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jagged flare
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jagged flare
i know $c=a^2+b^2$
using AM-QM, i can get
$$\sqrt{\frac{a^2+b^2}{2}}\geq\frac{a+b}{2}$$
$$\frac{a^2+b^2}{2}\geq\frac{(a+b)^2}{4}$$
$$\frac{2}{a+b}\geq\frac{a+b}{a^2+b^2}$$
soft zealotBOT
Skill_Issue
jagged flare
is this correct? do i answer like 2/a+b
languid yoke
Well you have c^2 on the RHS denominator, not c
languid yoke
$$\sqrt{\frac{a^2+b^2}{2}}\geq\frac{a+b}{2}$$
$$ \implies \frac{\sqrt{a^2+b^2}}{a+b} = \frac{\sqrt{2}}{2}$$
soft zealotBOT
Ari
languid yoke
so just flip both sides
jagged flare
o
languid yoke
or it should be >= not = mb
Also generally remember equality holds when a=b, which usually helps you find the upper bound when you don't need to be really rigorous
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ember maple
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ember maple
,rotate
soft zealotBOT
ember maple
Did I interpret the question properly
scarlet sequoia
you did, but your computation is wrong
you didn't multiply denominators
and forgot about one of them
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ember maple
<@&286206848099549185>
dusky spade
<@&286206848099549185>
(I used gauth since idk this level of math) the answer is -weird ass symbol = 0, 1
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@ember maple Has your question been resolved?
ember maple
<@&286206848099549185>
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@ember maple Has your question been resolved?
ember maple
<@&286206848099549185>
split socket
LMAO
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tranquil pine
integrate the following
cot^-1 ( 1 - x + x^2)
final saddleBOT
integrate the following
cot^-1 ( 1 - x + x^2)
gritty solar
you're gonna have to split it
tranquil pine
how
jagged flare
integrate the following
$\cot^{-1} ( 1 - x + x^2)$
soft zealotBOT
Skill_Issue
jagged flare
this?
tranquil pine
yeah
gritty solar
[ \arctan \left ( \f{x - (x - 1)}{1 + x(x - 1)} \right ) ]
soft zealotBOT
Sadie Carnot (η = -1)
gritty solar
does this look familiar
final saddleBOT
tranquil pine
thanks
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radiant spoke
at what R does a circle with a center (2; -4) and radius R have 2 common points with a straight line passing through point (6; -3)
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at what R does a circle with a center (2; -4) and radius R have 2 common points ...
radiant spoke
.close
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meager violet
how many ways to split n people into 2 groups which may (all or any) be empty
meager violet
my brain is fried
covert tree
how many ways to split n people into 2 groups which may (all or any) be empty
clarification: if i have 3 people a,b,c, does {a,b},{c} and {c},{a,b} count as different or the same
jagged flare
are the people distinct
covert tree
2 unlabelled groups
then you can consider an alternative process: let each person choose what group they want to go to, and then make the groups unlabelled
meager violet
are the people distinct
yes
jagged flare
then you can consider an alternative process: let each person choose what group ...
this
meager violet
what do you mean make the group unlabelled
covert tree
what do you mean make the group unlabelled
labeling the groups 1 and 2 is the same as labling by 2 and 1 so you counted each possibility twice
meager violet
still
so each person has 3 options (group a or b or none)
so 3^n/2
thats not right
covert tree
so each person has 3 options (group a or b or none)
isnt it separated into 2 groups?
does every person have to be in a group?
meager violet
yeah but they can be empty
meager violet
does every person have to be in a group?
no
meager violet
why n-1
sturdy cypress
(3^n)−1
meager violet
also why haha
meager violet
what if 3^n-1 is odd?
sturdy cypress
so you divide only that part of it
meager violet
oh wait
sturdy cypress
3^n is odd
covert tree
what if 3^n-1 is odd?
odd number times odd number is odd so 3^n is odd
meager violet
yeah yeah
meager violet
because there's one split, namely {}{} that has no pair
what do you mean?
covert tree
what do you mean?
in our counting process, both ({a,b},{c}) and ({c},{a,b}) are counted, so we essentially counted {a,b},{c} twice. However this is not the case for {},{}.
we only counted ({},{}) once
because that is exactly when everyone chose to be left out
there is only one possible way of doing that
in all other cases you can have a paring: when all the people who chose group A chose group B instead, and all the people chose group B chose group A instead.
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fast salmon
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fast salmon
This is a normal textbook question, not even a competition one... But I do not understand how to do it
And this is apparently the answer
But I cannot follow the steps...
Also by first thoughts were herons formula but I found it pretty disgusting to deal with
<@&286206848099549185>
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fast salmon
<@&286206848099549185>
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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).
