quite so
#help-33
dry prawn
dry prawn
So now I got 2x+6 over x + 3
no you don't
scarlet raft
Wait
You right I don't
I forgot the x-5 and x+11
So now I got 2x+6/(x-5) (x+11) / x+3
elfin berryBOT
Steakanator
scarlet raft
Now im stuck dang it
dry prawn
only now must we deal with the compound fraction
scarlet raft
Wait
Isn't the opposite of dividing multiplation?
So I could just multiply x + 3 to the top
dry prawn
Isn't the opposite of dividing multiplation?
yes
dry prawn
So I could just multiply x + 3 to the top
no
scarlet raft
Alright now I am really stuck
dry prawn
remember dividing by t is the same as multiplying by 1/t
dry prawn
much better
dry prawn
(2x+6), parentheses needed
dry prawn
factor what?
dry prawn
you sure do
scarlet raft
Alright, I got the answer. Thank you very much for the help
dry prawn
scarlet raft
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marsh citrusBOT
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cold idol
why is this the angle?
marsh citrusBOT
why is this the angle?
marsh citrusBOT
marsh citrusBOT
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solar ether
Need someone to explain the whole solution
marsh citrusBOT
Need someone to explain the whole solution
solar ether
I don't understand why even the very first step was done
And how did we come to the conclusion in the very first step that we need to prove that the limit is 2
devout mauve
hindsight
spark otter
And how did we come to the conclusion in the very first step that we need to pro...
The intuition comes from supposing it does converge, and finding out what would be the limit
devout mauve
questions arent solved like this. just because the solution presents it that way does not mean that the way to go about solving it would also start like this
spark otter
With recursion sequences u(n+1) = f(un), the intuition is always that if (un) does converge, then l = f(l), with f continuous
devout mauve
thats always important to keep in mind
spark otter
Order in which we personally find the solution ≠ Order in which things are written in the solution
solar ether
With recursion sequences u(n+1) = f(un), the intuition is always that if (un) do...
Alright. I haven't been taught this concept yet
spark otter
Alright. I haven't been taught this concept yet
It's a recurrent thing for sequences defined recursively
solar ether
Order in which we personally find the solution ≠ Order in which things are writt...
Well can you guide me and help me solve this question or just understand the solution
fair pond
Well can you guide me and help me solve this question or just understand the sol...
\FT
Suppose the sequence converges to $L$, then you can solve the equation
[\wrb{
L = \s{2+L}
}]
elfin berryBOT
Cooly
solar ether
**Cooly**
Um how can L be equal to root over 2+L
Alright i understood the first few steps but
cunning fiber
Um how can L be equal to root over 2+L
$\lim_{n \to \infty} x_{n+1}=\lim_{n \to \infty} x_n$
elfin berryBOT
Civil Service Pigeon
marsh citrusBOT
Available help channel!
finite forum
marsh citrusBOT
finite forum
for the DFS(4,7) row
why isn't CompletelyExplored[4] = True
Discovered[U] = True, so it should fall down into CompletelyExplored[V] <- True and not recursively call the DFS function?
jagged relic
It calls DFS(5,7) before setting CompletelyExplored[4]
Same reason 2 isn't completely explored when DFS(4,7) is called
Or 1 when DFS(2,7) is called
finite forum
It calls DFS(5,7) before setting CompletelyExplored[4]
it doesn't though
jagged relic
... yeah, it does
finite forum
jagged relic
2 isn't the only vertex connected to 4
finite forum
so it loops through 2 and 5?
jagged relic
Yes
finite forum
okay that makes sense
it just looks weird though, why for each vertex 'U'
like U is a variable used elsewhere already?
jagged relic
Where?
finite forum
it comes with a "preset" value at the start of each call
which is one of the adjacent nodes
jagged relic
No, it doesn't, this column just lists what it equals on each iteration of the loop, during the call
finite forum
No, it doesn't, this column just lists what it equals on each iteration of the l...
yeah im tripping my bad
also one more thing
what are these empty rows?
jagged relic
It's the same call, but a different loop iteration, hence the different U value
marsh citrusBOT
marsh citrusBOT
Available help channel!
fossil pebble
Is this PFD?
marsh citrusBOT
Is this PFD?
chrome jacinth
Is this PFD?
If by PFD you mean Partial Fraction Decomposition, then yes.
chilly mica
If by PFD you mean Partial Fraction Decomposition, then yes.
Thanks GL 2 U 2
chrome jacinth
Thanks GL 2 U 2
I already finished my HSC but thanks :)
wicked cave
Is this PFD?
And a simple one at that which can you do it manually: 7x = 2(2x-3) + 3(x+2)
fossil pebble
how do you know that?
chilly mica
I already finished my HSC but thanks :)
:/ got chem like rn
chilly mica
Nup phys next fri
chrome jacinth
Nup phys next fri
You got this 👍
fossil pebble
wtf is hsc
chrome jacinth
wtf is hsc
Higher School Certificate. Its the final exam equivalent for students in Australia.
