dude i am honestly having a mega hard time teaching you when i say things but it is like you don't read them at all
#help-19
wooden python
viscid kite
my friend i am just hella confused and running on 2 hours of sleep with no coffee
i am trying my hardest right now
viscid kite
i dont know
wooden python
go get some proper sleep and only THEN come back to this problem.
tomorrow, if need be.
literally, don't put yourself and others through this torture.
wooden python
come back to this after school lol
odd edgeBOT
@viscid kite Has your question been resolved?
blissful hornet
I dont understand how to differentiate this question. I've put the solution on here too and appearently you need to use the product rule and then chain rule. When I do the product rule, I get: (x^2 + 4x)^3 + (2x^2 + 4x). So far, am I correct?
cold sage
I dont understand how to differentiate this question. I've put the solution on h...
no, youre not
we have u=x and v=(x^2+4x)^3
youre main issue seems to be the dv/dx
could you try compute that?
blissful hornet
Alright let me try:
I've used g(x) here as opposed to v, just for your info:
g(x) = (x^2 + 4x)^3
g'(x) = (2x + 4)^3
cold sage
not quite, you dont just differentiate the stuff inside
do you know how to apply the chain rule?
blissful hornet
Oh yeahh, ok let me have a go
y = u^3, u = x^2 + 4x
y'(u) = 3x^2 and u'(x) = 2x + 4
chain rule: y'(x) = y'(u) x u'(x)
so -> y'(x) = 3x^2 x 2x + 4
y'(x) = 6x^3 + 4
cold sage
not quite, in the second line y'(u)=3u^2
y'(x)=y'(u)*u'(x)
=[3(x^2+4x)^2]*[(2x+4)]
blissful hornet
yes! just tried it again. got the same answer as you
right so, we've got =[3(x^2+4x)^2]*[(2x+4)]. And we've got 1 (differenetiated x). How do we go from here
blissful hornet
just to clarify, what we're doing here is using product rule on 1 + (x^2+4x)^3 where f(x) = 1 and g(x) = (x^2+4x)^3 right?
cold sage
just to clarify, what we're doing here is using product rule on 1 + (x^2+4x)^3 w...
product rule isnt used on addition anyway
blissful hornet
how do we use the product rule here though, so f'(x) = 1, right, but with g(x)=(x^2+4x)^3 do we just use our chain rule result: [3(x^2+4x)^2]*[(2x+4)]?
blissful hornet
no no, i think i got you
so we have f'(x) = 1 and g'(x) = [3(x^2+4x)^2]*[(2x+4)]
and then we multiply both right
cold sage
no
blissful hornet
wait ye thats dumb
cold sage
thats not what the product rule states
given f(x)g(x)
the derivative is
f'(x)g(x)+f(x)g'(x)
blissful hornet
not sure how i forgot that lol, right so what we do is:
f(x) = x, f'(x) = 1, g(x) = [3(x^2+4x)^2]*[(2x+4)]. g'(x) = something
and then just apply the product rule right? i say something because im not sure if we're differenetiating [3(x^2+4x)^2]*[(2x+4)] for g'(x), seems a bit complicated but i could give it a go if thats what we're meant to do
odd edgeBOT
@blissful hornet Has your question been resolved?
blissful hornet
no worries lol, respond whenever convienent
cold sage
f(x)=x f'(x)=1
g(x)=(x^2+4x)^3 g'(x)=[3(x^2+4x)^2]*[(2x+4)]
remember we started with f(x)g(x)=x(x^2+4x)^3
blissful hornet
applying the product rule to that (as per my understanding) would then be:
y'(x) = f'(x) * g(x) + f(x) * g'(x)
which translates to:
y'(x) = 1 * (x^2 + 4x)^3 + x * [3(x^2+4x)^2]*[(2x+4)]
cold sage
perfect
blissful hornet
wohooo, let me give that a go then
cold sage
youve now reached the second line/first line,
derivative is done, the rest is just supplementary
blissful hornet
Ok, I think i've created a monster
cold sage
i really dont recommend writing x for multiplication, it just gets confusing
blissful hornet
sorry about that
cold sage
,w expand (3x)(2x+4)(x^2+4x)^2)
clever fjordBOT
cold sage
you expanded (x^2+4)^2 wrong
though i dont see the need to do any of this in the first place unless its a 'show that'
blissful hornet
,w expand (1)(x^2+4x)^3 + x(3(x^2+4x)^2)(2x+4)
clever fjordBOT
blissful hornet
though i dont see the need to do any of this in the first place unless its a 'sh...
