B
#help-0
earnest saddle
<PRQ = 40 -----(angle sum property of triangle)
<PRS = r1 = <SRQ = r2 = 20 ---------(RS is angle bisector of <PRQ)
lone heartBOT
@sweet hemlock Has your question been resolved?
sweet hemlock
Yes
blissful lantern
lone heartBOT
stuck loom
Complex roots always exist in pair
therefore for all three complex roots there will be conjugate of those
thus providing you in total of 6 complex roots
polynomial degree is 9
therefore by the Fundamental Theorem of Algebra, You can find number of Zeros
As for the last one , i think you can find it by yourself now
lone heartBOT
@blissful lantern Has your question been resolved?
grave pagoda
lone heartBOT
abstract quest
lone heartBOT
abstract quest
I need help
abstract quest
can you simplify this?
what do you mean
earnest saddle
reduce it to simplest form...
reef verge
abstract quest
thank you
lone heartBOT
@abstract quest Has your question been resolved?
north hemlock
I've gotten this a bit far but have gotten stuck.
lone heartBOT
I've gotten this a bit far but have gotten stuck.
north hemlock
Since 119 and 17 are factors of 2023, I used those and then made the equation into
$$x^2-z^2=\left(\left(\frac{119+17}{2}\right)^2 - \left(\frac{119-17}{2}\right)^2\right)^2$$
$$\implies x^2-z^2 = (68^2 - 51^2)^2$$
ocean sealBOT
Juke | ping me if no response
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chrome salmon
Kraken is here
mellow grail
Mm can't u use Pythagoras triplets? Just find a triplet with 2023 as one term
chrome salmon
Nice 
vale wigeon
Mm can't u use Pythagoras triplets? Just find a triplet with 2023 as one term
how do you envision "using" pythagorean triplets
north hemlock
^
vale wigeon
think before you speak
north hemlock
yeah... I know that's what the goal is but I'm not sure how to do that
mellow grail
how do you envision "using" pythagorean triplets
Pls don't ask me if i chatgpted, i guessed. Also he can set 2023 = m^2 - 1, or m^2 + 1 or 2m, then find an integer solution
vale wigeon
Pls don't ask me if i chatgpted, i guessed. Also he can set 2023 = m^2 - 1, or m...
i wasn't going to ask if you GPT'd it
chrome salmon
You can use 119² and 17² instead
@north hemlock
mellow grail
Oh..well i kinda thought u would ask since u did that the last time I tried to help, sorrryy
north hemlock
You can use 119² and 17² instead
Lemme try this
chrome salmon
What are you apologizing for?
mellow grail
What are you apologizing for?
Well i think i judged her and judging is wrong
chrome salmon
What was your judgement?
mellow grail
Also what if he subtracts 2023^2 from both sides
mellow grail
What was your judgement?
Ask me if gpt'd it
wind cloak
How nice of the question to say please
north hemlock
nope
Maybe I went the wrong direction but I didn't get anywhere by distributing the square before expanding
chrome salmon
Wait lemme write down
keen plinth
show your work
north hemlock
chrome salmon
Since $119²$ and $17²$ are factors of $2023²$, I used those and then made the equation into
$$x^2-z^2=\left(\left(\frac{119²+17²}{2}\right)^2 - \left(\frac{119²-17²}{2}\right)^2\right)$$
ocean sealBOT
fäf
north hemlock
,calc (119^2+17^2)/2
ocean sealBOT
Result:
7225
Yeah
chrome salmon
Find zed
keen plinth
zed
chrome salmon
zee*
wind cloak
z
chrome salmon
Forgive my enlgish
wind cloak
,w prime factorize 2023^2
ocean sealBOT
wind cloak
2023 is such an ugly year man
keen plinth
lol
north hemlock
ahhh
north hemlock
How would I find the other integer solutions
keen plinth
use the other combinations of factors
iron leaf
How do I graph semi circles? Like:
x=√(2y-y^2)
And:
y=-√(25-x^2)
iron leaf
More specifically. How do I find the radius? How do I find what side is missing?
And where is the center?
wind cloak
Convert it to a circle, graph it, and then get rid of the top or bottom portion depending on the sign outside the radical
iron leaf
Convert it to a circle, graph it, and then get rid of the top or bottom portion ...
I tried that with the first one and just ended up with:
x^2 + y(2-y) = 0
And I have no idea where to go from there
Also what about left and right semi circles?
like horizontal I mean
chrome salmon
I tried that with the first one and just ended up with:
x^2 + y(2-y) = 0
And I...
