yeah
#help-27
near jolt
near jolt
can you show me the whole table
onyx badge
near jolt
i would recommend doing ~A v B first before ~(~A v B).
yeah i think you did ~A v B instead of ~(~Av B)
onyx badge
uh how do i do ~(~Av B)
onyx badge
so T and T = F?
near jolt
so T and T = F?
not T=F, T turns into F
its exactly like every other example you did
just insert another column ~A v B
its easier to do it one operation at a time
onyx badge
alright wohooo
time for the last question
since i can do the problem 3 and 4
since its just words now
so the question is 2. Which combination makes the output true.
how do i do that
near jolt
so the question is 2. Which combination makes the output true.
what does this even mean, is this multiple choice
oh
onyx badge
what does this even mean, is this multiple choice
i have no idea but its not a multiple choice
near jolt
they meant what combination of A,B makes the Q true
onyx badge
how does that work
near jolt
well you have the truth table
truth table tells you, for example, if A is true, and B is true, then Q is true
onyx badge
so do i choose one of the top like (A n B)?
near jolt
the whole purpose of this is telling you what Q is given A and B
if A=1, B=1, then Q=1 by the table
near jolt
so do i choose one of the top like (A n B)?
no, you pretty literally just say what (A,B) returns Q=1
all comes from the table
near jolt
look at the table and check which (A,B) gives Q=1
we established that Q= (A n B) v ~(~A v B)
near jolt
yes?
^using this table
its asking: "what truth value of A,B would make (A n B) v ~(~A v B) true"
if my phrasing is better
near jolt
so 1 is Q=1, 2 Q=0, 3 Q=0, 4 Q=0?
isnt second row Q=1
onyx badge
oh wait
near jolt
yeah
onyx badge
so if its true and false its still q=1?
near jolt
looks like it
onyx badge
oh alright
near jolt
just list them all
onyx badge
oke so Q=1 Q=1 Q=0 Q=0
near jolt
yeah
they want you to answer: what what values (A,B) will Q=1
for example when A=1,B=1,then Q=1
list them all, and that would be your answer.
all can be inferred from the truth table
onyx badge
list them all, and that would be your answer.
u mean like (A n B) , ~(~A v B) aswell?
i just need to choose 1 combination right
time to write it
near jolt
u mean like (A n B) , ~(~A v B) aswell?
no
(A n B) you can think of as "inbetween steps" to deduce the truth value of Q
the value of Q is solely determined by value of A,B
if that makes sense
onyx badge
oh u mean list all of this Q=1 Q=1 Q=0 Q=0 not the other top ones
onyx badge
oke
near jolt
the other ones don't matter
cuz they're there only to make our lifes easier in computing the truth value of Q
onyx badge
do i list it like this
A T = 1 B T = 1 A T = 1 B F = 0 A F = 0 B T = 1 A F =0 B F =0
?
near jolt
A T = 1 B T = 1 A T = 1 B F = 0 A F = 0 B T = 1 A F =0 B F =0
what does A T=1 mean
near jolt
just say A=1
onyx badge
oh okie
near jolt
either say A true, or A=1
onyx badge
time to write it on paper
near jolt
you didn't say the value of Q
near jolt
the point of our computation is to compute the truth value of Q in relation to A,B
onyx badge
i have no idea about how to get teh value of Q
near jolt
i have no idea about how to get teh value of Q
the table
Let us look at row one of the table. It means: if A=1, B=1. then ~A=0, (A n B)=1, ~ A v B=1, ~(~A v B)=0, and so Q=1
so its saying that when A=1, B=1, we must have Q=1
onyx badge
ohh
near jolt
the purpose of the table is to tell us the value of Q given A,B
onyx badge
Let us look at row one of the table. It means: if A=1, B=1. then ~A=0, (A n B)=1...
so this is the combination
near jolt
the four columns after A,B are the inbetween process we go through
near jolt
so this is the combination
end last column tells us what Q is given the A,B presented in the same row
if that makes more sense
onyx badge
end last column tells us what Q is given the A,B presented in the same row
since its T?
near jolt
since its T?
the first row tells us that. That whan A is true and B is true, then Q is trues
each row is sort of a deduction process to get the truth value of Q
so second row tells us that if A is true, B is false, we can do all these deduction (like finding the value of ~A, (An B) ) to get that Q is also true
does that clear things up?
onyx badge
does that clear things up?
yes that does clear things up
near jolt
each row is a deduction process
although it is easier to do these column by column
maybe that's why it's confusing: our goal is to make deduction for each row, it just turns out doing it column by column is easier
first row tells us what happens when A=1, B=1, second row tells us what happens when A=1, B=0, etc...
onyx badge
although it is easier to do these column by column
so the answer would be A and B True, A and B false?
onyx badge
so the answer would be A and B True, A and B false?
the combination
near jolt
so the answer would be A and B True, A and B false?
you mean when A is true and B is false for the second one?
