is there an easy way to do this?
#help-27
hollow glacier
devout snowBOT
is there an easy way to do this?
thorn cypress
you could use a calculator i guess
alpine python
you can subtract powers of two (without going negative)
keep track of which powers of 2 you subtract
thorn cypress
or divide repeatedly be 2 and keep track of remainders
alpine python
that works
thorn cypress
idk which is faster
sand quarry
you can subtract powers of two (without going negative)
i think this is the way
37 obviously has a 32 in it
5 obviously has a 4 in it
hollow glacier
you can subtract powers of two (without going negative)
oh shit that actually works
sand quarry
so and so
hollow glacier
the standard way is easy
the thing is I dont got time in exam, so like I wanted like a faster way
topaz axle
you can subtract powers of two (without going negative)
that makes sense, too
e.g. 405
256 + 128 = 384 (21 remaining)
256 + 128 + 16 + 4 + 1
if you know the powers by heart, it's probably a tiny bit faster like that
celest lantern
If small numbers you can even do by fingers 😂
But anyways, jokes aside, do more problems and you might find it faster to solve with similar questions.
topaz axle
bin to dec you can do in your head, but not this
hollow glacier
bin to dec you can do in your head, but not this
yes I wanna ask about that now
topaz axle
like, you read it left to right
hollow glacier
how to do this?
maybe like just guide for first qn
then I follow suite for the remaining
topaz axle
7 times 8 +4 = 60
60 times 8 + 3 = 483
feels like maybe you don't need paper
oh my bad
to binary
hollow glacier
7 times 8 +4 = 60
60 times 8 + 3 = 483
how do you even get this?
topaz axle
this means you just write 3 bits for each digits
7 4 3 = 111 100 011 and remove spaces
hollow glacier
7 4 3 = 111 100 011 and remove spaces
how did you arrive at this tho?
topaz axle
how did you arrive at this tho?
you will eventually learn binary up to 8
convert manually otherwise
this way only works if bases are powers of each other, it's like rarely usable
celest lantern
how to do this?
Group them by three.
Each octal bit is represented by 3 smaller bits (0,1). Maximum is 111 and mininum is 000 in binary.
Then can do mental calculation to turn these octal bits back.
devout snowBOT
@hollow glacier Has your question been resolved?
hollow glacier
Each octal bit is represented by 3 smaller bits (0,1). Maximum is 111 and mininu...
so for 743, is it 111100011?
celest lantern
Correct.
It works similarly to other octal numbers as well.
And this way of solving can be used for hex, etc.
hollow glacier
And this way of solving can be used for hex, etc.
wait how many are there even?
hollow glacier
You can use it for hexadecimal too.
I mean like the prefix hex, oct etc
solid perch
the common ones are bin(ary), oct(al), dec(imal), and hex(adecimal). other bases are usually referred to by their full names (ternary, quinary) or just by the base number (base-32, base-64).
(sorry for intruding, and I apologize if I answered the wrong question.)
celest lantern
Well, if octal is 8, then hexal is 16.
You split by 4 for hex, 3 for oct.
No worries Chiaki, I can step back if you want.
solid perch
no, it's fine! I thought the OP was asking about why we abbreviate some bases.
if it is not, I apologize.
celest lantern
Out of the line, that explanation by Chiaki is correct for the definition of bases.
celest lantern
if it is not, I apologize.
It is relevant enough and still helpful 
hollow glacier
the common ones are bin(ary), oct(al), dec(imal), and hex(adecimal). other bases...
oh, those are on the calculator
celest lantern
Yes.
hollow glacier
bruh
solid perch
yes! these four bases are usually present on basic scientific calculators.
hollow glacier
wait so if octal is 8
celest lantern
But for higher educational exam, i.e. University, you won't have chances to use calculators.
hollow glacier
wait so if octal is 8
what about the rest?
celest lantern
Hexal is 16, binary is 2.
Sometimes they do introduce to you quaternary, which is base 4.
solid perch
if you do computer science, base64 will show up a lot. both as a base, and as an encoding.
celest lantern
Yes, pretty helpful.
hollow glacier
if you do computer science, base64 will show up a lot. both as a base, and as an...
what if its digital electronics?
solid perch
binary.
and hexadecimal is also important, because nobody wants to read a string of 1s and 0s all the time.
celest lantern
They are used to store numbers and memory, with data.
solid perch
hex allows you to compress numbers and make them more readable.
the use of base64 (or lack thereof) would then depend on what kind of digital electronics you do.
celest lantern
But up to this level, base 16 is the highest base relevant.
hollow glacier
what about decimal?
solid perch
the prefix dec(i)- (10) already says as much.
if you're asking whether you use decimal numbering in digital electronics, of course, depending on context.
celest lantern
It is pretty much the numbers we are working with in Math.
solid perch
but if you're interfacing with assembly, where you're constantly working with bytes, words, memory addresses, etc., then you're going to see binary and hex more often. don't abandon decimal counting, of course.
alright, I think I've interrupted enough. sorry for suddenly stepping in, and all the best, OP.
celest lantern
Oh, no, you didn't do bad, that information pretty much explained what OP needed to know.
Looking good here.
hollow glacier
by the way how do I convert binary to octal basically reverse order
solid perch
- group the binary string into groups of 3 bits each, starting from the right. if the leftmost group has fewer than 3 bits, prepend leading zeroes until it has 3 bits.
(reason: 8 = 2^3, so one octal digit is equivalent in value to three binary digits with no remainder.) - convert each group of 3 bits into one octal digit separately.
- reassemble the new octal string.
sturdy fiber
1. group the binary string into groups of 3 bits each, starting from the right. ...
