Yeah
#help-27
lone stirrup
So in x^2 + 3x + 2 3 = b and 2 = c
vernal monolith
Every complex polynomial can be factorized given the degree is vreater than 1
lone stirrup
So in that example, what would d and e be?
vernal monolith
But every real polynomial doesnt have such property
lone stirrup
So how did you get to 2 and 1?
woven radishBOT
Cyrenux
vernal monolith
also 1.2 =2 so d.e = c is satisfied too
lone stirrup
Ah alright
vernal monolith
This only solves quadratics with integer root though
vernal monolith
but d can't be 3
Yeah, thats not a factor of 2 definitely
lone stirrup
So d and e are basically uncertain
vernal monolith
This only solves quadratics with integer root though
You cant solve x² + 4x + 1 with this knowledge
lone stirrup
we kind of need to figure out
vernal monolith
You cant solve x² + 4x + 1 with this knowledge
You need to learn completing the square for this
vernal monolith
You said b=2 tho?
vernal monolith
What about it
lone stirrup
in that equation b=4 and c=1
vernal monolith
That method you are trying only works if polynomial has a rational root
This one doesnt
lone stirrup
so if i understand now
because for some reason this is really confusing for me
if we have
x^2 + 7x + 6 we would need to find the sum that becomes 7 which is 6 + 1 therefore that d = 1 and e = 6
vernal monolith
Yes
lone stirrup
so we basically need to find the sum for b with the number we have at c
so in x^2 + 5x + 6 we'd need to get to 5 by making 6 - 1 = 5
d = -1 and e = 6
vernal monolith
(-1)*6 = -6 is not 6 though
Try again
Nice guess though
d*e =c and d+e=b must satisfy
lone stirrup
ah alright b = d + e and c = d * e
vernal monolith
Yes
lone stirrup
so in ```x^2 + 5x + 6``` we'd need to get to 5 by making 6 - 1 = 5
d = -1 and ...
so if i guess correctly now i found out that this cant be solved?
lone stirrup
hm i think im starting to understand slowly what they're trying to make me do
so 5 and 6 needs to be refactored
5 can be 2 + 3 and 6 can be 2 * 3
lone stirrup
hey i think im starting to get it
vernal monolith
As well as x²-x-6
vernal monolith
So you are saying x²-7x+12 = (x+4)(x+3)
lone stirrup
can i put d as 3 or 4, or doesnt it matter
vernal monolith
Order doesnt matter
.
lone stirrup
I believe it's true?
x(x+3) = x^2 + 3x
4(x+3) = 4x + 12
x^2 + 3x + 4x + 12 = x^2 + 7x + 12
or wait
no because its -7x
then it shouldve been -4 and -3
since -4 + -3 = -7 and -4 * -3 = 12
vernal monolith
Ye
lone stirrup
alright so we can basically choose what d and e is
-4 can be d or e
same goes for -3
vernal monolith
As well as x²-x-6
Try
lone stirrup
Try
so for when we have just x as b, what would be a good way to go about it?
or actually
vernal monolith
so for when we have just x as b, what would be a good way to go about it?
Wdym
Without x² ?
lone stirrup
i think i have figured it, but not fully yet
vernal monolith
Yes
lone stirrup
thank you for helping me, it really helped me understand it a lot more
so i just wanna sum up quickly
x^2 + bx + c = (x+d)(x+e)
d and e and refactors of b and c
d and e can pretty much be switched, no order
vernal monolith
Ye
devout snowBOT
vernal monolith
Also learn completing the square next day to maximize it out
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gentle warren
Why do you have to check if a point satisfies both lines of a linear system to verify that the point is the
solution to the system?
devout snowBOT
Why do you have to check if a point satisfies both lines of a linear system to v...
safe jasper
there are like 200k people in this server 😭 tagging everyone doesn't work
safe jasper
a system of two linear equations is specifically two equations that must simultaneously be satisfied
that's why they're also called simultaneous equations
sand dove
A system of equations means "... = ... AND .... = ... AND ........"
gentle warren
can u express the answer in a basic manner perchance?
safe jasper
so kind of by the nature of what simultaneous equations are, solutions must satisfy each equation
sand dove
so you're solution of a system if you verify the first equality, AND the second, AND the third, etc...
safe jasper
can u express the answer in a basic manner perchance?
wdym a basic manner?
gentle warren
like simply
eager nova
Your question is, why checking my own work or am I reading wrong?
safe jasper
like simply
are you asking if there's a way to algorithmically find the solutions to a system of equations?
whether or not you can simplify your answer depends on the answer you get
gentle warren
a system of two linear equations is specifically two equations that must simulta...
well that isnt the answer right
ofc they must fit properly
lusty sapphire
Why do you have to check if a point satisfies both lines of a linear system to v...
