ye
#help-13
wispy wadi
wispy wadi
ye
honest field
go ahead and kill the problem
honest field
what's wrong?
honest field
yep
wispy wadi
4root(3)/7, x are legs 32root(3)/7 is hypotenuse?
honest field
no
honest field
yep
wispy wadi
and green is 4root(3)/7
honest field
correct
wispy wadi
tysm
honest field
that was a hella lot of work
honest field
there def must have an easier way
wispy wadi
lemme send ss
floral arrow
All three colored triangles are similar
wispy wadi
well DB would've been easier to calculate
wispy wadi
I overcomplicated everything again
i couldn't find another way ngl
anyway, ty
.close
cedar kilnBOT
cedar kilnBOT
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keen meadow
I am playing a card game, if i pull a spade, i get $120, if i pull anything else, i lose $16. Its one deck. What is the most I should pay for an insurance policy that pays back at least HALF of what the expected value of the card is?
keen meadow
My answer is 9, because the ev is obvioously 120(0.25) - 16*0.75
which is 18
and then half
is 9
so thats the most i shoudl pay
does this make sense? idk why i my friend is telling me its 18.75.
deep nymph
I am playing a card game, if i pull a spade, i get $120, if i pull anything els...
what does "at least half" mean btw
upper laurel
deep nymph
does this make sense? idk why i my friend is telling me its 18.75.
i think this makes sense then
you should gamble against your friend
i think you would make money!
keen meadow
this is his explanation
even chatgpt says trhis
but i dont think this makes a lot of sense
@deep nymph
deep nymph
insurance payout shouldnt be 25 should it?
deep nymph
i think youre right
keen meadow
also a follow on question, was if the insurance costs 7.25, whats the new ev of the game? i just said 18-7.75 is 10.25
deep nymph
also a follow on question, was if the insurance costs 7.25, whats the new ev of ...
remember to add in the payout
deep nymph
insurance payout raises your ev
night wedge
!img
cedar kilnBOT
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deep nymph
if insurance always pays you, yes
deep nymph
yea you get it, idk the problem setup but this is correct
cedar kilnBOT
@keen meadow Has your question been resolved?
crimson sedge
Hi. Would the integral be 1 to infinity?
cedar kilnBOT
Hi. Would the integral be 1 to infinity?
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
night wedge
Maybe try it then we’ll see how you did (Since we usually check work if you know how to do it)
placid geode
Hi. Would the integral be 1 to infinity?
Not very important but there's a typo here, it should be t≥0 as the condition on the function
Not y
crimson sedge
Sure, I will try it
night wedge
There’s no y anywhere else
-# The magic of English: Writing a 4 letter word instead of a 4 word sentence
That was like 10 edits why am I like that
placid geode
That was like 10 edits why am I like that
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
Guys, you have been helpful. I am working with my group members, currently, so I am going to close this channel now. Thank you so much
celest badger
Where should I go from here any hints?
cedar kilnBOT
Where should I go from here any hints?
gritty viper
you should say "suppose that T is a surjective linear map"
not suppose that there exists such a T
anyways a hint is dont choose the basis in W
choose it in V instead
stiff totem
since T is surjective, you can find a preimage for each of the basis element in W
celest badger
you should say "suppose that T is a surjective linear map"
yes my bad
gritty viper
wait let me rethink my hint
stiff totem
you can start with a basis of V, but I think it's slightly cleaner to pull the basis of W back along T
either way works though
celest badger
V isn't finite-dimensional necessarily bud
in fact, I think it can be infinite dimensional in this case
stiff totem
infinite dimensional vector spaces still have bases (assuming axiom of choice)
stiff totem
and if V is infinite dimensional, you'll need AC to select a preimage anyway
W is given to be finite-dimensional so this direction doesn't require choice, actually
celest badger
we can't name a basis for an infinite dimensional vector space
that's illegal rn
until I get to functional analysis or something
I'm just telling you rn that axler isn't looking for something involving AC etc.
celest badger
~~and if V is infinite dimensional, you'll need AC to select a preimage anyway~~...
um okay but technically I can't know what a preimage is
since that was also not anywhere in the chapters
even though I have an idea of what it means
stiff totem
it just means some v such that T(v) = w
this should be assumed set-theoretic knowledge of some sort
since this is what it means to be surjective (that at least one such v exists)
celest badger
mhm
sure so
for all the w's
theres a Tv
such that w = tv
and we need S(w) = v
stiff totem
that defines S on the basis
celest badger
except v isn't unique
stiff totem
so you can linearly extend it
S won't be unique either
there are lots of possible S's
you just need to show that one exists
each one corresponds to a different selection of v's
celest badger
that defines S on the basis
on what basis
stiff totem
pick a basis of W first
stiff totem
you can't select a preimage for every w independently
or S won't necessarily be linear
celest badger
each w_1 = Tv_1
stiff totem
only need to select preimages for basis elements
celest badger
S(w_j) = v_j
stiff totem
yeah
stiff totem
yeah
should include a part like "by extending linearly, S is a well-defined linear map on W"
since as written, S is only a function from {w_i} to V
celest badger
wdym
once we show where it takes the basis vectors
we've defined the map
each linear map is uniquely determined by that
stiff totem
yes, that's a theorem, but you need to say that
celest badger
nahh thats trivial
stiff totem
you're implicitly invoking it
celest badger
I've defined all my linear maps like that
I've just shown what they do to the basis vectors either by T(v_j) = w_j or T(a1v1+...) = a1w1+...
