sin(85) = sin(180-85)?
#help-41
pulsar crest
pulsar crest
Yes
ionic nest
use that
pulsar crest
but the other 2 change
ionic nest
but still just as efficient
ionic nest
rlly?
ionic nest
I got 36.04 uh-oh
i got that too
pulsar crest
Yes it got 25.6
but then again it miswrote it
17 b (the second b. Itβs suppose to be a d)
ionic nest
yea
well
lemme try it the proper way
wait
hold on im too lazy to do that
ok lets do some reverse thinking
pulsar crest
Okay!!
ionic nest
use cosine law
u have an angle and 2 sides
find out the length of bc
see if it even matches what we were using
pulsar crest
25 degrees, 34 metres, and 36.04?
ionic nest
nah the answer
pulsar crest
or do i use 85 degree, 34 metre, and 15.29
ionic nest
25, 34 and 25.6
ionic nest
damn
ionic nest
i cant believe i got it wrong
ionic nest
yea
oak quartz
do you guys care about my work?
oak quartz
I did it without law of sines/cosines cuz that shit is stupid
oak quartz
send it
ok
ok can i say something annoying
ok im gonna say it anyways
this problem is easy, it's just the wording is cancer
ionic nest
lmao
oak quartz
my answer is used estimates too many times
pulsar crest
c = 15.28
oak quartz
so it's not as precise as i'd like it to be
pulsar crest
my brain is going to explode π
oak quartz
haha I've tangled with one too many middle school geometry problems to have this one get me
pulsar crest
so what was ur final ansswer?
oak quartz
ok i have no idea why you would need this lol
oak quartz
so what was ur final ansswer?
25.585
pulsar crest
i think u wouldve been right if it werent for ur rounding
oak quartz
what's the right answer?
I should be right to at least 2 decimal places
definitely 1 decimal place
pulsar crest
the book says 25.6 but i dont know
pulsar crest
i was jokinggg
oak quartz
oh
pulsar crest
i think u wouldve been right if it werent for ur rounding
^
ionic nest
ok i have no idea why you would need this lol
shush im thinking on how to make it work
pulsar crest
lets use probability
ionic nest
nvm i did not cook with that
oak quartz
here's my exact answer for your numerical precision fetishes: $AC=34\cos25-\sqrt{(\frac{34\sin25}{\sin70})^2-(34\sin25)^2}$
lmaooooo
grizzled pagodaBOT
00100000
ionic nest
wait
pulsar crest
Thank u but im too dumb to ever get that
oak quartz
oh come on. you're reconstructing the answer that you already know
ionic nest
i knew i wasnt tripping
oak quartz
send your closed form answer @ionic nest
oak quartz
desmos 8 decimal places: 25.58456886
pulsar crest
My answer:
ionic nest
lmao
oak quartz
34*sin45/sin110?
oh this is right
ionic nest
yea
oak quartz
that's a much shorter closed form that mine lmao
pulsar crest
on the test
ionic nest
ok i have no idea why you would need this lol
u can use sin 110 as the other angle at C instead of sin 70
then sin law and boom ur done
oak quartz
my what form
In mathematics, an expression or equation is in closed form if it is formed with constants, variables and a finite set of basic functions connected by arithmetic operations (+, β, Γ, /, and integer powers) and function composition. Commonly, the allowed functions are nth root, exponential function, logarithm, and trigonometric functions.[a] However, the set of basic functions depends on the context.
usually you say this for integrals and shit lol
ionic nest
> In mathematics, an expression or equation is in closed form if it is formed wi...
brother
oak quartz
ok actually i should have said "exact answer"
ionic nest
oak quartz
but closed form pretty much means the same thing
ionic nest
but boom
oak quartz
then sin law and boom ur done
ok this is the cringe part tho
ionic nest
im not stupid
oak quartz
this problem is absolutely 0 fun with law of sines π
pulsar crest
it makes it easy
ionic nest
this problem is absolutely 0 fun with law of sines π
its easy and fast
oak quartz
it was at least a little interesting to solve with the perpendicular construction
oak quartz
its easy and fast
well, to be fair, i got the correct answer before you.
ionic nest
but yea its quite abstract
ionic nest
well, to be fair, i got the correct answer before you.
shhh
pulsar crest
well, to be fair, i got the correct answer before you.
u make me think that ur like an 11 yr old prodigy
oak quartz
no my solution makes quite a lot of sense if you follow the flow
ionic nest
its been rlly long since i did those
oak quartz
u make me think that ur like an 11 yr old prodigy
nah bro im a college student
ionic nest
no my solution makes quite a lot of sense if you follow the flow
mine does too
oak quartz
mine does too
yeah but it's sooooo unfun
pulsar crest
im still confused on that question
ionic nest
but the flow is a bit harder to follow
ionic nest
yeah but it's sooooo unfun
but its easy
oak quartz
but the flow is a bit harder to follow
do y'all want me to explain my solution?