Because each line represents the set of solutions that satisfy that particular linear equation. And where the two lines intersect defines a point that solves both equations simultaneously.
If I gave you the equation 3y+4x=1, then every point on the graph of that line will be a solution to that equation.
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frosty gyro
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woven radishBOT
frosty gyro
Doing question 17.
jade hornet
Hello
frosty gyro
hi
jade hornet
I’ll try my best
frosty gyro
I'll show what I've done so far
so I'm supposed to use recursion
and the answer is probably going to be a fabonacci number
So let Tn be the number of minimal selfish subsets from 1-n
If n is not in the subsets, then there are Tn-1 such subsets
jade hornet
I reckon we try all of the fabonacci numbers first
frosty gyro
I reckon we try all of the fabonacci numbers first
wdym?
jade hornet
To find out so we use the numbers and then use the equation
frosty gyro
how do I do that?
jade hornet
So we need to find out the equation first
frosty gyro
the closed form or recursion?
jade hornet
Both
frosty gyro
So recursion is Fn=Fn-1+Fn-2
and Binet's formula is Fn = (1+sqrt5)^n-(1-sqrt5)^n all over 2^n *s1rt5
jade hornet
Let’s find out the numbers
frosty gyro
I don't think Binet's formula is helpful
F0=0, F1=1, and the rest of the numbers are 1, 2, 3, 5, 8, 13, 21, 34
and so on
jade hornet
Yes
frosty gyro
If n is not in the subsets, then there are Tn-1 such subsets
Continuing on from this, it means that there are Tn-2 subsets of n is in the set
but I need a reasoning as to why
and that's up to what I've done
jade hornet
I can help you find the answer just not a reasoning
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@frosty gyro Has your question been resolved?
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frosty gyro
.reopen
frosty gyro
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frosty gyro
,rotate
woven radishBOT
frosty gyro
Doing question 17
frosty gyro
I'll show what I've done so far
This is what I’ve done so far
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@frosty gyro Has your question been resolved?
frosty gyro
@fervent swallow
All I've got to do is figure out why there are Tn-2 subsets if n is in the subset
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@frosty gyro Has your question been resolved?
north summit
Other than using a graphing calculator, how can I get to the next step to solve for x?
devout snowBOT
Other than using a graphing calculator, how can I get to the next step to solve ...
north summit
sorry for messy ms paint
frosty gyro
Other than using a graphing calculator, how can I get to the next step to solve ...
maybe try for some values of x
starting from 1*
north summit
do you mean guessing a value for x?
north summit
uhh i have no clue but i came here to ask if there was a way not to use desmos
its just a textbook question so
frosty gyro
oh I think the only way would be to use a calculator
north summit
anyways thanks i think ill just use a graphing calculator
frosty gyro
or try out some values
there's a thing called binary search I think
where you try 1, 2, 4, and so on
and once you get a value that is greater on the right, you start decreasing
frosty gyro
np
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flint spire
@north summit theres a function specifically "invented" to solve this form of transcendental equations, and other forms
frosty gyro
oh
flint spire
its called the Lambert W function
frosty gyro
oh that
flint spire
yes
frosty gyro
Wait but don't you need a calculator for that
oh to actually solve it
is that what calculators use
flint spire
yes right, he wanted something without a graphing calculator
this is how, but must use a calculator
or the infamous wolfram alpha
hallow solstice
Yes
north summit
thank you 🙂
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lost crag
given v_1 and v_2, vectors of vectors space V
is v1 + v2 also in V?
lost crag
as in is v1+v2=v3, v3 is in V?
modest hemlock
yes. use the axiom of vector space
sand dove
a vector space is by definition...