-# congratulations on active!
last parrot
1. group the binary string into groups of 3 bits each, starting from the right. ...
(Quick addition to Chiaki's explanation, sorry for intefering, that this method can also be applied into other bases, for example, base 16, but in this case, it is a group of 16, since 16 = 2^4).
-# And congrats on getting active, can't wait to see you on the green side!
devout snowBOT
@hollow glacier Has your question been resolved?
clever sphinx
devout snowBOT
clever sphinx
Im trying to find the roots for -d/a but I keep getting it wrong and getting lost in my working 😭😭
Is there an easier way to do it
celest lantern
Yeah the sum of original roots is using Vieta.
The -b/a part.
Well, suppose 3 roots are x1=alpha+beta, x2=beta+omega, x3=omega+alpha.
Then can you apply sum of the roots fron the vieta step -b/a?
Hope this helps.
devout snowBOT
@clever sphinx Has your question been resolved?
clever sphinx
I have a theory
Yeah?
sage breach
I sent it in a help channel, i just known its best u create one
clever sphinx
Then can you apply sum of the roots fron the vieta step -b/a?
Wdym
long trout
btw for the new c/a equation, what is (-3/2)^2?
how you derived it was correct btw, but i think you plugged in both of those brackets as -3/4
long trout
Im trying to find the roots for -d/a but I keep getting it wrong and getting los...
also you are very close with deriving the new -d/a here. the only part that is incorrect is the "3"
long trout
also you are very close with deriving the new -d/a here. the only part that is i...
what i mean is the 3 in "3αβγ + (α+β+γ)(αβ+βγ+αγ)" that you had should be changed to something else
clever sphinx
Ok thanks I’ll have a look
long trout
Ok thanks I’ll have a look
np
unreal stream
since the question asks for a cubic equation that has those roots
you can just make a cubic equation's highest term's coefficient be one
example
$x^2 + 3x + 2 = 0$
woven radishBOT
caspikonline#1 (the becarsach)
unreal stream
has roots of -1 and -2
multiply all of the terms by lets say a
it will lead to
$a(x^2+3x+2)=0*a$
woven radishBOT
caspikonline#1 (the becarsach)
unreal stream
equals to 0
pay attention
since 1 and 2 are roots of x^2 + 3x + 2 = 0
which mean that $(-1)^2 + 3(-1) + 2 = 0$ and $(-2)^2 + 3(-2) + 2 = 0$
woven radishBOT
caspikonline#1 (the becarsach)
unreal stream
since the polynominal inside the bracket is the same as the previous one
it will have the same roots
which means
$ax^2+3ax+2a=0$
woven radishBOT
caspikonline#1 (the becarsach)
unreal stream
will have the same roots
clever sphinx
btw for the new c/a equation, what is (-3/2)^2?
Oh oops yeah it should be (-3/2)^2 I did (-3/4)^2
clever sphinx
what i mean is the 3 in "3αβγ + (α+β+γ)(αβ+βγ+αγ)" that you had should be change...
I expanded again and got the same values
Idk
long trout
Oh oops yeah it should be (-3/2)^2 I did (-3/4)^2
yep, thats correct
long trout
I expanded again and got the same values
well expand the (α+β+γ)(αβ+βγ+αγ) and this time only concern about the coefficient of αβγ (because that's the only part where youre off)
long trout
well expand the (α+β+γ)(αβ+βγ+αγ) and this time only concern about the coefficie...
and you can find the coefficient of αβγ without needing to expand the expression actually, just by observing the two brackets individually
youre essentially left with what you are looking for, but the coefficient for the αβγ part is off by a number
clever sphinx
Oh is the coefficient 2?
long trout
Oh is the coefficient 2?
no, well that's the coefficient of αβγ in (α+β)(β+γ)(γ+α)
clever sphinx
Also tbh I’m not sure how to factorise this further
long trout
Also tbh I’m not sure how to factorise this further
no need to factorise further, you are almost there
clever sphinx
Like from here
long trout
Im trying to find the roots for -d/a but I keep getting it wrong and getting los...
well the middle part of what you had from here is very close. you just need to change the 3
clever sphinx
Hmm
long trout
Like from here
well you can also do it another way if you wanted to factorise it. after expanding that, add αβγ and see if you can factorise it
long trout
Oh I can just do this
its not a 2 either
long trout
My expansion is still wrong ?
ill have a look
clever sphinx
What should it be? 1?
long trout
What should it be? 1?
oh wait, mb, nvm. the 4th line is correct
clever sphinx
Oh ok
long trout
now what i recommend next is to add αβγ from what you got, and then try and then factorise it
clever sphinx
Im not sure at all
long trout
Im not sure at all
oh wait a min. im very sorry, but you actually should add αβγ, not subtract it. mb
winged tapir
Do you know how to transform roots of polynomial
devout snowBOT
@clever sphinx Has your question been resolved?
clever sphinx
Do you know how to transform roots of polynomial
Yes but not using other roots
winged tapir
Yes but not using other roots
Wdym?
clever sphinx
Like ik you can shift using x=w+1 for example
But I’m not too sure about transforming with other roots
winged tapir
Say, i give you a polynomial with root a,b,c
can you find polynomial with roots 1/a, 1/b,1/c
Using transformation
@clever sphinx
winged tapir
And then substitue x --> 1/w
Right
Okay, so for your question we have alpha + beta + gamma = -3/2
And we have to find the equation with roots, alpha + beta, beta + gamma and gamma + alpha
winged tapir
Okay, so for your question we have alpha + beta + gamma = -3/2
You can find value of Alpha + beta = -3/2 - gamma
clever sphinx
Yep
winged tapir
one of the value of y will be alpha + beta after substitution
clever sphinx
Is x gamma
winged tapir
noo its like
winged tapir
Okay, so for your question we have alpha + beta + gamma = -3/2
after this, we have basically 3 roots... -3/2 - gamma, -3/2 - alpha, -3/2 - beta
winged tapir
Say, i give you a polynomial with root a,b,c
can you find polynomial with roots...
