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#help-27
restive river
Okay maybe this question is a bit too excel-y, but I am just looking to understand the Math behind it.
Here is the gist of it; there is a concept called cannibalisation in accounting, which is the number of customers that would transition from using an old product to a new product you just introduced (Think about Coca-cola and diet cola, for example)
This example I have here mentions a scenario of someone selling regular umbrellas and then introducing wide umbrellas to their sales; you know that 25% of the customers would end up transitioning to purchasing wide umbrellas, which ends up giving you a larger profit than when you had only just sold the regular umbrellas (You will be earning 1,150 instead of 1,000)
My question is relating to how they calculated the maximum cannibalisation rate, which is the percentage of how many customers could transition from buying your old product to your new product without giving you less profit than if you had only sold the regular umbrellas
devout snowBOT
Okay maybe this question is a bit too excel-y, but I am just looking to understa...
restive river
The way they calculated that is by taking the profit you got from your wide umbrellas (400) and divided it by the contribution margin of your regular umbrellas (10) and then further divided that by the sales of your regular umbrellas (100)
I can't quite seem to understand why those calculations make sense?
arctic field
you're actually here
devout snowBOT
@restive river Has your question been resolved?
restive river
<@&286206848099549185>
dull otter
hmmmm
devout snowBOT
@restive river Has your question been resolved?
dull otter
The way they calculated that is by taking the profit you got from your wide umbr...
the amount of sales is 400?
dull otter
The way they calculated that is by taking the profit you got from your wide umbr...
you can represent this by this
n stands for new product
e stands for old product
one second forgot somethin
@restive river
and your question is basically asking,
Why does this big formula equal this other simpler formula?
Well, if you recall
Contribution = S(F-V) where S is the sales, F is the fixed price and V are the variable prices
it should be easy to figure this out
ill leave this up to you
@restive river any minute now...
it should click
and you should go like "ohhhhh"
any minute now
the answer is like
right there
this is gonna be us
ill be drake and you will be lil yachty
lixera any minute now...
you may even close this channel instantly
since the answer
is right there
it makes total sense
super easy to understand
dull otter
and your question is basically asking,
Why does this big formula equal this oth...
right here...
you just need to figure out why they are equal
thats the question you asked
any minute now...
dull otter
in case you dont understand the formula...
its just a matter of notation
and rewriting...
dull otter
The way they calculated that is by taking the profit you got from your wide umbr...
you gotta look at the big picture...
and i mean the picture i sent
explains it all...
devout snowBOT
@restive river Has your question been resolved?
dull otter
@restive river any minute now...
tame bay
how to solve (-1-sqr2)^2 ? learning basic geometry (9th grade) and im not the proficient with square roots
devout snowBOT
how to solve (-1-sqr2)^2 ? learning basic geometry (9th grade) and im not the pr...
formal haven
how to solve (-1-sqr2)^2 ? learning basic geometry (9th grade) and im not the pr...
do u mean simplify
tame bay
yeah i do mean that
restive river
how can i prove that AE is a diameter?
devout snowBOT
how can i prove that AE is a diameter?
devout snowBOT
devout snowBOT
Available help channel!
restive river
if we have an improper intergral that is a discontinuous integrant, how do i know if it approaching from the left or right
devout snowBOT
if we have an improper intergral that is a discontinuous integrant, how do i kno...
restive river
for this improper intergral, how did we know it was approaching 3 from the left in the limit
warped relic
Okay so
We observe the function
And we find the locations of our undefined points within our bounds
restive river
yup so when x = 3
warped relic
Yepp
So when x = 3, the function is undefined
Now x=3 is exactly the upper bound
And if we drew a diagram, we will see that we will need to approach x = 3 from the left
restive river
so like for a lot of improper intergrals, its best to visualize the graph
warped relic
Yep
Later on with enough experience, you'll see that upper bounds need to be approached from the left
And lower bounds need to be approached from the right
But you will need experience to have that in your mind
restive river
experience because it doesnt apply to all cases correct?
devout snowBOT
@restive river Has your question been resolved?
restive river
nothing makes sense to me in math 💀
warped relic
Aww
Math needs a bit of focus and a good ol' cup of your favorite drink and a bit of time to solve the problems you have for homework
And it's all a game of using rules to your advantage
restive river
im not giving up
ever
on that topic, could i ask about the comparrison test as well
for improper intergrals
it is confusing me
warped relic
Oh sure :)
rugged kiln
If 20 / 5 = 4 groups each containing 5 parts. That means that 4 = 20 parts.