stiff totem
ok, but take care in the future, because sometimes the distinction matters (in other areas of maths in particular)
celest badger
ok, but take care in the future, because sometimes the distinction matters (in o...
of course
Thanks a lot for your help desync
you seem very smart
stiff totem
nw
stiff totem
category theory gang 🔥
celest badger
do you go to like a top 10 college
celest badger
category theory gang 🔥
I'm not close to that level but it looks really cool and I probably want to take a course in it at some point
stiff totem
I'm not US-based, but yes
stiff totem
I'm not close to that level but it looks really cool and I probably want to take...
it's very nice
I recommend doing some algebraic topology or algebraic geometry first
celest badger
I'm sure I will
stiff totem
or differential geometry
celest badger
I'm still in hs
stiff totem
or else a bunch of the results will just seem completely unmotivated
cedar kilnBOT
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Available help channel!
wary forge
Hello, I am working on this real analysis problem. I know that I can prove convergence if I get it into its explicit form, and I know what its explicit form is, but I'm not sure how to prove that the explicit form is correct
wary forge
the explicit form should be (xnot + 2^n - 1)/2^n
abstract pollen
Hello, I am working on this real analysis problem. I know that I can prove conve...
shouldn't need to
actually that's insufficient
two moments
wary forge
btw just for future reference, how do you go about proving a series' explicit form from this kind of form for one as simple as this?
abstract pollen
it's in the form = Ax+B so it should be in the form of A^n + something
cerulean sail
(if you want to prove that an explict formula you already found is true, you could do so by induction, no?)
wary forge
that is... a good idea yes, thank you!
I don't think I've ever done an induction proof for an explicit form before, but it shouldn't be too different from doing it for increasing/decreasing
abstract pollen
then make the conclusions yourself
as for the recurrence relation, one usually refers to a table of inhomogeneous recurrence relation
cerulean sail
I don't think I've ever done an induction proof for an explicit form before, but...
It isn't too difficult, it's pretty similar, assume that for some $k$ you have $x_{k - 1} = \frac{x_0 + 2^{k - 1} - 1}{2^{k - 1}}$, then from the definition of the sequence, show that $x_k$ has the same form with $k - 1$ replaced with $k$
wraith daggerBOT
@cerulean sail
abstract pollen
something that looks like this
it's a bit stickier to prove that these are true though
wary forge
Yeah I'm doing the induction proof right now and it's super simple, I just wasn't thinking about it before
cedar kilnBOT
Available help channel!
ancient lodge
$\int^{1}_{0} \frac{1+x-x^2+x^3-x^4-x^5}{1-x^7} \dd{x}$
cedar kilnBOT
$\int^{1}_{0} \frac{1+x-x^2+x^3-x^4-x^5}{1-x^7} \dd{x}$
wraith daggerBOT
Civil Service Pigeon
floral arrow
You just had to didn't you
ancient lodge
😇
sacred iron
feral sapphire
**Civil Service Pigeon**
have you tried turning your computer on and off again?
floral arrow
$\int^{1}_{0} \frac{1+x-x^2+x^3-x^4-x^5}{1-x^7} \dd{x}$
1.18741, and no I cannot elaborate
feral sapphire
cleo moment
night wedge
!done
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
floral arrow
cleo moment
Would need to be "I will not" instead (or actually, just nothing)
night wedge
Can we .close this (if that’s okay)
feral sapphire
Can we .close this (if that’s okay)
prob just infinite series and integrate term by term.
floral arrow
Can we .close this (if that’s okay)
Change of heart? 
cedar kilnBOT
@ancient lodge Has your question been resolved?
feral sapphire
$\frac{\pi\sqrt{7}}{7}$
wraith daggerBOT
qwertytrewq
wicked mantle
No I just meant that from the start but phrased it badly
yeah, we’ll keep this channel opened until you get helpful
ancient lodge
$\frac{\pi\sqrt{7}}{7}$
cedar kilnBOT
Available help channel!
delicate temple
hi, can someone help me with this
cedar kilnBOT
hi, can someone help me with this
cedar kilnBOT
hi, can someone help me with this
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
1
flint plinth
probably you have some thought regarding the value of h?
delicate temple
i have no idea about any of it
delicate temple
oh... 1.5
flint plinth
no... be careful about the sign
delicate temple
-1.5
flint plinth
yes
delicate temple
mistype mb
flint plinth
ok, so now just plug that h value into this:
flint plinth
yw
delicate temple
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
thin harbor
polynomail factorization
gusty ridge
polynomail factorization
Do you still need help?
cedar kilnBOT
@thin harbor Has your question been resolved?
elder bobcat
isnt union use the word or?
cedar kilnBOT
isnt union use the word or?
dire geode
"x not in A or B" means "x not in A and x not in B"
try translating "x not in A or B" yourself to see if you disagree
fast osprey
isnt union use the word or?