Complete the squares
You get x²+y²-2y=0 btw
(x+a)²+(y+b)²=r² when expanded gives x²+2ax+a²+y²+2by+b²=r²
You have a good opportunity to compare a and b
lone heartBOT
@iron leaf Has your question been resolved?
iron leaf
You get x²+y²-2y=0 btw
Yeah and then I factored out a y
iron leaf
(x+a)²+(y+b)²=r² when expanded gives x²+2ax+a²+y²+2by+b²=r²
Also I have no idea how you got this
chrome salmon
Thats the expanded equation of circle
Find a and b then get the equation of circle
iron leaf
Find a and b then get the equation of circle
But there’s 4 variables
Am I supposed to find a or b in terms of like all the other variables
chrome salmon
Am I supposed to find a or b in terms of like all the other variables
No a and b are constant
lone heartBOT
@iron leaf Has your question been resolved?
iron leaf
No a and b are constant
So how do I find them
chrome salmon
So how do I find them
Compare the equation
lone heartBOT
@iron leaf Has your question been resolved?
ashen mantle
lone heartBOT
@ashen mantle Has your question been resolved?
lone heartBOT
@ashen mantle Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
rigid gate
I need help with finding domain and range
lone heartBOT
I need help with finding domain and range
lone heartBOT
Commands:
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factoids: .tag
help: .help
Type .help <command name> for more info on a command.
sour dove
I need some help please
Open your own channel #❓how-to-get-help
lone heartBOT
@rigid gate Has your question been resolved?
plush stump
Domain is not right
plush stump
range?
lone heartBOT
@rigid gate Has your question been resolved?
versed escarp
Why does it look like some people are talking to no one lol
rotund crater
why 2+2=4
lone heartBOT
rotund crater
no no, they misinterpreted my question because it is that amount if someone shows me
I wanted a more in-depth demonstration, I don't see any harm in asking if 2+2=4
I heard that the demonstration of that lasted several minutes, so I ask...
i can reopen?
rotund crater
please dont waste helper time
.
night geyser
it would be good if youd include more information when you ask a question
since this is a common format for troll posts
anyway i cant reopen this channel but you can open a new one so long as you include precise info what you want
lone heartBOT
Available help channel!
oblique jetty
I would like some help
oblique jetty
Close
vapid shuttle
.close
lone heartBOT
oblique jetty
.close
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Available help channel!
timid iron
lone heartBOT
timid iron
how do I solve this ?
naive valley
what's the problem statement? what are you trying to solve
timid iron
write an equation to match the graph
naive valley
ah
median oar
What have you tried
timid iron
nothing
naive valley
suppose you had the same graph but the vertex was at the origin
what would the formula be then?
timid iron
I have no idea
naive valley
I have no idea
like this:
sour dove
do you know graph shapes? Like what equation makes a parabola? A sin function? Absolute value? Cubic? Exponential?
timid iron
<@&286206848099549185>
naive valley
<@&286206848099549185>
any thoughts on the graph in the screenshot above?
naive valley
does "absolute value" ring a bell?
timid iron
yes
naive valley
can you see that the above is just the graph of f(x) = |x| ?
timid iron
kinda
naive valley
try plugging in some points for x to check
dawn cliff
for -3 i got -1.2 i dont understand how its wrong
lone heartBOT
for -3 i got -1.2 i dont understand how its wrong
dawn cliff
wah?
ocean sealBOT
dawn cliff
-3 + 2 is -1
dawn cliff
the cube root gave me -1 aswell
pine kettle
so -1/5 * -1 = 1/5 -1 = -4/5
dawn cliff
then -1 at the end
wary stream
You realized you typed in $\frac{1}{5}$ and not $-\frac{1}{5}$
ocean sealBOT
dldh06
wary stream
Negative 1/5
lone heartBOT
@dawn cliff Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
how come these are the same?
alpine sable
bring the coefficient into the exponent
wdym?
i mean i differentiated both of them and got tan x
ruby current
c ln(a) = ln(a^c)
ruby current
happy to help
alpine sable
.close
frank gorge
lone heartBOT
frank gorge
how do i find max revenue?
merry depot
it's at the vertex of the parabola you get when you find the revenue funciton
frank gorge
how would i find it without graphing
i know u have to add the vertex and divide by 2
and i got 2.5
when but i plug it in i get 18.75 but the answer should be 6.25
quick peak
For a?
frank gorge
yes sorry
merry depot
the vertex is at -b/(2a)
frank gorge
-(-1)/2(5)?
merry depot
-5/(2(-1))
frank gorge
okk i got 2.5 do i plug it in?
merry depot
yes
merry depot
,w calculate -(2.5)^2 + 5(2.5)
ocean sealBOT
merry depot
seems right
frank gorge
but -2.5^2 is 6.25
quick peak
The negative has to be outside the squared part
alpine sable
lone heartBOT
alpine sable
is the above step necessary when integrating this:
or can i just write the (36^x)/2 + c
as my final answer?
lone heartBOT
@alpine sable Has your question been resolved?
weak seal
depends on your prof
short steppe
Is this inductive proof okay or is it too self-referential?
lone heartBOT
Is this inductive proof okay or is it too self-referential?
short steppe
been a while since i had to do anything this rigorous
surreal meadow
what do you mean by self referential
short steppe
so it's clear that because the function will always degrade to T(1) that the -1 will always hold for any input
but im wondering if the algebra in the induction step
relying on the base case to account for the -1
is too self-referential
i know induction not a great way to do this proof but am wondering if the induction step is correct basically
mb mistake in one equation - reupped image
<@&286206848099549185> 🥹
placid zinc
Indeed, this is not a proof by induction. You are literally just stating the equation is true in the base case. Everything after is redundant
@short steppe
short steppe
Indeed, this is not a proof by induction. You are literally just stating the equ...
yeah thought so
is there actually a way to prove this by induction?