modest hemlock
or call it definition
lost crag
yes. use the axiom of vector space
yeah, i googled it too, it just doesnt seem to be in the listed axiom we got
.close
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lost crag
ty
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queen dirge
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queen dirge
Hello! Trying my hand on some introductory questions from the russian olympiad book, im not rlly good at this so idk if this is an okay proof
jagged harbor
sorry, what are you trying to prove? that the number of odd handshakers is even?
jagged harbor
no problem most of the content was in the initial image anyway
queen dirge
jagged harbor
ok one complaint I have is the argument that A shakes hands with an odd number of people actually, because A and a second person B could shake hands twice
queen dirge
oh true
jagged harbor
also, B could have shaken an even number of hands, with some of them being with A
queen dirge
also, B could have shaken an even number of hands, with some of them being with ...
oh i considered this too but i didnt really know how to extend my proof to generalize that
any techniques i could use to help? i think this is prolly just some simple logic but i just dk 😓 also the solution the book posted kinda does not vibe with me
jagged harbor
it doesn't vibe with me either, like, a single handshake between two people doesn't count as two, but yes it does contribute two counts of a handshake when summing up the number of handshakes each person has experienced
but that's not a critical fault
we can word it like a proof by contradiction, and give variable names to things
let a be the number of people who have experienced an odd number of handshakes, and b [...] even number of handshakes
argue that there is an even number of handshakes experienced
let x be the number of handshakes experienced from the odd crowd, y the number from the even crowd
then ax + by is even
argue that y is even
then that ax is even
idk that wasn't a contradiction lmao
queen dirge
where did y is even come from
jagged harbor
it came from me
I defined it
oh. sorry
I read that wrong lmao
there's b people who have shaken hands an even number of times
so y is a finite sum of even numbers, 2h_1 + 2h_2 + ... + 2h_b
hence y = 2(h_1 + ... + h_b) and is therefore even
jagged harbor
uhhhh I goofed this up in my head I'm sorry
queen dirge
its okay
jagged harbor
if x is the total number of hands shaken amongst people who have shaken hands an odd number of times
and y " "" an even number of times
then x+y encompasses all hand-shaking experiences
and we can argue that the total number of hand-shaking experiences is even, so x+y is even
now we have the logic that y = 2h_1 + ... + 2h_b = 2(h_1 + ... + h_b) is even
the difference of two even numbers is even, so we can show that x is even
but since x is a finite sum of odd numbers, e.g. x = (2k_1 + 1) + (2k_2 + 1) + ... + (2k_a + 1), we can find an argument that x must be an even sum of these odd numbers
so the whole proof can be phrased as a direct proof, rather than by contradiction
sometimes it's easier to phrase things in terms of a contradiction though so it's still good to think about
now I didn't really make an attempt to write the proof, and all this is is a highlighting of some ideas for a proof that could work
jagged harbor
in general you want to be writing your proofs in such a way that the logic is easy to follow (cite deductions, carefully define your things, etc.) while also trying to make it concise or otherwise pleasant to read
your target audience should be someone who is on your level, so if you're just starting out, don't leave out any details, but revise and trim it down when there's superfluous stuff or stuff that can be shortened
also, awkard wording
e.g. "... 2n+2, which is the definition of an even integer" is incorrect; that's not the definition, that's using the definition
so you can say "... 2n+2, which is even by definition"
and if you want to actually use the definition, say 2n+2 = 2(n+1)
queen dirge
I did use that i think
jagged harbor
the reader may see n+1 and think "yup that's an integer because n is"
but if you're still not comfortable with that, then you can just reiterate that n+1 is an integer, hence 2(n+1) is even by definition
queen dirge
*now* we have the logic that y = 2h_1 + ... + 2h_b = 2(h_1 + ... + h_b) is even
just a question, how did you get that y will be even?
