we need c and d to be equal and not in (a,b)
#help-36
left trail
proven elk
At this point:
- we know
f'(d) != 0for alldwithd != cin(a, b) - we want to show
f(d) = 0for somedin either(a, c)or(c, b)
because those contradict.
proven elk
we need c and d to be equal and not in (a,b)
we need c and d to be unequal zeroes in (a, b)
rolle's is what says a zero d exists
left trail
At this point:
- we know`f'(d) != 0` for all `d` with `d != c` in `(a, b)`
- we ...
wait where are you getting all of theses? I thought all we knew was that f(c) = f(d) = 0 and f'(x) = 0
warm tundra
please dont delete modpings
tulip coyote
(please don't delete modpings 
)
proven elk
okay
we know f(c) = 0 and f'(-1) = f'(1) = 0 and f'(x) != 0 on (-1, 1)
we know a distinct zero is either in (-1, c) or (c, 1) (prove it)
Case (-1, c):
We can use rolle's because f(-1) = f(c) and f'(x) != 0 on (-1, c). So there exists d with f'(d) = 0 in (-1, 1) (contradiction)
Case (c, 1):
We can use rolle's because f(c) = f(1) and f'(x) != 0 on (c, 1). So there exists d with f'(d) = 0 in (-1, 1) (contradiction)
left trail
so d is in (c,1)
left trail
We can use rolle's because `f(-1) = f(c)` and `f'(x) != 0` on `(-1, c)`. So ther...
I dont' see how f'(x) != on (-1,c) is relelvant. from the fact that f(-1) = c we have (c,c) and c!= d meaning d is in (c,1)
proven elk
I dont' see how f'(x) != on (-1,c) is relelvant. from the fact that f(-1) = c we...
it's what rolles would contradict
left trail
wdym?
left trail
that we have at least one f'(c) = 0
proven elk
And we already know there are none.
We know there are none, we conclude there is one.... contradiction!
We know "no zeroes in (-1, 1)" but rolle's says "must be one in both parts above and below c"
left trail
We can use rolle's because `f(-1) = f(c)` and `f'(x) != 0` on `(-1, c)`. So ther...
for this one isn't your interval nothing since it is (-1,-1)?
proven elk
well c is never -1 so that can't be one of the intervals considered
I'm realizing you don't need to consider both halves.
It is possible to prove both of them contain zeros.
Showing either leads to contradiction.
You can work it this way:
We know f'(-1) = f'(1) = 0 and f'(x) != 0 on (-1, 1) for all x.
Suppose f(c) = 0 for some c in (-1, 1).
We can use Rolle's on (-1, c) because f(-1) = f(c). So there exists some zero ||(some d with f'(d) = 0)|| in (-1, c), and hence in (-1, 1), contradicting f'(x) != 0 on (-1, 1) for all x.
That's it.
left trail
You can work it this way:
We know `f'(-1) = f'(1) = 0` and `f'(x) != 0` on `(-1,...
where are we getting f'(x) != on (-1,1)? Wouldn't that mean that (c,d) is a subset of (-1,1)
proven elk
where are we getting f'(x) != on (-1,1)? Wouldn't that mean that (c,d) is a subs...
Well that's something to prove separately from the givens.
You differentiate and + b drops out and then you can show the inequality directly.
proven elk
where are we getting f'(x) != on (-1,1)? Wouldn't that mean that (c,d) is a subs...
(-1, c) and (c, 1) are in (-1, 1) because c is in (-1, 1)
(c, d) isn't an interval you need to consider
left trail
how so? we create our rolle condition from the fact that f(c) = f(d) so f'(-1)=f'(1)=0 on (c,d)
from rolle defintion
proven elk
Suppose f(c) = 0 for some c in (-1, 1).
We can use Rolle's on (-1, c) because f(-1) = f(c).
The rolle conditions are on the interval (-1, c).
We don't have d yet because rolle will give it to us
left trail
ok let me look at your stuff again then
proven elk
you should try to follow that closely because i think i captured exactly the proof rafilouyear2026 was recommending
left trail
We can use rolle's because `f(-1) = f(c)` and `f'(x) != 0` on `(-1, c)`. So ther...
ok let me ask you about this again. We are using rolle on c and -1. meaning f'(x) = 0 on (-1,c) but we know that f'(x) = 0 only at -1 and 1
which is a contradiction. I don't see how you bring d there though
proven elk
d is the zero that rolle gives
rolle says "some zero exists" and i named it so i can say f(d) = 0
There I spoilered a part to clarify
left trail
but for our proof I thought we were using -1 and 1 and then c to get contradictions
proven elk
Yes, after we assume some c has f(c) = 0 our task is to obtain a contradiction with f'(x) != 0 in (-1, 1).