onyx badge
i mean A true and B false
near jolt
yeah thats right
onyx badge
WOOO
near jolt
to be a bit more precise you might want to say "for all other cases, Q is false"
onyx badge
to be a bit more precise you might want to say "for all other cases, Q is false"
after writing A and B is True, A is true and B is false for all other cases, Q is false?
near jolt
after writing A and B is True, A is true and B is false for all other cases, Q i...
yeah
its more clear
but i hope this would help you see the point of the truth table. Each row is giving you a different deduction to get the truth value of something we care (like Q).
onyx badge
but i hope this would help you see the point of the truth table. Each row is giv...
yes took me a while to understand it
near jolt
and it is much easier to do it column by column than row by row (although you could)
onyx badge
only could do it when im used to it
near jolt
only could do it when im used to it
i think the main lesson is to understand why we do this. If you simply do this without knowing the meaning behind it, then, to you, it is nothing but a useless table.
onyx badge
<:KEK:586240877358350341> i think the main lesson is to understand why we do thi...
needed those umbrella examples
near jolt
as far as understanding how q->r works, its fine to think that "if im not lying about a statement, that statement would be true"
onyx badge
as far as understanding how q->r works, its fine to think that "if im not lying ...
took a while to get out of that lol
thank you for helping me
onyx badge
just got introduced yesterday so yes
near jolt
just remember these things about what info you get from truth table, and these intuition behind logical conjunction. Then you will do just fine.
onyx badge
just remember these things about what info you get from truth table, and these i...
and how i would interpret it
near jolt
and how i would interpret it
the table?
onyx badge
the table?
nah like the examples u gave out the integer and everything ill just think of it like that
near jolt
nah like the examples u gave out the integer and everything ill just think of it...
its a generalization of english words. What does "or" mean? if i say (something false) OR (something false), This would always be a lie. So, in it's fullest generality, if p is false, and q is false, then (p or q), or what we write as (p v q), would be false
onyx badge
its a generalization of english words. What does "or" mean? if i say (something ...
ill save this
near jolt
and truth table are essentially deductions: if we know the initial condition (circled in red), the things circled in blue are the stuff we can deduce.
near jolt
its a generalization of english words. What does "or" mean? if i say (something ...
same thing goes for And, Not, -> (if... then), <->,...
i'd be lying if i said "Not (true statement)", lying if i said "(false statement) And (true statement)" ...
onyx badge
some part still confusing but still can process it
near jolt
without these truth tables, its hard to immediately tell whether "((true statement) and (false statement)) and Not(true statmenet or false statement)" is a true statmenet or not
onyx badge
without these truth tables, its hard to immediately tell whether "((true stateme...
it basically double checks it
near jolt
it basically double checks it
you could use truth table to double check it, yes
or simply use truth table to deduce whether the statement is true or not
essentially the same thing, just put into a table
in the case with Q, we really just used the table to get the relation between the truth value of A,B and the truth value of Q
onyx badge
in the case with Q, we really just used the table to get the relation between th...
so if the talbe is wrong i really couldnt get the Q
near jolt
so if the talbe is wrong i really couldnt get the Q
u would get the wrong relation
yeah
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idle vessel
this is what ive tried so far but im not sure what to do next im thinking of moving 2ab to the lhs but idk what to do with that then
devout snowBOT
this is what ive tried so far but im not sure what to do next im thinking of mov...
winter patrol
messed up the last three lines
idle vessel
i shouldnt have divided by 2?
winter patrol
you didn't seem to have divided by 2 at all
winter patrol
it looks like the 2 just disappeared completely
idle vessel
like a^2-ab+b^2 + ab ?
winter patrol
loud lava
u can only send ab to the other side of inequality without any problems because its given a,b > 0
loud lava
yes according to what u solved
idle vessel
(a-b)^2>= 0 then?
idle vessel
.close
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rustic ocean
.
willow helm
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dim perch
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dim perch
is it okay to utilize a specific sylow 2-subgroup since all of them are conjugate to each other?
i was having a bit of trouble in the arbitrary case, so i decided to use $P = \langle r^k, s \rangle = D_{2a}$
woven radishBOT
blanketism
vital patrol
Youβre on your own twin π₯
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@dim perch Has your question been resolved?
dim perch
halp
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@dim perch Has your question been resolved?
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@dim perch Has your question been resolved?
dim perch
<@&286206848099549185>
supple knot
can also try #groups-rings-fields
woven vale
is it okay to utilize a specific sylow 2-subgroup since all of them are conjugat...
i'll say yes, since the 3rd Sylow theorem says n_p = [G : N(P) ] for any P. so it'll be the same number for any P, and since it's proven for any P, it works for a specific P
P is a p-sylow subgroup, N(P) = N_G(P), etc. etc.
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timber pebble
ionic sail
Wait
glacial tide
How can I do this by hand?
subtle wadi
How can I do this by hand?
Basically you need to iteratively approximate the solution by decreasing the step size h until the results stabilize within the specified tolerance.