jagged harbor
ok, so let me be a bit more careful about that
we have y as the total number of handshakes from even crowd
jagged harbor
let's say there are b handshakers in this crowd, with m_k the number of handshakes from person k (1 <= k <= b)
renamed vars
each m_k is even, i.e. m_k = 2h_k for some h_k
queen dirge
each m_k is even, i.e. m_k = 2h_k for some h_k
AHHHH yea okay okay
jagged harbor
hence y = m_1 + ... + m_b = 2h_1 + ... + 2h_b = 2(h_1 + ... + h_b)
queen dirge
ahhh since each people from the even crowd got an even amount of handshakes then just sum up
jagged harbor
yup
queen dirge
oh ok i get it now kinda got clouded on the wording at first
jagged harbor
depending on your audience, you could simply say that y is a finite sum of even numbers and is therefore even, or something to that effect, without the introduction of these variables
but if you're uncomfortable with that, you should get experience with writing it out the careful / symbolic way
jagged harbor
no problem, thanks for bearing with my mistakes lmao
queen dirge
.close
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karmic yoke
hello guys i need to calculate the area of this, is it correct assuming that the red and green lines are exactly the same because they could be the Radius of the circle? (i did the colored shapes, and right side is exactly the same as the left side)
devout snowBOT
hello guys i need to calculate the area of this, is it correct assuming that the...
sudden yarrow
if they line up with the center of the circle then yes
but the figure you've drawns looks more rather like and oval
do you have it stated anywhere that they are radii?
karmic yoke
do you have it stated anywhere that they are radii?
no, im assuming that it is because i cant think of any other way to solve this
sudden yarrow
well, the cutted section kinda lines up with midle of the squares
it looks like it would be sqrt2b
so yeah looks right
karmic yoke
what does sqrt2b means sorry?
sudden yarrow
$\sqrt{2}$
woven radishBOT
Max-Cat
karmic yoke
oh so you mean the red line
sudden yarrow
and the green one
karmic yoke
yea
sudden yarrow
the green one almost intersects the horizontal line in the middle
but juuuust almost
like how sqrt2 is juuust almost 1.5
low flicker
.help someone check the red marks for me pls.
devout snowBOT
No command called "someone" found.
low flicker
.help
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Commands:
- clopen:
.close,.reopen - consensus:
.poll - factoids:
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Type .help <command name> for more info on a command.
low flicker
.help
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Type .help <command name> for more info on a command.
low flicker
devout snowBOT
low flicker
someone check the red marks for me pls (calc 1)
safe fractal
They sure are red
low flicker
by first I mean problem 2
i thought the antiderivative of lnx is xln(x)
topaz umbra
By false I mean u have marked the correct option
low flicker
Oh ok
topaz umbra
and btw isn't it xln(x) - x
low flicker
yes forgot abt it
lone stirrup
How is this the second square rule?
devout snowBOT
How is this the second square rule?
lusty sapphire
Expand (x-7/2)² to verify
lone stirrup
I understand that
a = x^2
b = (7/2)
lusty sapphire
I understand that
a = x^2
b = (7/2)
b=7, not 7/2
lone stirrup
Oh I see, so we in fractions we take the counter?
lusty sapphire
so we in fractions we take the counter?
lusty sapphire
I'm still not understanding what you are asking
lusty sapphire
yes
lone stirrup
how come that its not 7/2?
lusty sapphire
Because b represents the coefficient of x
If your quadratic were 3x²+423x-11, then b=423
lone stirrup
but if i were to expand the original equation
x^2 - 2x(7/2) + (7/2)
wouldnt that be basically it? since 2x(7/2) = 7x
warm breach
it would expand as:
x²-2x(7/2)+(7/2)²
lusty sapphire
but if i were to expand the original equation
x^2 - 2x(7/2) + (7/2)
I don't get how this is changing what b would be
lone stirrup
it would expand as:
x²-2x(7/2)+(7/2)²
yeah exactly, but in here b would be (7/2) then?
warm breach
are you talking about b of
(a-b)²
lone stirrup
yes
warm breach
yea and SWR was talking of b about quadratic
lone stirrup
miscommunication 
lone stirrup
So now I've verified it, and it's correct. but if i were to start here without the next step, how could I know what to do with 7x?
warm breach
aha wait, I asked same question to my sir once, he gave me general form
gimme a moment to fetch it for you
lone stirrup
or since i can see a = x and b = (7/2) in here it would be self explanatory to do 2ab = 2x(7/2)
lusty sapphire
So now I've verified it, and it's correct. but if i were to start here without t...