ye youre right tbh
blissful hornet
,w expand (3x)(2x+4)(x^2+4x)^2)
could i ask where you got that from
because my product rule thingy isnt the same
cold sage
thats just an expansion of f(x)g'(x), from your product rule
blissful hornet
though i dont see the need to do any of this in the first place unless its a 'sh...
is there a shorthand to getting the answer without expanding
cold sage
you had the answer already
cold sage
applying the product rule to that (as per my understanding) would then be:
y'(x...
this is the derivative
cold sage
nw
blissful hornet
.close
storm wharf
Why does the condition 0>y make the function 1/(x+4)(x-5) negative?
cold sage
if y is <0, then the function is always negative, f(x)<0
quasi sparrow
what's y equal to?
storm wharf
if y is <0, then the function is always negative, f(x)<0
Ok that makes sense actually
In this graph, how do you explain the parabola when it's greater than 0?
It seems like it breaks the rule?
cold sage
you havent restricted the actual function
youve just highlighted the region y<0
may i ask what youre doing this for btw? are you finding x such that is it <0?
storm wharf
So the book wantsme to write a reciprocal of a quadratic with the followng properties
HA: y=0
VA x=-4, x=5
Interval of y<0
cold sage
you mean a range of y<0?
could put absolute value signs around the denominator (if thats allowed)
storm wharf
you mean a range of y<0?
mystic saffron
I've done part (a), not sure how to do part (b)
odd edgeBOT
I've done part (a), not sure how to do part (b)
cold sage
do you know any formulae for triangle area?
mystic saffron
do you know any formulae for triangle area?
1/2 a b sin(theta)
cold sage
how does that work out for you
zealous obsidian
i need help understanding why
odd edgeBOT
i need help understanding why
zealous obsidian
even though this function is modeled with tons of numbers
why is the max on this wave still just half 365 which is 182.5?
the question is this
quasi sparrow
zealous obsidian
so 182.5 days into the year the population reaches a maximum of roughly 4500 deer
quasi sparrow
$\sin(x)$ is max when $x = ?$
clever fjordBOT
riemann
zealous obsidian
1 or -1 i suppose
zealous obsidian
1/2 turn
quasi sparrow
what
zealous obsidian
idk what is that just pi
quasi sparrow
,calc sin(pi)
clever fjordBOT
Result:
1.2246467991474e-16
so 2pi
quasi sparrow
which is what number?
zealous obsidian
1/2
quasi sparrow
no
zealous obsidian
1/2 pi
clever fjordBOT
Result:
1
find when your argument equals pi/2
zealous obsidian
ah okay the paramater of sin
zealous obsidian
"argument" is what's inside the sine function
okay..
i did this
i got 975.6
roughly
set pi/2 = argument
and solved for t
what does that represent ?
zealous obsidian
ill take a pic
zealous obsidian
what is this supposed to equal
quasi sparrow
,rotate
clever fjordBOT
quasi sparrow
,calc pi / 2 * 365 / (2pi) + 75
clever fjordBOT
Result:
166.25
zealous obsidian
my last question would be
quasi sparrow
?