now isnt it similar to this problem?
winged tapir
yeah, its way faster than manually computing everything for the new cubic
this will directly give you the cubic
clever sphinx
So what am I substituting in
winged tapir
w = -3/2 - x
clever sphinx
And that directly gives me the cubic ? Sorry I’m being slow I just only use substitution when it’s obvious to use it
winged tapir
And that directly gives me the cubic ? Sorry I’m being slow I just only use subs...
yep
when you finally put x = -3/2 - w
clever sphinx
Yeah?
clever sphinx
Ok thanks I’ll try it
winged tapir
<@&268886789983436800>
ripe grove
Wtf was that server name
slim axle
Goat mod
ripe grove
:/
devout snowBOT
@clever sphinx Has your question been resolved?
clever sphinx
after simplification, you will directly get the answer
I got the answer so thank you
Im not fully convinced abt the method tho
winged tapir
I got the answer so thank you
No problem
clever sphinx
No problem
Like I don’t fully instead the whole substuituon thing
devout snowBOT
@clever sphinx Has your question been resolved?
clever sphinx
.close
devout snowBOT
devout snowBOT
Available help channel!
junior heron
lost on where to go from here
devout snowBOT
lost on where to go from here
sand quarry
lost on where to go from here
Apply the initial conditions to find your constants
junior heron
Apply the initial conditions to find your constants
how would i do that?
dont i need 2 equations?
sand quarry
how would i do that?
You have $\ds y(0) = \mat{1 \ -1}$
woven radishBOT
sand quarry
This means 1- substitute t = 0 in your final expression 2- equate the entire expression with y(0)
ionic jasper
Can someone pls show me how to derivate this
devout snowBOT
Can someone pls show me how to derivate this
burnt lark
2 is a scalar on the function $e^{-4x+6}$ so we just multiply it out after
woven radishBOT
TestTickler
ionic jasper
Isnt it product rule i gotta use
burnt lark
then, the way i like to interpret taking derivatives like this is recall that the derivative of $e^{u} = e^{u}\cdot :du$, where $du$ is the derivative of the exponentiated term
woven radishBOT
TestTickler
woven radishBOT
TestTickler
burnt lark
recall chain rule is $(f\circ g)(x) = f'(g(x))\cdot g'(x)$
recall chain rule is $(f\circ g)'(x) = f'(g(x))\cdot g'(x)$
woven radishBOT
TestTickler
ionic jasper
Or just u' ×v' no?
burnt lark
if you look at chain rule definition, we take $g = -4x+6$ to be inner function, and $f = e^x$ to be outer
woven radishBOT
TestTickler
burnt lark
so then just apply chain rule, $g' = -4$
woven radishBOT
TestTickler
burnt lark
so then the derivative is $(-4)e^{-4x+6}$, since the derivative of $e^{u}$ is itself times derivative of $u$
woven radishBOT
TestTickler
burnt lark
and then multiply on the original 2 (just a scalar) and you get the -8
ionic jasper
Aight
burnt lark
hope i was able to help
devout snowBOT
devout snowBOT
Available help channel!
daring basin
Just give me hint of this
devout snowBOT
Just give me hint of this
dapper fable
im guessing to look at the difference between two consecutive squares, like (i+1)^2 -i^2
dapper fable
wait is that 1 or l
dapper fable
anyway, say these consecutive squares are m^2, m+1^2 so n-k = m^2 and n+l = (m+1)^2
daring basin
Ok
Ohh yeahh ,solved
Very ez
Why I didn't thought this simple approach😭 😭 😭 😭
.close
devout snowBOT
devout snowBOT
Available help channel!
silk panther
help I don't understand in the definition why do we need the "sup" and "inf" part
devout snowBOT
help I don't understand in the definition why do we need the "sup" and "inf" par...
silk panther
this is L(f, P) and U(f, P)
I understand why the "inf" and "sup" needed in 2nd pic, but not 1st pic
vital sedge
It's possible that a lower integral IS possible but an upper isn't.
Or they don't give the same value
young spade
More than that, the value of any of the two may vary depending on your partition.
Non-Darboux / Riemann integrable functions suffer from that problem.
silk panther
wait sorry but I don't get the explanation
so basically the lower integral is equal to the maximum value of L(f, P) yes?
young spade
In caveman terms, there are more than one lower/upper darboux sum.
And you want the least upper, and greatest lower.
and you want them to match
young spade
This ensures that there is only 1 valid sum to begin with once you let the amount of intervals tend to infty
silk panther
there can be more than one because of the choice of partitions right?
