a few basics down. I am so...
for fractional decomposition
muted stump
I wanna learn fraction decomposition integration, got a few basics down. I am so...
Need help ^
hasty moat
make sure the denominator is represented as a series of linear factors
so (x-1)(x+2).....
Javaman open a new channel
rapid mauve
not gonna explain it if you already got it and the channel was dead
“Screw probability” is just an unusual response, but anyways I will ask in another channel
muted stump
so (x-1)(x+2).....
mhm
hasty moat
and once you've done that, you can write each term seperately
actually this might be easier to explain
muted stump
and once you've done that, you can write each term seperately
im still not clear enough with ur explanation sir
hasty moat
$\frac{A}{(x+1)} + \frac{B}{(x+2)}$
muted stump
yeah i understand that
woven radishBOT
Zouni
hasty moat
yeah
hasty moat
provide an example?
muted stump
hold up
hasty moat
what
hasty moat
why
hasty moat
you'll be fine i doubt they'd dock you for using the correct method lol
muted stump
nah nah, u dont understand, my math teachers are different
can u show me a method without trig sub or no
final laurel
you can use a u-sub
muted stump
you can use a u-sub
eh, we didnt get to that part yet
hasty moat
multiply by $\frac{\sqrt{4x+12}}{\sqrt{4x+12}}$
woven radishBOT
Zouni
hasty moat
do that
final laurel
eh, we didnt get to that part yet
you're doing partial frac but haven't done u sub yet?
weird curriculum ig
hasty moat
you're doing partial frac but haven't done u sub yet?
lmao true
multiplying by that will get rid of the square root on the denominator
will make it possible to integrate without stuff you haven't learned yet
muted stump
you're doing partial frac but haven't done u sub yet?
OK LET ME EXPLAIN THIS NICELY
I am doing GCSE O lvls, where they make u do a few steps so that u can easily substitute an easy part into the complex part of the integral to easily integrate it, BUT I WANNA LEARN how to do it the hard way
hasty moat
highschool student explaining to college students about Gcse 0 levels 
final laurel
OK LET ME EXPLAIN THIS NICELY
I am doing GCSE O lvls, where they make u do a few...
okay...
hasty moat
you cannot do the question you've provided with partial fractions
muted stump
like for example
they give u the equation y = xsqrt(4x + 12), and u need to differentiate it
u get dy/dx = 6(x + 2)/sqrt(4x + 12).
and then they tell u to integrate what i just said above
ig u just multiply by 2 and the outside integral by 1/2
and boom ur done
muted stump
highschool student explaining to college students about Gcse 0 levels <:sully:65...
sorry i thought u might not know, this server might be filled with mostly americans
hasty moat
sorry i thought u might not know, this server might be filled with mostly americ...
lmao
but it is very weird to be doing partial fractions and to not have done u-sub yet
usually you learn u-sub in calc 1 intro to derivatives
muted stump
yeah GCSE O lvl syllabus for calc is different than american calculus courses
hasty moat
yeah and i'm not american
devout snowBOT
@muted stump Has your question been resolved?
cold granite
I need help with my physics hw
devout snowBOT
I need help with my physics hw
supple knot
I need help with my physics hw
#old-network for physics server
cold granite
oh
pastel pasture
I need help with my physics hw
What is it?
cold granite
the following questions
And when I say I understand nothing i mean im clueless
🙏
pastel pasture
What would the dimensions of tension be?
pastel pasture
Do you understand what tension is
cold granite
Scalar?
cold granite
💀oh
pastel pasture
In any case, I think you should revise the basics
Maybe read on what a wave is and stuff
pastel pasture
The standing wave thing is gonna be impossible without it
Or the chaps at the phsyics server can help you
balmy wasp
Guys I'm pretty confused as to why I must use the sine rule when I can just use the normal tan
devout snowBOT
Guys I'm pretty confused as to why I must use the sine rule when I can just use ...
balmy wasp
devout snowBOT
@balmy wasp Has your question been resolved?
fleet surge
devout snowBOT
@balmy wasp Has your question been resolved?
rough hatch
how do i get this anwser
devout snowBOT
how do i get this anwser
rough hatch
its for unit circle
rare mantle
tan(theta) = sin(theta) / cos(theta)
supple knot
its for unit circle
are you given the unit circle?