yes but the negation of it is and...
pastel vault
isnt union use the word or?
a Venn diagram shows why
elder bobcat
yeah im just not getting where the and came from...
pastel vault
what happens if you take the intersection of these 2?
elder bobcat
like its different from when i didnt have the negation
pastel vault
like its different from when i didnt have the negation
yes, you can think of the negation as swapping 'and', 'or'
elder bobcat
everything outside A and B
pastel vault
there you go, so that's $x \notin (A \cup B)$
wraith daggerBOT
south
elder bobcat
what if x is an element of A union B? it would be x is in A or x is in B right?
cause theres no negation
so it's or
elder bobcat
okay i get it now lol i had to not overthink xD
thank youuu
cause i was breaking it by case scerniao and i was like wut
.close
cedar kilnBOT
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Available help channel!
dim flame
I have tried approaching this many different ways, but can’t seem to find the right way to do it. I have to solve for x.
worldly chasm
@dim flame have you considered changing the right hand side to log_8 using the change of base formula?
The raising both sides by 8
dim flame
<@804563320031412234> have you considered changing the right hand side to log_8 ...
What is the change of base formula?
worldly chasm
To clear the log
dim flame
The raising both sides by 8
Oh.
pastel vault
a couple different ways exist
for instance, raise 8 to the power of both sides
and then note that $8^k = (2^3)^k = (2^k)^3$
wraith daggerBOT
south
worldly chasm
What is the change of base formula?
$\log_b(c) = \frac{\log_a(c)}{\log_a(b)}$
wraith daggerBOT
OmnipotentEntity
worldly chasm
For nice a.
dim flame
For nice a.
Wait, I am confused. Where did a come from?
worldly chasm
a is whatever you want it to be, provided it isn't a problematic value, like 1 or 0 or something.
In this case, we will select a = 8
(with b = 2 and c = 4x)
dim flame
a is whatever you want it to be, provided it isn't a problematic value, like 1 o...
Hmm.
How does this formula work?
dim flame
I'm not sure what you're asking
Like why does this formula work? How does $\log_b(c) = \frac{\log_a(c)}{\log_a(b)}$
wraith daggerBOT
Pillow
dim flame
How do those equal each other?
worldly chasm
\begin{align*}
y &= \log_b(c) \
b^y &= c \
\log_a\qty(b^y) &= \log_a(c) \
y \log_a(b) &= \log_a(c) \
y &= \frac{\log_a(c)}{\log_a(b)}
\end{align*}
wraith daggerBOT
OmnipotentEntity
worldly chasm
@dim flame
wraith daggerBOT
south
pastel vault
but yes, that's the derivation of change of base
cedar kilnBOT
Available help channel!
stark garnet
I'm currently having trouble with this logarithms task, in which you have to find x.
stark garnet
then product rule your way to victory
I think you may have to be a bit more specific 😭
stiff brook
do you know how log converts products into sums
ln(xy) = ln(x)+ln(y)
try applying ln on both sides and using this rule on the RHS
something nice cancels out!
wispy marten
No need for this
stiff brook
i mean its another natural way I just realized that it is 8 TIMES 2^x. i thought it was question 8... 2^x = blah blah blah
fossil dawn
I think you may have to be a bit more specific 😭
first convert the 8 to some power of 2
then on both sides, you have a product of powers of 2
what do you do when you have a product of powers of the same base?
stark garnet
what do you do when you have a product of powers of the same base?
You add the exponents and keep the base the same think? Like x³ • x⁴ = x⁷
fossil dawn
mhm
stark garnet
I think it's this: x = 8/3 or 2 2/3
chrome elk
Yeah that's correct
Would be nice to show your work so we can check that you did all the steps correctly too
stark garnet
indigo lagoon
looks good to me
chrome elk
Yup
stark garnet
yayy 🙂🙂 thank you guys
indigo lagoon
Anything else you wanna ask?
stark garnet
Anything else you wanna ask?
Not at this moment no
indigo lagoon
Alright @chrome elk can you abuse your power?
cedar kilnBOT
cedar kilnBOT
Available help channel!
dusty sail
[Predicate logic resolution]
In the second step, why does the solution say to replace d with x? d is a constant, thats not allowed right?
cedar kilnBOT
## [Predicate logic resolution]
In the second step, why does the solution say to...
@dusty sail Has your question been resolved?
cedar kilnBOT
@dusty sail Has your question been resolved?
pseudo merlin
am I on the right track..
cedar kilnBOT
am I on the right track..
chrome elk
You forgot to change the limits of your integral accordingly
An integral over x from 0 to π/4 would not be the same as an integral over u from 0 to π/4
The values would change
pseudo merlin
um
pseudo merlin
An integral over x from 0 to π/4 would not be the same as an integral over u fro...