W
I understand it now
leaden raven
You can consider function f(x)=1 for rational and f(x)=0 for irrational
silk panther
alr thanks all, I definitely learnt this b4 but my brain just shrinks after revisiting this
young spade
btw, riemann integrability is the same as darboux integrability
sometimes the darboux and riemann sum are considered the same type of integration
silk panther
yes
runic prawn
why are there different names then
young spade
why are there different names then
different guys came with different overarching ideas in different time
they just happen to be equivalent to each other once you consider the limit
silk panther
they just happen to be equivalent to each other once you consider the limit
the one where the mesh is tending to 0 right
young spade
if by mesh you mean "equally spaced samples with distance h -> 0", yea
In reality the riemann sum doesnt require samples to be equally spaced, but its usually said to be for the sake of simplicity.
runic prawn
help I don't understand in the definition why do we need the "sup" and "inf" par...
roughly speaking, the finer the partition, the larger the lower sum and the smaller the upper sum
devout snowBOT
void fox
btw, riemann integrability is the same as darboux integrability
riemann integrability is a seemingly stricter definition of integrability and it is a nontrivial theorem that it agrees with the darboux integral. I think it helps to keep in mind they are different definitions
void fox
the direction riemann => darboux integrable is trivial but the other direction is not
that is what I meant by seemingly stricter
violet wind
But I thought Darboux was over all partitions with small mesh while Riemann was only the equally spaced ones
void fox
riemann quantifies over all partitions and all possible tags with a mesh size <δ
violet wind
Oh I thought that's what Darboux did
Oh wait
no idk
I'll look it up
Oh ok
I guess I'm misremembering
Darboux is just the global sup/inf across all partitions and Riemann does the mesh thing
Makes sense
void fox
i think the riemann definition is also the more "intuitive" one
young spade
ig i should have clarified that theyre equivalent not equal, mb
void fox
as in if you just told a calculus student who has seen the ε-δ definition of limits or whatever and ask them to come up with a definition for integrability then the riemann definition is what they probably will come up with
void fox
ig i should have clarified that theyre equivalent not equal, mb
yeah no worries. I just mentioned this because when I learned it my prof introduced the riemann integral first and had us prove the integral of a simple function like x^2 and it was unimaginably horrible to do
devout snowBOT
Available help channel!
raven forge
What is your people's answer of the 2nd equation coming?
devout snowBOT
What is your people's answer of the 2nd equation coming?
raven forge
Isn't union in wavy curve compulsory? The answer must be in this form (-a,b) union (c,d)
The answer can't be (-infi, 1)
celest lantern
Your people?
Clearly look at the domain drew, every x in R except (-3,1).
Or, can write: (-inf, -3) U (1, inf).
trail eagle
The answer can't be (-infi, 1)
Once you get to (t+3)(t-1) > 0 you may use wavy curve to find that you need t < -3 or t > 1, but we know t > 0.
So the only actual choice is t > 1, which translates to x < 1.
In general, the wavy curve method doesn't necessarily give a union anyway.
Say x^3 > 0 iff x is in (0, infinity).
devout snowBOT
@raven forge Has your question been resolved?
raven forge
.close
devout snowBOT
devout snowBOT
Available help channel!
keen sundial
how do we do this?
devout snowBOT
how do we do this?
faint gorge
how do we do this?
Do you recall the cross and dot products?
keen sundial
yes
faint gorge
That's what we can do with vectors ig
Unless you have a special course, you should know that dividing by vectors is nonsense
keen sundial
dividing by vector is defined right?
keen sundial
I mean diving vector by scalar
faint gorge
yes that is true
keen sundial
dividing*
faint gorge
Ok so let's say a=(1,0), b=(0,1) and c=(0,2).
Then a.b=a.c but if we had something like "division" then b=c, but that would be false
keen sundial
ok ok i solved this now
faint gorge
You would also ask yourself what the result would be dividing vectors by vectors, a vector again, or a scalar
devout snowBOT
velvet geode
ok ok i solved this now
if you're done you can close this channel by .close
fah
devout snowBOT
Available help channel!
clever sphinx
devout snowBOT
clever sphinx
Not sure where to start with part ii but I’ve done part i
frozen aurora
use double angle formula on sin2theta
runic prawn
maybe divide both sides of i by sin(2theta)?
frozen aurora
and do the division yeah
clever sphinx
use double angle formula on sin2theta
Like this ?
runic prawn
yes
clever sphinx
I thought I was meant to divide by it
runic prawn
should be 3, not 3sin(theta)
clever sphinx
Yh
woven radishBOT
artemetra
frozen aurora
what is the maximum and minimum of $(4t-3)(4t-1)$ on $[0,1]$?
woven radishBOT
artemetra
clever sphinx
Hmmm min of 4t-3 is -7 max is 1
Min of 4t-1 is -5 max is 3
So max is 35 and min is -21
Oh wait
Nvm
clever sphinx
Min is 0.5
Yh sorry I got a bit confused
I just completed the square to find the min now tho
frozen aurora
Min is 0.5
min is -1, but yeah it's at t=0.5
wind mason
that'd be the t-value for the min, what about the actual minimum
frozen aurora
what about the max?
clever sphinx
3
devout snowBOT
devout snowBOT
Available help channel!
ornate flame
devout snowBOT
ornate flame
idk if it's bc I'm not thinking properly but how come on the first one we do ³√8
but on the second pic we just ³ it
tulip peak
In the first one, we use $\sqrt[3]{8}$ because 8 is the scale factor, but we found that scale factor while working in cubic units, so we cube root it to get to linear.
in the second one, we find the scale factor while working in linear units, so we cube it to get to the cubic units we need to find the volume.