zealous obsidian
why did we set it equal to pi/2 and not 1/2 pi
wait
no shit
pi/2
okay
i see it now
god this makes so much more sense
how did i not see this before
its so simple
wraith dune
odd edgeBOT
wraith dune
completely lost not gonna lie, i tried divergence test to no avail
not really sure what other test would fit to test convergence/ divergence
nocturne belfry
how about just the plain ol limit test
,w graph (2pi*x -1)/(3x+1) from x=0 to x=10000
👀
clever fjordBOT
nocturne belfry
what limit were you working with?
nocturne belfry
do you agree if you want $\sin(f(n))$ to go to 0 along $n \to \infty$ its sufficient to require $f(n) \to m\pi$ as $n \to \infty$ for $m \in \mathbb{Z}$?
clever fjordBOT
jan Niku
nocturne belfry
@wraith dune
wraith dune
yes id agree i think
nocturne belfry
okay
so whats a simpler limit we can work with
instead of $$\lim _{n \to \infty} \sin \qty( \frac{2n \pi -1 }{ 3n+1 })$$
clever fjordBOT
jan Niku
nocturne belfry
not really what im getting at
do you see we have a limit of the form $$\lim _{n \to \infty} \sin (f(n))$$
clever fjordBOT
jan Niku
wraith dune
yes
nocturne belfry
**jan Niku**
so does this apply?
$$\lim _{n \to \infty} \sin(f(n)) = 0 \leftrightarrow \lim _{n \to \infty} f(n) = m \pi$$
clever fjordBOT
jan Niku
clever fjordBOT
jan Niku
nocturne belfry
sin(m*pi) = 0 for any m
it corresponds to starting at (1,0) and moving forward or backwards 180 degrees some number of times
nocturne belfry
i think youre missing the thread 
nocturne belfry
heres how it goes
wraith dune
this is a relatively new unit
nocturne belfry
we feed a number into sin(x)
and it spits out a number
if we feed it pi
or 2pi
or 0*pi
or 100*pi
or any multiple of pi
sin(x) = 0
so if x = m * pi, then sin(x) = 0
wraith dune
so pi
clever fjordBOT
jan Niku
wraith dune
0
nocturne belfry
yea
because 1000pi = m*pi
lets say we feed a short sequence of numbers into sin(x) instead
lets feed in the sequence $x = 0,1,2,\pi$
clever fjordBOT
jan Niku
nocturne belfry
what is sin(x) at the end of this sequence?
wraith dune
its still gonna be 0??
nocturne belfry
yea
okay lets add some more terms
lets add a ton of terms
were gonna have a lot of terms that do whatever, and we dont care about them
wraith dune
always gonna be 0
nocturne belfry
lets say $x = 0,1,8,7,56,2,\dots, m \pi + 2 \epsilon, m \pi + \epsilon, \dots$
clever fjordBOT
jan Niku
nocturne belfry
epsilon is just some really really small number
wraith dune
gotcha
nocturne belfry
lets say after a certain point, all the terms look like that
eventually, all the x's look like $m \pi + \epsilon$, where we can make epsilon as small as we want
clever fjordBOT
jan Niku
nocturne belfry
what happens to sin(x) towards the end of the sequence?
wraith dune
as the numbers get smaller
nocturne belfry
well, theyre not getting smaller
wraith dune
i mean sin is gonna be 0 either way right
nocturne belfry
theyre getting really really close to m*pi
wraith dune
so theyre aproaching 0 then
nocturne belfry
yea
wraith dune
since m*pi =0
wraith dune
okok
nocturne belfry
now, you can apply this logic to your sequence
your sequence of numbers is $$\frac{ 2n \pi - 1 }{ 3n +1 }$$
clever fjordBOT
jan Niku
nocturne belfry
if this sequence starts to look like m*pi
for really really big n
and it gets closer and closer to m*pi
then sine of this sequence will go to 0
otherwise, it wont
wraith dune
i see
nocturne belfry
so whats the sequence go to?