$\frac{dy}{dx} = 1+y^2 \implies \frac{dy}{1+y^2} = dx$
Next up, you should integrate and solve this, which will give you the initial condition and exact function. Select a target value, then your goal is to find the largest h where the result is within Β±0.01 of the true value.
woven radishBOT
πΏππππππππππ
devout snowBOT
What answer format am i expercted to enter?
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@burnt yarrow Has your question been resolved?
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. What happened here
willow helm
.close
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lost laurel
Maybe I'm missing something, but what's really there to verify here
lost laurel
I basically have to show that every function of bounded variation is the sum of monotone functions right
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green delta
How do I solve it guys?
devout snowBOT
How do I solve it guys?
void fox
!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 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
bold cipher
How do I solve it guys?
My first help
This is the ncert.
You are probably in 9th grade right?
green delta
No 7th
bold cipher
First of all you should know to prove a triangle isosceles you need to have two equal sides
There are 3 triangles
Scalene (no sides are equal)
Isosceles (2 sides are equal)
Equilateral (all sides are equal)
In your case it is isosceles.
green delta
Yes
bold cipher
@green delta try to prove AC AND BC equal
Im pretty sure you have learnt about congruency?
green delta
Yeah
bold cipher
Yeah so put that knowledge to this question.
Get AC AND BC equal
bold cipher
Compare TRIANGLE PQA AND TRIANGLE PRB.
There are two sides given write them and then ANGLE PQA = ANGLE PRB (90β°)
By this you proved triangle pqa and triangle prb congruent.
By this write ANGLE A = ANGLE B
If angle a and angle b are equal then ab=ac as sides opposite to angles are equal
green delta
How do I prove that angle a = angle b means ac=bc? (Sry if I'm being stupid)
bold cipher
How do I prove that angle a = angle b means ac=bc? (Sry if I'm being stupid)
Its totally okay
After proving the two triangles congruent.
You can say ANGLE QAP = ANGLE PBR
These are corresponding angles
And by this if you see the diagram ANGLE QAP you would see that ANGLE QAP IS ANGLE A
And ANGLE PBR is ANGLE B
Put the two together
ANGLE A = ANGLE B
Then there is a statement which you need to memorise or likely learn.
"If two angles of a triangle are equal, there opposite sides are equal
green delta
TYSM man!
bold cipher
No problem
green delta
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wanton tiger
what do i do here? i cant understand how i use the info given
devout snowBOT
what do i do here? i cant understand how i use the info given
glossy pecan
Okay think of a parabola which is symmetric about x=0. Now rotate it such that it is symmetric about y=-x.
That should give you enough intuition to solve this
No wait
glossy pecan
Nvm. Parabola is not invertible
wanton tiger
Okay think of a parabola which is symmetric about x=0. Now rotate it such that i...
a simple y = ax +b can i take
glossy pecan
Yeah that works
drifting sierra
The wording is a bit ambiguous but I'm pretty sure it's saying the inverse of f is the image of f by symmetry about y=-x, not that f and f inverse are individually symmetric about y=-x
wanton tiger
The wording is a bit ambiguous but I'm pretty sure it's saying the inverse of f ...
yeah i understood this
thats why i thought a line would work
any line with a +ve slope can be symmetric abt y = -x
drifting sierra
...no
wanton tiger
ah mb
so symmetric to y =-x would be a line with slope 1?
like perpendicular to it
solemn hatch
y=x is an example ig
wanton tiger
sry im kinda not confident abt this topic
wanton tiger
y=x is an example ig
yep thats what i am talking abt
candid maple
perhaps you should draw y = -x on a coordinate plane and play with some graphs a little bit first, instead of trying to reason abstractly.
wanton tiger
i got desmos open , im doing that
drifting sierra
The wording is a bit ambiguous but I'm pretty sure it's saying the inverse of f ...
.
solemn hatch
yep thats what i am talking abt
Do you know f and f inverse are symmetric about y=x?
wanton tiger
Do you know f and f inverse are symmetric about y=x?
yes
wanton tiger
a/x is symmetric about y=-x (for any a)
how so?
drifting sierra
If f is symmetric about y=-x and (x,y) is a point on the graph, then (-y, -x) is also on the graph
wanton tiger
If f is symmetric about y=-x and (x,y) is a point on the graph, then (-y, -x) is...
uhh u mean (y,-x)? or im tripping
ohh ok got it
1st quad to 3rd quadrant
drifting sierra
You really shouldn't think in terms of quadrants but if it gives you some intuition then so be it
wanton tiger
You really shouldn't think in terms of quadrants but if it gives you some intuit...