||We obtain d having f(d) = 0 in (-1, c) for that contradiction||
left trail
ok so you are saying that f(d) = 0 in (-1,c ) and (c,1) but those both lead to the fact that f'(x) = 0 in (-1,c) and (c,1) but we know f'(-1) = f'(1) =0
I don't see how we make the expansion to (-1,1) for both
proven elk
well
if there's a zero in (-1, c) then there's a zero in (-1, 1)
that's because (-1, c) is a subset of (-1, 1)
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dapper stratus
geo proof
neon slate
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!15m
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neon slate
@dapper stratus have you tried drawing a triangle and then going through \ drawing the steps one by one to check they make sense to you?
thats what i would suggest
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delicate kiln
can someone give me a clue on how to start this question?
final saddleBOT
can someone give me a clue on how to start this question?
rustic wedge
uhhh i am not sure since i have done much probability but i presume we let P(A and B) = x/(x+13) and the others similarly?
nvm
that would lead to x+2 = x+13 ☠️
delicate kiln
im lowk confused where u get that
x+13 is the total number right
but isnt P (A and B) in a mutally exclusive just P(A) X P(B)
rustic wedge
that would lead to x+2 = x+13 ☠️
a) i am stupid, i applied demorgans wrong hence i got this
delicate kiln
hm its okay i suck at probability as well
rustic wedge
but isnt P (A and B) in a mutally exclusive just P(A) X P(B)
and b) in a mutually exclusive P(A and B) = 0
delicate kiln
in part a) you are GIVEN x=0
ohhhhh
then why is it telling me to find x
is part A just x=0?
rustic wedge
but isnt P (A and B) in a mutally exclusive just P(A) X P(B)
and it indeed this is correct for independent events
delicate kiln
yes i meant indepedent event for that
rustic wedge
is part A just x=0?
i mean yes as per my understanding
delicate kiln
okay so for part b where do we start
rustic wedge
okay so for part b where do we start
well can you tell me the probabilities you are given? (in terms of x)
delicate kiln
ye
rustic wedge
we are given x equally likely outcomes in the left,top box
delicate kiln
yes
rustic wedge
meaning that for the event A and B, we x outcomes
and total outcomes are x+13 (from the table)
delicate kiln
yes
rustic wedge
so by definition P(A and B) =?
delicate kiln
x / x+13
rustic wedge
yesh
tired walrus
brackets
rustic wedge
now can you relate P(A and B) and P(A' and B')?
delicate kiln
what
delicate kiln
now can you relate P(A and B) and P(A' and B')?
uh
rustic wedge
ann can u delete thatt the greens giving me a stroke
rustic wedge
relate them
anyhow
delicate kiln
how do we relate them
tired walrus
ann can u delete thatt the greens giving me a stroke
done, my bad
rustic wedge
well i am sure you're familiar with de morgans laws?
rustic wedge
done, my bad
its okay, ty
tired walrus
this is peak btw
delicate kiln
this is peak btw
thanks
rustic wedge
this is peak btw
get this sh pinned 
delicate kiln
well i am sure you're familiar with de morgans laws?
um ive done a few
but i forgot
it was
delicate kiln
P (A | B) = P (B AND A) / P (B)?
rustic wedge
P (A | B) = P (B AND A) / P (B)?
no thats conditional probability
rustic wedge
A' and B' = (A or B)'
A' or B' = (A and B)'
these are the set versions of demorgans laws
rustic wedge
its ok
rustic wedge
A' and B' = (A or B)'
A' or B' = (A and B)'
can u try and relate P(A or B) and P(A' and B') from here?
also draw a venn diagram if u find it difficult to make sense of why its true
rustic wedge
typo 😅
delicate kiln
P(A′ AND B′) = P (A AND B)′ =1 − P(A OR B)
rustic wedge
P(A′ AND B′) = P (A AND B)′ =1 − P(A OR B)
good now do u know a formula for P(A OR B)?
delicate kiln
or
ye
P(A) + P(B) -right beacuse its mutually excluse
or do we still need the P(A and B)
rustic wedge
P(A) + P(B) -right beacuse its mutually excluse
we r doing part b .?