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fast salmon
<@&286206848099549185>
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bleak forge
How?
bleak forge
I read one says to prove a function continous, it must be
lim f(number) = f(number)
or lim f(number) from left = lim f(number) from right
which one is correct?
warm ether
both
the second one is the limit existing
which is a condition for the first to even be checkable (otherwise its just not continuous)
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@bleak forge Has your question been resolved?
final tangle
second is insufficient
first is notated poorly
if $\lim_{x\to a} f(x) = f(a)$ then the function is continuous at $x=a$
soft zealotBOT
ℝαμΩℕωⅤ
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thick oracle
what type of angles are these
final saddleBOT
what type of angles are these
hollow sable
what type of angles are these
angle at the centre = twice the angle at the circumference
thick oracle
angle at the centre = twice the angle at the circumference
but like
what ttype
like
inscribed
hollow sable
insribed angle and a central angle
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quaint stratus
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quaint stratus
how do i solve this
i got one solution thats x=1
when x is between -1 and 1
but for the other case, i am getting a 4 degree equation
void valley
first of all
notice that two first terms starting from the left side are nonnegative for any x
well, square root as well, but there we have a minus sign
quaint stratus
yeah
void valley
mhm, looking for a smart solution, because as you've mentioned squaring both sides leads to some algebra stuff
and 4th deg polynomial
quaint stratus
and also the solution to the 4th degree is also 1 (from desmos)
dusty dock
okay so there's a way to simplify the left terms if we split it into two situations
where x^2 - 1 is positive, and where it is negative
when x^2 - 1 is a positive value, we get to keep x^2 - 1
but when it's negative, we flip it over the x axis
so we get
-x^2 + 1
quaint stratus
where x^2 - 1 is positive, and where it is negative
i know that, what im saying is that for the case when x^2 - 1 is positive, we end up with a 4th degree equation
dusty dock
when x is between -1 and 1
wait that's weird because the other solution is also between -1 and 1
i have the answer
so you can actually get two solutions out of the case between 1 and -1
now i have zero clue how to simplify the 4th degree polynommial and im honestly too lazy to try lmfao
but
what's funny is the 1 as a solution came out as an extraneous solution. it just appeared by squaring both sides
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@quaint stratus Has your question been resolved?
quaint stratus
so you can actually get two solutions out of the case between 1 and -1
..i know that
the problem here is the 4th degree polynomial
dusty dock
the problem here is the 4th degree polynomial
ic
did manage to decrease it down to a cubic
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tranquil pine
what is it ? a chessboard
what are those arithmetic signs all over it ?
okay i think i get it
tranquil pine
the operation should give the summation which matches to that of the end
onyx peak
yeah
whats the order of operations?
If there was e.g. 1 + 5 x 3 ÷ 1 - 2, what would this result to
can you use code?
or do you have to do this manually
it seems too complicated
backtracking could solve this quite easily
tranquil pine
its gonna take time
onyx peak
its gonna take time
hella lot of time
frank cloud
and 20 equations
onyx peak
theres 99 spaces
*98
frank cloud
no?... 100 spaces in total, but one is filled with 14
tranquil pine
isnt this somewhat like sudoku with toughness of ♾️
onyx peak
there are additional constraints
onyx peak
no?... 100 spaces in total, but one is filled with 14
there is one more number
onyx peak
yeah, and there are additional constraints (such as using only 1, 2, 3 ... 100)
so it might have an unique solution
show me the script
ah
frank cloud
show me the script
pov: the file is 20 TB
onyx peak
pov: the file is 20 TB
It's not gonna be that bad with backtracking I believe
It's kinda late for me, so I can't write the script
but I'd suggest you to look at backtracking
i think that it's gonna be helpful here
And doing it in this order will help too
(red first, then green, then blue...)
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@snow oak Has your question been resolved?
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@snow oak Has your question been resolved?
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@snow oak Has your question been resolved?
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ivory vessel
Given a pyramid $S.ABCD$, $SA$ is perpendicular to the base, the base $ABCD$ is a rhombus. Let $M$, $I$ be the midpoint of $AB$ and $AS$ respectively, $N$ belongs on $SB$ such that $SN = 3NB$. The plane $(\alpha)$ passes through $MN$ and is perpendicular to the plane $(SAC)$, $(\alpha)$ cuts $SC$ at $E$. Given that the volume of the tetrahedron $CMNE$ is V, calculate the volume of the tegrahedrom $IMNE$ in V.
final saddleBOT
Given a pyramid $S.ABCD$, $SA$ is perpendicular to the base, the base $ABCD$ is ...
soft zealotBOT
ivory vessel
this is my current diagram
i idealized ABCD to be a square, since technically square is also a rhombus
other than that im stumped
vital surge
unfortunate diagram
bright tangle
Chaotic diagram 💀
vital surge
it helps that the tetrahedrons CMNE and IMNE share three vertices
ivory vessel
yup
the diagram reveals the answer is ||2V/3||, but not sure how to arrive to this answer
vital surge
are you trying to a find a solution that doesn't make use of ABCD being a square
ivory vessel
no, i want ABCD to be a square
vital surge
alright
ivory vessel
i dont want to make my life harder
vital surge
then coordinate geometry is a pretty easy and accessible way to do this
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hollow trellis
How do I evaluate this
final saddleBOT
How do I evaluate this
dense coral
How do I evaluate this
what have you tried?
hollow trellis
dense coral
looks good to me 
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dense coral
hollow trellis
Is it wrong to think that the e and ln “cancel” each other out (bc their inverse)
hollow trellis
GET AWAY FROM ME
dense coral
the correct answer is xe
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slim olive
Can someone help me w the u substitution, not sure if i was supposed to choose x^2 or 3-4x
final saddleBOT
Can someone help me w the u substitution, not sure if i was supposed to choose x...