or should i just show that leaves = branches + 1 and call it a day
placid zinc
Yeah. Re-enter the inductive step using only the recursive definition
And the inductive assumption that T(k) = k - 1
Actually, now that I think about it, it may not be haha. Should this be possible?
short steppe
Actually, now that I think about it, it may not be haha. Should this be possible...
not necessarily
there's no requirement to prove this by induction
placid zinc
Because you can't really relate the statement on k to the statement on k+1
short steppe
i think if you can demonstrate algebraically that it will always degrade to T(1) then it's possible
short steppe
Because you can't really relate the statement on k to the statement on k+1
yeah
short steppe
i think if you can demonstrate algebraically that it will always degrade to T(1)...
not by induction but maybe by contradiction or something
placid zinc
What about T(6)? That doesn't really degrade to T(1)
short steppe
yeah it does i just havent been that rigorous in the proof cos the function only accepts 2^n as input
but in reality T(6)=T(floor(6/2))+T(ceil(6/2))+1
placid zinc
Well, if you're only going to plug in powers of 2, you don't need to induct over every integer
You only need to induct over powers of 2
short steppe
it's still gonna be self-referential though right?
placid zinc
So with the assumption that T(k) = k-1 holds, prove that T(2k) = 2k-1 holds
short steppe
won't that just be the same algebra with K+1 replaced by 2k?
as in I don't see how you can relate the base case to 2k if you can't to k+1
functionally it should be the same
short steppe
yeah that's true ig 2k is the next level of execution regardless of the input
but I'm still a bit confused about how this is demonstrable via a process that is redundant for k+1
placid zinc
If T(k) = k - 1
Then T(2k)
= T(k) + T(k) + 1
= (k - 1) + (k - 1) + 1
= 2k - 1
And that's the proof
short steppe
but how is this any different to:
If T(k) = k-1
Then T(k+1)
=T(k) + 1
= k-1+1
=k
cos it ignores how the function is defined?
placid zinc
T(k + 1) = T(k) + 1? How do you know that?
short steppe
yeah got you
placid zinc
Ye we have to use that somewhere
Big thing though is that this is only a proof for powers of 2
short steppe
yeah no that makes sense I'm just at pains to make this delineation so that I don't drown as hard in future
short steppe
Big thing though is that this is only a proof for powers of 2
yep
can probably start at the top with some coefficient m and show the for any input T(mk) that the function will degrade to T(1) for a more general proof?
or am i still off track
or that for any input k the recursive halving taking floor/ceil on either side will degrade to 1 where we acquire our -2 to offset the +1
placid zinc
Depends how you show this
You're saying it like it's easy, haha. I wouldn't personally know how
short steppe
yeah i dont know how i would, but if you were able to then that would constitute a general proof for n > 1?
im just trying to consolidate some ideas around what constitutes evidence for what
cos i knew what i posted initially was circular i was just struggling to view it in terms of what i actually needed to demonstrate
in any case you've been a massive help
🙏
lone heartBOT
@short steppe Has your question been resolved?
short steppe
If T(k) = k - 1
Then T(2k)
= T(k) + T(k) + 1
= (k - 1) + (k - 1) + 1
= 2k - 1
...
all good you reckon?
placid zinc
In the base case, you've written:
T(n) = (n/2 - 1) + (n/2 - 1) + 1
That was the fundamental problem in your other version. You can't assume any form for T(n). Doing so is skipping the induction proof.
.
Under induction, you've written:
T(k)
= (k/2 - 1) + (k/2 - 1) + 1
= k + 1
The problem is that you're trying to prove your inductive assumption. You don't need to (and shouldn't be able to) prove this.
@short steppe
Note that I wrote the inductive part exactly above.
short steppe
truuuuue
short steppe
.
Under induction, you've written:
T(k)
= (k/2 - 1) + (k/2 - 1) + 1
= k + 1
The...
yeah okay this makes sense
so we can't assume anything except that from the base case T(k)=k-1 and that by demonstrating T(2k)=2k-1 is consistent under our recursive definition we are then safe to extrapolate from the base case for any n=2^x
short steppe
<@217934695055228928>
fwiw including n/2-1 in the assumptive part seemed like a huge leap to me intuitively
is what made me question all this in the first place
(cos it was clearly what i was trying to prove)
I think the global case is doable, if you assume that recursive halving of any value > 1 will approach 0 and then demonstrate that taking the floor+ceil of any (0 < value < 1)/2 will always = 1 that the function will always degrade to the base case
placid zinc
Awesome, that's much better.
short steppe
Awesome, that's much better.
thanks so much
really appreciate the help
and the time spent on conceptual stuff in particular
legend
🙏
.close
lone heartBOT
lone heartBOT
Available help channel!
wide acorn
lone heartBOT
tacit arch
Exponent rules
tacit arch
Is that true for p=9 and t=25?
tacit arch
2sqrt(p) * 2sqrt(t)
This equal to 2sqrt(p)sqrt(t)?
wide acorn
i'm not sure, are you giving me numbers to try with?
if it works then it should work for all numbers
tacit arch
i'm not sure, are you giving me numbers to try with?