Or more specifically, students in NSW, Australia.
marsh citrusBOT
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lavish kestrel
are the bounds
marsh citrusBOT
are the bounds
left mesa
marsh citrusBOT
humble fog
i was evaluating the lower sum and got the summation of a sequence i-1, im not sure how to put this in terms of a summation formula, could someone help
marsh citrusBOT
i was evaluating the lower sum and got the summation of a sequence i-1, im not s...
humble fog
im sorry for the early ping but it's 5 am and my exam is at 8:30 so i wanted to quickly get some sleep in <@&286206848099549185>
teal adder
from what i've observed over the months ive been here - help is rare early in the day. if none responds in an hour then id say go to reddit for help
wind field
hello
I am taking algebra 2 this summer
should I get any textbooks
or rely on the normal curriculum work
marsh citrusBOT
hello
I am taking algebra 2 this summer
should I get any textbooks
or rely on th...
@wind field Has your question been resolved?
wise lance
A question like really depends on what the instructor is explaining from
And also on your personal needs, like if you really want to study something like that on your own from another reference to dive in.
marsh citrusBOT
@wind field Has your question been resolved?
marsh citrusBOT
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compact crescent
The direction vector
marsh citrusBOT
The direction vector
compact crescent
Thanks for correcting me
whole thorn
you're welcome 😂
compact crescent
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marsh citrusBOT
calm harbor
????
gloomy ore
is it just me or there is a bit of chinese in that question
plain trellis
is it just me or there is a bit of chinese in that question
yes that is mandarin
calm harbor
The direction vector is (3,-1,1)
gloomy ore
in maths?
marsh citrusBOT
Available help channel!
stiff rampart
marsh citrusBOT
stiff rampart
I am not getting the same answer but have retried doing it multiple times. I'm not sure what I'm doing wrong if anything at this point
Is what I am typically getting
I dont want to talk about it
i wrote the right equivalent to x^2
not x
godfuck
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stiff rampart
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next moat
is this an inflection point (x=0)
marsh citrusBOT
is this an inflection point (x=0)
rancid geode
does the concavity change sign?
stoic saddle
this function ain't even continuous at 0 💔
next moat
f'''(-1) > 0
stoic saddle
it would be quite a bureaucratic move to say that 0 satisfies the defn of an inflection pt on paper
next moat
this function ain't even continuous at 0 💔
i will follow my professor, he said f(x) doesnt have to be defined at critical point
coral furnace
bit of a tangent but can someone correct me if im wrong, is an inflection point defined to be when the first and second derivatives are equal to 0?
stoic saddle
first derivative isn't required to be zero
next moat
can i do limit of $2^(f(x))$ as $2^(limf(x))$
marsh citrusBOT
can i do limit of $2^(f(x))$ as $2^(limf(x))$
elfin berryBOT
Mystic
rancid geode
can i do limit of $2^{f(x)}$ as $2^{\lim f(x)}$
elfin berryBOT
k
stone pelican
depends on what you mean by 'do' here
next moat
depends on what you mean by 'do' here
how are there more than one interprations here
stone pelican
if 'do' means replace 2^(f(x)) with 2^(lim f(x)) then no
open kayak
We can generalize this: (this got a nice continuation by Ann and I wanted to say basically the same)
stoic saddle
can i do limit of $2^(f(x))$ as $2^(limf(x))$
the function 2^x is continuous
so yes
next moat
the function 2^x is continuous
is continuity a requirement
waaat
give an example where i cannot do this
stoic saddle
floor function
stoic saddle
is continuity a requirement
kinda, it can still be true by coincidence with discontinuous functions in special cases
but continuous functions can be "factored through" limits
stoic saddle
so i cannot do limit (floor(f(x))) as floor(limit f(x))
yes in general you cannot.
umbral oasis
$\lim_{x\rightarrow 0}\floor{x}$ does not exist but $\floor{\lim_{x\rightarrow 0}x} =0$
elfin berryBOT
Herzog
marsh citrusBOT
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Available help channel!
leaden peak
sad i got this wrong because i was so confident
marsh citrusBOT
sad i got this wrong because i was so confident
leaden peak
allow me a moment to show my work
ahh wait nvm
i found my issue
when i typed the x_1 into my calc
i did -3 + (1/2)
needed to -3 -(1/2)
just a silly mistake
.close
marsh citrusBOT
leaden peak
(also, this was clearly the reason they used those stupid fractions, and i fell right into their trap 😭)
marsh citrusBOT
Available help channel!
tiny wadi
I'm trying to solve past papers for a competition i want to enter but i cant figure out a solution to the 2nd and 3rd problem i checked the answers but it still doesnt make sense could someone explain to me the answers
question 2 translation:
Let 𝛼 be a positive integer such that the least common multiple of the numbers 24 and 𝛼 is 120. Determine the possible values of the greatest common divisor of the numbers 24 and 𝛼.
Question 3 trasnlation:
In the adjacent figure, triangle ABC is
isosceles with AB = AC. Point D belongs to the
side AC so that triangle BCD is
isosceles with BG = BD. Point Z belongs to the
line BC, so that line AZ is perpendicular
toward line BD at point E.
It is also given that: BA is perpendicular to AD.
(a) Calculate the angles of triangle ABC.