rough hatch
are you given the unit circle?
yea
supple knot
,tex .unit circle
woven radishBOT
riemann
supple knot
tan(theta) = sin(theta) / cos(theta)
then it's just this
find $\sin(150^\circ)$ and $\cos(150^\circ)$
woven radishBOT
riemann
supple knot
yup
rough hatch
so how do make it so i dont get a decimal on calc
supple knot
google your calculator model
rough hatch
ok
supple knot
not every calculator is capable of it
devout snowBOT
@rough hatch Has your question been resolved?
pastel pasture
Why does computing derivatives with logarithms over functions that can be negative work?
devout snowBOT
Why does computing derivatives with logarithms over functions that can be negati...
pastel pasture
And does it always work?
pastel pasture
$$y = \sin x$$
$$\ln y = \ln \sin x$$
$$y' \frac 1y = \cot x$$
$$y' = \cos x$$
woven radishBOT
NEONPerseus
pastel pasture
Like sine isn't always positive but it seems to work?
Same thing can be done for x^3
Despite being negative over certain intervals, you get the derivative alright with no domain restrictions
supple knot
Despite being negative over certain intervals, you get the derivative alright wi...
taking the log already assumes domain restrictions
the method would only yield the correct answer in that domain
supple knot
that's completely independent of doing the logarithmic derivative
lusty sapphire
I see
supple knot
using this method, y' = cos(x) doesn't have to be defined for all x
it just happens so
pastel pasture
Is there a function where this fails
woven radishBOT
SWR
pastel pasture
$$\ln z = \ln |z| + i\arg (z) + 2n\pi$$
$$n \in \mathbb Z$$
But nothing for real valued functions?
And technically that doesn't need to be the principal argument
Right
lusty sapphire
But nothing for real valued functions?
Technically, log(sin(x)) will not be defined for sin(x)<=0 if you stick to the reals
woven radishBOT
NEONPerseus
pastel pasture
Technically, log(sin(x)) will not be defined for sin(x)<=0 if you stick to the r...
I guess
lusty sapphire
**NEONPerseus**
I'm sticking to principal log. Plus, the 2npi would disappear once you do derivative
devout snowBOT
devout snowBOT
Available help channel!
ancient gull
I need some help
devout snowBOT
I need some help
ancient gull
I need help with this worksheet
and how area =base x hight
here I showed how I think you do it
that is number one
dense nymph
Imagine it on a number line
You start from -8
How many numbers would it take to get to 0
ancient gull
8
dense nymph
Yeah
In the first question you are adding 12
It takes 8 to reach zero
And then you have 4 numbers left
So what would your final number be
dense nymph
Yeah nice
ancient gull
thank you
dense nymph
Np
ancient gull
.close
supple knot
"decreasing" means the slope is negative
Where in this image is the slope negative
Show the formula for this
devout snowBOT
@mighty acorn Has your question been resolved?
devout snowBOT
@mighty acorn Has your question been resolved?
umbral trench
So I am currently trying to implement an Animation in my app. Basically I have a value that is clamped from 0 to infinity, and should become very "slow" at around 30-40. I want to interpolate it like the curve shown in this picture. Its very important that the angle at the start of the function is 45 degrees, because the value is the value of a swipe gesture by the user and its used to swipe a widget. so the widget should move in the speed of the users finger in the beginning, and then slowly the speed should decrease until its eventually near 0. Any Idead?
devout snowBOT
So I am currently trying to implement an Animation in my app. Basically I have a...
@umbral trench Has your question been resolved?
umbral trench
wait, i think i found the solution
its f(x)=1-ℯ^(-x)
should be
yeah I will try if it works well
devout snowBOT
naive estuary
hmmm you might want to ask your teacher...
wooden sequoia
Can someone help me with an incline plane question?
long fog
Is that a -4?
viscid talon
dusk sand
hi. Algebra problem. To solve for x , why cant u multiply the denominator (without the x) to the LHS?
devout snowBOT
hi. Algebra problem. To solve for x , why cant u multiply the denominator (witho...
dusk sand
is it bc youd still have 1/x left over?