Does this make sense?
woven radishBOT
Morgan
ornate flame
ohh
cuz in the first one, we already have the volume
so to find the linear scale factor we have to cube root
to get it back to the original place
tulip peak
Yep
And the same follows for the second one but the other way
linear to cube instead
ornate flame
ohh
so in the first we were working backwards in a way?
so if we already have the area or volume we need to √ or ³√
to get the LSF
tulip peak
Yeah! We need the LSF, and we have the CSF/VSF, so we cube root to get the LSF
ornate flame
ohhhh
that makes more sense now
there's also this other question that I don't rlly understand aswell
bc we already have the volume and size
and im kinda just confused now
ornate flame
Yeah! We need the LSF, and we have the CSF/VSF, so we cube root to get the LSF
btw what's the CSF
tulip peak
For these two to be "mathematically similar" we need LSF=cube (square actually) root of ASF (area scale factor) = cube root of VSF
So they are saying show that cube root VSF does not equal LSF. they just need you to do the math
tulip peak
btw what's the CSF
CSF=VSF I forgot they called it volume scale factor and wrote cubic scale factor, it's the same thing
tulip peak
Almost! $LSF=\sqrt{ASF}=\sqrt[3]{VSF}$
woven radishBOT
Morgan
ornate flame
For these two to be "mathematically similar" we need LSF=cube (square actually) ...
but you just said the cube root of ASF
or was that like a typo
ornate flame
**Morgan**
so we need to find the LSF
by 24/16 =3/2
then 3/2 ² = 9/4
for the ASF
ornate flame
so for this question we don't need the ASF
ohh
so LSF= 3/2
3/2³ =27/8
√27/8
=3 √6 /4
tulip peak
They want you to show that VSF does not equal LSF.
Now you just need to compute the VSF from the given volumes and show that it does equal (LSF)^3
tulip peak
So the VSF will be 1125/576
And the LSF will be 24/16
And they want us to show that (24/16)^3 does not equal 1125/576
ornate flame
wait what
ornate flame
So the VSF will be 1125/576
And the LSF will be 24/16
And they want us to show...
so the stuff I just did wasn't even needed?
ornate flame
I'm confused now
so
all we need to do for this question is:
LSF= 24/16
and
VSF 1125/576
and if the answers are different then they aren't mathematically similar
ornate flame
LSF= 3/2
VSF= 125/64
tulip peak
Almost, ^3 instead
ornate flame
oh shi
I thought I sorted ³
LSF= 24/16= 3/2³= 729/64
VSF= 1125/576= 125/64
so they are not mathematically similar
tulip peak
Correct!!
I think you made a small math error, LSF^3 is 27/8 but that's prob just a typo!
ornate flame
Correct!!
I think you made a small math error, LSF^3 is 27/8 but that's prob ju...
I keep forgetting that
tulip peak
Yep! That's the same thing!
tulip peak
Yep!
tulip peak
The questuon is asking for the depth, what you calculated is the LSF
tulip peak
That looks right to me!
tulip peak
Part b is basicly the same as the first questions we worked on
ornate flame
yeah I get part B
just I didn't like part A
I'm not good with combined shapes either
so hoping that won't come up in the exams
but thank you for the help I appreciate it
tulip peak
Of course!! Good luck with your exam!
devout snowBOT
devout snowBOT
Available help channel!
wet robin
devout snowBOT
wet robin
i do not understand part b at all
in other words, if i saw that in the exam id leave it blank
mystic scarab
You simply have to eliminate t from the equations defining x and y
Suppose I gave you:
x = 3t
y = -18t²
Can you prove that the curve corresponds to this one: y = -2x² ?
wet robin
Suppose I gave you:
x = 3t
y = -18t²
Can you prove that the curve corresponds ...
yes i can
i am able to do this
mystic scarab
Awesome
wet robin
it's just that, the wording is very off putting
is the question asking for cartiasn form? (not sure the spelling)
mystic scarab
it's just that, the wording is very off putting
Well I can assure you that this is very standard as it is written, there shouldn't be any unknown terms
mystic scarab
is the question asking for cartiasn form? (not sure the spelling)
Yup
In other words y = f(x)
wet robin
In other words y = f(x)
ah okay got it
u aware of any other phrases?
coz lowkey it sucks that i know HOW to do it but not understand the question phrasing lol
i think the main hint was no t was in the equation
mystic scarab
u aware of any other phrases?
Mmh I don't remember some specific wordings
wet robin
okay got it 🫡
mystic scarab
i think the main hint was no t was in the equation
Yes exactly
If you don't want to eliminate t, you can also substitute your x(t) and y(t) definitions inside the function y = √...
wet robin
i see
there was another question i found annoying, i am going to quickly find it and post
it was to do with the phrasing
mystic scarab
In other words:
$4\sin t =\sqrt{a\cdot 2\cos(2t )+ b}$
But since you have the parameters $a$ and $b$ I wouldn't use this last route
woven radishBOT
Alberto Z.
mystic scarab
$\Rightarrow 16\sin^2 t = a\cdot 2\cos(2t )+ b$
$\Rightarrow 16\sin^2 t = a\cdot 2(1 - 2\sin^2 t)+ b$
$\Rightarrow 16\sin^2 t = 2a - 4a\sin^2 t + b$
$\Rightarrow ( 16+4a) \sin^2 t = 2a + b$
$\Rightarrow 16 + 4a = 0 \wedge 2a + b = 0$
$\Rightarrow a = -4$ and $b = 8$
$\Rightarrow y = \sqrt{8 - 4x}$ (or $y = 2\sqrt{2 - x}$)
wet robin
i see
oh yes
i know that double angle rule
im trying to draw the parametric equation for this certain question i want to show u but
it displays 2 seperate graphs
woven radishBOT
Alberto Z.
wet robin
oh i see
mystic scarab
it displays 2 seperate graphs
Yeah because you're giving him 2 functions, the x(t) and the y(t)
I guess there's some command for plotting parametric equations, but I don't know the specific name
mystic scarab
You can also type the bounds
wet robin
i see
wet robin
my issue is this
i got 2/5 marks on that question
because i was confused what to do
all i did was find dy/dt and dx/dt
and then divided both to find dy/dx, but it was in terms of t
i was unsure what to do after, and im still unsure
wet robin
and then divided both to find dy/dx, but it was in terms of t
and normally for dy/dx i substitute x to get the gradient at that specific point
but i cant do that if it is t
mystic scarab
The slope for the tangent is: $m = \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$
wet robin
The slope for the tangent is: $m = \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx...