wraith dune
that makes more sense
clever fjordBOT
jan Niku
nocturne belfry
this will tell us if the sequence gets close to m*pi or not
nocturne belfry
so whats the limit equal to
thats your job
but you know
if its m*pi
then sine of this sequence will go to 0
if the limit is anything else, sine of the sequence wont go to 0, and the series will diverge
nocturne belfry
we already know kind of what will happen
jovial owl
probably a dumb question but I'm kinda confused about contour integrals,
you can get the classic 2πi result but I thought if you parameterize it differently you will end up with the normal dt/t integral from 0 to 2π which is undefined, but contour integrals are also independent of your parameterization so these should be equal and you end up with ln(0) = ln(2π) - 2πi
my question is, is this wrong or right and why, can you not represent normal integrals with a contour like this so the normal dt/t integral and the contour integral aren't equal? or is this right in a different branch of the natural log
quasi sparrow
that's because it's wrong
log(0) is undefined
use exponent rules to simplify this. also you're missing d phi
odd edgeBOT
@jovial owl Has your question been resolved?
jovial owl
oh yeah I wrote this in a hurry
jovial owl
log(0) is undefined
so does that make this a nonsensical statement to begin with
quasi sparrow
correct, that step and everything afterwards is wrong
quasi sparrow
yes, but z = t is a pointless substitution.
winged wharf
What is the probability of R compliment intersection F compliment when R= 40 and f=17
winged wharf
I got zero but im bog sure
odd edgeBOT
Available help channel!
keen vapor
In triangle ABC, AB=AC. D is a point on side AB such that AD=DC=BC. if BC=1, find AB.
keen vapor
this is what i think the figure looks like
i know bcd and adc are isosceles, so 2(sqrt(1-height of adc^2)) = ac
but i dont know how to proceed from that
odd edgeBOT
@keen vapor Has your question been resolved?
odd edgeBOT
late dust
@keen vapor
odd edgeBOT
Available help channel!
fallen prism
odd edgeBOT
fallen prism
,rotate 270
clever fjordBOT
late dust
What's the equation?
fallen prism
f(x)= a(x+1)(x-4)
fallen prism
What's the equation?
this one
late dust
So choose two values for a and write the corresponding functions
lime root
but how do i do the state two functions?
choose 2 random values for 'a'
lime root
yep
late dust
Not zero
fallen prism
no restrictions
lime root
no 0
fallen prism
why not 0
lime root
because then the function would be y = 0
fallen prism
so anything other than 0 works
late dust
Because then it wouldn't be a quadratic
fallen prism
okkk
late dust
Maybe expand it too
fallen prism
its expanded
late dust
a(x+1)(x-4) is factored
fallen prism
wdym by expand
late dust
What do you mean?
fallen prism
like
yk how u multiply
the x
wirh other bracket
do i start
with multiplying the a
or no
late dust
The a multiplies everything
late dust
It is if you expand it
late dust
That's not a quadratic
fallen prism
how
late dust
Expand it, you'll see you get a x^4 term
fallen prism
oh
late dust
It's called a quartic (or degree 4 polynomial)
late dust
a(x+1)(x-4)?
fallen prism
yea
late dust
It's not necessarily positive
fallen prism
how
late dust
a can be any non-zero real
late dust
You first want to determine the value of a such that the function goes through (5,9)
late dust
Hm you're wrong
fallen prism
they said sub in (5,9)
late dust
My bad
fallen prism
y is 9
late dust
I misread
late dust
Ok y intercept is -6 yes
late dust
That 1 is a -1
late dust
Yea
late dust
No
late dust
It can, just not here
late dust
Because a quadratic is symmetric about its min or max
late dust
You can just plug it in
fallen prism
in x?
late dust
3/2 (1.5+1)(1.5-4) = -9.375
fallen prism
-9.375
late dust
You don't need to be that precise to graph the function btw
I mean the question doesn't ask for it
late dust
?
late dust
fallen prism
.close
haughty skiff
Idk how to reliably find the foci of ellipses, i can convert the equations into the proper format and get the center and everything but when it comes to foci im lost, heres the current problem im on
odd edgeBOT
Idk how to reliably find the foci of ellipses, i can convert the equations into ...