Yes
tacit arch
if it works then it should work for all numbers
Does it work for the numbers I gave
wide acorn
no, it's double
i guess one of them can take it
it would be multiplied by it anyways
tacit arch
Correct
lone heartBOT
@wide acorn Has your question been resolved?
lone heartBOT
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Available help channel!
tropic rose
- so do we know its not a basis for M22 because of the second matrix?
vale wigeon
wdym by "becasue of the second matrix"?
vale wigeon
well, i'm not really sure what your argument is...
tropic rose
because a standard basis for M2,2 would require only ones in each position and because we have [0 1 1 0 ] we automatically know its not a standard basis
vale wigeon
yeah but we aren't asked "is this a standard basis"
we are asked "is this a basis, and if not why"
a basis is a linearly independent spanning set.
so there are only two possible reasons why a set might fail to be a basis: either it fails to be linearly independent, or it fails to span our space. perhaps both at the same time.
tropic rose
holy cow i need to do some more studying because that made no sense
vale wigeon
uh yeah you do
low pasture
can someone help me with this problem?
lone heartBOT
can someone help me with this problem?
naive valley
which part?
low pasture
P(STS-1) = I + STS-1 + (STS-1)^2..., but like how I can get to the other side, and what this all means intuitively. I know that if a linear transformation is invariant on a subspace then that subspace is like an eigenspace I think?
naive valley
notice that $(STS^{-1})^2 = (STS^{-1})(STS^{-1})$, which can be simplified to...?
ocean sealBOT
Bungo
low pasture
oh that makes sense! so repeating this pattern, for some K term of p(STS-1) we have (STS-1)^k = ST^kS-1 as the middle S-1S terms cancel, which is easy to show, but as far as what part b is asking. If applying STS-1 to itself only changes T then S must be invariant under V right?
naive valley
well S is a transformation, not a subspace, it doesn't really make sense to ask if S is invariant
suppose U is a subspace of V that is invariant under T
what can you say about SU, which I'm defining as {Su | u in U}
i.e. the image of U under S
low pasture
okay I think I got it, the range of S-1 is invariant under T? This is because for some v in V, S-1 maps it to some w in its range then no matter how many times we apply (STS-1) to it, it will always be in the same range. But what insights does that give?
naive valley
basically i claim the following:
if U is a subspace of V that is invariant under T, then SU is a subspace of V that is invariant under STS^-1
and similarly, if W is a subspace of V that is invariant under STS^-1, then S^-1W is a subspace of V that is invariant under T
so there's a one to one correspondence between the subspaces invariant under T and the subspaces invariant under STS^-1, and that correspondence is given by multiplication by S in one direction, and multiplication by S^-1 in the other
(obviously you should prove these claims, but i'm writing them here because i'm probably gonna be taking off soon)
naive valley
pleasure
btw
the reason intuitively that this is true is that you can think of T and STS^-1 as the same linear transformation, expressed with respect to different bases
low pasture
yeah like diagonalization?
naive valley
that's a special case yea
low pasture
that's what you want to find bases for S of
naive valley
in general neither T nor STS^-1 need be diagonal, but they are by definition similar matrices
which essentially means that they're the same linear map expressed with respect to different choices of basis
low pasture
omg this makes so much sense this way
naive valley
a diagonalizable matrix is one that happens to be similar to a diagonal matrix
vapid shuttle
linear algebra never ceases to give me the warm fuzzies
naive valley
i do love LA
similar matrices have the same eigenvalues, but not necessarily the same eigenvectors
low pasture
for some reason I'm having a lot better time in my abstract algebra class
we're using hungerford and it makes a lot of sense
naive valley
what (b) is showing is that they do have the same eigenspaces if you express them with respect to appropriate bases
abstract algebra is quite nice too
i like how linear algebra fits into field theory among other things
low pasture
wait what if T is not invertible? Does this just mean that the dimension of the invariant subspaces are going to be less than V? Also if T is invertible are the dimensions of V and the invariant subspace W under T equal?
lone heartBOT
@low pasture Has your question been resolved?
naive valley
wait what if T is not invertible? Does this just mean that the dimension of the ...
sorry, just noticed this (was chatting in #linear-algebra in fact haha), let me process...
yea it's still valid, we don't need to invert T anywhere
if T is not invertible, then zero will be one of the eigenvalues, that's about it
in general (whether or not T is invertible), the sum of the dimensions of the eigenspaces need not be dim(V), it could be less
it will be equal to dim(V) if all of the eigenvalues have full geometric multiplicity (i.e. equal to their algebraic multiplicity).. this is equivalent to T being diagonalizable
however with regard to your other question, the answer is yes: if T is invertible, then dim(U) and dim(TU) will be equal
that's true for any subspace U even if it's not invariant
low pasture
got it! Thank you! oh yeah that last part makes absolute sense because obviously range(T) has to equal V where T is the linear operator on V in order for it to be invertible.
.close
lone heartBOT
naive valley
got it! Thank you! oh yeah that last part makes absolute sense because obviously...
yea, and more generally, T preserves the dimension of any subspace, basically because of rank nullity (recall that the null space is trivial for an invertible matrix)
lone heartBOT
Available help channel!
boreal surge
Could I get some help with it? I need some explanation on how to do it
boreal surge
I see there is the same argument and coefficient but have no clue what to do with it
Maybe turn sin into the cos or something like this
Oh so smth like this? 5√2(1-sin(7π/8))
Sorry for late responses, getting distracted
harsh girder
use double angle formula
hushed locust
you would want to use the pythagorean identity
boreal surge
Lemme writr down that formula in my notebook rq
Cos2x
Ok lemme
Answer is 5
Got it, tysm
lone heartBOT
@boreal surge Has your question been resolved?
charred plank
Hey guys, still couldnt figure it out so any help will be appreciated
Any help with the following?