long fog
long fog
Idk who srs is
winter patrol
you can do valid manipulation, whether it helps you is a different story
why cant u multiply the denominator (without the x)
wdym by without the x
devout snowBOT
@dusk sand Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
proper violet
finite inlet
Hey, quick question
devout snowBOT
Hey, quick question
finite inlet
[ \lim_{x \rightarrow 0} |x|^2 \cdot f(x) ]
woven radishBOT
madmike
pseudo basin
not if f(x) = {1/x^3 for x ≠ 0, 69 at x=0} it isn't.
woven radishBOT
madmike
finite inlet
and then I wanted to do sandwich
but I can't find a function that is <= |g(x)|
[
|g(x)| = |x \cdot f(x)| = |x| \cdot |f(x)|
\ \text{ and then } \ 0 \leq |x| \cdot |f(x)| \leq \ ?
]
woven radishBOT
madmike
finite inlet
I thought maybe ? := |x|^2 * f(x)
pseudo basin
well I have this function and need to show that it is continuous in x=0
is anything known about f(x)?
finite inlet
but as you said that is not going to work
pseudo basin
beyond it being a function from R to R, that is
finite inlet
f: R \ {0} -> R is limited (restricted?)
up and down
what's the english word
so I guess I could choose some y that is > f(x) for all x
pseudo basin
can you find the german word and its definition
pseudo basin
okay yeah that means bounded
finite inlet
ahh okay ty
pseudo basin
so you know there exists a constant M such that |f(x)| ≤ M
that's exactly what you need for your sandwich
the bread, if you will
pseudo basin
wdym generic
finite inlet
uhhh without actually giving a number
I guess that would be impossible
sorry brain fart
can I use 0 for the bottom bread though?
I think not?
Because x * f(x) could be less than 0 in some x
right?
yeah
ty
.close
grand meadow
how would i solve a logarithmic inequality that has a logarithm as the argument?
balmy wasp
give example
grand meadow
for example:
pseudo basin
10^(both sides) turns this into log_10(x) < 10^(1/2)
balmy wasp
i thik change whatever in the brackets into x aybe/
grand meadow
i'll have x >0 and x>10^sqrt10, right?
grand meadow
for example:
and the answer to this inequality would be x<10^sqrt10?
low holly
and the answer to this inequality would be x<10^sqrt10?
just this, or also x > 0?
can we have x = 1/10?
grand meadow
wouldn't i have x>0 and x>10^sqrt10? why x=1/10?
low holly
wouldn't i have x>0 and x>10^sqrt10? why x=1/10?
how are you getting x>10^sqrt10?
also if x>10^sqrt10, then x > 0 is redundant
x < y implies 10^x < 10^y, i.e. the direction of the inequality is preserved when raising 10 to power of each side
low holly
x > 10^sqrt10 seems correct
how? the left-hand side is increasing to infinity
final storm
sry not greater
low holly
yeah...
final storm
mb
low holly
that's the part they have wrong
final storm
ye, my lazy ass didnt scroll up to read the question again
grand meadow
where would i get x=1/10?
low holly
where would i get x=1/10?
i'm asking you to consider what happens when x = 1/10 since you seem to include that in your solutions
(assuming you have fixed the mistake x>10^sqrt10 to x<10^sqrt10)
grand meadow
and the answer to this inequality would be x<10^sqrt10?
i thought the answer to the inequality is x<10^sqrt10, is this wrong?
low holly
i thought the answer to the inequality is x<10^sqrt10, is this wrong?
well you pointed out that we must have x > 0 otherwise the inner logarithm is undefined
but does x = 1/10 satisfy the inequality?