(β) Prove that: BÂΓ = 2 ∙ DÂE.
(γ) Prove that: AG = BZ
(I Will check back on this in a bit i can't right now)
marsh citrusBOT
I'm trying to solve past papers for a competition i want to enter but i cant fig...
plain trellis
what have you tried for Q2?
First off, think why would be the LCM of 24 and $\alpha$ be 120?
elfin berryBOT
Annie Maqionde
elfin berryBOT
Annie Maqionde
tiny wadi
First off, think why would be the LCM of 24 and $\alpha$ be 120?
this might sound dumb but maybe because α factor(like idk if thats the word but u can divide it perfectly) of 24
plain trellis
no but then wouldnt the LCM be 24 itself?
tiny wadi
oh
elfin berryBOT
Annie Maqionde
plain trellis
**Annie Maqionde**
start with this
tiny wadi
i don't really understand 😅 what i should put in the place of a
elfin berryBOT
Annie Maqionde
plain trellis
$b = 24$
elfin berryBOT
Annie Maqionde
tiny wadi
120,24?
plain trellis
120 is the LCM
elfin berryBOT
Annie Maqionde
tiny wadi
is g a variable?
elfin berryBOT
Annie Maqionde
plain trellis
how can i find the gcd of a and 24 though
we'll do that later.
marsh citrusBOT
@tiny wadi Has your question been resolved?
proven saddle
Hello, how can I find the whole demostration of Rouche Frobenius's theorem? How can I represent it with lines and vectors as well as with the augmented matrix in 3 dimensions at least. As far as I now, you first do the determinant of the matrix because you want to know if the different vectors expand through the different dimension, but what with the augmented matrix. How can I link both concepts in the space? I have done some progress, Maybe if you know the expansion based on the dimensions of the vectors and link the vector with their covectors in order to find the inflexion point or... I am lost.
marsh citrusBOT
Hello, how can I find the whole demostration of Rouche Frobenius's theorem? How ...
@proven saddle Has your question been resolved?
main idol
what do you mean "whole demonstration"
proven saddle
It's because I want to demonstrate geometrically the theorem, but I am bewildered when it comes to the augmented matrix, what is that?
proven saddle
Yeah but you know that the square matrix is a group of vector in an n-dimensions which can be the basis vector (I am from Spain, so maybe I say some concepts wrong), then why when you do the rgA* you add the last column and do the the determinant with that?
main idol
not sure what rgA* means
proven saddle
The range of the augmented matrix
So, you know that we are dealing with linear equations, so linking vector with planes is a matter of what, covectors?
main idol
do you mean rank
proven saddle
yeah
main idol
not understanding your question. the rank of the agumented matrix (A|B) doesn't always equal the rank of the square matrix A
main idol
https://en.wikipedia.org/wiki/Augmented_matrix
following the notation from here
proven saddle
yeah, but as there is a demonstration to Cramer, in which B in (A|B) seep into A because you want to find the area of x,y,z... there must be a demonstration in which you add the B in order to find if the expansion of the vector is the same to the expansions of the planes
This would be the vectors
Each vector has a plane, if the number of independent vectors is the same as the number of independent planes the system of equation is SCD, or rectify me
main idol
what's SCD
proven saddle
when the system of equations has an unique solution
proven saddle
Well, that was my reflection, each plane has a direction which is denoted by a vector, if there are three vector in 3 dimensions and a rank of 2, then it has infinitives solutions which depends on the basis vectors, only if the rank of the augmented matrix is 2 as well. It would mean if the augment matrix reprensent the linear equations, then you are doing the determinant with the others vector and another vector which is the solution of the linear equation, then the question is why you do that
proven saddle
what does "each vector has a plane" mean
I suppose that that thing exists thanks to the covectors.
marsh citrusBOT
@proven saddle Has your question been resolved?
marsh citrusBOT
@proven saddle Has your question been resolved?
marsh citrusBOT
@proven saddle Has your question been resolved?
marsh citrusBOT
@proven saddle Has your question been resolved?
sand bear
marsh citrusBOT
sand bear
Why is answer D, shouldnt acceleration spike up
maiden edge
Why is answer D, shouldnt acceleration spike up
the acceleration will increase in which direction?
sand bear
the acceleration will increase in which direction?
the negative. but its a vector quantity so its decreasing for example -9.8 to -12 for spike down and -9.8 to -8.2 or something for spike up.
or
wait
Right im dumb
Thanks
.close
marsh citrusBOT
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wooden lintel
find the minimum of
wooden lintel
<@646604276336033793> looks like some AM-GM question
i tried
wooden lintel
No use
calm harbor
find the minimum of
wooden lintel
Can you show what you tried?
i dont know latex so cant type
But all i did
is just apply the ineq directly
calm harbor
I'll write it for you, just briefly explain
iron marlin
find the minimum of
i think it's rather clear the minimum < 2
looks like the most obvious thing to do is differentiate wrt x
wooden lintel
looks like the most obvious thing to do is differentiate wrt x
f'(x)=0 is a transcendetal equation
how could we solve it
wooden lintel
but seriously, where did you get this problem from
so my math teacher show us a 11th grade problem
iron marlin
how is this even an 11th grade problem
wooden lintel
he said it's a simple one
yeah idk why
he must've been kidding
11th graders know nothing about exponential function
dusk wharf
lofty gyro
Random thought, would it actually be
find minimum of 27^(cos(x))+81^(sin(y))
this would be much easier and more like a 10th grade Question
spark halo
the sin one?