Prove that for each natural n,m:
$n \in m$ or $m \in n$ or $n=m$, for all $n,m \in \mathbb N$
ocean sealBOT
meitar5674
charred plank
this is what I tried using induction but I'm stuck at the second case
young patio
How should I go about finding the shaded area of this triangle?
young patio
For some reason I can't seem to recognise it, but I'm sure I will over time just by looking at it long enough,
alpine sable
you are given the height and base
young patio
Is 33 the base or the whole top length?
alpine sable
33 is the base
young patio
Oh, I see, so it doesn't include that extra part on the end?
alpine sable
yeah, it doesnt
young patio
I see,
alpine sable
its centred on only the base
alpine sable
np
young patio
.close
modest needle
I am trying to solve the 3x3 matrix equation for the vector x: [0 1 1] [ 0 0 0 ] [0 0 0 ] x = [1 0 0]
modest needle
I took x3 as a free variable so made it equal to some value t
And then solved the equations x2=-t +1
but not sure how to get x in a vector of [x1 x2 x3 ] by solving
surreal meadow
$\begin{bmatrix}
0 & 1 & 1 \
0 &0&0\
0&0&0
\end{bmatrix}x = \begin{bmatrix}
1\0\0
\end{bmatrix}$
ocean sealBOT
maximo
surreal meadow
is that it
modest needle
yes thats the matrix
surreal meadow
if so, you have x_2 + x_3 = 1, and x_1 free
modest needle
Ohh so x1 would be the free variable, I got confused by the row of 0's
surreal meadow
you can also phrase it as
x_3 = 1 -x_2, x_1 and x_2 free
so you actually get 2 free variables
modest needle
so the way I do it is substitute the 'free variables' for some values of t, u for example. so here would x1= t and x3 = u
And does free variables have anything to do with linear independence like does it mean they are linearly dependent
surreal meadow
x1 and x3 are also variables, but if using t and u helps you then sure
surreal meadow
And does free variables have anything to do with linear independence like does i...
not really
it just describes the dimension of your solution space
modest needle
so from x1 = x1 and x2+x3 = 1, how do we write that as a vector form
surreal meadow
[x1, x2, 1-x2]
modest needle
OHHH IVE GOT ITTT thank you so much! So then u can separate it out and get the vectors x1[1 0 0] + x2 [0 1 -1] + [0 0 1]
.close
snow nest
The area of a circle is increasing at the rate of 4 cm2 per second. At what rate is the
circumference increasing at the instant when the radius is 8 cm?
snow nest
Doing a chapter on related rates
Here's my working out
dA/dt = 4
A = r/2 * c (c is circumference)
dA/dc = r/2
dc/dA = 2/r
dA/dt * dc/dA = 4 * 2/r = 8/r
i'm getting dc/dt = 1
but the answer is 1/2, why?
cinder tundra
What is A for you?
last ether
Area
You need to differentiate each variable with respect to time
So product rule on the rc/2 side
surreal meadow
dA/dc = r/2
this assumes r is constant wrt c, which is not the case
last ether
I would instead do:
A = πr^2
C = 2πr
cinder tundra
yes, that's what I was thinking about
last ether
Find dr/dt first
cinder tundra
rate of the radius first
snow nest
i'll try it
okay so dr/dt is 1/pi*r?
wait no
okay right i got it
i just want to ask
there's no way i can directly relate circumference to area?
without including r?
surreal meadow
A = r/2 * c (c is circumference)
then sub that into this
snow nest
oh yeah it works out in the end
but yeah the r method is probably better
thanks for the help guys
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lone heartBOT
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somber dune
What is the derivative of the function f(x) = sin(x^2 + 3x) at x = π/2.
somber dune
into f’(x)
f'(π/2) = cos((π/2)^2 + 3(π/2)) * (2(π/2) + 3)? this?
surreal meadow
yes
lone heartBOT
@somber dune Has your question been resolved?
gray isle
simplify
alpine sable
x^2 +3x -40 <----- MIDDLE TERM SPLIT THEM PLEASE
lone heartBOT
x^2 +3x -40 <----- MIDDLE TERM SPLIT THEM PLEASE
last ether
We don't give out answers
Also that just seems like a personal issue
Have you tried anything
alpine sable
Have you tried anything
i cant
i cont find any number
pls
pls give me answer @last ether
PLEASE
i just wanna pass
i have 3 mins
ocean hawk
we don't give out answers
lone heartBOT
last ether
Be more responsible next time
alpine sable
OH NO
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karmic cedar
Hi, I need help on number 7 a and b
lone heartBOT
Hi, I need help on number 7 a and b
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
1
vale wigeon
can you write down what g(4) is using the formula g(x) = (px+q)/2 that they give you?
karmic cedar
g(4)= (p(4) + q)/ 2
vale wigeon
better to write 4p rather than p(4) so as not to make it look like p is a function
but yes, ok
so you have g(4) = 6, or now that you plugged 4 into g, it becomes (4p+q)/2 = 6
are you able to do a similar thing to the equation g^-1(7) = 5?