dense coral
I wouldn't use a u-sub personally
well, not if the integral is in this form at least
I suggest distributing the x^2
i cant tell where i supposed to use u sub or nah
dense coral
usually one uses u-sub when there is a composition of functions
in this case, there is a product
so algebraic tricks (like distributing) or IBP will probably be your best bet
slim olive
Would i need for this problem then?
slim olive
Which one do i take tho
dense coral
well, first things first
we should simplify before any tricks like u-sub
the integrand is a sum rn
that's hard to work with
can you think of a way to make it so we don't have that sum as our integrand?
dense coral
ehh
I was thinking simpler
the integral is linear
so $\int_{a}^{b}f(x) + g(x)$ = $\int_{a}^{b}f(x) + \int_{a}^{b}g(x)$
soft zealotBOT
higher!
slim olive
oh
how would i take antiderivitive of g(x) tho cos i have x^-1 doesnt that become a zero?
dense coral
how would i take antiderivitive of g(x) tho cos i have x^-1 doesnt that become a...
what do you mean?
slim olive
Like this part
slim olive
is the inner func the u?
dense coral
dense coral
sub it back into the integrand
slim olive
im not sure how to get rid of the 7 though
dense coral
the integral is linear, so $\int_{a}^{b} c \cdot f(x) = c \cdot \int_{a}^{b} f(x)$
soft zealotBOT
higher!
slim olive
Like this?
slim olive
would the u become lnu?
dense coral
the u doesn't become ln(u), but the antiderivative of u^-1 is ln(u)
slim olive
i am taking antiderivitibe of u right when i want to integrate it?
grave hatch
hey ! that's the formula 1/(a^2 - y^2) isn't it..
slim olive
wdym
grave hatch
it's just the formula of integration for the u^-1
where (a ) is constant ( y) is a function of y
grave hatch
just type special formulae for integration...... you will find a list of 6 formulae which are in fraction.
this is from google.
you have 2nd type of problem..
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@slim olive Has your question been resolved?
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olive burrow
in the b part of this sum i am getting the wrong answer
final saddleBOT
in the b part of this sum i am getting the wrong answer
olive burrow
but whats wrong in what i did
olive burrow
why cant i just move 100 from RHS and make it -100 is LHS
safe spindle
t=(100A-100P)/PR?
soft zealotBOT
faiyrose
olive burrow
$\frac{100A}{PR} - 100 = T$
soft zealotBOT
Rohith M
safe spindle
this is simple algebra..
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steep cargo
someone help me understand how to do differential equations using Laplace transform
final saddleBOT
someone help me understand how to do differential equations using Laplace transf...
marsh temple
You'll have better luck if you post a specific question you're stuck on
hybrid heath
steep cargo
how do u get the bottom part
I know u gotta write out the y's and the put their coefficients in but idk how I'm supposed to get the bottom part
like I look at videos and they do different stuff idk what anything is reffering to
why did it go from b^2 to s^2
why is the s only what
does anyone have a name for what this stuff is called so I can like Google it
I really don't get it
wait I kinda get it bow
now
so like
whats this subject called with the Laplace transforms so I can go in the channel and talk ab it there
sour umbra
steep cargo
oh nice ty
I still don't get this specific exercise though
wrong pic
why is Y(s) equal that
<@&286206848099549185>
why is Y(s) equal to that
2/(s+b)^2+4*(s+b)^2
frosty cedar
steep cargo
Last one idk if it's right
(s+b)^2 +4
how do i recover the original of an thing
I feel like I'm close to getting the logic of it
.close
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shadow garnet
What is the area of the region bounded by y = 4 - 2x^2 and y=0.
(My answer is (16sqrt(2))/3)
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What is the area of the region bounded by y = 4 - 2x^2 and y=0.
(My answer is (...
shadow garnet
I just want to check my answer
odd rivet
I just want to check my answer
its correct
wet drum
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tranquil pine
i dont see m anywhere
spring haven
,rccw
soft zealotBOT
warm python
translate 58 please
wet drum
58 says in the expansion of (1+x)^2n the greatest term coffiecient will be greatest and x>0 then x will be in interval
@warm python
Is there any short idea like fake solve?
Putting random numbers n=1 and satisfied?
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olive burrow
I found the answer to (a) which is 25x² + 60x + 36 but i cant figure out how to equate the second one
final saddleBOT
I found the answer to (a) which is 25x² + 60x + 36 but i cant figure out how to ...
final tangle
first consider area addition/subtraction
woven slate
Seems enough
olive burrow
Seems enough
where did you get the 15x's from
woven slate
where did you get the 15x's from
3*5x
woven slate
i did not understand anything
The 3 is the thickness
The 4 is the sides
olive burrow
The 3 is the thickness
The 4 is the sides
how did you get 60x + 36 = 396
and your answer is wrong
the answer is 900cm²
final tangle
first consider area addition/subtraction
area of picture PQRS + area of shaded frame/border = total
right?
olive burrow
> first consider area addition/subtraction
area of picture PQRS + area of shaded...
yes
i used that formula itself
final tangle
wait, your a) is wrong
final tangle
who says
olive burrow
the textbook sats
final tangle
which isn't what you wrote
woven slate
So the x is 6….