So if you multiply 4 x 5 = 20. You are actually multiplying 20p x 5p = 100p.
20 = 100p
So multiplication doesn’t seem to be “reverting” division it just seems to increase it.
How am I wrong?
wooden zodiac
rugged kiln
So each group contains 5 parts
Since there are 4 groups, there are 20 parts
So if I were to multiply, 4 x 5, it wouldn't be inverting it, it's just increasing it's already set quantity
So how is multiplication inverse to division?
rugged kiln
You're dividing 20 into 4 groups. But there's still 20 in the total of the groups
rugged kiln
So if I multiply 4 (Which still has 20 in it) by 5 it would give you 100
cosmic trail
each group has 5 in it
so if you're multiplying 20 by 5 you're multiplying each group by 5
20x5 = 4x5x5
like fucktalogist said, you're treating the group as a part, which it isn't
rugged kiln
Why?
rugged kiln
But wouldn't the "new" 1 become some sort of unit? Since we divided 20 into 4 groups. The 1 represents 5 parts no?
cosmic trail
1 group represents 5 parts
1 does not represent 5
you can not just drop terminolgoy like that
which is how you get 20= 100
rugged kiln
But isn't that how division is defined? 20 is divided into 5 equal groups of 4
rugged kiln
But the result will be 4, and in each one there will be 5
Since 20 is divided into 4 groups, and the groups in total all contain 20, which would give you 5 in each group. And each 1 thereafter would represent 1 group
And each group, represents 5
cosmic trail
I don't understand your problem
rugged kiln
Where does the 5s in each group go
nova idol
Where does the 5s in each group go
in the group...
if there are 20 people
and group A, B, C, D
in group A there are 5 people
in group B there are also 5 people
same for C and D
rugged kiln
So there are 4 groups of 20 people. So in total there are 20 people
Every 1 represents a group with 5 people in it
nova idol
Every 1 represents a group with 5 people in it
yes
what
no
there are 4 groups with 5 people each
rugged kiln
So every group has 5 people in it
nova idol
yes
rugged kiln
So 1 (5) + 1(5) + 1(5) +1(5) = 4(20)
nova idol
incorrect
rugged kiln
why
rugged kiln
No its not multiplication
rugged kiln
Yeah my bad: 1 (people in group 5) + 1(people in group 5) + 1(people in group5) +1(people in group 5) = 4(people in group20)
nova idol
Why is there a one there
rugged kiln
The 1 represents each group
nova idol
It’s still multiplying
rugged kiln
4 groups with 5 people inside it
rugged kiln
20 / 5 = 4
nova idol
=20
rugged kiln
20 / 5 = 4
(5 people in 4 groups.)
20 / 5, is 20 divided into four groups. In each group there is a portion of 20
Which is 5
rugged kiln
So there are 4 groups, with 5 inside each of them. Meaning there is 20 in total.
So if I were to multiply those 4 groups with 5 inside of each of them, times 5, it would give you 100
since the 4 groups represent the value of 20
wooden veldt
sure, thats just 20*5
rugged kiln
So if 20 / 5 = 4 groups each containing 5 parts. That means that 4 = 20 parts.
nova idol
So if 20 / 5 = 4 groups each containing 5 parts. That means that 4 = 20 parts.
4 is the number of groups
20 is the number of parts
you cant just say 4 = 20
rugged kiln
And inside each group, there are 5 parts
rugged kiln
20 / 5 = 4 . Aren't you already saying that in this expression? Since its 20 divided evenly into 4 groups of 5
rugged kiln
So if were to multiply this, it would be 4 groups, 5 times. Each group, has 5 in it.
So it would give you 100 parts, and 20 groups of groups
It wouldn't give you 20 parts
So meaning, the 20 you started dividing with. And the 20 you ended up with after multiplying. Is not of the same value
cosmic trail
4 groups = 20 parts
multiply both sides by 5
20 groups = 100 parts, each group has 5 in it by definition
20 x 5 = 100
please tell me what is not clear in these steps
rugged kiln
Yes so. If we have 20/5(5) You would get 100 parts and not 20 parts
rugged kiln
Since 20/5 = 4 groups. And each groups has 5 parts. Meaning it has 20 parts
rugged kiln
So if you were to multiply 4 groups 5 times, you would get 100 parts
cosmic trail
4 groups = 20 parts
multiply both sides by 5
20 groups = 100 parts, each group h...