yep however
woven radishBOT
Alberto Z.
wet robin
it is in terms of t
mystic scarab
Sure
wet robin
but
mystic scarab
Because your equations are in terms of t
mystic scarab
**Alberto Z.**
Using this 😅
wet robin
the issue is all i know that x = 16, i dont have t
mystic scarab
You said you had already found the derivatives of x and y
wet robin
yes
mystic scarab
the issue is all i know that x = 16, i dont have t
Did you do part (a) of the question?
wet robin
this is part a 😅
wet robin
I meant, how did you use the fact that C(16, 11) **lies** on the curve?
i didnt
mystic scarab
At a certain value of t (between -3 and 2 of course), your x will take on the value 16, and the y will be 11, do you agree?
devout snowBOT
@wet robin Has your question been resolved?
rigid quarry
construction of triangles where ab=8cm bc=5cm ac=3cm help pls
devout snowBOT
construction of triangles where ab=8cm bc=5cm ac=3cm help pls
winter patrol
is that the full wording of the question
scarlet sequoia
mild sorrel
construction of triangles where ab=8cm bc=5cm ac=3cm help pls
The triangle is not a true triangle but rather a line segment.
It will have no area, and so it appears as a line segment
lament prawn
i am confused on why Q is inverted
devout snowBOT
i am confused on why Q is inverted
lament prawn
givens
devout snowBOT
@lament prawn Has your question been resolved?
lament prawn
.close
devout snowBOT
devout snowBOT
Available help channel!
coarse flume
construction of triangles where ab=8cm bc=5cm ac=3cm help pls
Thats just a line
devout snowBOT
Available help channel!
loud spade
how do we figure out the boundaries of this question
devout snowBOT
how do we figure out the boundaries of this question
solid perch
find the intersection points of the two curves/lines.
loud spade
find the intersection points of the two curves/lines.
so x = 0 and x = + - 1?
solid perch
I have not worked it out but if you wish to show me your work, I can check it for you.
solid perch
take your time.
loud spade
sharp adder
,rccw
woven radishBOT
final spade
-1 to 1 integrate the y
loud spade
integrate the function from -1 to 1
thats sin-1 x right
loud spade
why from 0?
final spade
because -1 to 0 will be down the x-axis
loud spade
is that a problem
final spade
yes
loud spade
okay
loud spade
why not just do the absolute
final spade
welcome
i also completed areas a week back
loud spade
also root1-x^2 is just sin^-1x right
loud spade
u substitution?
why
why not just solve the 1-x^2 as an inverse
aahhh
yes thank you again
loud spade
so we just double it and make 1-x^2 a u and just solve
final spade
true
loud spade
i love you
final spade
do it ig u ll get 2/3
loud spade
bet
final spade
i love you
Thanks bro!
loud spade
.close
devout snowBOT
loud spade
❤️
final spade
u dm me personally if u hv any doubts regarding areas
loud spade
u dm me personally if u hv any doubts regarding areas
bet
final spade
it's one of my fav topics
devout snowBOT
Available help channel!
spring oasis
devout snowBOT
lavish prawn
this is fantastic for my spanish practice
que esta te problema amigo
FUCk it's cual es
spring oasis
p | a => a = pk
a = 3 (mod 4)
=> pk = 3 (mod 4)
=> pk - 3 = 0 (mod 4)
=> 4 | (pk - 3)
=> ???
lavish prawn
i think you gotta give us some context to this chain of statements
spring oasis
p | a => p = 3 (mod 4)
how to prove
lavish prawn
as stated, that's not necessarily true; you're trying to prove that if a = 3 mod 4, then there exists some p with p = 3 mod 4 that divides it. for example, a = 15 is 3 mod 4, but it's divided by 5 which is 1 mod 4
constructing such a single p seems hard, so i'm wondering if you can get somewhere by contradiction instead
lavish prawn
p | a => p = 3 (mod 4)
how to prove
in other words: "p | a => p = 3 (mod 4)" is not true, but "a = 3 mod 4 -> there exists a p with p | a and p = 3 mod 4" is true
spring oasis
p => q = not q => not p
lavish prawn
yea
spring oasis
forall p prime with gcd(p,a) = 1 or p ≠ 3 (mod 4) => a ≠ 3 (mod 4)
lavish prawn
i wouldn't start getting the gcd involved, you can just start with "for all prime p with p | a it's true that p =/= 3 (mod 4)"
and then from there prove a =/= 3 (mod 4), correct
spring oasis
no
a = 3 mod 4 -> there exists a p with p | a and p = 3 mod 4
is what you said
the negation of there exists a p with p | a and p = 3 mod 4
is forall p prime with gcd(p,a) = 1 or p ≠ 3 (mod 4)
devout snowBOT
@spring oasis Has your question been resolved?
spring oasis
a = 3 (mod 4) -> there exists some p prime with p = 3 (mod 4) s.t. p | a
a = 3 (mod 4) -> there exists some prime p , p = 3 (mod 4) and p | a
not(there exists some prime p , p = 3 (mod 4) and p | a) = forall prime p , p ≠ 3 (mod 4) or gcd(p,a) = 1
forall prime p, p ≠ 3 (mod 4) or gcd(p,a) = 1 -> a ≠ 3 (mod 4)
devout snowBOT
@spring oasis Has your question been resolved?
