.close
#help-0
raven field
sharp wharf
lone heartBOT
quartz relic
What is 1+1
lone heartBOT
What is 1+1
night geyser
.close
lone heartBOT
chrome spade
what is cardinality of n ?
vale wigeon
what is cardinality of n ?
!occupied
lone heartBOT
what is cardinality of n ?
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).
Available help channel!
orchid perch
only total functions can have inverses right?
lone heartBOT
only total functions can have inverses right?
orchid perch
because if its not a total function it cant be injective?
glacial patrol
total functions can be injective. Injective just says $\forall y_1,y_2 (f(y_1) = f(y_2) \implies y_1 =y_2))$
ocean sealBOT
992qqoloy
glacial patrol
If f(y1) or f(y2) doesn't exist then obvs theyre not equal
So the implication is true since the start is false
lone heartBOT
@orchid perch Has your question been resolved?
mortal trellis
you can just make the domain smaller and then you have a total function
swift tangle
How can I graph the function F(n) = the sigma notation formula above in Geogebra?
stark crater
That summation makes no sense
You are summing from 0 to 0. Idk about geogebra but if you thought you knew how buts it not working, that is probably the issue
vale wigeon
How can I graph the function F(n) = the sigma notation formula above in Geogebra...
are you sure you didn't screw up this notation
cause it looks screwed up to me
median oar
How can I graph the function F(n) = the sigma notation formula above in Geogebra...
You’ll just have 18x, 36x, 54x, …
Wait what
n to n
swift tangle
Sorry, yes you're right it's a problem of variables.
18n is the intended equation
swift tangle
You are summing from 0 to 0. Idk about geogebra but if you thought you knew how ...
I haven't tried putting it in Geogebra as I have not found a way of doing it
stark crater
This still makes no sense
swift tangle
hm
stark crater
You do not sum from n=smth to n
Cuz that would just be 0
Maybe you want something like k=0 to n of 18k
swift tangle
I'm not sure I do understand what you're saying
starts at n=0. f(0) would be 0, yes. f(1) = 18. f(2) = 0+18+36
the pattern continues
stark crater
For f(1)=18 example, you are saying n=1, but the sum says n=0, which is it?
swift tangle
what sum are you refering to
stark crater
You do not sum from n=smth to n
Whoops did not mean to reply to that
Basically what im saying is your defining the same variable as 2 different values
swift tangle
n=0 indicates that, for example, f(3) would be f(0)+f(1)+f(2)+...
if n=1 then we would have f(3)= f(1) + f(2) +...
this is how I understood this at least
stark crater
n=0 indicates that, for example, f(3) would be f(0)+f(1)+f(2)+...
if n=1 then w...
I get what you are trying to do, im just pointing out a notational error
That if you try to enter in geogebra or any other calculator will cause errors
stark crater
Basically what im saying is your defining the same variable as 2 different value...
I think you just need to stare at it for a minute and think about this
swift tangle
I think you just need to stare at it for a minute and think about this
Yeah I fail to grasp what I have done wrong
do you mind showing what the correct notation is supposed to look like?
stark crater
Yeah I fail to grasp what I have done wrong
do you mind showing what the correct...
Change the circled n’s to any letter besides n
normally we use i,j,k
but as long as its not n it is fine
swift tangle
Change the circled n’s to any letter besides n
The majority of the sigma notations do look indeed like you're way of doing it, okay
can you explain why putting n here doesn't work, though?
stark crater
Yeah
Tell me what the n at the top of the sigma is equal to
If you are trying to do f(3)
swift tangle
okay, then I believe I got it
stark crater
Btw from my 1 minute google search it appears you would do something like
f(n) = Sum(18i, i, 0, n)
Ok I have came to the conclusion that plotting it is impossible (you can still calculate values though, it just wont plot it). ChatGPT also agrees with me but its knowledge only goes back to sept 2021
lone heartBOT
@swift tangle Has your question been resolved?
swift tangle
Ok I have came to the conclusion that plotting it is impossible (you can still c...
apologies for late reply
thank you for going through the hassle for me, it’s a bummer tbh that it doesn’t allow it
maybe converting it to one of those (n-1)n functions will work for some of the notations
.close
rocky crescent
Percent changes
$____ increase by % = $
$_____ increase by %= $_
$____ decrease by % = $
$_____ decrease by %= $
10,20,25,35,40,50,60,70,75,80,90,100
Rules:Use each number once
Fill in the gap with the given number
dreamy osprey
chill
rocky crescent
alright
dreamy osprey
dont ping anyone till 15 min
rocky crescent
sorry
dreamy osprey
whats your question?