$Ax^2+Bx+C=A\left(x+\frac B{2A}\right)^2+\left(C-\left(\frac{B}{2A}\right)^2\right)$
warm breach
aha yes exactly
woven radishBOT
SWR
lusty sapphire
i fixed it
warm breach
oh okay
conan, if you don't understand general form
check out https://www.mathsisfun.com/algebra/completing-square.html
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charred tangle
anyone can check my work '
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anyone can check my work '
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olive snow
Third wrong too
cold bone
Third wrong too
bro destroyed
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viral lynx
Sry if this is a dumb question but is there another way of writing (ln(x))^3
viral lynx
Like 3ln(x) or ln(x^3) or something
viral lynx
Maybe there isnt, it would just be really convinient if I could get rid of that cube for this question 😅
viral lynx
ln²(x)ln(x)
Ok I guess not
faint gorge
!original
devout snowBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
frosty gyro
if the x^3 is in the log then it's 3ln(x)
viral lynx
if the x^3 is in the log then it's 3ln(x)
Its not
viral lynx
(ln(x))^3
woven radishBOT
𝔸dωn𝓲²s
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eager nova
**𝔸dωn𝓲²s**
Not always true
rose rock
When ln (x) < 0
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sterile cairn
If (x,y) is the only solution to the system of equations above and x is positive, what is the value of x? y = 22.56 + 4x y = 20(1.2)^x How do I do it, since x is an exponent?
devout snowBOT
If (x,y) is the only solution to the system of equations above and x is positive...
eager nova
Above?
junior trail
perhaps taking a logarithm of both sides?
eager nova
If (x,y) is the only solution to the system of equations above and x is positive...
!original
devout snowBOT
If (x,y) is the only solution to the system of equations above and x is positive...
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
@sterile cairn Has your question been resolved?
safe fractal
What do you think?
safe fractal
Help? Yes. Solve it for you? No
restive river
help yes
safe fractal
You're correct on this one
restive river
safe fractal
You think the first one?
restive river
Yeah
safe fractal
Correct
safe fractal
gud
restive river
junior trail
nah
safe fractal
gud
restive river
safe fractal
Why do you think this?
restive river
It doesn't look like it has a solution
safe fractal
hmmm... note that these lines extend to infinity
if you were to extend them a bit further to the right, what would happen?
restive river
They would meet
restive river
So consistant
safe fractal
ye
restive river
safe fractal
An easy way to determine this would be to first try and simplify them to the same form
if you express y from the second equation, what do you get?
restive river
how do i express y again
native trench
Basically add/divide/subtract/multiply to get y = something with x
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celest wadi
In statistics
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In statistics
restive river
@safe fractal i finished it
safe fractal
Outside of statistics please
celest wadi
Bayesian statistics as a philosophy seems pretty flawed compared to the frequentist perspective
safe fractal
<@1061691723828432968> i finished it
gj
celest wadi
Is bayesian statistics merely a way of getting useable results without a massive amount of data
And for pretty easy compute
Or is there something else
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celest wadi
Meow
celest wadi
!15m
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celest wadi
<@&286206848099549185>
frosty gyro
hi
frosty gyro
Is bayesian statistics merely a way of getting useable results without a massive...
what's that?
celest wadi
its an approach to statisitics where prior knowledge is valued
adds some zest of subjectivity maybe you can say
celest wadi
beliefs about something
which can be formed from previous data
but u can also pull it from ur ass
celest wadi
hm alright
for ex you can say: "50% of all emails are spam" for spam classification problems
before any analysis of a particular instance or whatever
its alright im just reading about it now
.close
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gentle thicket
im watching a video on binomial theorem, and i came across this- idk what he did
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gentle thicket
<@&286206848099549185>
worn flame
graceful cosmos
He actually wrote down what he did. 198 = 350 - 152
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eternal cliff
ahh sorry for asking this question again, but since then I've still got no idea how to solve it :/
Does the following series converge or diverge?
devout snowBOT
ahh sorry for asking this question again, but since then I've still got no idea ...
eternal cliff
plain old ratio test does not work with this series.
safe jasper
nth term test
if you take the limit as n approaches infinity, if you get any value other than 0, your series diverges
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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).