And the area is 25*36=900 my goodness
olive burrow
So the x is 6….
And the area is 25*36=900 my goodness
how did you conclude that
ok then?
5x
25x^2
but how does area of border mean the entire picture?
doesn't area of boarded mean just the outer boarder
oh ok
60x+36
oh i get it now
tysm i got the answer
.close
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warm python
so I'm doing linear algebra and this is one of the first exercises in the book ( LDR 4e) , I could use eular's formula but is there something else I'm expected to use
final saddleBOT
so I'm doing linear algebra and this is one of the first exercises in the book (...
warm python
other than painstaickingly multiplying it by hand
warm python
I know
but this is from a linear algebra book
am I expected to use vectors or lists or something ?
spring haven
but this is from a linear algebra book
ah, then I'll let someone else answer your question
ocean lintel
surely this is just chapter 1
no
warm python
surely this is just chapter 1
no
it is
ocean lintel
other than painstaickingly multiplying it by hand
it's also not that bad btw
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hoary meteor
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warm ether
have you found x?
warm ether
i dont believe so
hoary meteor
i thought it means complement of b and c
so everything that doesnt include b or c
not sure rho
warm ether
which includes the 4
warm ether
yeah
warm ether
its the same logic as a two way one really, i wouldnt overthink it
what do you think A and B is
hoary meteor
x+1 + 4?
warm ether
yeah
hoary meteor
oh yh i got it thanks
hoary meteor
yeah
1 more thing
yk how a sideways parabola is x = y^2
how would you write the vertical and horizontal dilation now
like for a normal parabola vertical dilation would be af(x) and horizontal dilation would be 1/a f(ax)
how would u write both of those for a sideway
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@hoary meteor Has your question been resolved?
silver pewter
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@hoary meteor Has your question been resolved?
wet delta
hey this is like a general question i have, so i get stuck at math a lot, i look at the solution and i do the question again, what do i do about this
final saddleBOT
hey this is like a general question i have, so i get stuck at math a lot, i look...
tranquil pine
don't look at the solution until you're done with the problem and have tried everything
getting "stuck on math a lot" is the essence of improving
wet delta
don't look at the solution until you're done with the problem and have tried eve...
my teachers tell me not to look at the solution at all and move on to the next problem and ask the question to them the next day
tranquil pine
my teachers tell me not to look at the solution at all and move on to the next p...
that works too
Because the solution actually gives you the step-by-step model answer. But your teachers will (hopefully) drop hints instead of doing that.
In fact, now that I think about it, that's even better
wet delta
so i just move on then?
tranquil pine
Yes, or ask for hints on the math server
wet delta
its just that i think what if i dont get that question either
what do i do
i mean the next problem
tranquil pine
its just that i think what if i dont get that question either
then you ask here
this is a friendly server, i'm sure people will be happy to help you
what's the question on?
wet delta
i mean i was asking generally
the concept part i usually get
but its the simplification
that i go wrong in
tranquil pine
can you give an example?
wet delta
find the common normal between two curves
i know what i need to do
but
i go wrong while simplifying
and sometimes i have no clue on where tos tart
tranquil pine
i think that's just an issue with algebra, no? that is something that improves with practice
wet delta
i think that's just an issue with algebra, no? that is something that improves w...
yeah how do i improve on that
tranquil pine
practice
do more problems
if you know how to do them but struggle with simplification
then focus on that part
wet delta
currently i write everything step by step to not go wrong
tranquil pine
focus on improving your algebra skills
wet delta
alright thanks
indigo pilot
anyone know the stepts to do this?
final saddleBOT
anyone know the stepts to do this?
indigo pilot
this too
ill try that
is this answer d-540/0.5=p or p=2d-1080
which one is correct?
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@indigo pilot Has your question been resolved?
hoary meteor
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green ibex
,rcw
soft zealotBOT
hoary meteor
i took 2 out and applied sin subtraction identity on the inside so far
idk where to go frm there
green ibex
what happens when you distribute the 2?
hoary meteor
wym
green ibex
green ibex
what is $\f{\sqrt{2}}{2} \cdot 2$ equal to
soft zealotBOT
🫎 Chmoosey 🫎
hoary meteor
yeah i got it thank you
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@hoary meteor Has your question been resolved?
visual wigeon
remote island
Show that the functions have local extrema at these points:
"dla" means for
remote island
f(1) = 2 = f(0) -> f(1) < f(x) : x > 0
so i don't really udnerstand this question
young bridge
Show that the functions have local extrema at these points:
"dla" means for
at which points?
remote island
because the interval isn't specified
remote island
at which points?
x = 1
young bridge
you can differentiate the piecewise function
so differentiate (x+2) and 2
then find where the derivative = 0
remote island
at 2
coral prawn
the function is not continuous at x=1 so it is also not differentiable at x=1
remote island
at x + 2 it's 1
coral prawn
therefore any conclusions made from the derivative are kinda sus
young bridge
the function is not continuous at x=1 so it is also not differentiable at x=1
hmmm true
remote island
f(1) = 2 = f(0) -> f(1) < f(x) : x > 0
.