rustic wedge
part A is kinda obvious from x=0
delicate kiln
P(A) + P(B) - P(A) X P (B)
rustic wedge
but yes they both have the same formula but different equations
rustic wedge
P(A) + P(B) - P(A) X P (B)
correct so P(A' and B') = (1-P(A)) * (1-P(B))
delicate kiln
is that times
rustic wedge
yes
delicate kiln
oh yes
tired walrus
is that times
the standard for multiplication is * and you should use that rather than x or X in plain text
delicate kiln
okay
rustic wedge
ok so now we have two equations:
P(A and B) = p(A)*p(B) = x/(x+13)
P(A' and B') = (1-p(A)) * (1-p(B)) = 2/(x+13)
BUT we have 3 unknowns so we need one more equation
delicate kiln
hmmm yes
rustic wedge
guh discord ate my asterisks
anyhow
now i want u to visualise what the sets A' and B, A and B' look like using venn diagrams
delicate kiln
hmmmm
rustic wedge
so that you can write the formulae for P(A' and B), P(A and B') on ur own
rustic wedge
wait what formula do u want me to get
either P(A' and B) or P(A and B') does not matter
delicate kiln
yess
rustic wedge
now u have 3 variables namely P(A), P(B) and x
and 3 equations (technically 4)
solve :))
since this is a question from a book, data is set in such a way that it doesnt matter if the 3rd equation is made using P(A' and B) or P(A and B')
delicate kiln
x= 15
delicate kiln
since this is a question from a book, data is set in such a way that it doesnt ...
hmmi see
okay let me check answer
rustic wedge
if its wrong i will be real sad >_<
delicate kiln
yessss x is 15
a is 0 and b is 15
ty for ur help
i am going to further do the questions and hopefully finish this entire chapter
rustic wedge
yessss x is 15
w
rustic wedge
ty for ur help
np
delicate kiln
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restive sinew
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lilac moat
How did they choose denominator?
what exactly do you mean
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latent pelican
A dust-free powder box in the form of a rectangular box can hold enough 10 cylindrical powders (arranged as shown in the illustration below). Know that each chalk has a bottom diameter of 1 cm, a length of 8 cm. What percentage of the box is the volume of 10 chalks? (Consider that the thickness of the box is insignificant)
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A dust-free powder box in the form of a rectangular box can hold enough 10 cylin...
shadow aspen
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
versed crater
Let’s try something simpler
Let’s do a box with 1 chalk in it
How might you solve that problem?
And also pretend we’re in 2d
So it’s just a square with a circle inside of it
What percent of the area of the square is covered by the circle?
latent pelican
Find the volume of 1 chalk?
leaden moon
Find the area of 1 chalk
i think we should only focus on the volume of the chalks first
as we already have the measures of it
and for the rectangular box, we don't have a measure yet
latent pelican
i think we should only focus on the volume of the chalks first
I found the volume of a chalk: it is equal to 2π
latent pelican
2π x 10 = 20π
leaden moon
🔥
leaden moon
A dust-free powder box in the form of a rectangular box can hold enough 10 cylin...
now we want to find the measures of this box
for the height, we can use the height of the chalk as a reference
leaden moon
A dust-free powder box in the form of a rectangular box can hold enough 10 cylin...
and for the width and height, we can use the diameters of the chalks as a reference
latent pelican
Ok
violet forge
hi everyone
leaden moon
hi everyone
!redir
final saddleBOT
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This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
violet forge
okay thanks
latent pelican
The length of the box is: 5 x bottom diameter = 5 x 1 = 5 cm
The width of the box is: 2 x bottom diameter = 2 x 1 = 2 cm
The height of the box is the height of the chalk = 8 cm
Is that true?
leaden moon
The length of the box is: 5 x bottom diameter = 5 x 1 = 5 cm
The width of the bo...
hell yeah
violet forge
well that was an easy question
violet forge
in that question we have to find the volume of a single chalk piece and then multiply it by 10, taking that number as x
we can proceed further
latent pelican
Ok
violet forge
find the volume of the box and divide 'x' by the volume of the box.
finally multiply it by 100 to turn it into percentage
latent pelican
in that question we have to find the volume of a single chalk piece and then mul...
The volume of single chalk is 2π
The volume of 10 chalk is 20π
violet forge
well ik my explanation is not good, i really suggest checking another channels for help..
latent pelican
well ik my explanation is not good, i really suggest checking another channels f...
Oh I understand
Thanks for help
.close
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latent pelican
latent pelican
Bro I’m closed channel
violet forge
Oh I understand
well what was the answer?
if it was not in digit then mine is 25pi
latent pelican
.reopen
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✅ Original question: #help-36 message
violet forge
i am new too
latent pelican
i am new too
Me too
harsh narwhal
i dont knwo how this server works im so so so so sorry
latent pelican
i dont knwo how this server works im so so so so sorry
Pls chat in #discussion
violet forge
!redir
final saddleBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
violet forge
well was the answer 25pi or something in irrational numbers ?
latent pelican
well what was the answer?
if it was not in digit then mine is 25pi
My answer is 5/2π%
violet forge
is the real answer provided ?
latent pelican
is the real answer provided ?