oh
uhhh how do I change my limits
Was
chrome elk
What is u when x = 0
loud gyro
that 1009 shouldnt be in the numerator
pseudo merlin
oh
chrome elk
And what is u when x = π/4
chrome elk
that 1009 shouldnt be in the numerator
Right, so focused on the limits I didn't notice the integration was wrong too
chrome elk
Still the wrong limits on the u parts
pseudo merlin
You forgot to change the limits of your integral accordingly
wait I checked the answer and they didn’t change the limits
chrome elk
Also why did the 1008 disappear
Cuz they've written it differently
They're integrating wrt dx all the time
pseudo merlin
oh
chrome elk
You're integrating wrt du
pseudo merlin
aw man
chrome elk
It shouldn't matter in the end cuz you'll just turn it back into x
chrome elk
But someone checking might cut a point for not writing the limits correctly
pseudo merlin
ohh I see
wow I haven’t been changing the limits the whole time
and I did my integration test last week
im scared for my mark now
chrome elk
It's okay it isn't that hard
chrome elk
What is u when x = 0
^^
chrome elk
And what is u when x = π/4
^^
Oh the test is in the past
Ehh you might lose one mark for it at most
jovial hornet
How do i calculate this
cedar kilnBOT
How do i calculate this
buoyant latch
Look at a graph
buoyant latch
Draw the graph?
high coyote
Properties of powers
wraith chasm
How do i calculate this
answer is 0
high coyote
$$\lim_{x\rightarrow\infty}\frac{1}{e^x}$$
wraith daggerBOT
Categorist
jovial hornet
answer is 0
I know, I'm trying to know how to get to that stage
high coyote
What happens when you divide an orange for infinitely many people? How many orange for a person?
jovial hornet
What happens when you divide an orange for infinitely many people? How many oran...
a very small ammount i suppose 😭
fossil dawn
answer is 0
!nosols esp without explanation
cedar kilnBOT
answer is 0
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
jovial hornet
what if the exponent is 2x then
jovial hornet
is it just 2 times infinity?
high coyote
answer is 0
Him ok
high coyote
is it just 2 times infinity?
What exact limit are you asking about?
fossil dawn
So don't warn me
that was not even remotely directed at you, dw. that's why i replied to him
jovial hornet
What exact limit are you asking about?
the limit of infinity
high coyote
$$\lim_{x\rightarrow\infty} e^{2x}$$
wraith daggerBOT
Categorist
high coyote
This?
jovial hornet
yepp
high coyote
that was not even remotely directed at you, dw. that's why i replied to him
Ok, sorry
jovial hornet
I got infinity, but its still very confusing to understand why
do I just change x for infinity?
high coyote
Yes, that's how we visualise it
jovial hornet
okay, one last question
if it is limit of x to infinity of (1/2)^x
The answer is 0 but why
jovial hornet
ohh
we've just started on the limits chapter and I barely had any time to ask questions
high coyote
The answer is 0 but why
The intuition is that when you multiply a small positive number (lower than 1) by itself repeatedly it goes to 0 for example (½)^∞ would be the limit of
½
¼
1/8
1/16
...
which is 0
jovial hornet
bruh, makes sense
high coyote
But if the base is greater than 1 for example 3 then
3, 3², 3³... tends to infintiy
The number e>1
wheat crypt
cedar kilnBOT
wheat crypt
Idk to do this icl
so im mapping 1 to 5 to 1 to 10
but i have make sure that f(5) is the larget value and f(1) is the smallest
but surely theres gonna be cases rgiht?
floral arrow
Do you know any combinatorics?
chrome elk
Yeah..
wheat crypt
but
chrome elk
Do you understand why
wheat crypt
they ahve to be in order
chrome elk
Yes
wheat crypt
no not rly
wheat crypt
wdym, say u have f(1) = 10 tho? that defo means that f(5) wont be greater
wheat crypt
yea
chrome elk
Then you arrange them in ascending order
Then you assign them to f(1), f(2) and so on
chrome elk
wdym, say u have f(1) = 10 tho? that defo means that f(5) wont be greater
So this case will never arise
wheat crypt
how do we know they will be unique?
wheat crypt
So this case will never arise
oh so we choose after
chrome elk
how do we know they will be unique?
Cuz we are choosing
chrome elk
Yes
cedar kilnBOT
wheat crypt
.reopen
cedar kilnBOT
✅
wheat crypt
Hi this is a diff q
I hvae a hard time trying to understand these:
and why they are true
how i think abt the choos function intuitievly
tropic oxide
these all have combinatorial explanations
wheat crypt
cause none of it makes sense
tropic oxide
so you know the basic idea of it is that $\binom{n}{k}$ counts the number of ways to pick $k$ objects from a pool of $n$, yes?
wraith daggerBOT
Ann
tropic oxide
ok
tropic oxide
I hvae a hard time trying to understand these:
which of these do you wanna start off with
wheat crypt
first one
wheat crypt
yep
tropic oxide
we want to count how many ways there are to pick out a team of k+1 people from these
wheat crypt
including Bob?
tropic oxide
we do not impose a requirement on Bob to be on the team
he may be on the team and he may also not be on the team
wheat crypt
so its just n+1 C k+1
tropic oxide
on the one hand that's just $\binom{n+1}{k+1}$, since Bob isn't special
wraith daggerBOT
Ann
tropic oxide
on the other hand, we can break the teams down into two types: ones that contain Bob, and ones that don't
wheat crypt
i see
tropic oxide
if a team contains Bob, it needs $k$ more people to complete it --- which means $\binom{n}{k}$ options.