is there another way
other than quadrants
js the name, ill look it up
drifting sierra
I'm just saying that because I never said (x,y) was in any specific quadrant
wanton tiger
ah so i assumed them to be in 1st which could be wrong
i understand now
so what do we do after this
drifting sierra
I don't really know how to explain this without basically giving the solution
wanton tiger
im a bit confused to what the questions kinda means
f(x) and its inverse and symmetric to eachother by y =-x
so can i relate these 2 in someway
i cant find a way to relate em
willow helm
Right
drifting sierra
If f is invertible and symmetric about y=-x then f(x) = -f^{-1}(-x)
Now in the question f is invertible but not necessarily symmetric about y=-x, rather f and f^{-1} are, together
willow helm
If they are symmetric about y=-x, what happens to the point (x,y)
Nevermind I didn't read
drifting sierra
And then you need to recall the definition of an odd function
willow helm
You already said that
wanton tiger
If f is invertible and symmetric about y=-x then f(x) = -f^{-1}(-x)
how did u get this relation
x,y turns to -x,-y
so i get the -ve outside
so by this we take x inside -ve too
ohhh
wait what did i get wrong
drifting sierra
(-y,-x)
wanton tiger
And then you need to recall the definition of an odd function
if f(x) = -f(-x)
wanton tiger
Now in the question f is invertible but not necessarily symmetric about y=-x, ra...
the way u got this equation im not getting
drifting sierra
Not sure how to formally derive it and too tired to look it up, I got it from intuition about symmetries and transformations
wanton tiger
lemme try to get what u did
drifting sierra
Maybe try working with f: (0,+inf) -> (-inf,0), f(x) = -1/x actually don't
wanton tiger
did we use x,y to -y,-x
drifting sierra
Then f^{-1}: (-inf,0) -> (0,+inf), f^{-1} = -1/x
wanton tiger
yes
willow helm
So where does (x, f(x)) go
wanton tiger
-f(x),-x
willow helm
Well your x is -f(x) and your y is -x
wanton tiger
yes
willow helm
So $f^{-1}(-f(x)) = -x$
woven radishBOT
USS-Enterprise
wanton tiger
ok im
willow helm
Get it?
wanton tiger
not able to relate
willow helm
Right
willow helm
The point (-f(x), -x) belongs to our function
wanton tiger
yes
willow helm
and our function is f^(-1)(x)
wanton tiger
this is after getting reflected
wanton tiger
and our function is f^(-1)(x)
so this is y?
wanton tiger
in this case
willow helm
it gives you the y coordinate yes
And for the point (-f(x), -x)
The point must satifsy the same condition
wanton tiger
yes
willow helm
we just think of -f(x) as the x coordinate and -x as the y coordinate
and g(x) must equal y
wanton tiger
ye
willow helm
Only our g is f^(-1)(x)
wanton tiger
so -x = g(x)
willow helm
And for the point (-f(x), -x)
.
wanton tiger
y
wanton tiger
oh mb
willow helm
right
wanton tiger
so the functions between the points
willow helm
of f^(-1)(x)
wanton tiger
i see
wanton tiger
ok so g(-f(x)) = -x
willow helm
So $f^{-1}(-f(x)) = -x$
woven radishBOT
USS-Enterprise
willow helm
We input -f(x) into f^-1(x) and get -x
wanton tiger
dang this si genius
willow helm
Because we know the point (-f(x), -x) belongs to the graph of f^(-1)(x)
And now what do we do
So $f^{-1}(-f(x)) = -x$
woven radishBOT
USS-Enterprise
wanton tiger
take f both sides
willow helm
Exactly
wanton tiger
so -f(x) = f(-x)
willow helm
Yes
wanton tiger
this is wild
willow helm
Do you get it though?
wanton tiger
ohhhh i get it
willow helm
It's just working with a "different" point than (x, y)
Normally you have f(x) = y
Only here your f is f^-1, your x is -f(x) and your y is -x
That's all that changes
And we got those coordinates from looking what happens to the point (x, y)
And that's it
wanton tiger
yea i get it
willow helm
π
wanton tiger
tysm
willow helm
No problem
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cedar bolt
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cedar bolt
This is my teachers answer but I dont understand why i cant use angle=pi
See this is what I got for x if i used angle is 0 or pi
Now I have three limitsπ§ββοΈ
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uncut crow
π§ββοΈ
cedar bolt
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teal tree
This is my teachers answer but I dont understand why i cant use angle=pi
what happens if you put t = pi into x?
made a mistake whoops
cedar bolt
what happens if you put t = pi into x?
0 but thats the same as t=0
Oh oops
Okay
X=-5
cedar bolt
But i just need to find the area of the curve so why does it matter???
cedar bolt
the value of your integral you do get depends on your t
Oh
cedar bolt
The questions just wants the shaded area and now the step im missing is the area under the curve but idk which limits to use now
teal tree
if you choose t = pi as one of your limits, you would end up doing this
that is bad
what is the value of at the other point?
that value of t is one of the limits which you should use
heres a hint in the form of a diagram
for what you might want to do to find the area
cedar bolt
In the question t=(5 square root 2) /2 from part b
cedar bolt
heres a hint in the form of a diagram
for what you might want to do to find the ...