No
final saddleBOT
oh
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
violet forge
my bad
leaden moon
let the master handle thin then
proceed
uhm
latent pelican
Oh wait a min
In the question, let π = 3,14
So that means
Volume of 1 chalk is 6,28 cm^3
Volume of 10 chalk is 62,8 cm^3
Volume of box is 80 cm^3
So, my answer is 78,5%
violet forge
great job
to make things easier, make the equation simplified and then put value of pi.
latent pelican
As a helper, please do not give out answers that could be copied as a homework s...
Remember that u can’t show me ur answer
latent pelican
Really?
violet forge
wait am i not allowed to tell teh answer either?
latent pelican
wait am i not allowed to tell teh answer either?
Yeah
latent pelican
ik
I’m new too
I came here with direct guidance from my friend
By the way, should I ping more people?
violet forge
well if your question is solved then no need to do it but if your answer remains unsolved then you can ping "helper" once in 15 minute
latent pelican
Oh
Why hasn't the bot asked me if I've solved it yet?
Like this #help-14 message
violet forge
Why hasn't the bot asked me if I've solved it yet?
idk
i think you should not have a conversation in this channel
violet forge
My answer is 78,5%. Is that right?
if you followed the steps correctly then you should be sure about that, but if not then you can recheck and ask again in any doubt
violet forge
that's very good!
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latent pelican
Good bye and have a nice day!
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patent grove
I have a DMS problem but no D do I just put 0 in its place ?
final saddleBOT
I have a DMS problem but no D do I just put 0 in its place ?
patent grove
like this 0d, 5m, 20s ?
tired walrus
i mean, yeah
it's less than a full degree innit
however keep in mind
5 minutes and 20 seconds here is time not angle
it's not 0°5'20" at all but rather 00h 05min 20s
tired walrus
fym you never learned that
do you not know how clocks work
and how like timekeeping works
no way you remained ignorant of that
patent grove
no we got digital now I just ask chatgpt for the time
final saddleBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
tired walrus
but also this is not even about analog clocks
surely you did know what a minute (of time) and second (of time) is??
patent grove
yes of course lol
patent grove
I just don't know what you mean by its not 0°5'20" but 00h 05min 20s
like I understand what your saying I just don't know how that changes the problem
tired walrus
when i said 0°5'20", i meant angle
like: zero degrees, five minutes of arc and twenty seconds of arc
what i was saying is that the problem DOESN'T give you any minutes or seconds of arc
no arcs only time
do you understand me or not
if not, what's your native language?
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winged flame
hushed imp
How do you set this up?
winged flame
hushed imp
hi, how do you set this up?
some of the channels need to be reset, they are all full yet some are hours old
copper linden
I have the function f(x) = x² + 50xlogx + 200logx
x² is the fastest growing term in this function, and I would therefore like to prove that f(x) = O(x²).
When I plot the function in Desmos, I found that the function g(x) = 15x² intersects with f at x = 8 (to be safe)
This gives me the witnesses C = 15 and k = 6. However f(x) ! >= g(x) for x > 8 and I can't figure out why? f and g never cross each other again as x approaches infinity (atleast i think, not sure...)
plucky rover
Oh god
plucky rover
How do you set this up?
plucky rover
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quaint wing
mb
restive sinew
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hidden marlin
Man what am i even looking at (i need help with Q9, 10 and 11)
final saddleBOT
Man what am i even looking at (i need help with Q9, 10 and 11)
soft zealotBOT
hidden marlin
wait is q 11 clear enough
hidden marlin
nop
tiny gorge
when in doubt, use the definition of the mean
hidden marlin
when in doubt, use the definition of the mean
sum(i=1 to n) x_i / n
safe kayak
the mean is sum by count
so if you want the common mean of x and y
then find the sum of x and sum of y
this will be (x mean) * n + (y mean)*n
now that you have the total, divide by count = 2n
so you get 0.5 ((x mean) + (y mean))
answer is B
you can use a similar process for the others
tired walrus
!nosols
final saddleBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
tired walrus
you're kinda encroaching on that territory there @safe kayak
hidden marlin
Why would the total count be
Ok no wait I got it
What about q11? I feel like I can do q10 by myself now
What even am I looking at for q 11 😭
hidden marlin
So
The no of observations would be the sum of n from 1 to n.