(you should see a problem)
grand meadow
wait in the system of inequalities i'll have x<0 and x<10^sqrt10 so the answer should be x<10^sqrt10. idk where to plug in x=1/10
low holly
how did you get x < 0
grand meadow
honestly im following this, and since it says that i should write A>0 i wrote x<0
low holly
honestly im following this, and since it says that i should write A>0 i wrote x<...
why would you write x < 0 if A > 0?
grand meadow
for example:
because here it's <
low holly
because here it's <
no
woven radishBOT
tushar
low holly
the logarithm of 0 or any negative number is undefined
the domain of the log function is the positive real numbers
grand meadow
the options to the question are : A) x<10 B)x<10^sqrt10 C)every real value of x D)1<x<10 E)1<x<10^sqrt10
low holly
yes
one of them is correct
you can repeatedly use the following property to derive one of the constraints: x < y implies 10^x < 10^y
so from log_10(log_10(x)) < 1/2 you get log_10(x) < sqrt(10) and hence x < 10^sqrt(10), as you have found
but this is not all, you also have the domain constraints of the log function
for the inner log to be defined, you must have x > 0
however there are tighter restrictions on x that must be placed, which you can see if you try to evaluate the left-hand side of the inequality when x = 1/10
in this case, the outer log becomes undefined, because you get log_10(-1)
thus you must also make sure that the output of the inner log is positive
this is as much guidance that i can give without outright solving the problem for you
devout snowBOT
@grand meadow Has your question been resolved?
pliant sierra
Please, help me 😦 <@&286206848099549185>
low holly
Please, help me 😦 <@&286206848099549185>
!help
devout snowBOT
Please, help me 😦 <@&286206848099549185>
Please read #❓how-to-get-help
@grand meadow Has your question been resolved?
Available help channel!
crisp cliff
Can I get help understanding the 5 steps mentioned in this video about recursive models? (Time stamp is at that part)
https://youtu.be/ynu0cpyVrto?list=PLhpOtgf9GbnRruVksD0qfd0obHUzJSc4f&t=425
devout snowBOT
Can I get help understanding the 5 steps mentioned in this video about recursive...
crisp cliff
Starting with Step 1, I don't understand this...Wouldn't the t values just be the same? What's the point of this?
devout snowBOT
@crisp cliff Has your question been resolved?
winged wagon
i understand how to do it i just need to know how to break the fraction into two
winged wagon
i got an idea on how but i feel like there is a better way
the 5pi/12 to pi/4 and pi/3 how can i get there with any equation
is there like a proccess i can use with any equation
scarlet sequoia
it comes from sin(pi - x) = sin(x)
where x = 5pi/12
it follows sin(7pi/12) = sin(5pi/12)
scarlet sequoia
yes
scarlet sequoia
do you mean how pi/4 + pi/3 is 7pi/12 or what
or how should you know to split it into them
scarlet sequoia
It's an identity
woven radishBOT
Modus
scarlet sequoia
generally
doing questions like this one
you should focus on how you can express given number as sum (difference) of pi/6, pi/4 or pi/3
because for them values of trig functions are well known
winged wagon
hmm okay
scarlet sequoia
might be also pi, pi/2 etc.
winged wagon
so try to stay with the numbers we already know and use
scarlet sequoia
e.g. sin(pi/12) is not "obvious"
scarlet sequoia
so try to stay with the numbers we already know and use
yeah
scarlet sequoia
that's 7pi/12, but in this case it seems harder than pi/4 + pi/3
but might be used
then some trig identites are required
winged wagon
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wary hound
Is this right?
devout snowBOT
Is this right?
final storm
yes
final storm
14 * 2
wary hound
And when you multiply 0.5 by -2 it should be -1 not 2
final storm
multiplied by 2 on both sides
wary hound
Oh
wary hound
multiplied by 2 on both sides
But you only do that if there was a fraction right?
final storm
but there is a fraction?
wary hound
No I mean for example
final storm
i dont understand what you mean
wary hound
i dont understand what you mean
Let's say it was 2 instead of 1/2 for example
You still multiply both sides?
final storm
no, you multiply by 2 to get rid of the fraction because it looks nicer
but you dont have to multiply if you dont want to
y - 14 = 0.5x - 1
y = 0.5x + 13
just having your answer in this form is fine too
wary hound
just having your answer in this form is fine too
But would the outcome still be the same even tho the answer is completely different?
final storm
it'd be the same
multiplying by 2 for both sides would give 2y = x + 26
-x + 2y = 26
x - 2y = -26
wary hound
Oh now I get it
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ripe portal
In this exercise, i know that when a>3 the limit=inf and when a<3 the limit=0 but what happens when a=3, indetermination?