@haughty skiff Has your question been resolved?
Available help channel!
fiery hedge
anyone know how to do this?
odd edgeBOT
anyone know how to do this?
fiery hedge
kinda stuck here
brittle beacon
Think about the definition of the factorial 
haughty skiff
anyone know how to do this?
im only in alg 2 but just looking at this makes me want to c r y
fiery hedge
Think about the definition of the factorial <:catThink:1073406415575728200>
ive tried but i cant seem to get the hang of it
i dont really know where to begin lmfao
brittle beacon
ive tried but i cant seem to get the hang of it
Well what do you have as the factorial definition?
Of course, take note that $\prod_{i=1}^{n} f(i)$ is the product of all the $f(i)$'s with $i$ from 1 to $n$
clever fjordBOT
@brittle beacon
brittle beacon
How would you find something like 4!, for example?
brittle beacon
And say 5!, how about that?
brittle beacon
4! x 5
Yep, and equivalently, 5 * 4 * 3 * 2 * 1
Do you notice anything similar to those and how they defined the product notation?
fiery hedge
each factorial is just the previous factorial multiplied by the next integer
so 6! is 720
since 5! x 6
brittle beacon
Yep, and equivalently, 5 * 4 * 3 * 2 * 1
That is true of course, but also, notice how this 5! is the product of all integers from 1 to 5
brittle beacon
4x3x2x1
and similarly 4! is the product of all integers from 1 to 4
And we're dealing with products
With that, what do you think $\prod_{k=1}^{2025} k$ is?
clever fjordBOT
@brittle beacon
haughty skiff
i feel like im watching an advanced math lecture and im all here for it
fiery hedge
With that, what do you think $\prod_{k=1}^{2025} k$ is?
2025!
odd edgeBOT
odd edgeBOT
✅
light zodiac
odd edgeBOT
light zodiac
odd edgeBOT
fiery hedge
probably a
light zodiac
Wat is magnitue
fiery hedge
wait nvm its e
light zodiac
It says almost there pick all that apply
light zodiac
wait nvm its e
It says pick all the options
fiery hedge
e
light zodiac
If I pick just e
fiery hedge
as in 2.718
light zodiac
Wat
light zodiac
<@&286206848099549185>
fiery hedge
but its E
light zodiac
No
light zodiac
<@&286206848099549185>
odd edgeBOT
@light zodiac Has your question been resolved?
odd edgeBOT
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
grim sluice
What did you start with?
light zodiac
Umm I thought it was like A
Cuz like 360/8
Buttt idk what else
Or if that's even right
grim sluice
So 360/80 is 45 so it can be rotated 45 degrees and nothing will change
Does that part make sense?
grim sluice
So is it all of them
Not all of them
light zodiac
😔
grim sluice
Just the multiples of 45
grim sluice
Since you can rotate it 45 degrees, you can rotate any multiple of 45 degrees
And 45 degree rotations can make up everything else
grim sluice
So A C and D
I think so
light zodiac
Also wat is magnitude
grim sluice
I’m not good at geometry
grim sluice
Also wat is magnitude
Of a vector?
light zodiac
OMG I got it right
grim sluice
Of a coordinate?
light zodiac
Of a vector?
Wat
light zodiac
grim sluice
It’s like the size of the rotation
light zodiac
It’s like the size of the rotation
Wat does the line and arrow on top of the letters mean
grim sluice
Probably a line segment here. I’m used to seeing that above vectors
grim sluice
Probably a rat
light zodiac
Reflection
grim sluice
For this it probably doesn’t matter
grim sluice
I think it is reflection
Probably not
Look at what happens to lengths during reflections
light zodiac
Look at what happens to lengths during reflections
To the lengths
grim sluice
I mean the length from a point a to a’
Let’s say you are reflecting across the y axis
light zodiac
They call me the y axis
grim sluice
They call me the y axis
Why?
grim sluice
Idk I lied
Lol
grim sluice
Is it rotation
Why do you think that?