rocky crescent
i am new
Percent changes
$()increase by % = $
$()increase by %= $_
$()decrease by % = $
$()decrease by %= $
10,20,25,35,40,50,60,70,75,80,90,100
Rules:Use each number once
Fill in the gap with the given number
this
rocky crescent
i don’t think so
dreamy osprey
is this off a worksheet?
dreamy osprey
ah gotcha
rocky crescent
tysm
dreamy osprey
ok, easy peasy
rocky crescent
alright
dreamy osprey
can you use a calculator in your exam
rocky crescent
yae
dreamy osprey
super easy peasy
rocky crescent
:0
dreamy osprey
fill in the numbers where ever
rocky crescent
mhm
dreamy osprey
then we will calculate the money
rocky crescent
exactlyyy
dreamy osprey
thats so stuipd
rocky crescent
that what i was saying
rocky crescent
alright
dreamy osprey
do you know how to do percents?
dreamy osprey
how fast can you do 25% of 60
rocky crescent
pretty much
dreamy osprey
lol
dreamy osprey
alright well an obvious one is 10,100,20
rocky crescent
mhm
dreamy osprey
25,60,75
dreamy osprey
figured
dreamy osprey
write those down and cross them out
rocky crescent
done
dreamy osprey
cool
rocky crescent
now for decrease
dreamy osprey
alright, what do you got
rocky crescent
so now 10,100,20,25,60,75 is gone
rocky crescent
oh alright
dreamy osprey
so, what's a trio that would work?
dreamy osprey
i mean, if you know how to do percents really well and your confident in your abilities, then I would ask an ai to just do it for you, as this is a pretty usless and tedious assignment
rocky crescent
ik
i am confident
but the ai
isn;t working-
he doesn't understand the assimignet
dreamy osprey
im sure you can figure it out
rocky crescent
alright
lone heartBOT
lone heartBOT
Available help channel!
uneven moss
how to get to the answer?
lone heartBOT
how to get to the answer?
uneven moss
wild umbra
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
uneven moss
well i tried it
uneven moss
fbd?
wild umbra
the free body diagram?
uneven moss
oh i havent learnt that? just draw the triangle separately?
wild umbra
ok no
uneven moss
oh-
split mantle
well i tried it
Usually you would like to have the triangle towards up.
wild umbra
what do you think the measure of this angle would be?
uneven moss
25?
wild umbra
yea good
now, can you do components of normal vector along horizontal and vertical axis?
uneven moss
of vector n?
wild umbra
yes
split mantle
now, can you do components of normal vector along horizontal and vertical axis?
Remember that drawing components, it should be drawn as dotted lines.
wild umbra
for x ais wouldnt that be Nsin25 and for y axis that would be Ncos25?
wild umbra
Remember that drawing components, it should be drawn as dotted lines.
i drew that from snipping tool lol, i cant handle my mouse for making line dotted lmao
wild umbra
yes
from n1 you can get the value of n from that you can then find F from second equation
vast sonnet
lone heartBOT
vast sonnet
Question number 3
When finding out a series of function
Do you first work out the difference between f(1), f(2), f(3) then work with the resulting ratio
Or is there a better method?
lone heartBOT
@vast sonnet Has your question been resolved?
vast sonnet
.close
jade wasp
A person tried by a three-judge panel is declared guilty if at least two judges cast votes
of guilty (i.e. a majority verdict).
Suppose that when the defendant is in fact guilty, each judge will independently vote
guilty with probability 0.85, whereas when the defendant is in fact not guilty (i.e.
innocent), this probability drops to 0.25.
1
If 70% of defendants are guilty, compute the conditional probability that judge number
3 votes guilty given that:
(a) judges 1 and 2 vote guilty
alpine sable
is it 0.85×0.7?
jade wasp
no idea
basically I use bayes theorem
so probability that judges 3 vote guilty given the others have
is equal to probability that the others vote guilty given three does times probability 3 voted guilty over probability 1 and 2 vote guilty
i have probability 3 votes guilty
it’s 0.7*0.85
it’s not given 1 and 2 vote guilty tho
alpine sable
<@&286206848099549185>
lone heartBOT
@jade wasp Has your question been resolved?
jade wasp
<@&286206848099549185>
these helpers aren't helping xD
jade wasp
<@&286206848099549185>
lone heartBOT
@jade wasp Has your question been resolved?