OHHHHHHH
Okkkkkkk
Tysmmmm i get it so much now from your pircture
teal tree
In the question t=(5 square root 2) /2 from part b
oh nononono thats not t
thats x
uhoh
cedar bolt
Wait what no
From the previous wuestion they said thag t was that
Omg im so confused again
teal tree
ok so what your teacher has done is write out the integral in terms of x
but we want to integrate parametrically
wait.
are we doing the bottom question or the middle one
oh no
replace every mention of t i said before with theta
cedar bolt
I know but we can continue with t if u want i understand why u mena
cedar bolt
No i think shes done something wrong or i have
I know 10 is from the area under he line
But my area is a different value from hers
But its ok iβll just double check my answers later. Right now i just need to know where to go for the process
teal tree
imma point back to the useful diagram
you would need this basicallt
i meant area of triangle
and thats the process
you get the triangle area from knowing the coordinates of P and R, then you need the values of t at P and M for the integral limits
teal tree
frank current
how do I solve this with parametric form
devout snowBOT
how do I solve this with parametric form
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high basalt
If theres a queue at the bank of people who want to deposit and withdraw cash, there are as many people who want to deposit money (A) as people who want to withdraw (C) and they deposit or withdraw the same amount (the bank starts at 0) how many ways are there of arranging the queue to make every transaction successful?
devout snowBOT
If theres a queue at the bank of people who want to deposit and withdraw cash, t...
icy terrace
tΓΌrk var mΔ±
high basalt
Say that count(A) and count(C) are how many people of that kind have already done their transaction
lunar harbor
Dyck paths 
high basalt
Whenever a C person comes through, count(A) must be equal to atleast count(C)+1
night rune
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neon thunder
Hi
neon thunder
I did that and got 123deg 37' it says i'm wrong like did i mess something?
frank current
I did that and got 123deg 37' it says i'm wrong like did i mess something?
im getting 123 deg 97'
is that the answer
frank current
i guess it simply the fact that minutes don't work like decimals
neon thunder
frank current
they add a +1 to the degree whenever the first minute digit reaches 6
neon thunder
they add a +1 to the degree whenever the first minute digit reaches 6
Yes
123 37? Is right, no?
frank current
yeah I think so
neon thunder
That's what i thought idk why it says i'm wrong ok ty bro
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oblique bramble
is this the correct way of making histograms
devout snowBOT
is this the correct way of making histograms
oblique bramble
if yes then i have a counter question
winter torrent
yea that seems fine to me
crystal dawn
though I would like to note
q i) is a 4-marker
this may be just an exercise but you don't want to just slap an answer for a 4-marker anyway
winter torrent
yea especially given the space i'd expect to see at least a little working there
crystal dawn
esp. when the instructions are to calculate an estimate for the mean, not state it
as for the histogram, it looks fine
oblique bramble
this may be just an exercise but you don't want to just slap an answer for a 4-m...
yeah ik i just did it in calculator
and i will obv do the working in exam
anyways so my question is
the part ii is pretty confusing
cus the answer should be 3.6
pseudo basin
aight so you're working w histograms
oblique bramble
while the mark scheme shows 10.8
oblique bramble
aight so you're working w histograms
correct
pseudo basin
you should know the bar heights are proportional to frequency density and not to frequency
pseudo basin
ok
aight hang on though. have you computed the FDs in your frequency table yet?
cause i don't see where, if anywhere, you've written them down
oblique bramble
FDs?
oblique bramble
oh well i just do that in my calculator
pseudo basin
you should write these things down
oblique bramble
n keep it in my head
oblique bramble
ummtheres not really enough space soo
pseudo basin
you can write to the right of the table or sth
oblique bramble
also how is it 3 cm (in yhe question)
pseudo basin
i mean at least the results of calculating freq densities
oblique bramble
3x10 is 30
pseudo basin
or get another piece of paper (for now)
oblique bramble
not 10
pseudo basin
also how is it 3 cm (in yhe question)
we'll get to cm in a moment.
oblique bramble
okay
pseudo basin
i want you, right now, to:
- CALCULATE the frequency densities
- RECORD them
- SEND a PHOTO here
oblique bramble
i want you, right now, to:
* CALCULATE the frequency densities
* RECORD them
* S...
frequency density is just the height though
how do i calculate frequency density..
pseudo basin
mrmhrghrh.
pseudo basin
is this the correct way of making histograms
how did you calculate them here for this histogram
oblique bramble
how did you calculate them here for this histogram
i didnt
i just know when you multiply the x and the y you get frequency
eg 10x.3 is 3
the frequency is also 3
pseudo basin
so you know that area is prop to frequency.
native gyro
Xd
oblique bramble
yes
pseudo basin
10 * 0.3 is 3
that 0.3 is your frequency density.
it is equal to frequency divided by class width.