i don't understand the interval it wants me to use
because i guess, if x > 0, then it's a local minimum
in previous problems this is self-evident, for example:
f(x) = x^20 - 3 at x_0 = 0
f(0) = -3 < f(x) : x != 0 -> local minimum
here it doens't matter what interval we choose, it's the smallest attainable value by the function
scarlet sequoia
global minimum => local minimum yes. Here the interval you choose will matter
remote island
yeah so what exactly is it asking me
coral prawn
It does matter which interval you choose. Consider for instance epsilon=3. Now there do exist values within that interval that are in fact smaller than h(1)
remote island
it doesn't specify an interval
It just says to show that they have local extrema at these points
scarlet sequoia
it doesn't specify an interval
yeah, you have to find an interval that fits the point
it's up to you
remote island
okay but then tehre are different types of extrema
coral prawn
Here's the definition. Note that d_X(x, x0) = |x0-x|
remote island
like idk what it's called in english, but an extremum can either be >= or >
the latter is translated to "proper extremum" here
and i'm guessing there's only one correct answer
coral prawn
I haven't heard of that distinction before
scarlet sequoia
well a local proper extremum is possible
coral prawn
but h(1) is a proper local extremum point
remote island
yeah so here the correct answer is that it's a local proper extremum
scarlet sequoia
yes
remote island
f(1) = 2 = f(0) -> f(1) < f(x) : x > 0
which fits the above
but what if i would choose that x>= 0
then f(1) <= f(x)
scarlet sequoia
so you have to find an interval $I$ centered around $a$ such that $h_{|I}$ has a proper extremum at $a$
soft zealotBOT
rafilou2003
remote island
so you have to find an interval $I$ centered around $a$ such that $h_{|I}$ has a...
it doesn't say that tho
it just wants me to prove that local extrema exists at these points
scarlet sequoia
well if you want to prove that
scarlet sequoia
**rafilou2003**
you have to do exactly this
remote island
i don't think you udnerstand
scarlet sequoia
you want to prove that there is a local extremum at point 1 for example
scarlet sequoia
**rafilou2003**
this is a way to prove it
remote island
my point is that i can prove it for either the proper or "improper" (?) extrema
scarlet sequoia
if you have another way then go with it
remote island
which fits the above
.
f(1) = 2 = f(0) -> f(1) < f(x) : x > 0
proves it for local proper minimum extremum
f(1) = 2 = f(0) -> f(1) <= f(x) : x >= 0
proves it for local improper minimum extremum
coral prawn
You have to find epsilon such that |x-1|<epsilon implies h(1)<h(x) for all x in R
(this would show that x0 is a proper extremum, and obviously that also means that it's a "regular" extremum as well)
remote island
the corerct answer is "local proper minimum extremum"
scarlet sequoia
> f(1) = 2 = f(0) -> f(1) < f(x) : x > 0
proves it for local proper minimum extr...
the second one doesn't prove that it's improper
it just proves that it's a local minimum
remote island
wut
scarlet sequoia
if you want to prove that it's improper
you have to prove that there DOESN'T EXIST
remote island
wut no
scarlet sequoia
an interval where it's proper
coral prawn
note that proper implies improper
remote island
so like my issue is that if they're giving me choice, then i can prove it for either proper or improper extrema
coral prawn
well take that choice then
scarlet sequoia
then with those definitions, proper => improper
coral prawn
Of course you should prove whichever is easier if you're given both options
remote island
whenever i have these quedstions i can just try to prove it for proper
coral prawn
and improper is easier to prove
scarlet sequoia
it doesn't make a lot of sense though
improper should be the opposite of proper
meaning there doesn't exist an interval where it's proper
coral prawn
but of course you can also notice that the proper extremum is also incredibly easy to prove and you can flex on your teacher by proving a possibly stronger result than what they wanted
coral prawn
I don't think so
it's good practice to get used to writing some stuff out "manually"
remote island
like
∃ local min(f(x))
or something lolz
coral prawn
math in school tends to be 95% algebraic symbols and equations and expression manipulation
whereas math in the "real world" is more like 80% text 20% math
remote island
isn't it just a linear algebra textbook
coral prawn
I mean the text is also math but basically it makes no sense to try to define a special symbol for everything and just have like logical symbols
coral prawn
isn't it just a linear algebra textbook
it's a snippet from my bachelor thesis
scarlet sequoia
Another example, still 80% text
remote island
okay ty all
i will close this channel and ask new quesitons in another
once i have any
.close
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simple mauve
@coral prawn can u help me
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errant thistle
This was a multiple choice, product, question that appeared in am exam I wrote yesterday. Unfortunately I can't remember 'd', but if I recall, option d was >= 1 (provided value).
My assumption, using the following working-out, is that the correct answer is 'a', however, I'd appreciate it if someone could confirm or support my answer.
final saddleBOT
This was a multiple choice, product, question that appeared in am exam I wrote y...
errant thistle
I suspect that the product tends towards 1/2, but never quite gets there, am I right or wrong?
shell skiff
I suspect that the product tends towards 1/2, but never quite gets there, am I r...