jade wasp
<@&286206848099549185>
jade wasp
<@&286206848099549185>
subtle flame
yes
jade wasp
hey man I'm stuck on this question
subtle flame
tell me
jade wasp
so basically I know I have to use Bayes theorem
I explained it above
@subtle flame Are you still here?
next brook
Cool it with the multiple Helpers pings. Those tend to make helpers annoyed at you, and therefore less likely to want to help at all, which is not in your interest.
lone heartBOT
@jade wasp Has your question been resolved?
green reef
Yeah then thag becomes k^2+16 for the discriminant I think?
jade wasp
yes
k^2+16 is strictly positive so discriminant is positive so two real roots
btw u need to go in the available channels for help
.close
eager iron
stealing this :D
lone heartBOT
stealing this :D
eager iron
going through old exams trying to make sure im all ready for next week
a spiral is drawn with halfcircles with centrum alternating at A and B. Start with centrum in A with radius (?) r > 0 för the smallest halfcircle and continue with bigger and bigger halfcircles like in the picture. what's the total curvelength for a spiral that's built from n halfcircles? the answer should be as simplified as possible.
so, my attempt at this was something like this
first off, paint it on my own
and name each halfcircle L1, l2 etc
then make a small table to see the trend
and since the circumference is 2pir, this is pi * r
and then the radius increases with R each time, starting at 1 going up.
so now I want an expression for this that's applicable to the N'th halfcircle
so since we can see that we're just increasing by 1, we want to start at 1 and go up until n, multiplying m* pi* r and adding them together
which gives us this beautiful little thing
feeling all good about myself i decided to check the grading paper aaand
is my answer not good enough? or is it even possibly wrong?
would i possibly lose points for the way i wrote this? is there a better way to write this mathematically?
fallen verge
$\sum_{m=1}^n m = \frac{(n)(n+1)}{2}$
ocean sealBOT
GarlicB
fallen verge
This is what is called a closed form
Generally, you want to get rid of sums, and most sums can boil down to a formula
eager iron
but the formula itself is correct?
fallen verge
Yes
You basically are one step away from what they consider the right solution though
eager iron
im looking at this and my brain outright refuses to accept that npir + 2npir + 3npir + 4pir is the same as 10pir
could also be that i've sat with math for too long today 😅
ok thank you for the help
wishing you the best <3
.close
alpine sable
How do you find the height of a shape when you only have the width and length?
gray isle
what's the original question
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
what's the original question
This one, its in french but in translation its asking me to find the total area of the ramp.
gray isle
are you given more info
alpine sable
alpine sable
are you given more info
This is the other page
But it doesnt really explain anything else..
Its just asking me to describe what type of shape these things are
It just basically gave me the width (1.2m) and length (2.4m)
I've asked it before, but to this day I'm still not sure
So I skipped it, but now I need to do this.
Help please 
Someone 
frosty oxide
tu connais la pente de la piste?
si c'est incurvé ça semble impossible à calculer sans autre information
alpine sable
tu connais la pente de la piste?
Non malheureusement.
alpine sable
si c'est incurvé ça semble impossible à calculer sans autre information
Oui , j'ai parlé avec mon prof
Il m'a dit que je peux sauter ce question
Merci bcp! Je vais fermè ce probléme
proven tendon
lone heartBOT
vale wigeon
these are two geometric series.
do you know what a geometric series is, and how to find the sum thereof?
vale wigeon
missing parentheses, but yes. they did.
slim chasm
please can someone explain how SUVAT equations link to graphs?
stark path
The formulas of motions right?
slim chasm
yeah
stark path
It'd be better to refer an indivitual formula's graph at a time
Mostly in those equations time 't' is used in the X axis where 's', 'v', 'a' are used in the Y one
lone heartBOT
@slim chasm Has your question been resolved?
weary abyss
Can someone walk me through this problem
lone heartBOT
Can someone walk me through this problem
tacit arch
Can someone walk me through this problem
,tex .FTC2
ocean sealBOT
riemann
weary abyss
can i replace my prime symbol with d/dx
tacit arch
yea try it
weary abyss
its not d/dt right
can i have d/dx in the front as well?
instead of the right hand side
tacit arch
...
tacit arch
instead of the right hand side
weary abyss
read
https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab...
i think i got it but im stuck on a part
i have d/dx[F(x^5)-F(x^3)]
so now i just do [ f(x^5)(5x^4) - f(x^3)(3x^2) ]
is that right
tacit arch
right
tacit arch
I have 5x^4 ln(1 + 4x^10) - 3x^2 ln(1 + 4x^6)
yes?
tacit arch
yes
alpine parrot
Anyone help
lone heartBOT
Anyone help
exotic canopy
do you understand what parallel and perpendicular mean?