spark halo
yeah that's basically it
wooden lintel
do you know the answer to it?
nah i dont
wooden lintel
<@646604276336033793>
how did you get this
i mean
how can you find the lower bound
spark viper
it's 2×3^(-5/2)
? You sure it 3^(-5/2) it should be positive
spark halo
? You sure it 3^(-5/2) it should be positive
the exponent is negative, not the answer.
spark viper
Why?
spark viper
Oh
I wrote the result and forgot the next second😭
Sorry
@wooden lintel does this count as resolved?
wooden lintel
<@646604276336033793> does this count as resolved?
yes thank you all
spark viper
Yayyyy
unkempt venture
marsh citrusBOT
unkempt venture
how have they expanded the LHS like this in step 1
shouldn't it be x((x-a)+(x-b))
leading to x(2x-(a+b))
which is completely different to the result of x(x-b) + x(x-a)
late geode
same thing
late geode
show your work
unkempt venture
okay
nevermind i got the correct answer
i think ur reassurance helped me or smthng
thank you
.close
marsh citrusBOT
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timber yoke
Hey there!
I've just started studying arithmetic progressions at school
While solving a few problems, this idea spontaneously popped up that there is an easier way to find the common difference(d) of an AP, when given any two terms of it.
I took a while to make an equation
Here's what I came up with:
marsh citrusBOT
Hey there!
I've just started studying arithmetic progressions at school
While so...
hidden gale
what are those variables in the context of AP
timber yoke
what are those variables in the context of AP
Those are any two terms of an ap
Like, if an AP is 2, 4, 6, 8
a2 is 4, a4 is 8
that way
past maple
Is this right?
Yes it is
timber yoke
Yes it is
How do you prove it though?
I have no idea why this works, i just made it myself
hidden gale
you should realize that AP is basically a linear equation
and the gradient is the common difference
past maple
You can rewrite $a_x$ as $a_0 + dx$
elfin berryBOT
d
past maple
Where $a_0$ is a common number for the whole sequence
elfin berryBOT
d
past maple
Those are any two terms of an ap
Like, if an AP is 2, 4, 6, 8
a2 is 4, a4 is 8
For example here a0 is 0
But in 14,17,20,23,..., a0 is 11
So with that formula, you get
$$\dfrac{a_y-a_x}{y-x}=\dfrac{(a_0+dy)-(a_0+dx)}{y-x}=\dfrac{d(y-x)}{y-x}=d$$
No wait
timber yoke
what i learnt is $a_n$ = a + (n-1)d
elfin berryBOT
d
past maple
what i learnt is $a_n$ = a + (n-1)d
Yes you can use that as well
elfin berryBOT
Vihaan Vikas
timber yoke
It is almost the same as this
doesnt look same to me though 😅
I'm pretty new to ap to I don't know much
I just thought this up
past maple
If you have $a_n=a+(n-1)d$, replace the $n$ with an $x$ and obtain $a_x = a+(x-1)d$
elfin berryBOT
d
past maple
Now it looks more similar right?
timber yoke
no i get this part
past maple
$$a_x=a+(x-1)d$$
$$a_x=a_0+xd$$
elfin berryBOT
d
past maple
i'm talking about this
You can do the same
Rewrite a_y and a_x using the formula
And do the same steps
Try to do it yourself
past maple
Well, I am not sure whether it has a name
I have never seen it as an actual formula actually
But the idea of dividing those two things has been known for quite a long time, yes
It is actually one of the oldest ideas in math
timber yoke
ohh
i just made this up today at school
just a curiosity
i'm 15 so well, doing something felt good
past maple
ohh
i just made this up today at school
That is great, the fact that it is not new does not matter
Nowadays it is actually very difficult to do something new
You have to study some very obscure areas of mathematics because the more well-known areas have already been researched to exhaustion
But if you rediscover something by yourself, that's great!
marsh citrusBOT
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ornate leaf
f'(x) < f(x) => f(x) < f(0) e^x
Proof?
marsh citrusBOT
f'(x) < f(x) => f(x) < f(0) e^x
Proof?
novel juniper
$f'(x)<f(x)$ for all $x$?
elfin berryBOT
wai
stoic saddle
f'(x) < f(x) => f(x) < f(0) e^x
Proof?
feels like we are missing a bit of context here 
is there nothing else given?
novel juniper
I feel like we need this to greater than 0 to be able to do a lot of thigs
stoic saddle
!xy @ornate leaf
marsh citrusBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
@ornate leaf Has your question been resolved?
ornate leaf
feels like we are missing a bit of context here <:thonk:406575732563902485>
No nothing else
I went and rechecked
stoic saddle
false as stated
ornate leaf
When is it true ?
stoic saddle
i think maybe you can say f(x)<f(0)e^x for x > 0 at most?
ornate leaf
Its probably a typo can you guess the correct problem ?
stoic saddle
Its probably a typo can you guess the correct problem ?
i refuse to engage in such guessing-games.
but i am gonna give you a CE to this
f(x) = e^-x
f(0)e^x = 1, but e^-x is not upper-bounded by 1
f(-1) is not less than 1
ornate leaf
but i am gonna give you a CE to this
What's a CE
ornate leaf
i refuse to engage in such guessing-games.