FD = freq / width
oblique bramble
> 10 * 0.3 is 3
that 0.3 **is** your frequency density.
so the height
pseudo basin
m. almost.
pseudo basin
you're currently conflating like
height as measured on the y axis scale, and height as a physical measurement
oblique bramble
well the wuestion is kinda asking the height aswell though
this confuses me cus
10*3 is 30 not 10
pseudo basin
1 cm β 1 unit of freq. density.
pseudo basin
the height of a bar in a histogram is PROPORTIONAL TO frequency divided by class width
it may happen that these two are equal but they don't need to be
oblique bramble
this confuses me cus
10*3 is 30 not 10
the frequency density is like 30-20 is 10
and frequency is 10
so 10/10 is 1
hence frequency density is 1?
pseudo basin
like...
that's the FD for the first class
you need to calculate it for the other classes as well
pseudo basin
,rccw
woven radishBOT
pseudo basin
"kinda the same"
no they aren't the same
they are, once again,
proportional
but not the same
oblique bramble
okay
pseudo basin
you understand that the y axis in a histogram grid can be scaled any way we want right
like
oblique bramble
you understand that the y axis in a histogram grid can be scaled any way we want...
yes
pseudo basin
1 unit of FD can be represented by a segment of any physical length, any number of centimeters
oblique bramble
yes
pseudo basin
in this case, based on the first class,
we have FD 1 <-> 3 cm
oblique bramble
it physically can be 10 or even 0.1
pseudo basin
so now you need to work out the heights, in centimeters, that represent FDs 3.6 and 0.72
devout snowBOT
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oblique bramble
why does the mark scheme say 5 is the answer
devout snowBOT
why does the mark scheme say 5 is the answer
native gyro
,rccw
woven radishBOT
native gyro
the range is 20 - 15 = 5
hushed oyster
why does the mark scheme say 5 is the answer
What does the "15," mean?
Is that a typo?
sand fable
Hello quick question, why is this not right?
I dont get what I am doing wrong.
thorny bloom
Hello quick question, why is this not right?
I dont get what I am doing wrong.
looks correct to me
maybe the small p and capital P is the problem?
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warped turtle
In number 2 and 3, I don't know how
devout snowBOT
In number 2 and 3, I don't know how
candid maple
from what I can see of both figures in 2 and 3, they both look like quadrilaterals of some sort. that should be more than enough for you to deduce the missing angles.
loud lava
from what I can see of both figures in 2 and 3, they both look like **quadrilate...
in 2
i think u can use quadrilateral property
sum of angles of a quad = 360
warped turtle
Umh whut?
candid maple
you can use that property in both questions, but I'm not sure why you are replying to me with that. I'm not the OP.
loud lava
sry
warped turtle
you can use that property in both questions, but I'm not sure why you are replyi...
I mean how
loud lava
in 2
the angles of quad are
72, 30, 25 and 360 - h
candid maple
I'll let tishu take over. my screen reader cannot follow too many people. sorry.
loud lava
sure
karmic basalt
I mean how
Justiiiceeeee
warped turtle
in 2
the angles of quad are
72, 30, 25 and 360 - h
I thought it was 180 cause that was how it was taught to me
loud lava
I thought it was 180 cause that was how it was taught to me
for a triangle its 180
for a quad its 360
and i think 3 has missing information
warped turtle
What's a quad?
crystal dawn
3 is solvable.
loud lava
What's a quad?
quadrilateral is a 4 sided figure
like square , rectangle
loud lava
3 is solvable.
are the 2 trinangles formed isosceles?
crystal dawn
don't need to. the big shape is a quadrilateral.
warped turtle
quadrilateral is a 4 sided figure
like square , rectangle
Oh a polygon
loud lava
don't need to. the big shape is a quadrilateral.
yes , but 115 is not the full angle right
its the angle of the small quad
crystal dawn
hm
crystal dawn
still enough
loud lava
u can solve it
crystal dawn
wait where's hyposelenia
crystal dawn
its not his doubt
her* and I know she's not the OP
candid maple
wait where's hyposelenia
I yielded to tishu. it's fine.
loud lava
In number 2 and 3, I don't know how
um
warped turtle
So what do i do?
loud lava
In number 2 and 3, I don't know how
in q3 , use the 2 big triangles and the small quad, use all of their sum properties u will get 3 equations with 3 variables
loud lava
So what do i do?
did u understand q2? or should i explain in more detail?
warped turtle
Ye explain more in detail pls
loud lava
basically u get the point right its a quadrilateral
a 4 sided figure
basically if u dont know about quadrilateral sum, just divide it into 2 triangles
something like this
drifting sierra
Here's a method that always works for any number of edges:
If you start at A and follow the lines through B, C, D, and then back to A, the turns you make correspond to the green and red angles. If you turn clockwise, it's green, and if you turn counterclockwise, it's red. If you add all the green angles and subtract the red angle (because it's going the other way), you do a complete 360ΒΊ.
loud lava
Oh then get the missing angle for each triangle and add?
yes
drifting sierra
All these colored angles are paired with a gray one, and each pair makes 180ΒΊ
The rest is just calculating
loud lava
Then minus it to 360?
yes
loud lava
Oh okok then what about number 3?
in that there are 2 triagles ( big one
wait leme draw
drifting sierra
Here's a method that always works for any number of edges:
(this also works for question 3 jsyk)
warped turtle
Ye
loud lava
and one more quad
warped turtle
Yep
loud lava
so if u try to solve it
u will get 3 equations
and 3 variables
and one of those variables is e, which is your answer
loud lava
in this , 30 + a + e = 180
loud lava
and in this a + b + e + 115 = 360
warped turtle
I just got stuck on how to identify
loud lava
np
warped turtle
Forgot what quad is
loud lava
a 4 sided figure
warped turtle
Ye thx
crystal dawn
!done?