Use difference of squares for the numerators
errant thistle
I'll check that out quickly
I find I get the same result as prior, unless there's a way to develop it further with diff. of squares
shell skiff
Write down more terms
native flame
dont look for a pattern, look for cancellations
shell skiff
Try to find a pattern
errant thistle
I do wonder if there is a way to prove without calculating the entire product equation, or if multiplying it out is the only way
native flame
oh
errant thistle
uh oh
native flame
I do wonder if there is a way to prove without calculating the entire product eq...
there is
errant thistle
I am conflicted
shell skiff
Yeah no look for a pattern so you can use cancellation
Don't look for a pattern to guess the answer
native flame
yeah like dont look for something like "tends to 1/2" or anything is what i meant
errant thistle
I see now, the initial difference across the Numerators and Denominators is 5, then 7, then 9 ... d+2
can I use this?
My brain is not computing rn 🥲
native flame
I find I get the same result as prior, unless there's a way to develop it furthe...
try keeping the n - 1 and n + 1 factors separate. for example on top you have (1)(3)(2)(4)...
errant thistle
try keeping the n - 1 and n + 1 factors separate. for example on top you have (...
I see what you mean
I'm seeing this ...
native flame
I'm seeing this ...
hmm...
it should be simpler than that
but youre on the right track
errant thistle
I'll keep digging for a couple minutes, otherwise, I'll have to contact the university lmao
This, that I found, does confirm my answer, although it has no explanation ofc ...
woven slate
try to make a^2-b^2=(a+b)(a-b)
gives you the solution
native flame
This, that I found, does confirm my answer, although it has no explanation ofc ....
yeah this is what i got
errant thistle
I find I get the same result as prior, unless there's a way to develop it furthe...
Snowtuna, I did over here ^
errant thistle
no
native flame
so on the bottom you have 2 copies of each natural number except for n + 1 (no copies) and on the top you have two copies of each natural number except for n and 2 (one copy of each). you also have only 1 copy of n + 1 on the top. everything in the middle cancels out, so youre left with 101/2(100)
errant thistle
give me one, just one, minute to understand 😂 😭
native flame
yeah sure. if you need clarification on anything, just ask
errant thistle
I'll be back in 5, I think i've got it
Showing a classmate the progress to get his input haha
My friend gets it, I don't, I may need a visual representation of the cancelling-out
He says its "difficult to explain in words" 🥲
Okay, after a long look, I finally get it, thank you @native flame 🙏
native flame
Okay, after a long look, I finally get it, thank you <@1054611986463342694> 🙏
npnp 👍
glad you got it
errant thistle
.close
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mental root
Determine whether the set of rational numbers in lowest terms whose denominators are odd under addition is a group.
final saddleBOT
Determine whether the set of rational numbers in lowest terms whose denominators...
stone wagon
Determine whether the set of rational numbers in lowest terms whose denominators...
!status
final saddleBOT
Determine whether the set of rational numbers in lowest terms whose denominators...
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
I don't know how to approach the problem
stone wagon
let me think how to give you a hint without giving away the answer
mental root
i have reached $\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$
soft zealotBOT
The د
mental root
it must be odd
mental root
but this might not be in lowest terms
ohh you cant divide any odd number to get an even one!
so yeah
stone wagon
Determine whether the set of rational numbers in lowest terms whose denominators...
the set of rational numbers in lowest terms
this is a bit confusing to me tho
mental root
right?
stone wagon
like 1/3 = 3/9
muted prairie
probably they mean the set of rational numbers which have odd denominators when written in lowest terms
well i shouldn't say probably but obviously
stone wagon
probably they mean the set of rational numbers which have odd denominators when ...
ah
in that sense
stone wagon
like the fractions must be in lowest terms
then yeah closure is satisfied
stone wagon
associativity, identity and inverses come for free from rationals
mental root
yeah makes sense
mental root
but for example if it was even denomiatots I would nit have closure
muted prairie
correct
muted prairie
you should justify identity and inverses too though
they aren't free
though i mean they're pretty easy
mental root
yeah they're quite simple
muted prairie
but {0, 1, 2, ...} is closed under addition without being a group due to problems with inverses
but ye u got the hard part
final saddleBOT
muted prairie
np
digital steeple
bd an two angles should be enough to calc everything in bcd.
final saddleBOT
@tranquil pine Has your question been resolved?
safe spoke
first, do you know all of the info you have about bcd
Is it a bad idea to use integration for this
You know calc?
muted prairie
Is it a bad idea to use integration for this
yes
muted prairie
not without using the exact same trig you could just use to solve it instead
refer to my first 2 messages here
safe spoke
not without using the exact same trig you could just use to solve it instead
I forgot how to do trig
calculus unironically seems simpler to me
muted prairie
good luck lmao
you know all lengths?