Then sum of the numbers if their mean is n_1 would be (n_1)(x_1)
safe kayak
yeah
hidden marlin
From i = 1 to n?
safe kayak
yes
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stable viper
for this q does anyone get y = -1/13, x = 73/12
final saddleBOT
for this q does anyone get y = -1/13, x = 73/12
stable viper
tired walrus
x = 73/12? you're sure? @stable viper
stable viper
x = 73/**12**? you're sure? <@538904028709519393>
13 sorry
onyx peak
for this q does anyone get y = -1/13, x = 73/12
you can verify your sols with wolframalpha or sth like that
stable viper
wth how did u solve that that fast
onyx peak
,w (73/13 - 1/13 i)*(3 + 2i)
soft zealotBOT
tired walrus
real part seems to be wrong
can you show your work for how you got your values? @stable viper
tired walrus
hmm. you haven't learned how to divide complex numbers?
it might make your life a lot easier than trying to solve this as a real system
that said i see the issue
tired walrus
33 - 9y - 4y = -32 gives -13y = -65 and not -13y = 1.
you made a sign error
-32 - 33 = -65 not 1
tired walrus
$x+yi = \frac{-16+11i}{3+2i}$
soft zealotBOT
Ann
tired walrus
achieved from your original equation in one step
tired walrus
i literally just divided both sides by (3+2i).
stable viper
wait
ok
so to do this do i
multiply by the complex conjugate
from what im reading
tired walrus
you work out the complex number division the same way you'd work out any other complex number division, and yes it involves multiplying the top and bottom by the complex conjugate of the bottom.
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pallid sundial
I need help working out understanding some hexagonigal graph map. Context is that I am trying to code catan as a personal project but I cannot figure out how to setup the grid for verticies and edges. The math for going between hexes and positions has been coded using the Cubic coordinates (this includes all the information for the axial system). But what I cannot figure out is the math for the edges and nodes. I am using this site for the math:
https://www.redblobgames.com/grids/parts/#hexagon-relationships
final saddleBOT
I need help working out understanding some hexagonigal graph map. Context is tha...
pallid sundial
i am going crazy
This is the cordinates for the map, in the form q,r,s
And this is how the cordinates change in each given direction
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stable viper
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brazen stump
hello is this right what do i do from here
final saddleBOT
hello is this right what do i do from here
tired walrus
the formatting is poor
it looks like you're trying to solve the quadratic 2x^2 - 10x + 5 = 0 by completing the square, yes?
brazen stump
it looks like you're trying to solve the quadratic 2x^2 - 10x + 5 = 0 by complet...
idk if its right and how to carry on
tired walrus
so one thing i'll say is that you should prefer to work with fractions over decimals in this sort of question. not in a "decimals are wrong" way, but in a "this makes your life easier" way.
tired walrus
anyway, ok, i checked your arithmetic, everything checks out
2(x - 5/2)^2 = 15/2 so far is correct
brazen stump
then what do i do
tired walrus
if the (x - 5/2)^2 were replaced with a single letter would you know what to do
coral prawn
If your goal is to solve the equation then note that the equation
2(x - 5/2)^2 = 15/2
is easily solvable
brazen stump
If your goal is to solve the equation then note that the equation
2(x - 5/2)^2 ...
so far is right?
then i just bring the 2 to the other side so 7.5/2?
coral prawn
yess excellent
brazen stump
like this
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stable viper
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final tangle
|z| = |z*|
stable viper
|z| = |z*|
does this mean the conjugate thing
coral prawn
yes
stable viper
the *
final tangle
yes
final saddleBOT
coral prawn
np
ocean herald
Number Systems, Algebra, Coordinate Geometry, Geometry (Lines & Angles, Triangles, Quadrilaterals, Circles), Mensuration, and Statistics
(These chapters I have to cover them in 15days)
9th grade
tired walrus
final tangle
Number Systems, Algebra, Coordinate Geometry, Geometry (Lines & Angles, Triangle...
or if you have specific problems you're stuck on,
claim your own channel and post those problems
ocean herald
or if you have specific problems you're stuck on,
claim your own channel and pos...
Number system
Pretty much
ocean herald
or if you have specific problems you're stuck on,
claim your own channel and pos...
Oh ok
final saddleBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
woven ledge
<@&268886789983436800>
halcyon night
What's a "partition" of R
final saddleBOT
What's a "partition" of R
halcyon night
brisk lion
a partition of any set is a collection of non-empty subsets, such that their union equals the set itself, and any intersection between any two or more sets is empty.
halcyon night
Okay I suppose I understand it a bit
So it's like breaking the set into disjoint non empty subsets
So what's up with that search problem there
brisk lion
yes, exactly so.
unfortunately I don't understand enough of what is written here to answer the question, sorry.
but I hope someone can build off the definition of a partition to help you with that.
halcyon night
Okay thanks for the help!
🐙 
Im guessing the structure here is like a binary search tree?
And does a binary search
Over the sorted array ?