devout snowBOT
@spring oasis Has your question been resolved?
lavish prawn
forall prime p, p ≠ 3 (mod 4) or gcd(p,a) = 1 -> a ≠ 3 (mod 4)
yea but you can rewrite this one in the way that i stated it by using (A or not B = B -> A)
so "p = 3 mod (a) OR p does not divide a" is the same as "p | a -> p = 3 mod a"
i just don't want you to start bringing gcd things into this because that makes it more complicated than it needs to at this point
devout snowBOT
@spring oasis Has your question been resolved?
trail cairn
Guys I have been on 2nd question for an hour, and have progressed a lot it would mean a lot if some1 can help.
devout snowBOT
Guys I have been on 2nd question for an hour, and have progressed a lot it would...
trail cairn
My progress:
sharp adder
okay sooo did u draw diagram yet?
trail cairn
trail cairn
okay sooo did u draw diagram yet?
I'm on 2nd
trail cairn
okay sooo did u draw diagram yet?
On the right page upside diagram
I extended a side
To make it a rhombus
frm being a parallelogram
@modest maple
spiral raptor
<@1116136739090743296>
This is a person's account
trail cairn
This is a person's account
Nvm
trail cairn
WAIT dont pin
K
sharp adder
alright so
trail cairn
alright so
Take time
sharp adder
trail cairn
Hmmm
trail cairn
okay so we know that DC is parrelr to AB
Ya
sharp adder
okay so we can say that traingle ABC is congruent to ADC
trail cairn
okay so we can say that traingle ABC is congruent to ADC
Hmmm
@sharp adder bro take ur time don't hurry
I can wait
sharp adder
we can then say that these angles are the same right?
so blue = blue
purple = pruple
and green = green
trail cairn
oh u used af/cf
hm
sharp adder
okay well what u did is corect but we need to find the ratio of AT to AC
i dont know how getting AF /AC can help us..
maybe it is another way of solving it i just do not realise it-
trail cairn
i dont know how getting AF /AC can help us..
Yea, ik, but I wasn't able to get anywhere
sharp adder
do u want me to share of how i think of it?
trail cairn
so uhh..
trail cairn
I JSUT GOT AN IDEA-
Okay
molten roost
@trail cairn
trail cairn
<@1387825888963596311>
Yea?
sharp adder
know ing twe get triangle
ABE and we have traingle APT
molten roost
Hay can u help me to learn advanced mathematics
sharp adder
!occupied
devout snowBOT
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).
molten roost
@trail cairn i am from 9th class
sharp adder
Then it may
trail cairn
<@1387825888963596311> i am from 9th class
Okay, but not rn
trail cairn
Clever
molten roost
Okay, but not rn
So when
trail cairn
I THINK U CAN SOLVE IT NOW RIGHT?
Leme see
trail cairn
lmk if uneed hints!!
K bro
sharp adder
also btw if it waasnt for ur DE line i would have went for another wayy longer solution so well done!!
trail cairn
Tysm
sharp adder
npnp!
molten roost
@trail cairn can give me tution
sharp adder
also just ralized i made s malle mistakes wait-
and AC will just be 2x AF cause AF = FC
trail cairn
NOW ITS RIGHT
molten roost
@trail cairn i need to talk to you parsal
wind mason
<@1387825888963596311> can give me tution
do this in dms or something, not here pls. this is an open help channel
trail cairn
and AC will just be 2x AF cause AF = FC
Bro, good idea, but F isn't midpoint of AC
sharp adder
Bro, good idea, but F isn't midpoint of AC
yes it is ABCD IS PAARERLOGRAM
trail cairn
yes it is ABCD IS PAARERLOGRAM
Bro F IS COMING FRM E NOT B
sharp adder
ah wait- 
trail cairn
ah wait- <:blobcry:971797574916907028>
But good idea
sharp adder
wait awit but i can model it so wait-
trail cairn
Hm
dark sable
Guys I have been on 2nd question for an hour, and have progressed a lot it would...
I'm pretty sure there's a theorem for no 2
sharp adder
APT is countruent to AB(midpoint of AC)
trail cairn
here is a correct diagram and via this we know that
Bro this won't be helpful bcoz we can't have AB/AP =AQ/AD
@trail cairn
trail cairn
<@1387825888963596311>
Checkout values of ratios given
dark sable
Bro this won't be helpful bcoz we can't have AB/AP =AQ/AD
wut
sharp adder
nautlilus hi come save me this q kinda hard
trail cairn
nautlilus hi come save me this q kinda hard <:blobcry:971797574916907028>
Sob
Me too
I couldnt
sharp adder
wait i am tinkin-
trail cairn
nautlilus hi come save me this q kinda hard <:blobcry:971797574916907028>
But we understood the ques right
dark sable
nautlilus hi come save me this q kinda hard <:blobcry:971797574916907028>
I've been trying to remember the thing
sharp adder
But we understood the ques right
OR WAIT MAYBE IT IS HELPFULL. cause imagne with me we find the ratio of AB/AD WELL we know that DC and FB are equal..
so that means we can apply the ratio to AD and AB respectivelly..
to gett
AT/AF
trail cairn
W8
sharp adder
since side AQ is just some ratio of AD
and side AP is just some ratio of AD
and WE WOULD already know the ratio of AF for each AB and AD
we can solve it!!
sharp adder
no ignore this
trail cairn
But we need AC/AT
sharp adder
i think this might be not true..
trail cairn
i think this might be not true..