Well i meant if you have seen such problem somewhere
stoic saddle
counterexample
ornate leaf
For some specific interval
stoic saddle
no
correct course of action is to email your prof with the counterexample
it's THE PROFESSOR'S responsibility to give meaningful questions in your problem set
ornate leaf
Im pretty sure its x>0
stoic saddle
no
stoic saddle
the third one...?
ornate leaf
Second
stoic saddle
the one asking you to calculate the limit of x^(1/x) as x -> +∞?
ornate leaf
Ok so
stoic saddle
email prof and force her to give you correct questions for proof!
stoic saddle
no, you have to refuse to do it outright
ornate leaf
Im am not trying to correct the professor
novel juniper
Im am not trying to correct the professor
why not
ornate leaf
Im trying to spend time on problems to have more experience
novel juniper
you can only do that if the problems are right
ornate leaf
Ok so i rephrased the problem
x>0
This is right and im still not sure how to solve
So id like to understand this one now
Could this be a MVT solution ??
stoic saddle
well ok alright let me take my maliciously compliant hat off.
i think what you might wanna do is consider the function g(x) = f(x)e^-x
with the ultimate goal of showing g(x)<g(0) for x>0
which, yeah, it'll be mvt at the last step
stoic saddle
i think you overcomped
stoic saddle
overcomplicated.
stoic saddle
rather (g(x)-g(0))/x with g defined as i wrote
but also mvt is really a stepping stone to say "negative derivative therefore decrerasing" in a more formal way
and im trying to communicate that but you're kinda stuck not seeing the forest for the trees i feel like
ornate leaf
and im trying to communicate that but you're kinda stuck not seeing the forest f...
Wdym
ornate leaf
but also mvt is really a stepping stone to say "negative derivative therefore de...
Why negative
Wait i think i made some mistake give me a sec
stoic saddle
when someone "doesn't see the forest for the trees" it means they are over-focused on the little details and are missing the bigger picture / basic idea.
ornate leaf
With g you get g(x) < f(0) on the right side
Then f(0) = g(0)
Oh here is where x >0 matters
Yea i solved it
Basically you get f'(c) < f(c)
Which is true because f'(x) < f(x)
But why did you use that sub g(x) = f(x) e^-x
stoic saddle
my idea was that the inequality f(x) < f(0)e^x is equivalent to f(x)e^-x < f(0)
but the latter has the advantage of being easier to think about bc it's function vs. constant rather than two functions being compared.
marsh citrusBOT
@ornate leaf Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
elder wing
help
elder wing
solve for x
hidden gale
i think you need to take the log on both sides
knotty trellis
either take log, or rewrite everything to have base 3
marsh citrusBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
indigo nest
!show please
marsh citrusBOT
Show your work, and if possible, explain where you are stuck.
crude flax
Wagwan
elder wing
wait sending my work
knotty trellis
can someone do this and send me their working
yeah, btw this is not how this server works. We can help u do it on ur own, but we wont do it for u
elder wing
yeah, btw this is not how this server works. We can help u do it on ur own, but ...
correct answer should be 2n-6 for x
crude flax
correct answer should be 2n-6 for x
Yo
elder wing
correct answer should be 2n-6 for x
someone help !
crude flax
but im dumb
Alr
warm osprey
elder wing
in the first step
i got sqrt 3^3 and multiplied it with 0.5
knotty trellis
!nosols
marsh citrusBOT
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.
knotty trellis
i got sqrt 3^3 and multiplied it with 0.5
okay so sqrt(27) = sqrt(3^3) = 3^(3*0.5) = 3^1.5
is that what u tried to do?
for some reason you wrote 3 + 0.5 and not 3 * 0.5
elder wing
for some reason you wrote 3 + 0.5 and not 3 * 0.5
yea but then u add them right
elfin berryBOT
MathIsAlwaysRight
elder wing
is this wrong or what we are supposed to do
knotty trellis
what you wrote is wrong
warm osprey
Someone explain triple integration
stoic saddle
Someone explain triple integration
!occupied
marsh citrusBOT
Someone explain triple integration
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
elder wing
what you wrote is wrong
uhm i might actually have to go rn..got exam in 30mins...i still dont get it but tnks for helping
knotty trellis
is this wrong or what we are supposed to do
u can surely start by rewriting $\sqrt{27}$ as $3^{1.5}$ or $3^{0.5 \cdot 3}$
elfin berryBOT
MathIsAlwaysRight
knotty trellis
uhm i might actually have to go rn..got exam in 30mins...i still dont get it but...
alr, sure. U can come back after the exam if u want
elder wing
alr, sure. U can come back after the exam if u want
alr
marsh citrusBOT
@elder wing Has your question been resolved?