what do you disagree with in these steps
just tell me explicitly so I can help you faster
cosmic trail
So if you were to multiply 4 groups 5 times, you would get 100 parts
yes
rugged kiln
So 20/5(5) is equal to 100
The 20 you start with, is not the same as you end up with
The first 20 is parts, the one you end up with is groups
cosmic trail
So 20/5(5) is equal to 100
how are you getting that
rugged kiln
how
But we're putting 20 into 4 groups, each with 5 of the 20
So each 1 has 5 in it
rugged kiln
so 20/5 = 20 parts
cosmic trail
is 20 one fifth of 20
rugged kiln
No, it'd be 20 parts and 20 in total for the 4 groups
wooden veldt
the value of 20/5 is "how many groups are there, when we split 20 parts into groups of 5?"
rugged kiln
There are 5 groups, each with 4 in them
But 20 is still there
Since each group has 4
5 groups is not = 5
rugged kiln
But 4 parts per group (which there are five) is 20
4 parts per group. There are 5 groups, So the value of this is 20
wooden veldt
(4 parts *per* group) * 5 groups = 20 parts
yes thats what this says
rugged kiln
But there are already 5 groups
wooden veldt
rugged kiln
I already watched this
wooden veldt
you need to go and watch all these videos and do the whole course pretty much
rugged kiln
20 parts / 5 groups = 4 parts *per* group
Ill go watch it fully. But thanks, I think after this I might be getting closer
.close
edgy owl
can someone help me go about wrapping my head around this problem? It's an optimization problem. As far as I understand I need to get the height of the rod in terms of r, but in order to do that I need the volume, which I don't have.
devout snowBOT
can someone help me go about wrapping my head around this problem? It's an optim...
edgy owl
It just to me doesn't seem like enough information to find the length, I know that the rods have a maximum height of 1 but I don't see how that could be relevant
I can also post the answers if needed
any help is appreciated!
wooden veldt
i think you want to express the volume of the cylinder in terms of the height of the rods
and then maximise that with respect to the height of the rods
edgy owl
how would I be able to do that for V = pi r^2 h? Wouldn't volume already be isolated?
wooden veldt
let R be the rod length
you know that h = R
and you can determine the radius of one of the circles (r) in terms of R
edgy owl
How would the rod length help find the radius of one of the circles though? Aren't they both independent of each other?
wooden veldt
because the length of the rods and the circumferences of the circles must add up to 4m
edgy owl
ahhh I thought that the circles would be a constant and weren't made up of the bendable rod aswell.
I wrote an equation like this: 4 = 4R + 2C where C is the circumference
Then subbed in C = 2pi r
then isolated for r and got (1-R)/pi = r
am I on the right track or no?
so V(R) = pi((1-R/pi)^2)R?
wooden veldt
yes yes
now maximise V(R) wrt R
within some constraints on R that you've already mentioned
devout snowBOT
woven radishBOT
LeftySam
devout snowBOT
@tidal haven Has your question been resolved?
devout snowBOT
@tidal haven Has your question been resolved?
restive river
um
more simpler terms?
i mean how would you explain functions to a complete newbie
like a high schooler
i do have some kind of a source to understand this but, i wanted to understand it in more layman terms
thank you for your time
aight thank you
devout snowBOT
@tidal haven Has your question been resolved?
devout snowBOT
@tidal haven Has your question been resolved?
woven radishBOT
LeftySam
LeftySam
LeftySam
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
LeftySam
green gulch
James wants to design an optimal weekly time table which satisfies the following requirements over a time period of 9-10 months:
•Number of periods per week: 13
•Subject A: 156 lectures.
•Subject B: 148 lectures.
•Subject C: 181 lectures.
devout snowBOT
James wants to design an optimal weekly time table which satisfies the following...
azure patio
James wants to design an optimal weekly time table which satisfies the following...
is it linear programming?
green gulch
How do i make the most optimal time table
green gulch
is it linear programming?
???
azure patio
maybe finding the hcf would help
green gulch
maybe finding the hcf would help
I am getting 1 as a hcf
azure patio
I am getting 1 as a hcf
hmm
do we have to make the timetable for 9 months or 10months??
green gulch
hmm
But like they have mentioned a range 9-10 months so i think can we manupulate the values a bit?
Of the lectures i mean
So that it fits perfectly
Acc according to the needs
azure patio
But like they have mentioned a range 9-10 months so i think can we manupulate th...
that means we can have 36 to 40 weeks
azure patio
get the natural number between them
green gulch
Yes for optimal we should take average right?