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In this exercise, i know that when a>3 the limit=inf and when a<3 the limit=0 bu...
glacial wyvern
Wolfram Alpha says that it diverges to infinity but I have no idea why
ripe portal
in my solutions too
glacial wyvern
how did you attempt to tackle it?
ripe portal
so what can i do, apply the log?
glacial wyvern
yeah and then take out the x^3 and then simplify it a bit and then use l'hopital (nvm I have actually no clue if that would work lmao)
glacial wyvern
diverge = does not converge to a value
low holly
,w lim x to infinity ((3x^2+4)/(3x^2+2))^(x^3)
glacial wyvern
it diverges to positive infinity
woven radishBOT
ripe portal
but it's a indetermination no?
glacial wyvern
The limit is indeterminate yes
ripe portal
and to solve it, i applied the ln, taking out the x^3 and then the result is (x^3)ln(0) ?
low holly
$$\lim_{x \to \infty} \left(\frac{3x^2+4}{3x^2+2}\right)^{x^3} = \mathrm{exp}\left(\lim_{x\to\infty} \frac{\ln\left(\frac{3x^2+4}{3x^2+2}\right)}{1/x^3}\right)$$
woven radishBOT
tushar
ripe portal
i don't know doing by this way
i show you how i do it
i think that is what you write
but could u explain me the step of dividing x^3?
woven radishBOT
tushar
Compile Error! Click the 
reaction for more information.
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ripe portal
is the method that i used changing the e for A
low holly
essentially equivalent
ripe portal
but then, how can i solve the intedermination 0*inf?
low holly
rewriting $f(x)^{g(x)}$ as $e^{\ln(f(x)^{g(x)})} = e^{g(x)\ln(f(x))}$
woven radishBOT
tushar
low holly
then since e^x is continuous, we can pass the limit into the exponent
woven radishBOT
tushar
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(You may edit your message to recompile.)
low holly
but then, how can i solve the intedermination 0*inf?
formally, you would be arguing: assume that the limit in question exists. then this limit must also exist, which you seek to contradict
ripe portal
okey, now i see it clearly
and then, i transform my 0*inf in a 0/0 indetermination right?
low holly
0 * infinity is just 0 / 0 when you bring the infinity to the denominator
ripe portal
which by l'hopital is easy to solve
low holly
but could u explain me the step of dividing x^3?
just dividing by 1/x^3 instead of multiplying by x^3
to get 0/0
low holly
which by l'hopital is easy to solve
yes
late gull
Solve this (D^4+D^2+1)y=e^-(x/2)cos(sqrt3/2 *x) how to solve?
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Solve this (D^4+D^2+1)y=e^-(x/2)cos(sqrt3/2 *x) how to solve?
late gull
D=d/dx
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brazen spire
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brazen spire
Is this correct
<@&286206848099549185>
Also do I need to find extra points
Hello
<@&286206848099549185>
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carmine swallow
Is my answer correct?
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Is my answer correct?
carmine swallow
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carmine swallow
<@&286206848099549185>
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maiden tree
how do you graph E
devout snowBOT
how do you graph E
lusty sapphire
Maybe it's a typo. Or maybe it's -2
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umbral raft
waxen harness
@maiden tree are you here?
maiden tree
yea
last imp
https://cdn.discordapp.com/attachments/1051010769300496437/1103876849622327326/i...
Find the midpoint of PQ and use the coordinate of the midpoint and coordinates of S to find the coordinates of R that are inline
waxen harness
https://cdn.discordapp.com/attachments/1051010769300496437/1103876849622327326/i...
This is quite simple. Property of parallelogram is that the diagonals bisect each other. Using this, we can apply midpoint formula to find the point of intersection and then point R as well. Should I do it on paper?
Mid point of SQ would be M ( -6-3/2 , 1-4/2) so M (-4.5,-1.5) then take R (x,y) and x+4 = -9 , y+2= -3. So x = -13, y = -5.
Hope this helps.
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mossy gale
I'm struggling with questions like these. What chapters should I learn before I have strong basics of these
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I'm struggling with questions like these. What chapters should I learn before I ...
pastel pasture
You really only need to know about complex numbers for these ones
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distant shore
Hello Could I please have some help with this question
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Hello Could I please have some help with this question
distant shore
distant shore
the answer is 36
quaint citrus
Right and then what would half of a hashtag be worth?