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faint breach
marsh citrusBOT
faint breach
siny=cosx then cosy=√1-cos^2x
cosy.y'=-sinx
y'=-sinx/cosy=-sinx/√1-cos^2x
Now put values
-sin(5π/3)/√sin^2(-5π/6)
=√3/2 / √(3/2)^2
2/√3
Is this correct?
hard gull
,w differentiate y=arcsin(cos x) at x=5pi/3
elfin berryBOT
hard gull
siny=cosx then cosy=√1-cos^2x
cosy.y'=-sinx
y'=-sinx/cosy=-sinx/√1-cos^2x
No...
whats up with 4th step after putting the values
faint breach
,w differentiate y=arcsin(cos x) at x=5pi/3
What a creativity you choose wolfram alpha instead of looking at my solution for confirmation so you have doubt on your brain
faint breach
assuming yk the diffrentiation of arcsin
Could you see my work?
twin pike
lemme check
faint breach
It would be better if you look at my work and highlight the mistake
faint breach
,w sin^2(-5π/3)
elfin berryBOT
faint breach
@hard gull
The written thing could be wrong but overall result?
Check the next step
late geode
you want sqrt(3)/2 not 3/2
hard gull
3/4 and (3/2)^2 isnt same
marsh citrusBOT
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echo mirage
can anyone help with this question? I've done the first part of b, but the resulting matrix seems very messy, so i dont know if ive done it right, and im not sure how to use it to find a
marsh citrusBOT
can anyone help with this question? I've done the first part of b, but the resul...
cunning fiber
can anyone help with this question? I've done the first part of b, but the resul...
What did you get for your inverse
echo mirage
1/(0.82a-0.012)*(this is hard to type but ill try) |0.82 -0.15|
(bottom half of the matrix) |-0.08 a|
cunning fiber
yeah it's just rlly ugly
anyway for part ii
they give you all of this
can you convert these into equations
hello?
cunning fiber
ok
echo mirage
So I got this, but I'm not sure how that helps
cunning fiber
the subscripts should be 0, not n
echo mirage
Oh yeah sorry
cunning fiber
but do you see how your matrix equation gives you $J_0$ and $A_0$ in terms of $a$
elfin berryBOT
Civil Service Pigeon
cunning fiber
ok
echo mirage
cunning fiber
,rotate
elfin berryBOT
echo mirage
So if I do the other one, can I create three equations I can solve?
The third being 1 $J_0$ + 1 $A_0$ +0a
elfin berryBOT
ThanduilShrike
cunning fiber
I mean you could but why
echo mirage
To solve to get a
cunning fiber
finding J_0 and A_0 in terms of a is trivial from your inverse multiplication
actually did you do that
echo mirage
Unless there is an easier way to get a I am missing
cunning fiber
finding J_0 and A_0 in terms of a is trivial from your inverse multiplication
and they add to 64000
so you get an equation in only a for free
echo mirage
Oh ofc, yeah I completely missed that somehow thank you!
cunning fiber
anything else?
cunning fiber
!done
marsh citrusBOT
If you are done with this channel, please mark your problem as solved by typing .close
cunning fiber
you can't edit it after (bot doesn't register)
echo mirage
.close
short zinc
Hi
marsh citrusBOT
red nimbus
Bye
marsh citrusBOT
Available help channel!
lost steppe
How did they come to so many conclusions from the second inequality - i understand that they square rooted both sides but i don’t understand how to know which pair of x<_0 / x>_0 goes with which inequality with the root 3s
marsh citrusBOT
How did they come to so many conclusions from the second inequality - i understa...
lost steppe
The red boxed bit is the solution btw
analog elm
How did they come to so many conclusions from the second inequality - i understa...
well do you realize that after square rooting both sides
you end up with
elfin berryBOT
kizzyyy
lost steppe
Not rly
analog elm
never seen $\sqrt{x^2} = \abs{x}?$
elfin berryBOT
kizzyyy
lost steppe
Uhh ik what mod means? Do u mean just considering the positive root then
analog elm
since if x > 0 then \sqrt{x^2} = x
and if x < 0 then \sqrt{x^2} = -x
analog elm
Uhh ik what mod means? Do u mean just considering the positive root then
no more like
if you had to solve something like x^2 = 9
lost steppe
Yh
analog elm
you'd square root both sides
but sqrt(x^2) = |x| not just x
unless x > 0
so it'd be something like $\sqrt{x^2} = |x| = \sqrt{9} = 3$
elfin berryBOT
kizzyyy
analog elm
and |x| = 3 gives x = 3 and x = -3
lost steppe
Ohhh! Yea got u
analog elm
**kizzyyy**
yeah so "square rooting" both sides gets you here
now if x >= 0, you'd have x >= sqrt(3) |y|
since |x| = x for x >= 0
then presumably you know how that translates to |y| <= x/ \sqrt{3}
lost steppe
Yea
analog elm
yeah and so -x/sqrt(3) <= y <= x/sqrt(3)
and yeah multiplying by sqrt(3) gets you the first inequality
u can extend that logic to get the x <= sqrt(3) y <= -x as well
by noting that |x| = -x for x < 0
lost steppe
Oo ok i get where they got those bits from now but how do yk the ways to do the inequality
As in
The upper limit for the first is +ve x and the lower is -ve x but then that flips for the second inequality
analog elm
Oo ok i get where they got those bits from now but how do yk the ways to do the ...