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
warped turtle
. close
crystal dawn
no space
robust bobcat
For number 9 I am trying to minimize the area of the circle. I have the sides of the rectangle inside the circle are c and d meaning c^2+d^2=4r^2. The area of a circle is minimized when r =0. But then we have c^2=-d^2 which makes no sense. What is the error in my thinking
devout snowBOT
For number 9 I am trying to minimize the area of the circle. I have the sides of...
near jolt
For number 9 I am trying to minimize the area of the circle. I have the sides of...
"the area is minimized when r=0" sure. but that ignores the condition: "area of the rectangle is fixed"
r is dependent on c,d, and c,d is dependent on the area
you can't just modify r all you want
and you basically showed that r=0 when c=d=0, which is correct. But this already diverges from the original question
robust bobcat
"the area is minimized when r=0" sure. but that ignores the condition: "area of ...
So your saying this is a contradiction unless the area of my rectangle is 0
near jolt
So your saying this is a contradiction unless the area of my rectangle is 0
no im saying that if r=0 then the area of your rectangle is 0
im saying that the claim "the area of the circle is minimized when r=0" forgets the condition that you are fixing the area of the rectangle
so, for example "if the area of the rectangle is 1, then the area of the circle is minized when r=0 " is incorrect
robust bobcat
I see
near jolt
so basically you've ignored the constraint the problem set when you said "minimized when r=0"
pure kelp
For number 9 I am trying to minimize the area of the circle. I have the sides of...
you have a given condition btw. that is the area of the rectangle is "given" or fixed. so using that as a constraint, you need to minimize the AREA of the circle
near jolt
so we have c^2+d^2=4r^2. and you know cd is fixed, how do you minimize 4r^2
brittle coral
hint: try to fish out a cd term in the equation:
c^2 + d^2 = 4r^2
pure kelp
this problem is easily solved with lagrange multipliers too. idk if you've learnt about this
brittle coral
frankly i find it quite laughable that this qn doesnt require differential calculus and only requires at most basic algebra and geometry
robust bobcat
this problem is easily solved with lagrange multipliers too. idk if you've learn...
I have not.
brittle coral
hint 2:
cd is constant, want to minimise area Οr^2, meaning we can minimise 4r^2
we also have:
4r^2
= c^2 + d^2
= (c-d)^2 + 2cd
robust bobcat
Ok give me a sec
Ok I just need to isolate for r and minimize that
Ok so both c and d are equal do sqrt cd
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winter ivy
Markscheme did it in a really weird way but it just seems like integrating factor? or am i mistaken
devout snowBOT
Markscheme did it in a really weird way but it just seems like integrating facto...
loud lava
Markscheme did it in a really weird way but it just seems like integrating facto...
indeed it does seem like integrating factor
after dividing by 2x^2 both lhs and rhs
u can use IF
winter ivy
yeah thats what I did but im stuck rn im with 2 * ln |x| * y = integral(1/2x^2 *f(x) dx)
it doesnt lead to the answer
loud lava
leme try one sec
supple knot
yeah thats what I did but im stuck rn im with 2 * ln |x| * y = integral(1/2x^2 *...
Show your full work
supple knot
Markscheme did it in a really weird way but it just seems like integrating facto...
Show the mark scheme
winter ivy
wait lemme write it in legible handwriting
winter ivy
2ln x
loud lava
thats incorrect
winter ivy
Oh wait
loud lava
what formula did u use to find IF?
winter ivy
its x^2
loud lava
yes
winter ivy
oh shit lol
loud lava
ye u got it now
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Available help channel!
summer harbor
"A marketing firm surveyed 120 college students about their subscriptions to three major streaming services: Netflix (N), Disney+ (D), and Max (M). The data collected is as follows: 65 students subscribe to Netflix, 50 students subscribe to Disney+, 45 students subscribe to Max, 20 students subscribe to both Netflix and Disney+, 18 students subscribe to both Netflix and Max. 15 students subscribe to both Disney+ and Max. 8 students subscribe to all three services."
Draw the Venn diagram and answer the following questions.
How many students subscribe to only Netflix?
How many students subscribe to exactly two of these services?
How many students do not subscribe to any of these three services?
devout snowBOT
"A marketing firm surveyed 120 college students about their subscriptions to thr...
summer harbor
"A marketing firm surveyed 120 college students about their subscriptions to thr...
and for the first question (only netflix) my answer is 19 because i assumed the 65 students who watch netflix also encompass those that have another service subscribed (netflix and disney; netflix and max)
65 - 20 - 18 - 8 = 19
is this correct so far?
is my venn diagram correct as well?