Not saying if it’s right or wrong because there are two options left
light zodiac
WAIT
Is it translation
Cuz like everything is like the same fr
But in diff spot idk
light zodiac
OMG it was correct
grim sluice
Nice
grim sluice
Looks correct but my eyes might be failing
light zodiac
Got it right fr
grim sluice
Gimme a min. Random pains
grim sluice
Gimme a min. Random pains
Ok they are over
light zodiac
Ok they are over
Idk if I picked the right points
Idek what a point mapping to another point means
Tbh
grim sluice
There are a few errors I think
So if a point is reflected across a line twice what happens
grim sluice
So since E reflected is G, E reflected should be what?
light zodiac
Wat Abt 3
grim sluice
So h maps to h
grim sluice
So EH->GH because E->G and H->
grim sluice
This is probably the final quesion i can help with because I have. Spanish test tomorrow
So what did you get for the final problem
grim sluice
The one about the length of GH
grim sluice
I just put GH
You can find a number answer
grim sluice
Since EH and GH are reflections their lengths are the same
light zodiac
Duh
grim sluice
So it’s just EH or 4
eternal aurora
odd edgeBOT
eternal aurora
z = a - bi and w = c - di right
fair prism
You can use that yeah
eternal aurora
.close
south solstice
odd edgeBOT
south solstice
I already did the work for #6 but since the normal line is the line perpendicular to the tangent line, would I just follow the same procedure but have the negative reciprocal slope?
Would it be this then?
.close
mystic saffron
why
novel crater
Are you aware of the inclusion exclusion principle?
mystic saffron
not really
novel crater
It states that for two finite sets A and B
|AUB| = |A| + |B| - |A intersection B|
Where |X| denotes the cardinality (# of unique elements) of X
You can check this via Venns diagram
Take for example 10
You count it once since its divisible by 2 and you count once more since its divisible by 5, so you are double counting
There is only a single 10, and thus you cant count 2 times
manic lichen
Is this equal to A^Ty?
odd edgeBOT
Is this equal to A^Ty?
manic lichen
I think the 2 outer matrices are symmetric, so I tried to prove using spectral decomposition but didn’t make progress
.close
odd edgeBOT
odd edgeBOT
Available help channel!
stiff wagon
i know that:
x | 0 | 1 | 2 |
Pr(X=x) | | | |
odd edgeBOT
i know that:
x | 0 | 1 | 2 |
Pr(X=x) | ...
stiff wagon
however, i dont know how to find the possibilities of X
ive tried using a tree diagram, but it didnt work
odd edgeBOT
@stiff wagon Has your question been resolved?
odd edgeBOT
@stiff wagon Has your question been resolved?
stiff wagon
.close
odd edgeBOT
odd edgeBOT
Available help channel!
odd edgeBOT
I don’t understand any of this question
tardy lagoon
why so blurry
orchid ravine
Uhh
Not really
I’m in grade 9
but going into gcse early entry
and i need help with this
tardy lagoon
the maximum/minimum distance from equilibrium
orchid ravine
Uh 2?
orchid ravine
a?
tardy lagoon
not 3
tardy lagoon
(try to plug in x=0)
^
orchid ravine
Sorry my mind is blanking
orchid ravine
Sorry i dont jnow how😔
tardy lagoon
plug in (x,y)=(0,3) into y=2cos(bx)+c
orchid ravine
Oh
tardy lagoon
so it becomes 3=2cos(b*0)+c
tardy lagoon
properties of trig + functoin transformation
orchid ravine
properties of trig + functoin transformation
Thank you
orchid ravine
what next?