@eternal cliff Has your question been resolved?
eternal cliff
should i substitute with a variable?
twilit comet
it's 0 * (infinity)^0
eternal cliff
it's 0 * (infinity)^0
okay.. well then how do we calculate (x!)^(1/x)?
eternal cliff
actually im not sure, honestly
thats alright, i personally dont know how to deal with x! in these situations to begin with
i think there is an equation of approx. x! out there
but idk how good that would do here
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spring oasis
I tried ratio test
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@eternal cliff Has your question been resolved?
tender cobalt
ahh sorry for asking this question again, but since then I've still got no idea ...
use #calculus message saying that you can prove that this series is increasing
eternal cliff
use https://discord.com/channels/268882317391429632/326138772477575180/126811113...
its alright! i found the answer
turns out you can use Stirling's approximation to substitute x!
after using laplace's method, asymptotic approximation etc it turns to be divergent
lusty fox
Can someone explain me how to check the validity of an argument
devout snowBOT
Can someone explain me how to check the validity of an argument
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restive river
Quick question before my exam
devout snowBOT
Quick question before my exam
restive river
The answer is 13/30 (it's a practice test ik it's the right answer)
How do I get to that answer? I've shown my work here
after getting common denomenators i get to 13/36 divided by 30/36
but how does that get me to 13/30
rustic laurel
when dividing by a fraction its the same as multiplying by the inverse of that fraction
rustic laurel
no problem
restive river
Well when i multiply i get 390/2376 and i cant use a calculator so OH BOY CANT WAIT
rustic laurel
nono
well actually sure if you want
but now if you divide this big number by 36 you should get 13/30
restive river
Divide both num and denom by 36?
rustic laurel
wait how did you get 390/2376
rustic laurel
no it should be 468/1080
rustic laurel
let me save you some time though
when you have something like this
you could basically rewrite it as 36/36
which is 1
restive river
ty so much man
rustic laurel
no problem
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restive river
Can someone tell my why this is the correct answer?
devout snowBOT
Can someone tell my why this is the correct answer?
restive river
When solved the Answer 0 put into 2x + Y = 0 you get 0
But when 2 is put in you get -1
So why is that right?
dense jay
y=0 leaves you with 5x^2=9 x^2=9/5
and 2x=0 x=0, those arent compatible
restive river
Compatible how?
restive river
Wait so both the top and bottom have to be true?
dense jay
theyre the same variables, both equations have to hold
dense jay
the square root of 1 is +1 or -1, if x^2=1
restive river
so despite them being different it still works?
oh yeah youre right
alright thanks man
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thin geode
Number 10
thin geode
,rotate
woven radishBOT
clever pine
First find the derivative of the function
thin geode
Thats the tricky part
thin geode
split?
thin geode
Have you not learnt this?
im self taught
clever pine
It’s quite simple but do you get what I’m saying?
clever pine
If the numerator has multiple terms all over the same common denominator, you can split each term of the numerator into fractions over the same denominator
Of course make sure you get the + or - symbols correct!
clever pine
Yea
thin geode
and i take derivative of that?
thin geode
So i got 1-3x^-2 +2x^-3
clever pine
Yeah
thin geode
but how i solve it when i put equal to zero?
thin geode
So fraction?
clever pine
I.e -3/x^2
thin geode
Which is 3/x^2
clever pine
No keep as separate terms
thin geode
yeah forgot the sign
clever pine
But you get that right?
thin geode
Yeah got 1- 3/x^2 +2/x^3
thin geode
even with x^2?
clever pine
Yeah
You have to times all the fractions by the same number to ensure there’s values are the same ratio
thin geode
but i get 3/x right? For the x^2
clever pine
It’s a cubic
thin geode
Oh so its gon be x(x^2 -3) = -2
clever pine
Just put it into your calculator
thin geode
Just put it into your calculator
i dont know how to do that on my calc
clever pine
Show me your calculator
thin geode
clever pine
The answer is x=-2 and x=-1(repeated)
thin geode
is it the calc button?
thin geode
can i solve it algebraicly?
clever pine
You can but it’s very long and to be honest I don’t know how
When you get these exams expect you to put it into a calculator
thin geode
ok ill figure that out later, but so i get the extreme points. I then put into org equation to get the y value
clever pine
Yeah
thin geode
then i differentiate the equation again to get infection point, can we go over that
clever pine
Then find the second derivative
thin geode
3x^2 -3
clever pine
1st derivative finds the gradient function
2nd show the gradient of the gradient function
thin geode
In the second derivative equation?
clever pine
Sorry I wrote negative earlier
clever pine
In the second derivative equation?