(set theory btw)
please help someone π
willow helm
I don't won't check answers because I don't have time right now sorry π
But why don't you fill the data you got in the diagrams and see if it is correct
You know how many are subscribed to each
And then also see if the intersections you got match up
summer harbor
You know how many are subscribed to each
i.. dont know how to present them π
do i just write 65 for the netflix ppl
50 for disney+
willow helm
Well if 65 people are subscribed to Netflix, then 65 goes into the Netflix circle
Yes
summer harbor
i see
willow helm
And if 18 are subscribed to both netflix and max
Put 18 in the intersection of Netflix and max
And then fill everything else
And see if it works out
If it does it's correct, otherwise it's not
Anyways I gotta run good luck
summer harbor
i see i see
willow helm
Right if you get 18 subscribed to both netflix and max, and 90 subscribed to botj netflix and Disney that can't be correct
summer harbor
90?
willow helm
Because that would mean at least 108 people are subscribed to Netflix
Just sn example
also have to take in account people being subscribed to all three but you get it so that was a bad example
summer harbor
and if 8 people are subscribed to all 3 that would mean
116 people subscribed to netflix
willow helm
No
This is a common mistake
Those are already counted in both netflix and max AND netflix and Disney
So you actually have to subtract
I will let someone else explain though
Really gotta go
summer harbor
i see
willow helm
Sorry π
summer harbor
its fine
i think i get it
8 people watch all 3 services, 18 watch netflix and max, 15 watch max and disney, and 20 watch netflix and disney
that means within those 18-15-20, 8 of them watch all 3 services
devout snowBOT
@summer harbor Has your question been resolved?
devout snowBOT
@summer harbor Has your question been resolved?
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Available help channel!
frank wagon
Hello, i have 2 questions. Is this right? And when do i have to shade the whole graph
devout snowBOT
Hello, i have 2 questions. Is this right? And when do i have to shade the whole ...
frank wagon
I need to shade the sets of solutions
olive snow
Hello, i have 2 questions. Is this right? And when do i have to shade the whole ...
Yes, and wdym by the whole graph
frank wagon
Yes, and wdym by the whole graph
Like the lower part
I'm curious
Is it untouched or
olive snow
Like the lower part
As far as you want to
frank wagon
So my solution is still right?
olive snow
Yes, we understand clearly what you mean with that current sketch
frank wagon
I just need to show my work to the teacher
Is this satisfying the answer? (I dont have answer book)
olive snow
Well then the best is to ask them about the drawing, and how they want it, but the inequality part is correct yes
frank wagon
Well then the best is to ask them about the drawing, and how they want it, but t...
And drawing too or no?
That what concerns me most
olive snow
And drawing too or no?
Teachers dependant, ask them
frank wagon
In your opinion?
olive snow
Thats the correct side, maybe you can go a down a little to show its "infinite"
olive snow
rather extending the lines already made
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Available help channel!
vivid fern
i need help doing this, it cannot possibly be 19 steps, what i did so far was convert the zeros and got the multiplicity. x=0 and multi 2 and x= 2 at multi 1
devout snowBOT
i need help doing this, it cannot possibly be 19 steps, what i did so far was co...
wicked turtle
how accurate does this graph need to be
a reasonable next step would be to find the maxima and minima, and determine where it's increasing and where it's decreasing
vivid fern
how accurate does this graph need to be
vivid fern
a reasonable next step would be to find the maxima and minima, and determine whe...
how do i do that
patent ruin
how do i do that
Do you know derivatives?
if you know derivatives, take the ddx of the original polynomial and you can find the increasing and decreasing points.
vivid fern
Do you know derivatives?
idk ngl, maybe i do but i dont know the name
could you explain pls
patent ruin
$f'(x) = \frac{d}{dx} f(x)$
woven radishBOT
Maddie
patent ruin
That would be the best to find your functions rate of change,
If you dont know this, take 5 different points and you should get a rough estimate
devout snowBOT
@vivid fern Has your question been resolved?
vivid fern
im so confused, its fine tho ig ill use chatgpt to explain
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zinc siren
can anyone help me calculate the integral of this function on [0,2] by darboux definition
devout snowBOT
can anyone help me calculate the integral of this function on [0,2] by darboux d...
zinc siren
I've been thinking on taking my partition around the point 1
quiet steppe
zinc siren
dw
devout snowBOT
@zinc siren Has your question been resolved?
zinc siren
can anyone help me calculate the integral of this function on [0,2] by darboux d...
or is there any other way to solve it? i'd do by splitting the interval into parts but since that works when the interval is split into closed intervals and there's the semi-closed interval [0,1) then i thought I shouldn't use it
devout snowBOT
zinc siren
it didn't close lol
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rain coral
what is c
rain coral
like i did part b and a
runic prawn
like i did part b and a
can u show ur answer to b
runic prawn
i can send ms
yes
rain coral
rain coral
yes
here
i assume its like, from point to y axis right?
like centre of circle
to y axis
runic prawn
the center of the circle is not on the y-axis
runic prawn
anyways, think of arg(z) when z is in R (the shaded region)