If one hashtag is 18, what’s half of it?
distant shore
27
whole lake
wise marsh
Ex.
If () = 4, then () () () = 3 * () = 3 * 4 = 12
Which means half () = ( = ½ * 4 = 4/2 = 2
() ( = 4 + 2 = 6
distant shore
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loud spindle
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loud spindle
An i on the correct step
I don't know what to do after that assuming I did everything correctly till that point
$e^xsec(x)=0$
woven radishBOT
ilikecats
loud spindle
$Tan^-1(1)=\pi/4$
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supple knot
,rotate
woven radishBOT
loud spindle
I tried it another way
I got pi/4
I don't know how to solve the questions after this?
Because that's not within the interval
I think
I mean 3pi/4
I miss wrote
No idk
They are both values for tan^-1 (1)= pi/4,3pi/4
Idk
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restive river
how do I take notes in maths
devout snowBOT
how do I take notes in maths
restive river
I seem to remember really well using questions
But I would like advice from someone more experienced
And generally how to approach questions and worked examples
I just try to solve a question till I get it
But I find that very slow and ineffective is there a better way
If so I would really appreciate any advice
karmic quarry
For me, I usually like to look at a couple examples to see if there's a certain pattern or pattern of steps when it comes to specific kind of questions before I approach a problem by myself. I also like to reason why they needed to do that step in the problem to get the end result.
karmic quarry
I just try to solve a question till I get it
honestly, sometimes this is just a thing that you have to do. A lot of getting good in math is working through problems, and just overall practicing
karmic quarry
I seem to remember really well using questions
maybe like when taking notes or working through problems question why that step is needed.
restive river
I suck at highschool maths so badly tbh
Also what about focus and effort
I cant seem to completely focus on the problem and that leads me to skip or forget a step
karmic quarry
have you tried like marking the problem with a star to indicate that you have to go back and try again?
or like mark it with a question mark to ask a teacher
karmic quarry
I suck at highschool maths so badly tbh
i mean it's okay to struggle. you wouldn't learn anything if you were able to breeze through
restive river
or like mark it with a question mark to ask a teacher
I dont think i can do that cuz my o level gce exam is on 9 may
karmic quarry
ah i see
restive river
I tried improving my basics
And got a bit better
But still suck
Any advice on atleast scoring a C
Anything would really help
karmic quarry
while you still can use your school's math resources to get in-person help, they can help narrow down where you are getting stuck
when working through a problem when you get stuck try to solve the problem through other methods for 5-8 minutes, if that can't seem to get through, look up the problem, and work it through the problem with them, and try to understand why they did that step or method
restive river
Ok i will try to fix my basics completely in six hours
Then i will try to cover all the main topics
karmic quarry
most math follow a set of pattern and reasoning, so knowing that can help with problems
half of the battle is understanding why and how
restive river
If its ok could u talk to me in dms about improving and feedback
restive river
most math follow a set of pattern and reasoning, so knowing that can help with p...
So how can i know that
karmic quarry
it's hard to explain
it just kind of clicks
i know it's not the greatest thing to say, but it will eventually happen
just be patient with yourself, practice a lot, it will eventually click
karmic quarry
for me i personally if i get stuck and spend more than 7 minutes trying to figure it out, i usually stop and either look at my notes to see if it helps or look up a step by step answer guide to see how they got there
restive river
for me i personally if i get stuck and spend more than 7 minutes trying to figur...
Is explaining a given example step by step a good way to gain understanding
Cuz thats something i learned recently too
karmic quarry
yeah
bright gulch
M
bright gulch
How do you know the components of a vector field?
How did you get <-y+z, -x+z, x+y>?
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rich helm
been trying to figure out this problem with trig and i'm confused on if ur supposed to subtract 20 from 90 because it's a depressing angle and input 70 in the calculator or use 20.
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been trying to figure out this problem with trig and i'm confused on if ur suppo...