lone heartBOT
@alpine parrot Has your question been resolved?
exotic canopy
parallel means they do not intersect
alpine parrot
What does that mean
Keep in mind I got a 0 on my maths test
And I’m in year 22
I mean 11
alpine sable
Should you not be on discord if you are 11?
lone heartBOT
@alpine parrot Has your question been resolved?
plucky chasm
How exactly do we get (sinu)/(1+cosu) and (1-cosu)/(sinu) from tan u/2 = +-sqrt((1-cosu)/(1+cosu))?
real wind
inside the sqrt
if you multiply the top and the bottom of the fraction by 1+cos u
u get 1-cos^2 u on the top
which is the same thjng as sin^2 u
and on the bottom you get (1 + cos u)^2
real wind
u get 1-cos^2 u on the top
this is difference of squares btw
real wind
which is the same thjng as sin^2 u
this is pythagorean identity
real wind
and on the bottom you get (1 + cos u)^2
and this is just cuz ur multiplying it by itself
so if u have sin^2 on the top
and (1 + cos)^2 on the bottom
the square root of that is just sin / (1 + cos)
same principle for the other one
except this time multiply both sides by 1 - cos^2
top will become (1 - cos)^2
oops made a mistake
i’ll edit those portions
ok yeah
and bottom will become 1 - cos^2
or sin^2
same principle square root it
and you get (1 - cos) / sin
does that make sense sorta??
plucky chasm
It makes a ton of sense!
plucky chasm
A clarifying question if you've got the time: I'm trying to write this out so that I can see how it works.
real wind
go for it
plucky chasm
Oh wait, no. I made a math error.
So we're eventually left with sqrt((sin^2u)/(1+cosu)^2), which we then take the square root of and are left with just sinu/1+cosu
real wind
yep
plucky chasm
Sick.
real wind
that’s if you multiply both sides by 1 + cosu
plucky chasm
Indeed, and if you multiply by 1 - cosu, we're left with 1-cosu / sinu.
real wind
yep
plucky chasm
Rad. Hey, thanks a ton! You've answered this exactly the way my brain needed it to be answered. I really appreciate it!
real wind
lol no problem
plucky chasm
.close
empty bough
I am not sure the purpose of the proof. What am I trying to find and why am I trying to find it? Also how do we choose what value to shove in?
empty bough
Please ping me if you reply
lone heartBOT
@empty bough Has your question been resolved?
lone heartBOT
@empty bough Has your question been resolved?
empty bough
<@&286206848099549185>
lone heartBOT
@empty bough Has your question been resolved?
lone heartBOT
@empty bough Has your question been resolved?
quartz lance
I tried implicit differentiation, which is essentially adding y' to y in the function
quartz lance
x^2 * y - 4x^2 = 0
First the Product rule
2xyy' + x^2y' - 8x = 0
send the 8x over and organize the y
y'(x^2 + 2xy) = 8x
y' = 8x/x^2 + 2xy)
now I'm not sure if I should factor the denominator, which would give me x(x+2y)
if I plug in (2,4). I get either 1.6 or 0.8
but it says both answers are wrong, did I make a mistake somewhere, perhaps when differentiating
alpine sable
im getting -8
quartz lance
what did you do differently to me?
alpine sable
quartz lance
well we have completely different answers for the differentiation
let me try yours
cause here it's asking for y' not dy/dx
alpine sable
same thing
quartz lance
ok
quartz lance
yea cause it's supposed to cancel out the x
alpine sable
yea cause it's supposed to cancel out the x
You dont have to but u can
quartz lance
does it give the same answer?
alpine sable
yes
quartz lance
quartz lance
I'll do it again
alpine sable
I'll do it again
alr
dark hull
i forgar on how to do the steps in i think pre algebra
lone heartBOT
i forgar on how to do the steps in i think pre algebra
subtle birch
I'm still not completed with my telepathy skills
So for now you have to send a pic of the problem for more context
subtle birch
Okay so you are supposed to solve for z?
dark hull
i think
subtle birch
What have you tried?
dark hull
well my friend said to just multiply the variables
subtle birch
MULTIPLY?
dark hull
idk
subtle birch
Since we need to solve for z, we must isolate it on either side LHS or RHS
so what can you think of?