3.9
Which is roughly 4
For subject A its stated that there are 156 lec so: 3.9 to 4.333
azure patio
Which is roughly 4
basicaly you get a range that for lecture of b you can watch between 3.7 to 4.1 lectures per week
green gulch
For subject A its stated that there are 156 lec so: 3.9 to 4.333
Average is 4.1 here
azure patio
so optimal one here means that you can watch 4 complete lectures per week of subject b
green gulch
basicaly you get a range that for lecture of b you can watch between 3.7 to 4.1...
But there i have to make a weeky timetable too
green gulch
so optimal one here means that you can watch 4 complete lectures per week of sub...
Oooh hmm yes
azure patio
But there i have to make a weeky timetable too
yes
sum of per week lectures of each subject should be 13
green gulch
For subject A its stated that there are 156 lec so: 3.9 to 4.333
Average is 4.1 which is rougly 4
azure patio
Average is 4.1 which is rougly 4
you need not take average
cuz how will you manage to watch exactly 4.1 lectures
green gulch
True
green gulch
For C: 4.52-5.02
azure patio
ya
azure patio
And 4+4+5=13
ya
green gulch
Now how do i optimally arrange these in a week
azure patio
Now how do i optimally arrange these in a week
ig the ques just asked to arange it week wise
or else number of lectures per day would also be given
green gulch
But isnt the range given?
azure patio
But isnt the range given?
yes
green gulch
If it is there has to be limited number of lectures that a person can watch per day
azure patio
but how he manages to watch them is not given
green gulch
So i should report weekly readings right?
azure patio
So i should report weekly readings right?
yes
restive river
Hey can you help me with Question 6) I can translate it from German, it says
Given is the Point P (1 -2 1) and the point Q (13 13 17)
a) Calculate the midpoint M of the line segment PQ
b) Calculate an equation of the plane that is perpendicular to PQ and passes through M."
devout snowBOT
Hey can you help me with Question 6) I can translate it from German, it says
Gi...
@restive river Has your question been resolved?
long fog
Hey can you help me with Question 6) I can translate it from German, it says
Gi...
are you having difficulty finding mid point
restive river
yeah
The midpoint between the point of PQ
I think I have a way but im not sure if its right
My Idea is
M = 1/2 * (P + Q)
woven radishBOT
fäf
long fog
My Idea is
M = 1/2 * (P + Q)
good
restive river
ah
okay thank you
so
M = 1/2*(P+Q)
M = 1/2*(14,11,18)
M = (7, 5.5, 9)
so that leaves the b)
woven radishBOT
fäf
long fog
god dyslexia
restive river
is X a stand in for M ?
long fog
is X a stand in for M ?
X=(x,y,z)
restive river
okay thanks
coral tulip
devout snowBOT
magic pine
for 1, what is the diameter of the complete circle?
for 2, find the area of the non shaded region to find the area of the shaded region
devout snowBOT
@coral tulip Has your question been resolved?
magic pine
@coral tulip can you elaborate on what you’re still unsure about
coral tulip
for 1, what is the diameter of the complete circle?
Complete circle is the one which is inside the largest semi circle?
magic pine
oh
i misunderstood the question
no the complete circle would be the full circle let me take another look
coral tulip
Ok
magic pine
ok i’m actually not sure how to do that one
there’s probably an easy geometric trick
do you happen to have the answer?
coral tulip
do you happen to have the answer?
Yes
coral tulip
No its 13
magic pine
ok then i’m not super sure how to do it sorry
coral tulip
Ok
coral tulip
for 2, find the area of the non shaded region to find the area of the shaded reg...
How do we do this?
magic pine
focus in the top left of the rectangle
find the area under the shaded section
it should be a triangle with base of 4 and height of 3/2
you have 4 of those, and then 2 rectangles with base 4 and height 5/2
the sum of all of those gives you the unshaded area
is the answer 6?
to make sure i’m not spouting off wrong stuff
devout snowBOT
@coral tulip Has your question been resolved?
weary granite
i need df(A, b, λ) / dλ for a propagation of uncertainty
devout snowBOT
i need df(A, b, λ) / dλ for a propagation of uncertainty
@weary granite Has your question been resolved?
devout snowBOT
@weary granite Has your question been resolved?
devout snowBOT
@weary granite Has your question been resolved?
devout snowBOT
@weary granite Has your question been resolved?
devout snowBOT
@weary granite Has your question been resolved?
coral tulip
is the answer 6?