wdym
isn't that what we did
unless you're talking about something else
analog elm
,, (\abs{y} \leq k) \iff (-k \leq y \leq k)
lost steppe
Yea
elfin berryBOT
kizzyyy
analog elm
if that's what you didn't catch
lost steppe
No i got that bit
But yk how there’s 2 sep inequalities, one for x>_0 and one for less than
lost steppe
And the inequalities that they’re paired with have opp upper and lower limits
analog elm
we showed that for x >= 0, we get x <= sqrt(3) y <= -x
lost steppe
so there are two cases to consider
Yes but how do yk when to set x as the upper and when to set it as the lower limit of the inequality
lost steppe
we showed that for x >= 0, we get x <= sqrt(3) y <= -x
Oh in the mark scheme thats flipped around - the lower limit is -x and the upper is +ve x
The inequality u mentioned is for x<_0
analog elm
Yes but how do yk when to set x as the upper and when to set it as the lower lim...
😭 just repeat the process we did for x < 0
|x| = -x for x < 0 so our inequality is -x >= sqrt(3) |y| or otherwise
-x/ sqrt(3) >= |y|
now translating that in a similar fashion gets us to x <= sqrt(3) y <= -x
lost steppe
Yea i get how to get to the numbers but dont get the -x and x limits, why do they flip around 😭😭😭
analog elm
Yea i get how to get to the numbers but dont get the -x and x limits, why do the...
so you don't get why -x/sqrt(3) >= |y| turns to x <= sqrt(3) |y| <= -x?
cuz otherwise the lower and upper bound
are self explanatory
lost steppe
Sorry where did we get -x/sqrt3 from
lost steppe
Yh
analog elm
|x| suggests that we need to consider two cases
-
x >= 0
-
x < 0
if x < 0 then |x| = -x
so far so good?
lost steppe
Yh
analog elm
if x < 0 then |x| = -x
^ by definition
so -x >= sqrt(3) |y|
divide both sides by sqrt(3) to get -x/sqrt(3) >= |y|
if we swap it so that it looks easier on the eyes
it's just |y| <= -x/ sqrt(3)
recall that we established this earlier
which u were in agreeance with
lost steppe
Oh ok
analog elm
so |y| <= -x/ sqrt(3) can be equivalently expressed as - (-x/ sqrt(3)) <= y <= -x/ sqrt(3)
finally multiply by sqrt(3)
that gets you to -(-x) <= sqrt(3) y <= -x
x <= sqrt(3) y <= -x
lost steppe
so |y| <= -x/ sqrt(3) can be equivalently expressed as - (-x/ sqrt(3)) <= y <= -...
Why is the lower limit bracketed with a negative outside
lost steppe
Oh right okay
lost steppe
x <= sqrt(3) y <= -x
Ok i get up to this now!
analog elm
yeah that was for x < 0
u do exactly the same thing
to get -x <= sqrt(3) y <= x
for x >= 0
analog elm
lost steppe
.close
marsh citrusBOT
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Available help channel!
slow pasture
anybody good with mesh analysis and thevenin?
marsh citrusBOT
anybody good with mesh analysis and thevenin?
slow pasture
like the theory
marsh citrusBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
@slow pasture Has your question been resolved?
vivid beacon
hello i dont get this conversion
marsh citrusBOT
hello i dont get this conversion
fervent rampart
no, the chart is a bit confusing but it is trying to say 1 kJ = 1000 J
the way to read it is "1 J x 1000 = 1 kJ" (i.e. 1000 J = 1 kJ)
marsh citrusBOT
marsh citrusBOT
Available help channel!
ancient parrot
need help solving problems like this
marsh citrusBOT
need help solving problems like this
lavish kestrel
need help solving problems like this
for the maxima?
ancient parrot
1/2 for theta?
lavish kestrel
close
ancient parrot
or is it pi
lavish kestrel
pi/2
ancient parrot
ok
lavish kestrel
that is when sine is at its peak
ancient parrot
its 8 * pi/2
lavish kestrel
yeah
ancient parrot
ok
lavish kestrel
so you find 8 * sin(pi/2)
ancient parrot
right cause we are inputting the equation
ancient parrot
so you find 8 * sin(pi/2)
and thats our y?
ancient parrot
ok
lavish kestrel
and then since you've an inflection point, you'll have a mirror
ancient parrot
and then do we do -pi/2?
lavish kestrel
correct
that'll give you a negative y value, but bc of the inflection it's positive
like how you see on the graph
lavish kestrel
yes but
lavish kestrel
do you know that value of sin(pi/2)?
lavish kestrel
npp
lavish kestrel
haha
ancient parrot
so its 8 and -8 resoectively
ancient parrot
no
ancient parrot
tried this and it said i was wrong ;-;
lavish kestrel
chrome jacinth
tried this and it said i was wrong ;-;
Um, isnt there more than two local extrema?