IT IS
Rhombus
BASIC PROPORTIONALLY THEOREM
So parallel
sharp adder
then its no longer a parrlerogram
trail cairn
then its no longer a parrlerogram
Bro
First it was. A parallelogram
Then I made side equal
So
....
sharp adder
alright then lets solve this!!
sharp adder
I took 2 hours
🫂
dark sable
<@1387825888963596311>
this is probably a vector problem
trail cairn
this is probably a vector problem
Idk abt that
sharp adder
ALSO I JUST REALIZED THIS WOULD SOLVE FOR AF AND THE PROBLEM WOULD BE FINDING AC SINCE IT WOULDNT BISECT ANYMORE BUT WHAT U SOLVED EARLIER WAS AF/AC WHICH IS WEXACTLY WHAT WE NEED AFTER WE FET AT/AF
ITS PERFECT
WAIT U JUST SOLVED IT THATS IT no?
trail cairn
ALSO I JUST REALIZED THIS WOULD SOLVE FOR AF AND THE PROBLEM WOULD BE FINDING AC...
Wait
sharp adder
WE CAN GET AT/AF AFTER U MADE THE SIDES EQUAL IN THE RHOMBUS
AND BECAUSE ITS EQUAL WE GET TRAINGLE APT AND ABF CONGRUNCY
AND SO WE SOLVE FOR AT/AF AND THEN JUST USE UR SOLUTION EARLIER TO TURN AT/AF INTO AT/AC
(i think?)
trail cairn
AND BECAUSE ITS EQUAL WE GET TRAINGLE APT AND ABF CONGRUNCY
ABF?????
trail cairn
AND SO WE SOLVE FOR AT/AF AND THEN JUST USE UR SOLUTION EARLIER TO TURN AT/AF IN...
Bro it's good but they are similar
I have anth idea
W8
dark sable
Idk abt that
let A be the origin yadda yadda
let AB (arrow)= b and AD (arrow) =d
AC (arrow) = b+d
AC, AB, and AD are some multiple of AT, AP, and AQ respectively wherein AP=61/2022 b and AQ=61/2065 d
point T also lies on the line segment PQ so AT=the triangle thing
best to ask in competition math I'm sure they have far more competent people
I hate geometry
trail cairn
I hate geometry
velvet geode
hmm
trail cairn
My progress
sharp adder
i spent like 10 mins doin random stuff anf got an answer of 0.029854 which is probably wrong
trail cairn
i spent like 10 mins doin random stuff anf got an answer of 0.029854 which is pr...
Ohhh
sharp adder
i am sorry prithvi but i dont think i am smart enough for this
i wishh u best of luck!
trail cairn
i am sorry prithvi but i dont think i am smart enough for this <:blobcry:9717975...
Same here
dark sable
let A be the origin yadda yadda
let AB (arrow)= b and AD (arrow) =d
AC (arrow) =...
so the triangle thing is that AT=nAP+(1-n)AQ=n(61/2022)b+(1-n)(61/2065) d
which should have the same direction as AC hence n(61/2022)=(1-n)(61/2065) giving an n value which you plug back in to get AT and then u just divide
yadda yadda
self explanatory
I hate geometry
anw if you wanna ask questions I can help answer
trail cairn
so the triangle thing is that AT=nAP+(1-n)AQ=n(61/2022)b+(1-n)(61/2065) d
which ...
Oo
dark sable
what I said is prolly wrong tho
trail cairn
I THNIK I FOUND SOMETHIN
Hmm
dark sable
someone correct me on the triangle thing I hate vectors
azure parrot
there's a lemma in vector that say, for any 3 collinear points A,B,C in that order, and a random point M then
MB= x MA + y MC such that x+y =1
which is extremely useful here
trail cairn
there's a lemma in vector that say, for any 3 collinear points A,B,C in that ord...
Oh
trail cairn
WOULDNT AP/AB = TP/TB
Nah bro
trail cairn
was stuck w someone else
Np man
dark sable
there's a lemma in vector that say, for any 3 collinear points A,B,C in that ord...
WE hate geometry
trail cairn
WE hate geometry
Wait I solved ig
azure parrot
trail cairn
Oh my
azure parrot
you won't need this anyway but this's what I would do
dark sable
AHA
I WAS ONTO NOTHING
trail cairn
you won't need this anyway but this's what I would do
Ty bro but Idk vector, si yea...
dark sable
does this even have a name
velvet geode
Ty bro but Idk vector, si yea...
you'll learn basics in 11th, nd core vector in 12th
azure parrot
Ty bro but Idk vector, si yea...
you should find [AQP]/[ADB] first
trail cairn
you should find [AQP]/[ADB] first
I'm onto smthin
azure parrot
you should find [AQP]/[ADB] first
then expresses [ATP]/[AOB] and [ATQ]/[AOD] in term of AI/AO
[ATP]/[AOB] + [ATQ]/[AOD] = [AQP]/2[ADB]
sharp adder
WOULDNT AP/AB = TP/TB
this wwould be true i belive..
dark sable
WOULDNT AP/AB = TP/TB
feels like math is being betrayed by this
trail cairn
I got 3 equations
Every1 of them having some part of or complete AC
trail cairn
Every1 of them having some part of or complete AC
involved
dark sable
there's a lemma in vector that say, for any 3 collinear points A,B,C in that ord...
wait so P T Q, and point A then oh hey thanks so that was the triangle thing
dark sable
so the triangle thing is that AT=nAP+(1-n)AQ=n(61/2022)b+(1-n)(61/2065) d
which ...
this is right I think
trail cairn
The values of ratios given
trail cairn
This ain't enough
sharp adder
-# maybe the geomtric mean therom can help?
trail cairn
-# maybe the geomtric mean therom can help?
No circle here bro
sharp adder