^
tardy lagoon
so it becomes 3=2cos(b*0)+c
solve for c
tardy lagoon
so we get 3=2cos(0)+c
tardy lagoon
yes
orchid ravine
Okay
orchid ravine
3=cos0?
tardy lagoon
nope
orchid ravine
90?
tardy lagoon
no
tardy lagoon
yes 2pi radians = 360 degrees for a normal cosine wave
tardy lagoon
count how many times the graph repeated from 0 to 360 degrees
tardy lagoon
umm no
orchid ravine
My mind is blanking again
orchid ravine
so a=2 b=3 and c=1
tardy lagoon
correct
tardy lagoon
no problem
odd edgeBOT
@orchid ravine Has your question been resolved?
orchid ravine
maybe check out khan academy
Alright
odd edgeBOT
odd edgeBOT
Available help channel!
snow solstice
hiii
swift rock
shouldnt it be like this?
snow solstice
hmm why
swift rock
nvm im dumb
snow solstice
dont worry, me too
swift rock
dont worry, me too
yeah that seems correct
odd edgeBOT
ionic pine
so could anyone please tell me where i went wrong
here's my process
and im supposed to get two free variables
but i got only one?
here's what i diddd
and i put all four equations to solve the equations
odd edgeBOT
@ionic pine Has your question been resolved?
ionic pine
<@&286206848099549185>
mint mirage
Your last equation,
Where did the c and d terms come from? Because you have -24b + 27d in the left matrix and -72c + 27d in the right one since you were creating an equation based on element 2, 2 in the matrices
ionic pine
oh my lordddddd
that makes so much more senseee
thank you so muchh ;-;!
now i have two variables that are freeeee
yyaaaaaayyyyy
mint mirage
thank you so muchh ;-;!
No problem, btw if you're done with the channel, you can close it using .close
ionic pine
.close
odd edgeBOT
hey bdw what is that program that you are using ?
pearl tundra
odd edgeBOT
pearl tundra
how do you go about this 
weary pelican
how do you go about this <:catThink:526983414226747393>
this is a hidden polynomial equation of degree 3
you just have to let y = f(x) where f is a mystery function for you to find
pearl tundra
where did the y come from?
weary pelican
<:NervousSweat:789206248419491900> where did the y come from?
it's just a "change of variables"
like for example, if we were to solve $\sin^2(x) - 6\sin(x) + 5 = 0$, I solve $y^2-6y+5 = 0$ where $y=\sin(x)$
clever fjordBOT
rafilou2003
pearl tundra
ah i see
weary pelican
here it requires a bit of manipulation, but as a hint : make sure $\cos(x) \neq 0$
clever fjordBOT
rafilou2003
keen vapor
Two diagonals of a regular polygon intersect at an angle of measure 147 degrees. What is the minimum number of sides of the polygon?
keen vapor
Since the max angle of intersection i think is gonna be the interior angle of the polygon i think the number of sides has to be greater than 120/11
Im not sure how to proceed
odd edgeBOT
@keen vapor Has your question been resolved?
keen vapor
<@&286206848099549185>
odd edgeBOT
@keen vapor Has your question been resolved?
round citrus
Any help for this
odd edgeBOT
Any help for this
round citrus
This is what ive been doing but wolfram gives the other solution
Any pros here to let me know where I made that mistake
never mind figured it out
odd edgeBOT
Available help channel!
round citrus
can anyone tell me which one of the answers is correct or is it even correct.
odd edgeBOT
@round citrus Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
tropic shadow
odd edgeBOT
tropic shadow
how eval
south plume
geometric series
mystic saffron
infinite geometric series
south plume
yes
mystic saffron
yeh
south plume
i asked how to eval
we gave you a hint
tropic shadow
i dont want a hint
south plume
use the formula from infinite geometric series
tropic shadow
a/(1-r)
south plume
mhm
tropic shadow
a = 1/3
south plume
yes
tropic shadow
r = 5/6
south plume
yes
tropic shadow
(1/3)/(1-5/6)
tropic shadow
so
south plume
so a=5/18