(perhaps you should first rewrite it in a simpler form)
karmic cedar
Oh
karmic cedar
are you able to do a similar thing to the equation g^-1(7) = 5?
Yes
vale wigeon
do you understand how to continue from here?
lone heartBOT
karmic cedar
.reopen
lone heartBOT
✅
karmic cedar
do you understand how to continue from here?
Sorry, actually I don't know how to continue...
vale wigeon
ok so what do you have after you write down g(4) = 6 and g(5) = 7 in terms of p and q
karmic cedar
ok so what do you have after you write down g(4) = 6 and g(5) = 7 in terms of p ...
How about the g^-1?
vale wigeon
what do you mean?
i rewrote g^-1(7) = 5 as g(5) = 7 just now, and thought you had done the same
karmic cedar
Oh yeah
karmic cedar
ok so what do you have after you write down g(4) = 6 and g(5) = 7 in terms of p ...
I would get
6 =(4p + q)/2
5 = (7p + q)/2
vale wigeon
your second equation is incorrect
karmic cedar
Should it be in inverse
vale wigeon
g^-1(7) = 5 translates to g(5) = 7, NOT to g(7) = 5 as you did.
vale wigeon
yes
so now you have a system of two equations in two unknowns
(4p+q)/2 = 6
(5p+q)/2 = 7
do you know how to solve these in general
karmic cedar
Not really
vale wigeon
what if i told you it was a system of linear equations?
maybe you know of methods such as substitution or elimination
vale wigeon
you cannot solve this system of equations by elimination?
karmic cedar
Is it for the first equation for p and the second equation is q?
karmic cedar
you cannot solve this system of equations by elimination?
Yep cant
vale wigeon
Is it for the first equation for p and the second equation is q?
this question doesn't make sense.
karmic cedar
Sorry don't mind the question
karmic cedar
12 = 4p + q
karmic cedar
14 = 5p + q
vale wigeon
ok
4p + q = 12
5p + q = 14
do you now see how to proceed?
there are multiple different ways to do so
karmic cedar
For linear equation?
vale wigeon
there are multiple different ways to go about solving this system of linear equations yes
vale wigeon
yes thats correct
burnt meadow
How does
lone heartBOT
@burnt meadow Has your question been resolved?
lone heartBOT
@burnt meadow Has your question been resolved?
lone heartBOT
@burnt meadow Has your question been resolved?
lone heartBOT
@burnt meadow Has your question been resolved?
lone heartBOT
lyric fable
help
finite relic
lyric fable
lone heartBOT
potent garnet
sure, ur gonna wanna do ".reopen"
lyric fable
.reopen
potent garnet
hmm, weird, hopefully it doesnt go to available help channels
lyric fable
its already my channel
potent garnet
for the last step, the desired statement would be the statement and the reason is ||CPCTC||
actually, thats the abbreviation for congruent triangles
Corresponding Parts of Congruent Triangles are Congruent
lyric fable
Yeah
potent garnet
so for the reason you can just say "Corresponding Angles of Similar Triangles are Congruent"
potent garnet
its instant grading?
lone heartBOT
Available help channel!
copper pendant
what website is that
north hemlock
Hi, I have no idea how to start this limit... any ideas?
$$\lim_{n\to \infty} \left( \cos{\left( \frac{\theta}{n}\right)}^{n^2t}\right)$$
lone heartBOT
Hi, I have no idea how to start this limit... any ideas?
ocean sealBOT
Juke | ping me if no response
north hemlock
this is where how I got here
I just realied I wrote that cosine is odd and sine is even, I meant to switch them. the actual math part is fine though
marsh rapids
Try to use the fact that (1+1/n)^n -> e
north hemlock
Try to use the fact that (1+1/n)^n -> e
I see.. gimme a sec
north hemlock
Try to use the fact that (1+1/n)^n -> e
idk how to get this
north hemlock
Oh, sorry. I understand that limit but I don't know how to get my limit into that form
that's what I meant, mb
( side note: I don't really understand it, but I have come to accept it after doing it like twice )
also I have an issue since the inside part just goes to 1 right so why isn't the entire limit just 1
,w 1^inf
ocean sealBOT
tacit arch
the intuition is $\cos(x) \approx 1 - \frac{x^2}{2}$ for small $x$. then when you raise that to the $x^2$ power it looks like the definition of $e^{...}$
ocean sealBOT
riemann
north hemlock
interesting
how is that approximation made?
also what if x isn't nessisarily small
marsh rapids
Taylor-Young theorem
tacit arch
also what if x isn't nessisarily small
it is in your problem
north hemlock
,w taylor cos(x)
tacit arch
x = theta / n
ocean sealBOT
north hemlock
OHH ( pea brain moment )
I see
okay
okay cool, I think this got a lot easier from here
thanks a ton guys!