wraith daggerBOT
Ann
tropic oxide
if a team \textbf{doesn't} contain Bob, then it's just a team of $k+1$ chosen from among the other $n$ people --- which makes $\binom{n}{k+1}$ options.
wraith daggerBOT
Ann
wheat crypt
wdym by if it needs Bob?
wheat crypt
if a team contains Bob, it needs $k$ more people to complete it --- which means ...
so when u say a team that contains Bob, what does the choose function do here exaclty
tropic oxide
a team of k+1 people that contains Bob == a team of Bob and k other people
tropic oxide
yes
wheat crypt
and then the team that doesnt contain Bob, there would be n people, given bob isnt on the team, but then it would need k+1 more people to complete the team?
hm now abt the second one
tropic oxide
choosing k people from a pool of n to make a team
is essentially the same thing as choosing which n-k people WON'T go on the team
wheat crypt
waitttt
this is mind boggling hold o
is this some contrapositive thing
😭
like we're saying, given we have n people and k are needed to amek a team, then LHS is saying the ones we pick, the RHS is saying the ones we dont pick?
wheat crypt
oh damn
wheat crypt
And there's a one-to-one correspondencs
idk what u mean by this
chrome elk
Like for every selection of people you pick, there is a selection of people you don't pick
wheat crypt
ah okay
chrome elk
And it all pairs uniquely
chrome elk
Combinatorially, what does 2^n represent
wheat crypt
u can always choose 2 ppl?
chrome elk
Nooooo
wheat crypt
hm
chrome elk
Okay let's do smth lile
If a person is chosen we assign them 0
If a person isn't chosen we assign them 1
Now what would 2^n represent
wheat crypt
each person will hvae a partner?
waitt
are we saying that, there are n options for group of 2 people?
oh wait no
If you add up all the ways to make groups of size 0 to n from n people u have 2^n groups
which is basically the statement
floral arrow
Which question are you on?
chrome elk
If you add up all the ways to make groups of size 0 to n from n people u have 2^...
Yes
floral arrow
Okay, do you need an explanation from zero or do you have some intuition already
wheat crypt
Yes
yea but this is the statement i wanna understand
like its not making sense intuitively
wheat crypt
Okay, do you need an explanation from zero or do you have some intuition already
yea pls
floral arrow
Would you prefer thinking about groups of individuals or about binary strings?
wheat crypt
individuals
floral arrow
Okay, given n people, the total number of ways to make a group of any size (from 0 to n included) is:
- the sum of [ the number of ways to make a group of k people ] with k going from 0 to n,
- 2^n because each person can be either chosen to be in the group or not, so that's two options for each of the n people
Let me know if that isn't clear enough, and which part exactly
wheat crypt
Okay, given n people, the total number of ways to make a group of *any size* (fr...
ohhh shit
that was so nicely said
tysm
now i just need to let these ideas marinate
do u guys reccommmed any books/vids to learn combi from
literally from scratch cause im so bad
floral arrow
No clue sorry
chrome elk
Milkos Bona maybe?
I'm not sure how from scratch it is
But I've been told it's a nice book
topaz osprey
Can you guys help me with this?
cedar kilnBOT
Can you guys help me with this?
topaz osprey
Just the first part for now. The one with the graph
A can’t be distance since you can have a negative distance right?
cedar kilnBOT
@topaz osprey Has your question been resolved?
cedar kilnBOT
@topaz osprey Has your question been resolved?
ancient lodge
neon crystal
A can’t be distance since you can have a negative distance right?
You can have a negative position
lethal lintel
cedar kilnBOT
lethal lintel
idk why this isn't right, I've tried doing it out 3 times
and got the same answer each time
tender ore
it appears to be correct
just that they used fractions and you used /
if they are the same numbers its the same thing
lethal lintel
Yeah but it says I'm wrong sooo
livid hound
unnecessary () maybe
livid hound
oh, 1 sec
tender ore
my bad i thought the answer on the right was correct and yourse was on the left
cabn you show how youve come to your answer
livid hound
have you had any other syntax issues in other questions
tender ore
i think the answer is just plain wrong unless i am missunderstanding the question
floral arrow
-190/81 x + 271/81 is correct
Maybe the software doesn't like that the x is grouped with the -190 (in the numerator)
livid hound
try
-190/81 * x + 271/81
cedar kilnBOT
@lethal lintel Has your question been resolved?
earnest dock
Hello! I am stying to solve this but I am doing something wrong all this time >.< Can I ask you guys for a hand how would you solve this?
gray hamlet
!status
cedar kilnBOT
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
sacred anchor
Hello! I am stying to solve this but I am doing something wrong all this time >....