15
magic pine
15
ok yeah you should have 2 triangles with base 4 and height 1.5, 2 triangles with base 3 and height 2.5, and 2 rectangles with base 4 and height 2.5
summed up you get 6 + 7.5 + 20
the area of the whole rectangle is 8*5
so the shaded area is 40 - 33.5 = 13/2
so p + q = 15
sorry for the mixup, i was thinking it was a square for some reason
devout snowBOT
@weary granite Has your question been resolved?
frosty cradle
!help
devout snowBOT
Please read #❓how-to-get-help
devout snowBOT
@weary granite Has your question been resolved?
nova idol
.close
devout snowBOT
devout snowBOT
Available help channel!
ancient nova
devout snowBOT
echo sandal
Still need help I can help
ancient nova
yes
ancient nova
👍
echo sandal
So basically you find what one cup to one glass is
Can you find? The ratio of what one cup is to one glass
ancient nova
yes
echo sandal
Then find
ancient nova
isit 3 : 4 or smt
echo sandal
Is so basically one cup is 0.75 of a glass
ancient nova
mhm
echo sandal
So take the
24 then calculate it as cups
So the 24 glasses is how many cups
You know how to find?
ancient nova
yes
echo sandal
Answer?
ancient nova
isit 32
long fog
What grade are you?
passed out
ancient nova
11
echo sandal
Year?
ancient nova
no
long fog
I learned that shit in 6
surprising
echo sandal
Rly?
echo sandal
cus i dont use grade in my country
Wait then what do you use
long fog
Sg?
long fog
same
devout spruce
devout snowBOT
jagged lily
Hi.
devout spruce
Hello
devout spruce
Tbh I just don't know
jagged lily
Ok.
jagged lily
Do you seriously need help to voice call, cause I can work swiftly with that,
or do you want me to explain it?
devout spruce
Sry
devout spruce
or do you want me to explain it?
It's ok
jagged lily
Did you figure it out already?
jagged lily
Do you want help?
devout spruce
Yh pls
devout spruce
devout spruce
This
devout spruce
K
jagged lily
We can label the inner rectangle as ABCD for now,
And label the outer rectangle as 1234
Rectangle ABCD has length 18 and width of 12
devout spruce
Hm
jagged lily
And
Rectangle 1234 has length 30 and width 24
All you need to do is find out if the ratio is the same, and that is how you solve it.
devout spruce
216:720
jagged lily
terse remnant
QUESTION
terse remnant
what is (sin45˚) (sec60˚) equals to??
pseudo basin
what's troubling you with this expression?
terse remnant
what's troubling you with this expression?
well
idk how to solve it
i need help with solving it
magic sun
use scientific calculator
terse remnant
use scientific calculator
but idk how to
pastel pasture
do you not know the values of sin 45 and sec 60?
terse remnant
do you not know the values of sin 45 and sec 60?
nope
terse remnant
cmon bro
magic sun
I wonder if your teachers taught this?
terse remnant
i just started out with trigonometry
pastel pasture
there's really not much that can be done here
terse remnant
I wonder if your teachers taught this?
i dont have one
pastel pasture
you need to memorize the values
terse remnant
im self learning
pastel pasture
ah
magic sun
you should start on angle measures
terse remnant
you guys ARE my teachers
terse remnant
look up a table with the angles
ok
pastel pasture
its how it starts in trig 
terse remnant
but i can just use a science calc to solve it?
pastel pasture
i suppose
terse remnant
if so what do i put in the calc do i just put sin45˚ sec 60˚?
pastel pasture
tbf you need only the values of sin and you can derive everything else quickly
pastel pasture
if so what do i put in the calc do i just put sin45˚ sec 60˚?
yeah
magic sun
yes you can. And even without one you can as long as you know their values
terse remnant
yes you can. And even without one you can as long as you know their values
ohh
does sec have a value?
terse remnant
raise cos to -1
i see
terse remnant
sec and cos are reciprocals
ok
terse remnant
special?
pastel pasture
raise cos to -1
honestly just say reciprocate
pseudo basin
whose trig values should be on instant recall
magic sun
Cos X = 1/sec(X)
Sec X = 1/cos(X)
pseudo basin
like the multiplication table
terse remnant
like the multiplication table
oh
woven radishBOT
NEONPerseus
magic sun
no that's different
magic sun
That inverse
tropic current
does sec have a value?
just memorize the 30, 45, 60 and 90 values of each trig. sec, cosec and cot are reciprocals of cos, sin and tan anyways so u don't need to memorize that much. it will become instant as u practice anyways
magic sun
(cos X)^(-1)
Not cos^(-1) x
terse remnant
just memorize the 30, 45, 60 and 90 values of each trig. sec, cosec and cot are ...