.clode
.close
final saddleBOT
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brittle drift
This working out correct?
final saddleBOT
This working out correct?
narrow dirge
yes
brisk lion
correct.
brittle drift
what if i used 2n+1 and 2m+1
expand each of them to get 4nm+2n+2m+1
factorise to get 2(2nm+n+m)+1
narrow dirge
still even cause 2(2nm+n+m)+1
brittle drift
that still acceptable as an answer?
opaque ember
what if i used 2n+1 and 2m+1
those would not necessarily be consecutive
opaque ember
what you already have is fine
tired walrus
did op switch to a different problem without telling anyone
opaque ember
idts
brittle drift
You just multiplied (2n+1) and (2m+1)?
got it from some video
brisk lion
please show the video.
opaque ember
my suggestion is just extra wording to "properly" introduce the relevant quantities
brisk lion
because what you did was to prove that the product of two odd integers is odd.
tired walrus
my suggestion is just extra wording to "properly" introduce the relevant quantit...
key word here is WORDING.
brittle drift
i thought the part he was talking about had the word consecutive
tired walrus
proofs, by and large, involve words. and they read like English prose.
brittle drift
turns out it didnt
brisk lion
if it is allowed, I can show OP a sample wording of the proof in his original question.
brittle drift
brisk lion
yeah, that is a whole other problem entirely, OP.
brittle drift
i misread and thought consecutive was in the question
so consecutive would be like n+1,n+2 or like m+1,m+2
brisk lion
consecutive integers differ by 1.
tired walrus
here is something else that you should know
which is quite obvious to the point of absurdity
when writing a proof, you should know the thing you are proving
opaque ember
you should also make it clear to whoever's helping what problem youre working on
brittle drift
i dont read properly
boreal lichen
always* know
brittle drift
i need to relearn reading
opaque ember
looks like you switched to a new one without telling us
brittle drift
my bad
brisk lion
are there any further questions you'd like to ask?
brittle drift
no
boreal lichen
Then do .close
final saddleBOT
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brazen stump
hello this is the markscheme answer im confused ho they got the green triangle
gritty flume
Mb
tired walrus
hello this is the markscheme answer im confused ho they got the green triangle
can you uncrop so we see 100% of the page
including the question numbers
brazen stump
tired walrus
i want to see the ENTIRE page, and i don't want you to try and be clever in following my instructions.
but if you wish to know why
i want to see if there is like a part b to this question that your green triangle would relate to
tired walrus
there isnt
then the green-highlighted triangle shall remain unexplained.
tired walrus
it's a reflection of B in the line x=0
it's not a reflection in y=x of anything else that's drawn
ripe seal
i think, purely by intuition, that to get C directly from A, we can rotate A 90deg clockwise
it about the point (1.5, 1.5)
@brazen stump what do you think?
brazen stump
im not sure
ripe seal
hmm
ripe seal
i know it is correct but idk how to formally proove it. wait ill try
ripe seal
but ann said is wrong
which it is
ripe seal
wait wait wait
brazen stump
so i can say reflection in the line y=x?
ripe seal
yeah you can
i see now why i was confused
cause rotating A about (1.5, 1.5) 90deg clockwise looks very similar to reflecting A about line y=x
ripe seal
see dotted triangle is rotation of A 90deg clockwise about (1.5, 1.5) and C is rotation about x=y
ripe seal
so is right?
yes, y=x is correct
final saddleBOT
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Available help channel!
twilit granite
Hi, I'm unsure on how this question is solved, part ii to be specific.
vital crag
can you solve it for n=4?
vital crag
did you use the "standard results for ... and ..." ?
vital crag
you should
use sum(a - b + c +d) = sum(a) - sum(b) + sum(c) + sum(d)
a = r^2, b = 2r, c = 2n, d = 1
twilit granite
but for that, r must be 1 right?
and would sum(c) be 2 * sigma 1
nvm ive got it
thanks for the help
.close
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rain sentinel
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void valley
When the polynomial has real coefficients then complex roots appear in conjugate pairs
aka Complex Conjugate Root Theorem
hence the brackets, the algebra is obvious, I guess?
rain sentinel
yh second step we are expanding
i dont know why they've written it like this
<@&286206848099549185>
vital crag
i dont know why they've written it like this
It's because you're told r1 and r2 are roots
Any quadratic can be factored into a(z-root1)(z-root2) by fundamental theorem of algebra
Here a=1
vital crag
This is a trig problem
3-3i is equivalent to (3,-3) in Cartesian plane. Do you know what angle (3,-3) makes with the x axis
rain sentinel
tan^-1(-3/3)
vital crag
Did you know that yourself or did you use the solution
void valley
this doesnt make sense
Another typo maybe?
void valley
Yeah, I mean here it's correct
But over there I think they did the opposite quotient
void valley
so its 2/sqrt2
And I think it also should be -13/12 pi, since -3/4pi - 1/3pi is -13/12pi
or 11pi/12 after adding 2pi
shadow river
does anyone know this to make sure i got it right
vital crag
does anyone know this to make sure i got it right
!occupied
final saddleBOT
does anyone know this to make sure i got it right
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).