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obtuse pulsar
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finite briar
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finite briar
Isnt the answer just infinity?
pseudo basin
how so
finite briar
you have a constraint
right...well i tried solving the constraints
like obtaining x in terms of y
i got $x=\frac{3y+8}{y-5}$
woven radishBOT
ItzKraken2
finite briar
but idk how to proceed from here
pseudo basin
i want to verify this before we proceed
finite briar
Okay 👍
pseudo basin
,w sqrt(x-5) + sqrt(y-3) = sqrt(x+y) isolate x
woven radishBOT
pseudo basin
!nosols
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
pseudo basin
so it sounds like you have fucked up your arithmetic somewhere
finite briar
so it sounds like you have fucked up your arithmetic somewhere
lemme see
pseudo basin
but in any case now you want to maximize y(5y+1)/(y-3) for y ∈ {4, 5, ...}
finite briar
but in any case now you want to maximize y(5y+1)/(y-3) for y ∈ {4, 5, ...}
but how can u maximize..? i mean doesnt this have infinitely many values?
pseudo basin
have you never done optimization problems before
finite briar
have you never done optimization problems before
nope
proud perch
you don't need calculus
proud perch
just some algebra and intuition
pseudo basin
so theres only so many values y can take given that
finite briar
square both sides
1 sec
i actually did the whole squaring thing
$x+y-8+2\sqrt{xy+8-5x-3y} = x+ y$
woven radishBOT
ItzKraken2
finite briar
$2\sqrt{xy+8-5x-3y} = 8$
proud perch
let's rewrite that, it's better to leave it factored
woven radishBOT
ItzKraken2
finite briar
let's rewrite that, it's better to leave it factored
mmm okay 👍
proud perch
$$2\sqrt{(x-5)(y-3)} + x + y - 8 = x + y$$
woven radishBOT
Mr. Gamer
proud perch
now get the square root by itself on one side
woven radishBOT
ItzKraken2
finite briar
we square again?
proud perch
divide by 2 first
woven radishBOT
ItzKraken2
finite briar
which gives $(x-5)(y-3)=16$, upon squaring
woven radishBOT
ItzKraken2
finite briar
right?
proud perch
yep, now here's where the geometric intuition comes into play
proud perch
nah nvm you just have to test the cases
finite briar
Sooo i do that by looking at factors of 16, find x and y, then xy, then compare?
proud perch
yes
finite briar
Okay lemme do that real quick
proud perch
(1,16), (2,8), (4,4), (8,2), (16,1)
it's not symmetric so you have to include both factor pairs
finite briar
it's not symmetric so you have to include both factor pairs
K
i got xy = 128
x=6, y = 18
from (1,16)
as the maximum
proud perch
how can y be 18
proud perch
yes...
finite briar
then its 114...
proud perch
there you go
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mortal depot
Max/Min f(x,y) = x^2 + y^2 under the constraint x^2+xy+y^2 = 3
I have a quick question regarding the task above. If we solve this with the lagrange-method we get multiple candidates for the optimization problem. But if I simply solve the constraint for x^2 and then insert it in the original equation I get completely different solutions. Why does that not work?
mortal depot
<@&286206848099549185>
Helperbros I need your help
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mortal depot
<@&286206848099549185>
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mortal depot
<@&286206848099549185>
When I solve x^2+xy+y^2=3 for x I get a solution for x that depends only on y. If I insert it into the original equation and maximize it I get the correct solutions. (although this is quite annoying to do)
When I solve x^2 + xy + y^2 = 3 for x^2 I get a solution for x that depends on x and y. If I insert it into the original equation and maximize it I get wrong solutions.
From a purely theoretical standpoint, why is the second approach invalid?
I am aware that solving via lagrange is much easier, simply curious.
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soft raven
mortal depot
rip
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analog trellis
As long as the extrema exist at points where x^2 + xy + y^2 = 3 define a function x in terms of y or y in terms of x you should be fine to use your approach.
fossil garden
could someone guide me on how to write a quadratic polynomial in standard form
fossil garden
Q=x^t(SDS^t)x+Px+c
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supple knot
Q=x^t(SDS^t)x+Px+c
That doesn't look quadratic
fossil garden
Q is a quadratic polynomial here not a quadratic form
@supple knot
or am i missing something
rapid jewel
i don’t know how to solve this
devout snowBOT
i don’t know how to solve this <:bleakkekw:913344117981999125>
rapid jewel
why is this part 0?