dark hull
umm canncelling something out
subtle birch
Hint:||It's just adding a number both sides||
subtle birch
Add such a number so that the RHS only contains the 'z'
the number -8 would cancel out with the number added
subtle birch
$-3=z-8$\$-3+8=z-8+8$
ocean sealBOT
B-eard
subtle birch
Adding '8' on both sides
dark hull
wait so its 5=z
subtle birch
yes
subtle birch
welcome 
dark hull
.close
alpine sable
lone heartBOT
alpine sable
How do I do part ii?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Struggling with problem 2 its not difficult I just dont understand what is happening
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
why is everyone but me and the other discrete math guy getting help
this is bullshit
lost wasp
@alpine sable Do you understand what you are being asked?
alpine sable
<@456226577798135808> Do you understand what you are being asked?
utterly no clue
also I cant do the truth table for P^S => R
lost wasp
We can start with #2
You have to come up with P, S and R such that P and S will imply R
I will give you an example, I think it's the best way
If you define
P : Visiting Canada
S : Visiting France
R : Visiting at least two continents
Then (P and S) implies R
Because if P and S are true, then R is necessarily true
alpine sable
so p and s have to be true
lost wasp
No, it means that if you suppose that they are true, then R will necessarily be true
alpine sable
No, it means that if you *suppose* that they are true, then R will necessarily b...
I have utterly no clue what your saying
it is binary
it is true or it is false
lost wasp
All statements are true or false
isn't synonym of
For every statements, we know if that is true or false
You are assuming the latter
If the latter was true, why would the course even exist?
lost wasp
What do you want me to reply then?
alpine sable
alpine sable
What do you want me to reply then?
ts
lost wasp
ts
alpine sable
ts = this shit
lost wasp
I replied ts
alpine sable
dude i just need to know how to write a truth table
idk how to write it if implies is involved
lost wasp
Do you think people will care to help you if you don't even care yourself?
alpine sable
im here bc I care
im trying to do math
not philosophy
for the love of god please help me
lost wasp
i dont care about math at all
That's not what you said here though
alpine sable
im actually begging
why are we arguing about why im in math
ts is irrelevant
ill write you a 10 page paper in a day math just isnt my thing
lost wasp
Would you help is a soccer player if they don't care at all about playing
I'm sure you would not
alpine sable
im a soccer caoch I have tons of players that dont wanna play
i stil help them
bc its my job
lost wasp
You waste your time though
alpine sable
<@&268886789983436800> bro is arguing philosophy with me I just need help
like holy fuck why are you being so petty
<@&286206848099549185> for the love of god
lost wasp
I was trying to help you but you didn't even try to understand what I meant and said right away you didn't care about math, all of this even after you were being impatient for getting help (see the beginning)
tardy stag
wlmmm i don't think you being here is helping at this point
lost wasp
Alright, sorry 👋
night geyser
i mean, their example was meant to help you understand the problem with a practical example
i dont think you have to be rude just for them trying to help
alpine sable
i didnt understand what he meant and then he barraged me with philosophy which I THEN PROVED WRONG
im on a time crunch
i was completely reasonable in what I said
I sent the example to get back on trakc but he wanted to continue shitting on me
liek holy fuck how are you defending him right now
alpine sable
If the latter was true, why would the course even exist?
with this
alpine sable
i mean, their example was meant to help you understand the problem with a practi...
it was math until this
and then I explained myself
night geyser
no need to keep pinging them after they left the convo
alpine sable
I pinged you
night geyser
regardless, the point is that the statement:
(P and S) implies R
means that, whenever (P and S) is true, R is also true
in implication statements, we don't care about situations where the premise (left hand side) is false
we just mark those as "true"
you may wish to check your truth table for implication
so when constructing a truth table for (P ∧ S) ⇒ R, whenever P ∧ S are false, the entire implication will be true
night geyser
that said, the truth table you wrote here does not have enough rows
there are 3 statement variables: P, S, and R
but you only have two variable columns (on the left of the table)
you should have 3 variable columns, for a total of 8 rows
i.e. your table should look more like this
i left out the entries for the implication (except the first one)]
note that we're considering all possible values for the three variables
there are 3 variables, and each have 2 options (true or false), so we expect to have 2^3 = 8 rows
and you can count the rows in my image to double-check that
in any case, as mentioned, for implication statements, whenever the premise (left hand) is false, the entire implication is true "by default"
so we can fill in all those
and are left with only one "blank", (true ∧ true) ⇒ false
as you correctly observed in your table, (true ∧ true) is just true
so this last remaining row is true ⇒ false
if you consult the appropriate row of your implication truth table, you should be able to fill in that last spot.