Show what you've done already
earnest dock
amma send a pic..... it ll look horrendous but its something xD
gray hamlet
xD
sacred anchor
We'll try
sacred anchor
okay so before telling you what I would do
i wanna tell you what you did wrong for some of your attempts
gray hamlet
you started of wrong in all attempts
earnest dock
one where x = 0, other when x doesnt = 0
I could replace x with something.... but I did not feel like thats what they wanted me to do 🤔
sacred anchor
First error: $x^{\frac{2}{3}} = 2^3x$ does not imply $\sqrt[3]{x^2} = \sqrt[3]{2^3x}$. The RHS just magically has a cube root. You did manage to successfuly express $x^{\frac{2}{3}}$ in root form.
wraith daggerBOT
gray hamlet
where x doesnt = 0, divide with $x^{\frac{2}{3}}$
wraith daggerBOT
Roy
earnest dock
First error: $x^{\frac{2}{3}} = 2^3x$ does not imply $\sqrt[3]{x^2} = \sqrt[3]{2...
I felt that
ooh my first time seeing texit. I got it hmmh mm
earnest dock
First error: $x^{\frac{2}{3}} = 2^3x$ does not imply $\sqrt[3]{x^2} = \sqrt[3]{2...
yes. that was a massive fluke
all of them I did so far went smooth. sommet aint right
sacred anchor
For your second attempt, everything looked alright however you need to consider the negative case as well. You also just didn't continue after $x = \sqrt{432}\sqrt{x^3}$
earnest dock
or am just overthinking it
gray hamlet
or am just overthinking it
its pretty easy
wraith daggerBOT
sacred anchor
And uhh that third attempt is like illegible im not even gonna try to read that
earnest dock
For your second attempt, everything looked alright however you need to consider ...
Yes. Because I felt like I did something very wrong already 🙈
earnest dock
And uhh that third attempt is like illegible im not even gonna try to read that
yeah u dont have to xD
🙈
sacred anchor
Hello! I am stying to solve this but I am doing something wrong all this time >....
you wanna divide both sides by x
it's really that simple
Then after that
gray hamlet
you wanna divide both sides by x
huh
where x doesnt = 0, divide with $x^{\frac{2}{3}}$
wraith daggerBOT
Roy
sacred anchor
where x doesnt = 0, divide with $x^{\frac{2}{3}}$
also works
my one youll need to take nth roots
gray hamlet
yea i like this cause it remains positive
sacred anchor
my one youll need to take nth roots
actually you can do without the nth roots
and just use indices
i think that's better
earnest dock
x^2 = 512x^3
I did 482 which threw me off.... I calculated 8*64 wrong 🙈
ty guys!!!!
sacred anchor
what's your value of x?
gray hamlet
huh
gray hamlet
x^2 = 512x^3
here you divide both sides with x^2 then with 512
earnest dock
OH!
1/512=x
👀
is.... that correct?
This was the second equation I had to do. Significantly easier for me tbh. 🙈
gray hamlet
This was the second equation I had to do. Significantly easier for me tbh. 🙈
thats not right tho
look at the 2nd arrow
you forgot something
gray hamlet
huh
earnest dock
you forgot something
thank you x'D I keep making mistakes like this....
gray hamlet
getting worse
gray hamlet
its just there a 2 you forgot about
earnest dock
earnest dock
you forgot something in the 3rd arrow
I feel ashamed. I should not rush and properly write things down.
gray hamlet
no dont be
this is good
it takes my classmates more tries than you and they are in the best high school of hungary
earnest dock
thats encouraging. thank you! ❤️
(but my.... poor classmates gonna have nightmare time later)
I shall close this one. thank you everyone (:
gray hamlet
np
earnest dock
.close
nocturne spear
cedar kilnBOT
nocturne spear
Good evening.
hello
potent echo
I'm here to help you
civic heron
Ominous entrance
nocturne spear
I'm here to help you
ok..
abstract breach
did you make a drawing? it usually helps with such problems
potent echo
Can we start?
marsh mesa
Do you know that this is not a physical discord?
potent echo
When solving this problem, we are essentially stepping into the rich history of motion and relative speed,
which dates back to the work of Galileo Galilei in the early 17th century.
nocturne spear
did you make a drawing? it usually helps with such problems
yeah
didn't help much tho
abstract breach
can you show it?
nocturne spear
yeah 1 sewc
potent echo
Galileo was one of the first to formalize the concept that the distance covered is the product of speed and time,
namely:
$$
\text{distance} = \text{speed} \times \text{time}.
$$
wraith daggerBOT
Henry Whitmore
potent echo
Now, let us apply this principle to Claire and Charles.
Are you ready? @nocturne spear
nocturne spear
im ready young sheldon
potent echo
Good.