Yeah
thin geode
How? I got the x values as 1 and -1
clever pine
I think you’ve found the wrong second derivative
clever pine
So i got 1-3x^-2 +2x^-3
Of this
clever pine
No
thin geode
But aint that the same thing?
clever pine
No
That’s when we times f’(x) =0 by x^3
We need to find the second derivative of the original function
clever pine
Then sub in -2 and +1
thin geode
Yeah fromt the first derivative
clever pine
Yeah
clever pine
Ok
thin geode
And 0 for 1
clever pine
That means it’s a maximum for -2
thin geode
Yeah because thats negative
thin geode
here ill send a pic
clever pine
He’s amazing at upper high school stuff
thin geode
thin geode
I recommend Bicen maths YouTube videos for the topics your doing
ill def check him out thnaks
clever pine
Did you get it right?
clever pine
We got that though didn’t we
thin geode
no because 6/1^3 -6/1^4 is just 0
clever pine
The second derivative
thin geode
Yes
clever pine
If f’’(x) = 0 it could be a point of inflection so we need to more investigation to ensure it is
Bicen maths has a good video on it. I probably can’t explain it well enough on text.
You essentially have to test points close to the stationary point to find the shape of the curve
clever pine
Have a good one
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primal quail
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gloomy gazelle
how do i solve this?
devout snowBOT
how do i solve this?
gloomy gazelle
i really dont know much of these 3d vectors and cuboids/cube questions, could anyone reccomend me any videos for these?
ashen stirrup
vectors are in the for of x, y and z right?
you can use the given vector to label the side lengths
rose rock
Idk any but the only knowledge needed here are the property of the shapes and some geometry
ashen stirrup
i really dont know much of these 3d vectors and cuboids/cube questions, could an...
have you done 2d vectors before?
gloomy gazelle
yes
i can do 2d vector questions for the 2d shapes but 3d vectors are very hard to solve
ashen stirrup
do you know what the length AB is?
gloomy gazelle
AG+GB?
ashen stirrup
use the given vector, you can then find the other dimension of the prism to
answer the questions
to get from A to G you go 12 in the x direction, 4 in the y and 2 in the z
gloomy gazelle
right
ashen stirrup
you can then say AB is 12 etc.
gloomy gazelle
right
ashen stirrup
A to M is AB + BM
gloomy gazelle
so
ashen stirrup
BM being half of BC
gloomy gazelle
AM would just be (12,2,0)?
ashen stirrup
yup
ashen stirrup
yeah
there are different ways to get from one point to another but they will give the same answer
ashen stirrup
all good
gloomy gazelle
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round sentinel
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unique stag
!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
interval is not given right?
soft umbra
is it correct?
It’s one of the answer
mystic scarab
devout snowBOT
@round sentinel Has your question been resolved?
rain bluff
this is wrong because secx isnt the reciprocal of sinx and csc isnt the reciprocal of cosx, if it was correct it would be secx=1/cosx and csc=1/sinx
devout snowBOT
this is wrong because secx isnt the reciprocal of sinx and csc isnt the reciproc...
rain bluff
am I missing any other parts were I am wrong?
if not does the rest of my work check out
the correct solution is tan^2(x). To get this you need to rewrite t he equation with the correct identities and then simply, use the pythag identity, and simplify again.
it's very difficult to type out lol
so i just wrote steps
round sentinel
It’s one of the answer
oh alr, thanks
devout snowBOT
@rain bluff Has your question been resolved?
rain bluff
<@&286206848099549185>
rose rock
am I missing any other parts were I am wrong?