(to clarify: the one between the white and red Ts. i know that my writing was messy)
as for coming up with an example, they already provided one, but the idea is that (P ∧ S) ⇒ R is saying "whenever P and S are both true, then R is true as well"
we do not care about cases where P is false or where S is false (as mentioned, the implication is true by default when its premise is false)
we only care about the case where P and S are both true
in that specific circumstance, the conclusion R must be true as well
for the implication to hold
night geyser
depends on convention.
unkempt birch
is there a difference?
night geyser
typically not
round geyser
depends on convention.
wait really? but wouldnt -> always just be something like 'approaches' or something
like in the limit
night geyser
wait really? but wouldnt -> always just be something like 'approaches' or someth...
no, you can usually distinguish from context
unkempt birch
yeah context wise
night geyser
well i mean in logic
in model theory, you sometimes see → for syntactic implication and ⇒ for semantic implication; but the distinction is not relevant to the question so i'd rather not occupy their help channel with discussing it
unkempt birch
alr mb
alpine sable
as for coming up with an example, they already provided one, but the idea is tha...
then whhy ar they all true
unkempt birch
because the only scenario when implication is false is when its TF
because then it would make no sense for the initial premise to be true but the implication to be false
night geyser
Think about it like this
Let's say Im a politician and I say "If I win the election, then I'll lower taxes"
This is an implication statement
I win election -> I lower taxes
Since there are 2 variables, we have 4 possibilities
I win the election and I lower taxes: I told the truth
I win the election and I did not lower taxes: I lied
So T -> T is true, and T -> F is false
Easy enough
But what if I lose the election?
unkempt birch
and if you didnt win the election, nothing happens
unkempt birch
^^^
night geyser
I only said I'd lower taxes if I won the election
So if the premise "I win the election" is false, the implication itself is true automatically
(careful not to confuse the entire implication with the premise or conclusion)
unkempt birch
so the only scenario when an implication is false is when the premise is true and the conclusion is false
so p is true, q is false, p -> q is false
night geyser
In other words, F -> T and F -> F are both T
unkempt birch
^^
night geyser
And yeah, the only situation in which an implication is false is when the premise is true, but the conclusion is false
This should match with how we use implications "in practice"
Like if I say "if x is an integer, then x² is an integer"
I can justify this statement by only considering the situation when x is an integer
I don't have to think about situations where x isn't an integer
Since the implication is true by default in those cases
In the case of (P and S) implies R, this means that the statement can only be false if the premise (P and S) is true, but the conclusion R is false
Hence every other row of the truth table will be T
unkempt birch
so we can fill in all those
second implication is false though
whys that not drawn
night geyser
Right, I omitted it
unkempt birch
oh ok
night geyser
Hoping they'd fill it in
unkempt birch
oh i did not read what you wrote lmfao
lost wasp
so we can fill in all those
It should be more clear about what are the last two columns actually are
night geyser
I wrote it informally with my mouse
Apologies if it's not entirely clear but I think if they actually read my text they'll understand what I'm trying to say
alpine sable
i cant get over that hist im actually still tripped pout i spent 30 minutes on problem 1A ill tank the test tomorrow
thank you for the help
alpine sable
It should be more clear about what are the last two columns actually are
go fuckl yourslef
night geyser
...
unkempt birch
just make sure you know the truth tables for the different functions
night geyser
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lone heartBOT
night geyser
Please don't be a dick to helpers even if you think they weren't helpful
lost wasp
and second collumn is the implication
Indeed, but my point was, it should be written because it can be confusing with R (instead of the implication) 😄
night geyser
Best of luck on your test
lost wasp
for the last column that is
At the first read I thought it was for R, since it was aligned with the R on the right
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marble crown
Can anyone tell where I’m going wrong
marble crown
Sorry bot
winged lava
Sorry bot
what happened to the (x+8)(x-3)
and it should be -8
also the limit does not exist as the denominator approaches inf as x -> -8
also this is wrong
it should be x^2/3 -4
marble crown
why the/3?
marble crown
what happened to the (x+8)(x-3)
i just havent written that yet as im seeng what to do
lone heartBOT
@marble crown Has your question been resolved?
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@marble crown Has your question been resolved?
subtle pewter
why the/3?