lavish kestrel
oh yeah
ancient parrot
caus -2pi and 2pi
chrome jacinth
If I'm not mistaken, there should actually be ||5.||
ancient parrot
got it
lavish kestrel
well hold on
ancient parrot
If I'm not mistaken, there should actually be ||5.||
only 4 :
ancient parrot
chrome jacinth
Reallly?
ancient parrot
only 2 maxima tho
cause of closed brackets
chrome jacinth
I would have argued that
ancient parrot
if it was open brackets there would only be 2
chrome jacinth
(0, 0) is a local minima
lavish kestrel
minima, it was asking for maxima
chrome jacinth
Since in the local neighbourhood, all the points are actually above that point
ancient parrot
max not min
chrome jacinth
need help solving problems like this
Well rip, badly formatted question.
ancient parrot
if it was inverse you would be right
ancient parrot
Well rip, badly formatted question.
It's a very pearson moment
me and my homies hate pearson
lavish kestrel
type shit
chrome jacinth
need help solving problems like this
ancient parrot
ts ts..
chrome jacinth
It's a very pearson moment
Oof
rough swallow
maxima...
ancient parrot
nobody fw it not even the teachers the administration just decided that everyone needs to do that 😭
and that every sheet of homework needs to have a font size of 42 just incase u have a disability which is crazy cause it's a college and they have accomidative services so you think it would be seperate sheets
ok now its asking for minima but i think theawnser lies with that dob was GLHSC was saying
ok i feel ive done something wrong here
oh its cause it's 3pi/2 instead of pi
chrome jacinth
Oof
ancient parrot
glad i didn't have to do the 2nd derrivative test to find that out lol
https://tenor.com/view/angry-angry-red-mad-mad-angry-guy-friday-night-funkin-gif-1221298022220267120
rough swallow
[-2pi, -pi] , [pi, 2pi]
rough swallow
notation is weird, im in the uk so i think its slightly different
ancient parrot
im doing math while you're doing maths
rough swallow
im doing math while you're doing maths
😆
ancient parrot
how tf do i tell when it's concave down and up cuz rn my brain hurty
and im looking at that middle point like wtf?!?!
got it doe.
rough swallow
concave up is like a bowl, concave down is like a cave
its easier with the british versions, concave (concave down) and convex (concave up)
vague jay
slim ginkgo
so uhm need help with these graphs
marsh citrusBOT
so uhm need help with these graphs
slim ginkgo
i ruled out D easily
my full solution to the difeq is 4/15 ( cos3.5t -cos4t)
how do i select from the 3
i ruled out B by taking the derrivative of the solution and guesstimating that a small tiny value past zero would give y'>0
so positive slope which B does not have
hazy lion
i feel like
youd have to reason about the period
you know that like, you're going to have two pieces right
it'll be a cos of the forcing function period
and then a cos of the unforced period
they should start out pretty much in sync, because they both start at 0 argument, but then drift apart, then back into sync, then back apart
hazy lion
so uhm need help with these graphs
all this besides just plotting the solution which you could do
@slim ginkgo do you get what i mean?
you have one part of the solution with a period of $\frac \pi 2$, thats the $4t$ piece
elfin berryBOT
jan Niku
hazy lion
then $\frac{4\pi}{7}$, thats the $3.5t$ piece
elfin berryBOT
jan Niku
hazy lion
then you'll have oscillations of the difference function contained within some wider periodic envelope, which wont be 0 again until the periods are integer multiples
seems like that'd be 7 oscillations of the 3.5t piece, and 4 oscillations of the 4t piece, at 4*pi, or just past 12
hten again at mAybe 24.5 or so
which is exactly what you see here
marsh citrusBOT
@slim ginkgo Has your question been resolved?
slim ginkgo
all this besides just plotting the solution which you could do
wait up
sorry mb i dipped
daym this question is pretty intricate
slim ginkgo
you know that like, you're going to have two pieces right
yes
slim ginkgo
they should start out pretty much in sync, because they both start at 0 argument...
is that cuz they are similar period values or just for any period values
limber trellis
marsh citrusBOT
limber trellis
i got 1/4 but the answers given pi /8
marsh citrusBOT
@limber trellis Has your question been resolved?
marsh citrusBOT
limber trellis
.reopen
marsh citrusBOT
✅ Original question: #help-33 message
@limber trellis Has your question been resolved?
marsh citrusBOT
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dusty kite
Five cuboid blocks of identical dimensions have been arranged to form a figure.
The shape and selected dimensions of this figure are shown in the drawing.
Calculate the volume of one block. Show your calculations.
Isn’t it 225 cm^3?
marsh citrusBOT
Five cuboid blocks of identical dimensions have been arranged to form a figure.
...
signal stream
Five cuboid blocks of identical dimensions have been arranged to form a figure.
...
yea 225 is correct
topaz narwhal
it seems to be correct, if I did not miss anything.
bright frigate
yes
marsh citrusBOT
marsh citrusBOT
Available help channel!
buoyant jetty
marsh citrusBOT