rain sentinel
im talking about the second step
void valley
i.e. how does cos(-θ) + jsin(-θ) become cos(θ) - jsin(θ)?
rain sentinel
void valley
cos(-x) = cos(x) and sin(-x) = -sin(x)
Basic properties of even and odd functions
cos(x) is even (symmetric about the Y axis), so for every x we must have cos(x) = cos(-x)
sin(x) is symmetric about the origin
final saddleBOT
@rain sentinel Has your question been resolved?
stable viper
how is |5i| = 5? isnt it sqrt5?
final saddleBOT
how is |5i| = 5? isnt it sqrt5?
lucid nymph
Its sqrt(5^2)
final saddleBOT
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final saddleBOT
whats the fastest way to do this
final saddleBOT
or is graphing theo nly method
tiny gorge
final saddleBOT
@stable viper Has your question been resolved?
stable viper
what is this in cis form?
final saddleBOT
what is this in cis form?
stable viper
i got 2 sqrt 2 cis -pi/6
stable viper
what abt this?
vital crag
,w sqrt(6) - sqrt(2)i == 2 * sqrt(2) cis(-pi/6)
soft zealotBOT
stable viper
ohh ok thx
vital crag
use cis = cos + i * sin
stable viper
so for a i just do 2 cos3pi/4 + 2sin3pi/4 i
stable viper
use cis = cos + i * sin
thats fastest method?
vital crag
fastest would be to use a calculator
final saddleBOT
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Available help channel!
stable viper
final saddleBOT
stable viper
can someone verify this
loud sundial
,w (-3+i*sqrt3)^(-3)=\frac{1}{24 sqrt 3}i
soft zealotBOT
loud sundial
,w 2sqrt3 e^(i*5pi/6)
soft zealotBOT
loud sundial
dropped sign on argument
loud sundial
,w true or false (-3+i*sqrt3)^(-3) = -\frac{1}{24 sqrt 3}*i
soft zealotBOT
loud sundial
so my answer but just negative?
yeah
final saddleBOT
stable viper
<:catthumbsup:614540188747563008>
sorryy if possible could you verify this too 😭
idk where i keep going wrong
i think just silly mistakes tbh
loud sundial
.reopen
final saddleBOT
✅ Original question: #help-36 message
loud sundial
what happened with your moduli here
$\frac{\left(2\operatorname{cis}\left(\frac{\pi}{3} \right) \right)^3}{\operatorname{cis} \left(\frac{\pi}{2} \right) \left(\sqrt{2} \operatorname{cis} \left(-\frac{\pi}{4} \right) \right)^5}$
soft zealotBOT
Civil Service Pigeon
stable viper
How are you so fast w
loud sundial
How are you so fast w
Idk learning to read fast was a skill that was emphasized in high school ig
and I'm fresh out so I still have it
actually idt that's something you really lose
idk I'm not in a philosophy mood lol
final saddleBOT
stable viper
.reopen
final saddleBOT
✅ Original question: #help-36 message
stable viper
oh wait i alr see the last step
but
ok -pi/4
but apparently my r value is still wrong
loud sundial
$\frac{2}{\sqrt 2}=\sqrt 2$ though
soft zealotBOT
Civil Service Pigeon
loud sundial
stable viper
Oh
wait
OHHhhhhhhhhhhh
shuodl i always rationalise my answers
is that like a unspoken rule
loud sundial
shuodl i always rationalise my answers
eh
if it reduces very easily like this then yeah
if it's something like $\frac{3}{\sqrt 2}$ that doesn't reduce down to a "singular" thing then depends
soft zealotBOT
Civil Service Pigeon
loud sundial
a lot of high school curricula want rational denominators for some reason
but it's rlly not that deep
trail mango
rationalizing the denominator is for noobs
loud sundial
lol hi
stable viper
.close
stable viper
is it acc possible to visually jump from lhs to rhs without solving the denominator of the LHS into polar form then using demoivers theorem
final saddleBOT
is it acc possible to visually jump from lhs to rhs without solving the denomina...
stable viper
i swear im doing too much
loud sundial
Eh it feels like something you should be able to do in your head since the $1-\sqrt{3}-2$ triangle is "nice" depending on how much experience you have. Perhaps the person writing solutions got a bit lazy lol.
soft zealotBOT
Civil Service Pigeon
hearty pulsar
so just experience
yeah
loud sundial
so just experience
and/or you've seen this exact representation before because it's so "nice"
which ig also counts as experience
hearty pulsar
is it acc possible to visually jump from lhs to rhs without solving the denomina...
though this is how like most ppl would do it i think...
stable viper
im spending like more than half a page for one q
so i thought my method must be so slow
or im just writing too many steps
.close
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Available help channel!