I would recommend constructing an altitude somewhere (probably from the obtuse angle for simplicity)
and then calculating the length of the altitude using trig
Yeah
safe spoke
muted prairie
construct a line going through B perpendicular to DC
safe spoke
Just go off this I guess
digital steeple
he means this: #help-48 message
muted prairie
Just go off this I guess
Doesn't give area formulas
safe spoke
Doesn't give area formulas
use cross product idfk
life of a college student I forgot how to do basic hs math
Then do this
muted prairie
yeah that's an area formula
It forms one side of a right triangle, you know the hypotenuse and the other angles
Those are line segments, so they don't have a base or height
ah
that's why I wanted to use CD
the other 2 altitudes lie outside of the triangle
it's the line from the top that's perpendicular to the line you get by extending the other side into an infinite line
if you google obtuse triangle altitudes you'll probably see it
still works in the base*height/2 formula though
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
May h ask where did I go wrong?
final saddleBOT
@crimson stirrup Has your question been resolved?
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@crimson stirrup Has your question been resolved?
jagged flare
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crimson stirrup
a
warm python
fathom walrus
clearly not lol
vocal forge
clearly not lol
wdym?
fathom walrus
looks like theyre solving for m, not k or a
also the number 3 doesnt show up in the problem u posted
vocal forge
umm these are images posted by OP, i just reposted them
fathom walrus
bro just read what his first picture in this channel has
crimson stirrup
<:helpjustask:371662163489718273>
i replied to it..
sonic crystal
i replied to it..
yeah but like whats the original question
crimson stirrup
plz start from here
first image is the insert
second image is my working for second last question
third image is my working for last question
I wanted to ask where did I go wrong
fathom walrus
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@crimson stirrup Has your question been resolved?
crimson stirrup
help?
final saddleBOT
@crimson stirrup Has your question been resolved?
barren basin
Given two different but similar plots (let's assume in 2d and the plot is Given by discrete values), translate plot A so that it overlaps on plot B with the smallest error possible.
final saddleBOT
Given two different but similar plots (let's assume in 2d and the plot is Given ...
barren basin
My question is what would an algorithm to complete this task would look like. What if we are allowed to translate in any direction ? What if we allow stretching ?
digital steeple
the question is too unspecific. which translations do you have in mind?
native flame
im guessing theyre talking about something like gradient descent?
barren basin
Well, think about it as if you have done the same experiment twice, the data should look similar, but it likely won't begin at the same origin.
native flame
so youre trying to find a function of best fit?
digital steeple
hmm if you have two sets of n points you can always translate errorless one into the other.
barren basin
In my actual case, I am trying to compare two curves. I can translate those curves on top of each other visually/manually, but I'd prefer to automate that part
barren basin
hmm if you have two sets of n points you can always translate errorless one int...
Well, since the data is taken experimentally, it won't be possible to have a perfect match because of noise and disturbances
digital steeple
Well, since the data is taken experimentally, it won't be possible to have a per...
if your set consists of n data points you can always fit a polynom of at least degree n-1 to get an errorless transformation.
barren basin
I'm not quite sure I understand.
I have two set of data that I'm trying to fit one on top of another
native flame
so wdym fit
i strongly suspect youre looking for gradient descent. but if you could clarify your problem statement a little bit it would be helpful
basically, youre looking for a way to generalize something like linear regression, right?
where you have a two sets of data points and you want a function that minimizes average error over both sets
digital steeple
you said you have given the function by discrete points, so you do not really have curves.
barren basin
Yes i don't have f(x) = y, I only have the coordinates of points making the curve
digital steeple
you have a set of n Points P1, ... PN and a set of Q1, ..., QN. and you want a function PI->QI.
barren basin
In my problem I kind of have to find irregularities in my data, in my example my data had two bumps, a larger one followed by a smaller one
Both sets of data have these characteristics
digital steeple
in this case you can find a polynom of (at least) degree n-1 which fits exactly to the gven points.
barren basin
Visually I could stretch and translate the shape so that they "sort of" fit onto each other
native flame
okay hold on is this what youre looking for
the green line is the function youre looking for, the red and blue points are different datasets
barren basin
Yes exactly, except the blue points are not necessarily aligned on top of each other already
forest ember
I think what is looking for is to keep the 2 curves separate, but have the points of interest on the curves align
barren basin
I think what is looking for is to keep the 2 curves separate, but have the point...
Yes that is my problem I am trying to solve
digital steeple
Yes exactly, except the blue points are not necessarily aligned on top of each o...
exactly? one common function for both sets?
native flame
Yes exactly, except the blue points are not necessarily aligned on top of each o...
mhm so the approach here is you take some error function E, and then you minimize E over f
mellow axle
native flame
I think what is looking for is to keep the 2 curves separate, but have the point...
so have the sampling intervals of the independent variable line up?
barren basin
exactly? one common function for both sets?