.close
lone heartBOT
marsh rapids
The hard part is rigorously handling the error imo
north hemlock
oh fuck.
tacit arch
very cumbersome
north hemlock
I'll just ignore it :D
lone heartBOT
Available help channel!
lone heartBOT
I'll just ignore it :D
lone heartBOT
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elfin ermine
Hello, I am a high-school student and I will take the EmSAT test soon, it’s a test that is required for the university. However, I saw an “differential equation” question, and I have a little knowledge about it. Can you please solve the problem and give me a detailed solution? Also, if you don’t mind I want you to give me a resource to learn how to solve this type of questions:)
tacit arch
Hello, I am a high-school student and I will take the EmSAT test soon, it’s a te...
no?
if you want to learn a new subject, just google resources
math channels are for specific problems
slender marten
I can provide resources I think are excellent but we can't just fully solve problems for everyone.
slender marten
elfin ermine
if you want to learn a new subject, just google resources
I don’t have time to learn everything related to differential equations, it’s a huge topic
elfin ermine
“What is the general solution of the differential equation shown below?”
I want to learn how to solve this one in particular
tacit arch
I don’t have time to learn everything related to differential equations, it’s a ...
indeed it is
elfin ermine
I don’t have time to learn everything related to differential equations, it’s a ...
plus I don’t have enough time and I won’t need in the future since I will apply for the college of Medicine
tacit arch
plus I don’t have enough time and I won’t need in the future since I will apply ...
nobody cares
slender marten
I care but I just don't see a good solution to help you. Other than very basic videos but they can't do much to condense it more than Lesson 20 in that book anyway.
elfin ermine
I care but I just don't see a good solution to help you. Other than very basic v...
thanks for trying to help:))) I appreciate it
alright send the videos if you don’t mind
wary stream
I want to learn how to solve this one in particular
How will you know that there is only that topic on your test? What if you learned this one topic from diff eq but then see a different topic? What are you going to do now?
slender marten
I don't have any videos. I can only vouch for that book. 😢
elfin ermine
How will you know that there is only that topic on your test? What if you learne...
Well, the EmSAT is “adaptive” which means if I solve a question correctly, the next question will be more difficult to solve, if I reach the Calculus II level of questions, I will certainly get a high score.
elfin ermine
I don't have any videos. I can only vouch for that book. 😢
No problem, thanks for the help 😄
north hemlock
diff eq is above calc 2 tho
well ig not really... depends
it's different from calc 2
vapid shuttle
usually it does end up coming after calc 2, although it is different material that doesn't necessarily follow calc 2
north hemlock
usually it does end up coming after calc 2, although it is different material th...
exactly
so idk what ur talking about here in terms of "calc 2 level" questions
elfin ermine
The EmSAT has variety of different types of questions: like algebra, calculus, probabilities and statistics, etc
elfin ermine
so idk what ur talking about here in terms of "calc 2 level" questions
nope
sorry for misunderstanding, I just wanted to clarify what “adaptive” means
north hemlock
I understand the format of the exam
but what does this DE have to do with that
in theory, u can just get this wrong and still be placed a good grade
anyways, the issue is that nobody wants to do ur work for u
out of curiosity, why do u need the detailed solution
elfin ermine
in theory, u can just get this wrong and still be placed a good grade
exactly but I am interested to know how it can be solved
wary stream
Then learn how to do it
north hemlock
this one is linear and so u just use the characteristic equation for it and you'll end up with a solution
elfin ermine
Then learn how to do it
Do I have enough time?
wary stream
That's up to you
north hemlock
Do I have enough time?
when is the "deadline"
elfin ermine
anyways, the issue is that nobody wants to do ur work for u
unfortunately 
north hemlock
and what level of math are u doing easily atm?
vapid shuttle
this one is linear and so u just use the characteristic equation for it and you'...
I don't think it is linear
north hemlock
I don't think it is linear
wym
elfin ermine
when is the "deadline"
my exam is scheduled for the next week
vapid shuttle
sorry, it is linear, but it's not homogeneous
north hemlock
my exam is scheduled for the next week
no shot
vapid shuttle
Is what I meant
north hemlock
sorry, it is linear, but it's not homogeneous
yep
but the general solution is the homogenous plus the particular
vapid shuttle
so characteristic eqn not completely solving it
elfin ermine
and what level of math are u doing easily atm?
well the current topic I am learning in the school is “integration by parts”
north hemlock
which shouldn't be too hard
north hemlock
so characteristic eqn not completely solving it
it solves the homogenous part
vapid shuttle
I am aware
north hemlock
and then he can easily guess the particular form and do from there I think
lemme try it...
elfin ermine
lemme try it...
thank you so much…
north hemlock
well the current topic I am learning in the school is “integration by parts”
no shot u can learn all of DE in a week
vapid shuttle
He could try to learn just basic linear ODE strategies
characteristic equation, undetermined coeffs, (maybe VOP)
that would get him far
vapid shuttle
basic and linear still so it'd work out
north hemlock
VOP is taught alongside undet coeffs I thought?
north hemlock
basic and linear still so it'd work out
perhaps
vapid shuttle
VOP is taught alongside undet coeffs I thought?