(x^1/3 -2)(x^1/3 + 2) = x^2/3 - 4
lone heartBOT
@marble crown Has your question been resolved?
tough lintel
lone heartBOT
tough lintel
with number (2)
im able to expand out the taylor polynomial to the 3rd order, set x = a+h
and subtract f(x+h) - f(x-h)
and get the equation for number 2
the rest after phi is just the error term
can i use the same process to dervive number 5?
i just do the same thing except i set x = a + h/2?
ripe mulch
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ripe mulch
how do i solve C
someon give me a hint
is it simultaneous equations?
cause i can make two equations
but like
i cant use eliminitation or substitution to solve it i think
vale wigeon
how do i solve **C**
have you solved parts a and b?
ripe mulch
yes
vale wigeon
ok right
so then you know the follwoing:
a + 2b - c = 1/2 d
-2a + 2b = d
multiply both sides of the first equation by -2 and see if you get any ideas from there
ripe mulch
oh wow
so i use the first and 2nd equation in the questions given to me
but i plug in value of x, y and k
and then through that
i add both of the equations
which gives me the equation very similar to this
which is uh
2a + b - c = 0
which means
p is 2
q is 1
and r is -1
strange fractal
Hello
echo socket
Are you dividing by a function?
echo socket
log_2(21)/log_2, this makes no sense
echo socket
Logarithms are injective, from log_2(21) = log_2(x) you directly have x = 21
stark path
U can just write x = 21
strange fractal
Oh
stark path
Since base is 2 in both sides
stark path
If u wanna add extra context u can go like this
log_2 (21) = y = log_2 (x)
=> 2^y = 21
log_2 (x) = y
=> 2^y = x
Hence x = 21
@strange fractal
But theres no need tbh
U shouldn't lose marks for that
lone heartBOT
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old sinew
Why is an empty set is an open set?
lone heartBOT
Why is an empty set is an open set?
old sinew
My gut says that it has to with false implication true or false is always true
vale wigeon
what's your defn of an open set
also like what class are you in so we don't saddle you with definitions irrelevant to it
old sinew
Let me define real quick
‘A’ subset of R is open, if for all a in A, there exists an epsilion neighbourhood of a which is fully contained in A
vague coral
an epsilon neighbourhood ???
old sinew
(a-e, a+e)
vague coral
more like there exists a ball of radius epsilon contained in A
vague coral
whats the notion of ball in a real line?
(a-e, a+e)
old sinew
more like there exists a ball of radius epsilon contained in A
there exists an interval of length epsilon from a?
vague coral
you work with only R ?
old sinew
I’m taking real analysis rn
but yeah i have complex too
So the ball is the just an interval in R right?
but a circle in C
vague coral
an open ball in R is like this :
B(a,r) = {x € R / |x-a| < r}, r>0
old sinew
makes sense, this is exactly my definition of epsilon neighbourhoods in R
vague coral
^
old sinew
Yeah, im trying to see if thats the case of being vacously true as I recall from logic and proof
I’ve seen cases if the antecedent is false, the implication will always be true
vague coral
if you take the complementary of the empty set in R which is R itself, R is neighbourhood of all his points and also contains all the limits of all his converging sequences
Therefore empty set is open and closed
quasi sand
if you take the complementary of the empty set in R which is R itself, R is neig...
yeah. also you can see it but definition of open set too. There's a definition " if every point's neighborhood is in that set then it is open" . so for Empty set every point satisfies it( to be more precise there's no point to check)
vague coral
yeah. also you can see it but definition of open set too. There's a definition "...
yea 🤔
quasi sand
also close since all limit point of that empty set is in that set right
old sinew
yeah. also you can see it but definition of open set too. There's a definition "...
so no points to check is same as being sufficient condition failing right?
The truth table of implication will be always true even if p is false
vague coral
so no points to check is same as being sufficient condition failing right?
i dont really like to reason like this tho but its a bit true 🤔
old sinew
idk, are they related?
vague coral
The best way to prove that a set is open is to show that his complementary is closed
old sinew
but i only have the definition of an open set
vague coral
ahh ?
old sinew
my textbook says the logical structure of open set definitions makes the empty set open
vague coral
then we can work by contradiction 🤔
vague coral
my textbook says the *logical structure* of open set definitions makes the empty...
hmm
old sinew
Here, even if p is false, the implication is always true
so here, p being if a element of A
‘A’ subset of R is open, if for all a in A, there exists an epsilion neighbourhood of a which is fully contained in A
quasi sand
‘A’ subset of R is open, if for all a in A, there exists an epsilion neighbourho...
yeah note that for all a in A
old sinew
yes
quasi sand
so here there's no a to check
old sinew
thats like getting into one of the last two rows in that table right?
quasi sand
thats like getting into one of the last two rows in that table right?
no how?
old sinew
because the statement is an implication?
quasi sand
actually truth table don't do anything here's atleast for your p
quasi sand
because the statement is an implication?
read it properly. we just have to check for all "a" right
so if there's no "a" means?