i see thanks
thanks
.close
devout snowBOT
pastel pasture
if you're star
devout snowBOT
Available help channel!
forest lily
devout snowBOT
forest lily
Hello
vernal monolith
where are you stuck?
vernal monolith
should have been 3 instead of 3³, other than that it seems correct
nah nvm its correct
forest lily
so
forest lily
?
vernal monolith
you can group 25^x and 40^x together since they have the same exponent
forest lily
so it's (1000)^x
vernal monolith
you can type that as 10^3x if you would'd like
take log base 10 on both sides, then it should be over
vernal monolith
np
forest lily
.close
proud nimbus
option A correct ans ?
devout snowBOT
option A correct ans ?
proud nimbus
dull otter
option A correct ans ?
yes
devout snowBOT
devout snowBOT
Available help channel!
rich barn
devout snowBOT
rich barn
can some one please help me understand this question
specfically the first part
the criteria for indepence is E[XY]=E[X]E[Y]
as i have written
and it meets it for this question
acoustic vault
it meets what?
devout snowBOT
@rich barn Has your question been resolved?
rich barn
it meets what?
the requirement E[XY]=E[X]E[Y]
acoustic vault
independance -> E[XY]=E[X]E[Y]
not the other way around
so in the 1st part they use contrapositive logic
not (E[XY]=E[X]E[Y]) -> not (independance)
they did it for X^2 and Y^2 though but its the same
acoustic vault
do you understand that logic doesnt necessarily go both ways?
independance -> E[XY]=E[X]E[Y]
rich barn
do you understand that logic doesnt necessarily go both ways?
i dont know what you mean by that
acoustic vault
this means that IF it is independant that implies the E[XY] part
but if the E[XY] part is true it doesnt mean that it is independant
the arrow only goes one way
not both ways
independance -> E[XY]=E[X]E[Y]
rich barn
still not following
acoustic vault
ok lets generalise then
A -> B
lets say A is you are in texas
and B that you are in usa
its clear that A->B right?
but B->A is not true
acoustic vault
its the same here
rich barn
like the texas and us example it amkes sense
but the this is math
it like saying 2=2*1
acoustic vault
yes but only one way has been proven to be true.
nooo
always be careful
when looking at theroems
$A\rightarrow B$ and $A\Leftrightarrow B$
woven radishBOT
Køter
acoustic vault
are very different things
acoustic vault
you are not dealing with =
rich barn
this is my chat
acoustic vault
you are dealing with an arrow
round crest
Sorry for interruption
rich barn
please delete and exit and open a new one for yourself
acoustic vault
yes so its inconclusive because the arrow goes only one way
the E[XY]=E[X]E[Y] part is true
but we cant conclude the LHS of the arow is true
because it only goes right
rich barn
what is the LHS of the arrow
acoustic vault
independance
in english it would usually be written
'if X and Y are independant then E[XY]=E[X]E[Y]'
rich barn
ok so shouldnt this apply to E[X^2Y^2]=[X^2]*E[Y^2]
acoustic vault
it does aswell but here they used contrapositive logic
so lets go back to our texas and usa example
do you agree that if you are NOT in usa then you are NOT in texas?
acoustic vault
so $A\rightarrow B$ is logically equivalent to $not B \rightarrow not A$
woven radishBOT
Køter
rich barn
yes
acoustic vault
in this case they showed NOT E[X^2Y^2]=E[X^2]E[Y^2]
so this implies NOT independant
rich barn
in this case they showed NOT E[X^2Y^2]=E[X^2]E[Y^2]
lol
i must be missing something
i stil dont ge it
okay back to texas =usa
example
acoustic vault
ok i mean if we assume it goes both ways your example right?
acoustic vault
yes
rich barn
so they are so they are independent?
acoustic vault
no
for the 10th time
E[XY]=E[X]E[Y] does not IMPLY independancy
independancy IMPLIES E[XY]=E[X]E[Y]
lets even look at your exmaple
if its not intuitive
you have E[XY]=E[X]E[Y]
acoustic vault
but $E[X^2Y^2]\neq E[X^2]E[Y^2]$
woven radishBOT
Køter
acoustic vault
so which one do we trust?
rich barn
so which one do we trust?
what are my optios?
acoustic vault
by your logic it would be both independant from the first result and dependant from the 2nd right?