taught near the same time yah
north hemlock
@elfin ermine u can still try tho tbh
elfin ermine
no shot u can learn all of DE in a week
I am learning lots of different random topics at the same time💀💀 like: reviewing conditional probabilities, taylor series, euler’s method
I know that it’s so random but I am certain that questions about these topics will come up if I do solve the first 20 questions correctly (which are usually easy)
north hemlock
that's not useful
unless ur somehow able to retain all that info
that's absurd
whatever floats ur boat man
elfin ermine
I am noting everything
plus
I have been learning for like a couple of months and I am reviewing them
vapid shuttle
Excel, I can try to quickly give you an idea for linear ODEs
(with constant coefficients)
elfin ermine
Excel, I can try to quickly give you an idea for linear ODEs
yes pls
vapid shuttle
Okay so a simple one would like like this $ay''+by'+cy=0$
ocean sealBOT
AustinU
vapid shuttle
this is linear
second order
homogeneous (equal to 0)
and has constant coefficients
a, b, c are constants and not functions
elfin ermine
(with constant coefficients)
well I faced this kind of differential equations and I learned how to solve them and I was able to
but the problem is that, the differential equation I sent is not equal to 0🥲
vapid shuttle
right
so you should learn the method of undetermined coefficients
and variation of parameters
you can find good youtube videos for those
I'm sure
vapid shuttle
sure thing
elfin ermine
.close
lone heartBOT
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hollow marsh
I need help with part C and D
lone heartBOT
I need help with part C and D
hollow marsh
lone heartBOT
@hollow marsh Has your question been resolved?
lone heartBOT
@hollow marsh Has your question been resolved?
lone heartBOT
@hollow marsh Has your question been resolved?
serene fiber
hell
lone heartBOT
@hollow marsh Has your question been resolved?
hollow marsh
hell
wet nest
lone heartBOT
vale wigeon
,rccw
ocean sealBOT
vale wigeon
!status
lone heartBOT
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
vale wigeon
wdym by "stoichiometric coefficient"
wet nest
wdym by "stoichiometric coefficient"
I tried to apply poac but the answer is not coming
vale wigeon
"poac"?
vale wigeon
you tried to balance that reaction equation?
wet nest
you tried to balance that reaction equation?
No
wet nest
what did you do if not that?
10= 80/100(n1+n2)
vale wigeon
what are n_1 and n_2 ... ?
wet nest
what are n_1 and n_2 ... ?
n1,n2 = no of moles of CO AND CO2
vale wigeon
then where does this equation come from...?
wet nest
then where does this equation come from...?
If no Carbon atom is formed other than co and co2 then this equation will be correct. But im not sure if c will react with h2so4
vale wigeon
ah so wait
wet nest
then where does this equation come from...?
Can you tell how many mol3s of co and co2 will be formed ?
vale wigeon
HOOC--COOH -> CO + CO2 + H2O
is what the equation should be
then it will be properly balanced
i am not a chemist but i do not think the carbons would react with the sulfuric acid
and since we had 5 moles of oxalic acid going in, in an ideal experiment we would have 5 moles each of CO and CO2.
but 80% yield means we only get 80% of that, so 4 moles each.
wet nest
Thanks dude
wet nest
.close
cyan drum
can someone help me with this?
lone heartBOT
can someone help me with this?
cyan drum
much appreciated
quasi vector
!status
lone heartBOT
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
I dont know how to begin with (a), do I take limit when x approach 2 from left and right? or is it some other way?
quasi vector
first tell me what you think $f_{+}'(2)=0$ means
ocean sealBOT
kheerii
cyan drum
first tell me what you think $f_{+}'(2)=0$ means
right-hand derivative of f(x) when x = 2
lone heartBOT
@cyan drum Has your question been resolved?
cyan drum
in terms of the piecewise definition of f(x)
4a + b?
when x>2, f(x) = ax^2+bx+c, so f'(x) = 2ax + b, f'(2) = 4a+b
is this right
cyan drum
6a+b -1 = 4a + b, 2a = 1, a = 1/2, therefore b = -2
cyan drum
so what does that tell u
help 😭 was I right
$\lim_{x\to2} f(x) = f(2)$, therefore $\lim_{x\to2^{+}} f(x) = \lim_{x\to2^{-}} f(x) = f(2)$
ocean sealBOT
Tangerine
wide gyro
how would you go about finding the length of the blue box
lone heartBOT
how would you go about finding the length of the blue box
wide gyro
so far i've just done t(table) + 2b(boxes) + a(ball) = 160
so t + 2b + a = 160
i dont know how to get another equation
hushed locust
you have a second diagram here
echo socket
Simply express the difference between table + ball and box
wide gyro
Simply express the difference between table + ball and box
im not sure how i could do that
oh wait
table + ball = 70 + box
is that right
echo socket
Yeah
lone heartBOT
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lilac thicket
i have a question on this situation again. The task is to redistribute the balls among the 3 boxes such that I maximize the probability to pick a white one. The only condition is that a box must at least contain one ball. I first chose a box , then a ball. All with closed eyes. Except for the redistribution , thats with open eyes
My question: How can I approach this systematically?
I made some guesses, and I know that I would try to maximize the elements of the formula but I dont really find a clear way to do this such that I can be 100% sure that its the best solution
lilac thicket
my current solution would simply be to have
B1 = w
B2 = w
B3 = w^9 and s^6
that would result in 86.666...% probability to pick a white one from what I calculated
but my main question is really about the systematical approach to this
alpine sable
lone heartBOT
echo socket
AB and DC are parallel to one another, meaning the angles B and C shall add up to 180 degrees
sage nebula
lone heartBOT
gray isle
!status
lone heartBOT
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
2