No
After applying that correction, the cos^2 (x) ends up as the denominator and the sin^2 (x) the numerator, which gives your answer
rain bluff
After applying that correction, the cos^2 (x) ends up as the denominator and the...
so I'm all correct?
rose rock
Yeah
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solid osprey
A,B,C is on a line, ABD and BCE are equilateral triangles, S is the intersection of AE and CD, fins ASD
devout snowBOT
A,B,C is on a line, ABD and BCE are equilateral triangles, S is the intersection...
solid osprey
not sure how to do this
solid osprey
trig is strictly not allowed btw
solid osprey
isnt it 60
boreal helm
A,B,C is on a line, ABD and BCE are equilateral triangles, S is the intersection...
Sry i meant the sum is 120
And the angle is 60
If I drop
A line from S to B
Will it be perpendicular to the straight line?
solid osprey
dunno
solid osprey
how do you know its 90
boreal helm
I said that if we drop a perpendicular bisector from s
solid osprey
ok go on
boreal helm
A,B,C is on a line, ABD and BCE are equilateral triangles, S is the intersection...
We consider this one
solid osprey
hold on
boreal helm
Ok
solid osprey
nvm
daring stag
Hi @boreal helm
daring stag
I'm stuck somewhere
What's the question
daring stag
Oo geometry questions
devout snowBOT
@solid osprey Has your question been resolved?
daring stag
A,B,C is on a line, ABD and BCE are equilateral triangles, S is the intersection...
Is angle asd 60
?
solid osprey
dunno
turbid cypress
We don't know whether the perpendicular line will intersept AC at B
It could be another different point
turbid cypress
Yes, they said it earlier
daring stag
Yes, they said it earlier
Now Take triangle ABE
From there you will get
Angle Bae be 30 degree
cold bone
how?
solid osprey
proof?
turbid cypress
No
solid osprey
no
cold bone
Ab and Be are equal
but not congruent
turbid cypress
Yeah
solid osprey
wait, but technichally this doesent have constraints on the size of them no?
turbid cypress
solid osprey
would it be valid to assume that BCE has some length such that AE is the angle bisector of BAD
solid osprey
nop
turbid cypress
Maybe from this we can prove that ACED is a cyclic quadrilateral
solid osprey
this?
solid osprey
hm
turbid cypress
But why do we need this
solid osprey
Maybe from this we can prove that ACED is a cyclic quadrilateral
does that acomplish anything
turbid cypress
I mean it could
solid osprey
absd or bces being a cyclic makes sense
turbid cypress
But I assume the problem intends to be solved using Geometry only
Not via Trigonometry
solid osprey
trig isnt allowed
cold bone
see from here we know that required angle is alpha + beta
cold bone
If ya'll observe, triangle ABE is congruent to the triangle DBC
from there we can conclude that alpha + beta = 60degrees
I am not sure if I am correct, but please check it once
solid osprey
you mean simmilar?
cold bone
you mean simmilar?
congruent
solid osprey
huh
cold bone
If ya'll observe, triangle ABE is congruent to the triangle DBC
from there we ca...
in the exact order that I've written
solid osprey
in the image bd=/=be
solid osprey
how did you get a+b=60
cold bone
and DB=AB
cold bone
how did you get a+b=60
you got the congruency point?
cold bone
damn thats smart
after that it's just sum of angles
cold bone
I literally hate geometry fr
solid osprey
.close
devout snowBOT
solid osprey
fr fr
turbid cypress
If ya'll observe, triangle ABE is congruent to the triangle DBC
from there we ca...
Wait
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Available help channel!
turbid cypress
SAS (side-angle-side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
devout snowBOT
SAS (side-angle-side): If two pairs of sides of two triangles are equal in lengt...
turbid cypress
So we need ABE = DBE
solid osprey
lmao
cold bone
Oh mb I read the triangles wrong
that was the point, to read the triangles in opposite sense
boreal helm
Yo
cold bone
ayo
glossy dew
whats the question?
cold bone
whats the question?
Anirudh's point gave me this idea'
turbid cypress
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cold bone
so credit goes to him
turbid cypress
A,B,C is on a line, ABD and BCE are equilateral triangles, S is the intersection...
.
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sick arrow
I want a function, such that the graph looks something like the attached image. How can I do this? my best attempt has been y=-abs(x)
devout snowBOT
I want a function, such that the graph looks something like the attached image. ...
topaz axle
sick arrow
thanks