Claire walks with speed
$v_C = 6 \ \text{km/h},$
while Charles cycles with an unknown speed
$v.$
wraith daggerBOT
Henry Whitmore
nocturne spear
Henry Whitmore
yes
potent echo
Normally, they meet at the library, at a distance L from the starting point.
nocturne spear
yes
potent echo
If Charles leaves $h$ hours later, then their times must be equal at the meeting point:
$$
\frac{L}{6} = h + \frac{L}{v}.
$$
wraith daggerBOT
Henry Whitmore
potent echo
Ok so far?
nocturne spear
Henry Whitmore
why the + h
potent echo
Because Charles starts later than Claire
ember heath
what is the question tho
nocturne spear
Because Charles starts later than Claire
okay makes sense
potent echo
If Claire’s walking time to the library is $\tfrac{L}{6}$, then Charles’ cycling time is $\tfrac{L}{v}$. But since he begins his journey $h$ hours after Claire, his “clock” is shifted forward by $h$. So to compare their total times (measured from the moment Claire leaves), we need to write:
$$
\text{Claire’s time} = \text{Charles’ delay} + \text{Charles’ riding time}.
$$
wraith daggerBOT
Henry Whitmore
potent echo
That's why
nocturne spear
what is the question tho
sorry, i thought i included it
nocturne spear
That's why
okay i agree
potent echo
Henry Whitmore
This equation reflects the simple but powerful algebra introduced in the Islamic Golden Age
by mathematicians such as al-Khwarizmi, who gave us the very word "algebra."
true plank
Sheldon?
potent echo
My name is Henry Whitmore.
ember heath
sounds like a madeup name no
ember heath
sorry, i thought i included it
i think claires speed is irrelevant to the question..
delay of claire(20 mins) = extra distance (3km) created
so speed of charles = distance/time
nocturne spear
i think claires speed is irrelevant to the question..
delay of claire(20 mins) =...
but what is the time for charles
nocturne spear
20 min?
nocturne spear
yes
potent echo
i think claires speed is irrelevant to the question..
delay of claire(20 mins) =...
No, it's not true
ember heath
No, it's not true
alr just glanced at it..if its wrong then u can continue
potent echo
The 20 minutes is a delay in time, while the 3 km is a difference in distance.
To connect time and distance, you need Claire’s walking speed.
potent echo
yes
On the special day when Claire is $20$ minutes late, i.e. $\tfrac{1}{3}$ of an hour,
they meet instead at the swimming pool, which is $3$ km before the library, so at $(L-3)$.
wraith daggerBOT
Henry Whitmore
nocturne spear
Henry Whitmore
yh
wraith daggerBOT
Henry Whitmore
potent echo
Yes?
nocturne spear
yes
potent echo
Now, by subtracting the second equation from the first, we eliminate $h$ and $L$
wraith daggerBOT
Henry Whitmore
potent echo
I have to make a clarification.
This is a technique reminiscent of the method of elimination used by Diophantus in Ancient Greece, did you know?
nocturne spear
This is a technique reminiscent of the method of elimination used by Diophantus ...
nope
this looks like simultaneous equations
night wedge
I thought Diophantus was all about integer equations?
potent echo
$\left(\frac{L}{6} - \Big(\tfrac{1}{3} + \frac{L-3}{6}\Big)\right)
= \left(\frac{L}{v} - \frac{L-3}{v}\right).$
wraith daggerBOT
Henry Whitmore
potent echo
Now, by subtracting the second equation from the first, we eliminate $h$ and $L$
From this
wraith daggerBOT
Henry Whitmore
nocturne spear
nice
potent echo
Thus, Charles cycles at a speed of 18 km/h.
cedar kilnBOT
potent echo
I thought Diophantus was all about integer equations?
Do you want to discuss this?
cedar kilnBOT
Available help channel!
karmic field
what is this setting coefficients thingy ?
cedar kilnBOT
what is this setting coefficients thingy ?
crimson delta
the things in front of the cos() terms have to be the same
and the things in front of the sin() terms have to be the same
flint plinth
to see why, try plugging in t = 0 and t = pi/(2 omega)
cedar kilnBOT
@karmic field Has your question been resolved?
karmic field
to see why, try plugging in t = 0 and t = pi/(2 omega)
i see ok ty
cedar kilnBOT
i see ok ty
karmic field
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
dense jewel
I dont know how to do this question and have a few hours pls help: A tennis tournament starts with 117 players. If a player is eliminated after losing three matches, what is the least possible number of matches played when 4 players are left?
cedar kilnBOT
@dense jewel Has your question been resolved?
rain idol
$117 - 4 = 113$ players have been eliminated throughout the course of the tournament. Since each player can only lose 3 matches before being eliminated we do as such: $113 \cdot 3 = 339$. Therefore, the minimum number of matches that have been played is $339$.
wraith daggerBOT
lily
rain idol
This obviously makes the assumption that the 4 remaining players did not lose a single match, which would result in the least amount of matches played
muted bear
!nosols
cedar kilnBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
muted bear
😮💨
rain idol
Oops sorry
glacial beacon
Suppose the number n, is described with lambda calculus format:
1 -> lambda f : lambda x : (f x)
2 -> lambda f : lambda x : (f (f x))
3 -> lambda f : lambda x : (f (f (f x)))
.
.
.