no element to check so it's obvious
old sinew
if for all a in A, there exists an epsilion neighbourhood of a which is fully contained in A then A is open
is this correct?
quasi sand
like (2,3) ... we only check for the elements inside the set. Honestly we don't care about other elements...
old sinew
no element to check so it's obvious
Makes sense
quasi sand
**if** for all a in A, there exists an epsilion neighbourhood of a which is ful...
yeah that's right
quasi sand
Makes sense
yeah it definitely would
quasi sand
as you didn’t give the sufficient condition
it is sufficient and necessary condition
lone heartBOT
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lavish holly
How do I rearrange the bottom intergral into the form of the first?
lavish holly
but that gives 1/lnx
in the bottom
wait nvm
i cant differnitate properly
let me try again
I get to the bottom left one, but there's still a u at the bottom
lone heartBOT
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lavish holly
<@&286206848099549185>
golden canyon
This is what you want right?
golden canyon
But there is also an x in the denominator in the original integral
Try adding the integrals
alpine sable
How is possible that ln(1+x) is an Infinite numbers of terms plus an arbitrary constant ?
alpine sable
The Infinite series stays the same but the constant can vary
So I can make ln(1+x) any value I want right ?
vale wigeon
no. at x=0 the thing is supposed to be 0 and that's how you fix C
alpine sable
Oh I see
Oh yeah I didn't read lol
to the end of the example
Thank you !
.close
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copper vigil
The two conditions are parallel I think(
And also in second condition, why "Ax = b has at most one solution x" can figure out "A has an left-inverse B"?
copper vigil
Why condition 1 is EXISTENCE and condition 2 is UNIQUENESS?
The context
<@&286206848099549185>
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empty bough
I am not sure the purpose of the proof. What am I trying to find and why am I tr...
Back at this…
lost wasp
Back at this…
The exercise is about writing a rigorous proof (with the definition of a limit) that $\lim_{x \to 1} 3x = 3$
ocean sealBOT
wlmmm
empty bough
The exercise is about writing a rigorous proof (with the definition of a limit) ...
I see
I tried to apply it the same way within this question
Would it still be applicable?
lost wasp
This looks good to me! 🙂
sand bolt
hi
sick garnet
x^2 was factored and cancelled out
sand bolt
bro i feel rllly dumb rn could u show this to me on paper or something
i rlly cant get my head around it
@sick garnet
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warm birch
a tv quiz program pays a contestant php 100 for each correct answer for 10 questions. if all 10 questions are answered correctly, bonus questions are asked. the reward for every correct answer is increased by php 50 for each bonus question correctly answered. any incorrect answer ends the game. if 2 bonus questions are answered correctly, the contestant receives php 200 for each of the 12 questions. if a contestant won more than php 3500, how many correct questions must have been answered correctly
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a tv quiz program pays a contestant php 100 for each correct answer for 10 quest...
@warm birch Has your question been resolved?
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warm birch
.close
neat mango
Try plugging in some real numbers. If, for example A = 3, then (5A - 3)^2 = (15 - 3)^2 = 12^2 = 144
swift grail
because (5x -3)^2 is not equals to 5x^2 + 3^2
theres a bracket there that you need to respect
no the ^2 dosent uh
not how it works
haha
you need to treat everything in the bracket as a whole
let me illustrate
neat mango
If what you're saying is true, then 25A^2 + 9 = 25*9 + 9 = 234 must be equal to 144, which is not the case
swift grail
the bottom is what your misconception is
its just not how it works
what the bracket means is that you need to take x + 1 as if its together
which means you cant put the square inside the bracket like the bottom example
its a common misconception, dont worry
no
its 25x^2
you need to square the 5 as well
yes
but
when you add something to the 25
and square it
such as 25 + 1
25^2 + 1^2 is not equls to 26^2
so the rule of thumb here is
any addition inside a paranthesis that is raised to a power, you cant bring the power inside the paranthesis
swift grail
as shown here
no
u cant
thats illegal
idk i dont speak math english
but (5+5)^2 is equls to 10^2
if you add the 2 fives together
then square
yes
correct
then you use whatever method thats taught to you
here we call it rainbow method
idk
dont see it as ^2 see it as whatever inside the paranthesis multiplied by itself n times
maybe itll be clearer though it means the same thing
wdym not variable
like integers?
like not x
yeah
so u can add those
and square the whole thing
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tepid prism
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tepid prism
been stuck for more than 30 mins ,help me try some other way to solve it
jagged cobalt
whats u=
tepid prism
(xsqr +ysqr +zsqr) -root