$E[XY]=E[X]E[Y]$ and $E[X^2Y^2]\neq E[X^2]E[Y^2]$
woven radishBOT
Køter
acoustic vault
which do we trust then?
rich barn
give me a min
are we going along with "If i calculate E[XY] to be 2" & "E[X]=2 and E[Y]=1"?
acoustic vault
no the problem you sent in you found that
$E[XY]=E[X]E[Y]$ and $E[X^2Y^2]\neq E[X^2]E[Y^2]$
woven radishBOT
Køter
rich barn
to me there both contradicotry
however my notes talked about the first one
so im going to go with the first one alhtough u have rpeatedl told me its wrong
acoustic vault
but the 1st one according to YOUR logic. should show independance
and the 2nd one according to YOUR logic should show dependance
but it obviously cant be both
so there is nothing wrong with the problem
its your logic
acoustic vault
exactly!
rich barn
all that it means is that it could be
so I would have to do E[X^2*Y^2]=E[X^2]E[Y^2]
and that would tell me whether its independent or not?
acoustic vault
if it was equal then it doesnt tell you anything either
its only because you found a case that wasnt equal
rich barn
i see
and also correct me if im wrong but E[XY]=E[X]E[Y] is not enough in this case because its dealing with non linear(sinusoidal) functions?
acoustic vault
it is never enough
let me give you an intuitive example
monday -> rains
i task you with finding out whether its monday or not
when can you actually get any good information?
if its raining or not raining?
rich barn
if its raining or not raining?
if its raining
acoustic vault
well no, because it can also rain on a tuesday or any other day
so you cant actually say its monday
rich barn
ohhw ait i read tht wrong
acoustic vault
just because its raining
rich barn
so when its not raining because then i know its definetly not monday
acoustic vault
yes
rich barn
when its raining it could be any day of the week
but it always rains on monday
that is certain
acoustic vault
so here you look for when $E[XY]\neq E[X]E[Y]$ so you can know for sure that its not independant
woven radishBOT
Køter
rich barn
so when its not raining you know that definetly not monday
acoustic vault
yes exactly
rich barn
ok i get it
acoustic vault
and obviously if X^2 and Y^2 are independant so are X and Y
rich barn
thank you
acoustic vault
np
restive river
may i get explanation on this question
devout snowBOT
may i get explanation on this question
restive river
i dont get how to probably start with this qs
weak cove
did you make that setup in blue inking there?
that's a good start
What would happen if you performed that matrix multiplication on the left, leaving the results in terms of "a" and "b", what would the two components you get be?
restive river
i have been watching a video and i didnt get what theyve done here, i mean y a and b has to be written?
weak cove
What they have done where?
restive river
the equation is xa = (4 -2)
restive river
yes
weak cove
The matrix on the left is a 1x2 matrix
lusty sapphire
Are you familiar with matrix multiplication in general?
weak cove
and the matrix "X" is unknown in dimensions, but the matrix A is 2x2
restive river
I am
weak cove
so you have to decide "X"s dimensions
what size matrix, multiplied from the left times a 2x2 will produce a 1x2 matrix
if you don't know, a m x n matrix times a n x m matrix will produce a m x m matrix. Additionally n must equal n for the multiplication to be possible
restive river
is this is how ive to think on it?
weak cove
Yes this is a good way to begin approaching this question
let me know when you decide what dimensions "X" should be
restive river
okay then I need to do these kinds of questions
lusty sapphire
if you don't know, a **m x n** matrix times a **n x m** matrix will produce a **...
You can generalize this more. A m x r matrix multiplied by an r x n matrix will produce an m x n matrix
restive river
thank you
weak cove
true
restive river
.close
visual urchin
How would I set this up
devout snowBOT
How would I set this up
lucid mulch
devout snowBOT
lucid mulch
do I have to integrate this whole thing for p3
nova idol
Bro what else could you do
lucid mulch
no clue
nova idol
It integrates nicely
lucid mulch
the issue is the algebra
cuz its not indefinite
i dont want to do all that work if its not even right
nova idol
It takes like 2 min
lucid mulch
ok ok il do it
nova idol
You could be waiting here for a while
lucid mulch
i cant integrate t
lucid mulch
You could be waiting here for a while
alr I got 1
it was pretty easy ngl
do you know what part D is tho
I think it would be the same
restive river
why do you think its the same?
restive river
approximation
wet zinc
Hi! I've got a question about map colouring. The question is:
Consider a map where each country may consist of up to $k$ disconnected regions. For example, Russia has a region bordering Poland and Lithuania that is disconnected from the rest of the Russian mainland. Prove that the minimum number of colours needed to colour such a map is no larger than $6k$. We require that all disconnected regions of a country be coloured by the same colour.