Now, let s be a lambda function, such that (s n) = lambda x : lambda y : x if n = 0, and (s n) = lambda x : lambda y : y if n is otherwise.
glacial beacon
For additional information, n is a Church numeral.
actually nvm i figured it out
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
honest jasper
Hey am I going in the right direction with this question?
cedar kilnBOT
Hey am I going in the right direction with this question?
honest jasper
Question 5
abstract pollen
Question 5
an easier way would just be to do $\varepsilon=\min(|y-1|,|y+1|)$
wraith daggerBOT
Xetrov
abstract pollen
there's not much reason for you to consider epsilon wrt x
honest jasper
an easier way would just be to do $\varepsilon=\min(|y-1|,|y+1|)$
Ohh makes sense
abstract pollen
often especially on problem sheets the chosen epsilon is quite simple
in fact, to be safe I'd even divide it by three
honest jasper
Wait so for this question we don’t need to include an arbitrary point (a,b) in our solution?
hazy yarrow
Can someone help me simplyfing this?
cedar kilnBOT
Can someone help me simplyfing this?
honest jasper
an easier way would just be to do $\varepsilon=\min(|y-1|,|y+1|)$
wait im so sorry but im having a hard time understanding this
abstract pollen
wait im so sorry but im having a hard time understanding this
hi
so U is just a horizontal band
and pick any point $u \in U$, then if you draw two vertical lines from $u$ to get to the boundary of $U$
honest jasper
yes
wraith daggerBOT
Xetrov
abstract pollen
their lengths are $|y-1|$ and $|y+1|$
wraith daggerBOT
Xetrov
abstract pollen
honest jasper
for my initial epsilon < dist((arbitrary poinit) - (x,1)) how should i rewrite it
cause you said making it with respect to x makes it harder
cedar kilnBOT
@honest jasper Has your question been resolved?
honest jasper
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
vale ermine
the v in braces represents scalars, is this a subspcae of r infintiy
crimson delta
"all vectors of the form"
silent scroll
is the answer for 9 1/square root of 2x+1? i alr answered 8 its 4
frail citrus
is the answer for 9 1/square root of 2x+1? i alr answered 8 its 4
!occupied.
cedar kilnBOT
is the answer for 9 1/square root of 2x+1? i alr answered 8 its 4
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).
wraith daggerBOT
fröööööken
cedar kilnBOT
Available help channel!
fleet coyote
yo
last apex
what is your concern
native heath
what is your question
fleet coyote
what is your concern
im not sure how to get from line 4 to line 5
i also dont understand what events to consider
last apex
what they did is they split into 5 cases on the first coin tosses
tail
head tail
head head tail
head head head tail
head head head head
these cases are disjoint, so we use the law of total expectation (correct me if I referene the wrong statement)
fleet coyote
what they did is they split into 5 cases on the first coin tosses
tail
head tail...
why not consider
tail tail
that still increases the value of e
last apex
it would be included in the first case
if you know there is a tail at the start then you are in the same situation as you are were at the beginning but you already made 1 coin toss
fleet coyote
if you know there is a tail at the start then you are in the same situation as y...
but why doe we consider head tail
and not
tail head head
last apex
we do consider head head tail
fleet coyote
we do consider head head tail
i meant other way around sry
i dont get why we necessarily consider head events
the objective is to get 4 heads
last apex
these are 5 cases where in each of them we can relate the expected value to the one in the beggining
exactly because we end in a tail or we reached our goal
fleet coyote
these are 5 cases where in each of them we can relate the expected value to the ...
why dont we consider tail head
because thats also a unique option
idk if im missing something sorry
i just odnt
i get for expected values you only consider the relavent events
but im not getting why tail head is irrelevant
last apex
why dont we consider tail head
its included in the first case
the cases cover everything
thats the point
fleet coyote
its included in the first case
is it because were considering how many consecutive flips hes getting
so the only thing that matters are consecutive flips
last apex
its because the first case contains all series of flips that start with a tail
and in your case we start with a tail
fleet coyote
so case 1 is first t
case 2 is second t
and so on
until we get to 4 t
because afte rthat it doesnt matter
and then its just p(case) * value of case
last apex
what they did is they split into 5 cases on the first coin tosses
tail
head tail...
these are the cases
fleet coyote
these are the cases
because nothing else would eb relevant to consecutive head flips
isee
last apex
and then its just p(case) * value of case
yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
latent citrus
I've deduced that it is not B or D, as if they are true, then A or C are also true. The answer is A, but I am unsure as to why, because surely if something is true for x^2+1<1 it is also true for <2?
floral arrow
Where did you get the answer? Is there an answer key? If so, does it only say that it's A without explanation?
Oh I think I misinterpreted it, all the options are about the same statement
Consider the statement [ x^2 < 1 or x^2 = 1.5 ], then only A is correct
(could also just be [ x^2 < 1.5 ] or even [ x^2 <= 1 ] )
@latent citrus
latent citrus
ahh ok
so if A is true for a statement, C is also true
wait the other way around
latent citrus
im still a bit unsure tbh
floral arrow
(could be true for other values too, but that doesn't matter)
latent citrus
surely if x^2=1.5 then C is true but not A
floral arrow
Well, the statement [ x^2 < 3 ] satisfies both A and C, for example
latent citrus
yes
floral arrow
surely if x^2=1.5 then C is true but not A
That's not how it's worded
If the statement is only [ x^2 = 1.5 ], then none of the options are correct
latent citrus
ah yes
floral arrow
Consider naming the statement, for example P
Option A says: x^2<1 => P
Option C says: x^2<2 => P
In option C, P needs to be true when 1 <= x^2 < 2 as well
So option A is less restrictive
latent citrus
i think its starting to make more sense