Well like I said, I am repeating the same experiment twice. It could be dropping a basketball and measuring the vertical height
mellow axle
if $f(x)$ and $g(x)$ are two discrete functions over set $A$, determine for which $a, b$ minimizes $\sum_{x\in A} f(x) - (g(x - a) + b)$
soft zealotBOT
pee norm maxxing
digital steeple
well it makes a difference if youre searching for a transformation from one line to another:
barren basin
If you drop the basketball at the same height and plot the height, which was measured discretely, then visually you could observe that the two curves are very similar
mellow axle
is that what you're trying to ask?
native flame
i think i see what you're getting at. basically you want to approach this by taking the mean at each point, and for that you want the points on the x axis to line up
digital steeple
or if your searching for a common function.
barren basin
native flame
youll want to get more than two samples for this
barren basin
In the simplest case, I have function 1 in blue and function 2 in purple. Visually we can see that the trapezoidal shape thingy is my region of interest, thus I could translate f2 so that the trapezoids are ontop of one another
Now, I have 200 such curves
native flame
right but how do you pick which one to translate
barren basin
Well, that wouldn't be too important since my goal is to compare them
digital steeple
i repeat this.#help-36 message this is (theoretically) errorless possible. but mostly it doesnt make sense (google overfitting), so you should typically say something about wanted transformations (linearity for example).
barren basin
Yes it would have to be linear translation or stretching
native flame
stretching?
so you want to compare them by analyzing the function that maps one curve to anothrr
digital steeple
the question is too unspecific. which translations do you have in mind?
therefore i asked this.
digital steeple
Yes it would have to be linear translation or stretching
linearity is a kind of matrix multiplication.
barren basin
For translation, you could likely try every possible translations possible(since you can't translate more than the size of the data), but I'm assuming there's a smarter solution than trying AxB possibilities
native flame
a naive approach could be mapping each point from A and B to their mean
instead of one function that takes A to B, you have two functions that take A and B to a common curve
native flame
For translation, you could likely try every possible translations possible(sinc...
okay okay i see what you're asking now
barren basin
linearity is a kind of matrix multiplication.
Yes in my scenario you can do multiplication on the data(which is what i call stretching/compression), or add (translate)
native flame
lets just consider translations first
$E = \sum |a_i - b_i|$
you want to find the translation of B that minimizes this error?
soft zealotBOT
esca (@ with reply)
barren basin
Exactly correct
digital steeple
Exactly correct
just for completeness: you also have to define your error function which you want to minimize. you can do the sum of the absolute errors, mostly its the sum of square of the errors. the result depends on the error functioon you choose.
you could measure by maximize correlation fore example.
native flame
in general for two variables youll just want to take the derivative of the error function and use that as your next translation
iirc
barren basin
just for completeness: you also have to define your error function which you wan...
I've mostly seen people use the sum of squares as you've said, so I'd be tempted to use that measure(I wouldn't be able to answer why, but that's likely a question on its own)
digital steeple
typically this decission depends on the structure of the data. sum of squares tends to give extreme outliners more impact then just taking the absolut errors. is like a mean vs. median discussion.
native flame
i think some error functions are also easier to minimize than others
digital steeple
i think some error functions are also easier to minimize than others
thats true, thats true.
to sum up (from my practie view): there is no general advice someone can give you. it really depends on your data, on your experiment generating the data, and the purpose you wanna to with this.
So to go on further I would need more details.
barren basin
In my experiment, I have measured the throttle cycle of a car going from 0 to 100 mph
On the x-axis you would have the time and the y-axis is the speed.
I have over 100 samples curves, taken with the same car, same pavement, same tires, and a bunch of other controlled variables.
I am trying to trace the envelope of possible outputs, and to do that I need to overlap those 100 curves.
The time of recording won't always be the same, and the speeds will slightly differ, but will look really similar
digital steeple
well you have something in the range of some seconds on the x-axis, a renge 0 to 100 on the y-axis and n general the same conditions (same car, same tires, etc.)
shouldnt it then be identical curves (nearly)?
barren basin
well you have something in the range of some seconds on the x-axis, a renge 0 to...
Yes that's what I've been saying, the curves are extremely similar, but not quite "positioned" correctly. Sometimes there's a few seconds before we see the curve, sometimes there's a little bit of roll before the tires latches into the ground and so on
digital steeple
well thats a completely different task fro my point of view. it looks for me that the experiment has some "troubles" (there's a little bit of roll before the tires latches into the ground and so on), so I wont do a transformation on the resulting data to fit similarity, i would try to adjust the data to get rid of this "experiment-troubles": So if youre not sure that the measure starts a the same point/time, try to adjust this.
for "there's a little bit of roll before the tires latches into the ground" it would just shift to the left with this "little bit".
barren basin
Well we can't control everything. I think people who've experimented on tensile tests have had to solve a very similar problem.
There's always irregularities in the material that changes slightly the values.
And you're right, it would shift to the left a little bit, the question is inherently about "how much" should you shift to minimize the error
digital steeple
i do fully agree. but handling errors in the setting of an experiment is a complete different task to "transform similar curves".
You can try to ignore this errors first, do so as wouldnt there such setting-errors and assume that the resulting curves should be nearly the same. the determine the "mean curve" of all resulting curves, determine the difference from each resulting curve to the theoretical mean curve. make a error distribution an then for example discard the most 5%, 10%, 15 % percent error curves.
Maybe the setting errors equals each other and you can ignore them therefore.
But as said before, i guess this needs much more time to spent with the settings, the data, and the purpose you want to achieve. thats much to detailed for discussing here I guess.
or you could do the following: if you curves go from 0 t0 100 mph, you could adjust all with a first value speed of your choive, eg initialize all curves with the time of the first value above 5mph.
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serene rain
help
serene rain
so
tranquil pine
so