I've tried approaching it with induction on $k$, or induction on the number of countries, but neither approach really seems to lead anywhere.
devout snowBOT
Hi! I've got a question about map colouring. The question is:
Consider a map whe...
woven radishBOT
Roberto Tan
wet zinc
<@&286206848099549185>
sand dove
!status
devout snowBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
tried a couple things but haven't managed to find anything substantial that might indicate I'm on the right track
sand dove
Have you tried recurrence?
wet zinc
No I haven't, how do you use that in this context? I know about recurrence in the context of algorithms mostly
sand dove
Try to prove the statement $P_k$ : "For any map with any number of countries having at most $k$ disconnected regions, then this map can be coloured with at most $6k$ different colours" for any $k\in \bN *$
woven radishBOT
rafilou2003
sand dove
(by recurrence)
wet zinc
I don't really know what you mean by using recurrence. I know recurrent functions: e.g. fibonacci where $F_n = F_{n-1} + F_{n-2}$, but that evaluates to a number. How do you use recurrence on a logical statement instead of a function that evaluates to a number?
woven radishBOT
Roberto Tan
wet zinc
As for the statement $P_k$: $P_1$ holds because of the four-colour theorem obviously, but I wouldn't know where to start using $P_k$ to prove $P_{k+1}$, or even just how to show that $P_2$ holds. I considered for example first treating all regions of a country as different countries, but then the "merging procedure", where you have to make sure each country gets the same colour for all its regions, is not at all straightforward as far as I can see
woven radishBOT
Roberto Tan
sand dove
**rafilou2003**
Basically, how recurrence proof works :
Step 1) Prove the very first statement of the list, here it is $P_1$ (called initialisation).
Step 2) Prove that for any $k\in \bN$, if $P_k$ is true then $P_{k+1}$ is true
woven radishBOT
rafilou2003
wet zinc
Ah I know this concept as induction
wet zinc
But yeah I tried using induction, but couldn't figure out how to do the inductive step
sand dove
you did the induction on the number of disconnected regions, and not the number of countries right?
wet zinc
Yeah so assume that $P_k$ holds. Then, consider a map with countries where each country has at most $k+1$ disconnected regions. Then, for each country with $k+1$ disconnected regions you could remove one region, and use $P_k$ to get a valid colouring for that map
woven radishBOT
Roberto Tan
wet zinc
But then how do you add the $k+1$st regions for all those countries back in
woven radishBOT
Roberto Tan
sand dove
Well, consider the map formed only by all of the regions you removed
wet zinc
Yeah that has a valid colouring by the four-colour theorem
So by using four colours you could colour that map
sand dove
ah I see
wet zinc
That makes sense, but the problem is that all the disconnected regions of a country have to have the same colour
So yeah not sure how to do the inductive step
devout snowBOT
@wet zinc Has your question been resolved?
devout snowBOT
@wet zinc Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
devout snowBOT
Available help channel!
molten hollow
devout snowBOT
molten hollow
why can't we use this formula in this question
i suppose it's because of the x in the integrated function but
i'm not really sure why we can't just set x as a constant and still proceed with this formula
therefore my question is when does this formula not work
<@&286206848099549185>
btw this is the answer
@pale ingot
left relic
Dream is trying to rizz up some girls. Each time Dream tries to rizz up a girl, there is a $0.01$ percent chance of the girl getting together with him. If Dream tries to rizz up $50$ girls, what is the probability that he will get together with at least $1$ girl? Assume that each girl's decision is independent from every other girl.
devout snowBOT
Dream is trying to rizz up some girls. Each time Dream tries to rizz up a girl, ...
woven radishBOT
LukeyThePookie
left relic
I tried doing casework with 1 girl, 2 girls, 3 girls, and so on, but that would take very long
astral beacon
Where did I go wrong?
devout snowBOT
Where did I go wrong?
brisk geode
weary void
lol
devout snowBOT
@astral beacon Has your question been resolved?
astral beacon
.close
frail igloo
devout snowBOT
frail igloo
pls don't laugh at me
for det(-3A) and det(A^T) i am unsure why i'm wrong
although 3^T seems pretty laughable to me
main gull
frail igloo
yea i just read that
lmao
i'm rushing. i should stop flooding the channels.
thank you.
.close
devout snowBOT
main gull
.reopen
devout snowBOT
✅
frail igloo
omg
main gull
Times by the det
main gull
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devout snowBOT
devout snowBOT
Available help channel!
restive river
can someone help?
devout snowBOT
can someone help?