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proper dagger
<@&268886789983436800>
worldly spruce
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Available help channel!
unkempt gazelle
Need help i am stuck in this
final saddleBOT
Need help i am stuck in this
crude cairn
i'd suggest you to define
initial income as x,
final income as y (if you need to define this)
then express new peecentage savings in terms of new income and new expenses
brisk lion
might be nice to see your attempts first though, since being stuck implies you had an attempt or an idea.
winter lava
i think one variable is enough
crude cairn
should be for most people
unkempt gazelle
might be nice to see your attempts first though, since being stuck implies you h...
Let x = income
brisk lion
sure. what's next?
also, might wanna clarify, initial or final income?
because you have two different income values here. you should make it clear.
winter lava
let it be the initial income. everything can be defined in terms of the initial income
brisk lion
you might get better mileage by letting x be the initial income instead.
winter lava
yeah that's the original expenses
worldly spruce
Still getting wrong answer
Show your work.
final saddleBOT
@unkempt gazelle Has your question been resolved?
final saddleBOT
@unkempt gazelle Has your question been resolved?
worldly spruce
Why do you have a channel open if you don't plan on engaging with people who want to help you
😭
unkempt gazelle
Sorry I got help in other server I almost forgot
That I had it open here
.close
final saddleBOT
worldly spruce
I meant more the reacting with ❌ ... but ok
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Available help channel!
sacred night
can someone check my solution to this equation please
final saddleBOT
can someone check my solution to this equation please
fossil kiln
can someone check my solution to this equation please
-# nice name
sacred night
,,\begin{aligned} \sin^2(\th) &= \frac{\sqrt3} \sin(\th) = \pm \frac{\sqrt3}2 \end{aligned}
soft zealotBOT
1.732050807568877293527446341505
hasty kiln
yo can somebody help me out
sacred night
,,\sin(\th) = \frac{\sqrt3}2 \ \th = 60^{\circ}, 120^{\circ}
soft zealotBOT
1.732050807568877293527446341505
fossil kiln
yo can somebody help me out
!occupied
final saddleBOT
yo can somebody help me out
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).
sacred night
yo can somebody help me out
!occupied
final saddleBOT
yo can somebody help me out
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).
sacred night
**1.732050807568877293527446341505**
,,\sin(\th) = -\frac{\sqrt3}2 \ \th = 240^{\circ}, 300^{\circ}
soft zealotBOT
1.732050807568877293527446341505
charred comet
can you send over the equation?
sacred night
can you send over the equation?
scroll
sacred night
rude?
sacred night
all good
sacred night
its
charred comet
i mean, you want to know all the solutions, if they are correct?
charred comet
got it! cheking up
soft zealotBOT
1.732050807568877293527446341505
charred comet
yea, your answers are correct
mind telling wich method you used, cuz you know sometimes, we get correct answers from incorrect methods.
sacred night
square root
charred comet
perfect
charred comet
your answer are correct.
sacred night
your answer are correct.
which state are you from
charred comet
you are welcome, if you have any other question, you may ask else close it.
sacred night
.close
final saddleBOT
sacred night
.reopen
final saddleBOT
✅ Original question: #help-36 message
soft zealotBOT
1.732050807568877293527446341505
sacred night
im not sure if its right
timber scroll
Is the answer theta equals to pi/2 ?
sacred night
,,\begin{align*} \sin^2\sec(\th)&= \tan(\th) \ \sin^2(\th)&= \sin(\th) \text{ but} , \sin(\th) \neq 0 , \therefore \th \neq 0^{\circ}, 180^{\circ} \ \sin(\th) &= 1 \ \th &= 90^{\circ} \end{align*}
oh it goes to the left
right?
soft zealotBOT
1.732050807568877293527446341505
odd seal
well, I hope you can also spot the clear trivial solution, sin theta = 0, coz I see that you ignored that part when cancelling it from both sides, but it still is a solution nonetheless
final saddleBOT
@sacred night Has your question been resolved?
sacred night
well, I hope you can also spot the clear trivial solution, sin theta = 0, coz I ...
if it equals 0 then the eq is undefined
wait how can i do yhis
i showed a
but idk how to do b
candid pulsar
if it equals 0 then the eq is undefined
if it equals zero then the sin theta cannot be cancelled out
sacred night
if it equals zero then the sin theta cannot be cancelled out
but isnt it domain
candid pulsar
if it does equal zero then the equation is already true
odd seal
if it equals 0 then the eq is undefined
0=0 is a valid equality
so it would be an answer
odd seal
however, it does mean that you cant cancel sinx in an attempt to find further solutions