I'm happy to
pulsar crest
Yes
oak quartz
aw :(
pulsar crest
I redrew it
oak quartz
sin(x)=sin(180-x)
what. no
pulsar crest
Yes
ionic nest
so u have 110 at C
25 at A
45 at B
now sin law
and ur done
u have three angles
2 sides
and just need the last one
oak quartz
I redrew it
construct a line segment $BD$ such that it is perpendicular to $AC$
grizzled pagodaBOT
00100000
oak quartz
then, clearly, $BD=34\sin25$
grizzled pagodaBOT
00100000
pulsar crest
construct a line segment $BD$ such that it is perpendicular to $AC$
stop
Ur murdering me
ionic nest
RIGHT
oak quartz
D is a point on AC
pulsar crest
pulsar crest
and just need the last one
THANK YOU!!
oak quartz
that's important to remember
oak quartz
oh COME ON. "sine law" is so lame
ionic nest
dude
pulsar crest
its a law π π»
ionic nest
u should become a teacher
pulsar crest
in sine law we trust
oak quartz
u should become a teacher
WHAT
pulsar crest
exactly
ionic nest
cause my old math teach made us learn ur way
pulsar crest
no way
oak quartz
but I like to think I'm a pretty good math explainer
ionic nest
and i hated it
oak quartz
but I'd rather be a professor
oak quartz
and i hated it
π
ionic nest
so i thought of this way
pulsar crest
albert einstein once said ermm
pulsar crest
if u cant explain it simply u dont understand it well enough but i fear
that is not the case in math
it seems
oak quartz
if u cant explain it simply u dont understand it well enough but i fear
ok idk if u r trying to tell me that i don't understand my solution or not
but like
I assure you I understand it
and also
I can explain it as simply as the language of geometry lets me
ionic nest
same thing happened a few more times but hey, i guess im just an out of box thinker
oak quartz
the sine law one is beautifully easy
I was trying to construct one without using a theorem like that
ionic nest
I was trying to construct one without using a theorem like that
yea ik what ur talking about
thats why i said u should teach
oak quartz
my solution is hella close to basic geometry operations/axioms except for using trig π
ionic nest
all mathh profs teach that method
pulsar crest
I got the area of QRS as 241.4 metres
oak quartz
same thing happened a few more times but hey, i guess im just an out of box thin...
that's good, however, you shouldn't ever shun rigor because of it!
ionic nest
that's good, however, you shouldn't ever shun rigor because of it!
if i find an easier way
without thinking about process
and steps
and whatnot
oak quartz
if i find an easier way
math is about being precise, however
ionic nest
im taking it
oak quartz
cs and physics is where you make leaps and bounds in assumptions because you see a pattern
ionic nest
math is about being precise, however
dude ima be real, i didnt do it my way cause of precision, i did it cause its two steps
oak quartz
your method is fine and precise. it rests on a proven theorem
ionic nest
:)
ionic nest
lmao
pulsar crest
I just find it uninspiring
it inspired me! ;)
ionic nest
it inspired me! \;)
thank you
oak quartz
π
oak quartz
oh god i hate all these questions
ionic nest
18 C and D
you do those yet?
pulsar crest
okay im not clocking this exam
oak quartz
they're literally just "use law of sines"
pulsar crest
you do those yet?
yes
ionic nest
oh god i hate all these questions
i love em
pulsar crest
im going to faint
ionic nest
super easy
pulsar crest
looking at the next page
ionic nest
and light
oak quartz
super easy
yeah but that's boring
ionic nest
yeah but that's boring
but thats what makes it fun
oak quartz
how
oak quartz
noooo π
pulsar crest
Just look at the next page π
ionic nest
Just look at the next page π
light work
oak quartz
part of why I'm not using law of sines is because I literally don't remember it
ionic nest
opposites attract π
oak quartz
lmao
oak quartz
but another big part is also that I just want to rebel against these obnoxious textbook problems
pulsar crest
Only electrostatically smh
oak quartz
by doing them in an unintended way
pulsar crest
but another big part is also that I just want to rebel against these obnoxious t...
I agree
ionic nest
by doing them in an unintended way
dude same
pulsar crest
I hate this textbook
pulsar crest
My bed looks like heaven rn
ionic nest
i did a problem so different
oak quartz
I hate this textbook
you need yourself a good copy of Knowing the Odds by John Walsh
pulsar crest
Great natures second course sleep π΄
ionic nest
that the teacher didnt have
pulsar crest
Balm of hurt minds
ionic nest
i got half marks for it since it was only half right, but she was mad impressed
pulsar crest
Iβm contemplating winging the exam
ionic nest
i rllygotta friend u man
oak quartz
i remember on my multivariable calc exam as a freshman, I forgot that I could do a problem that was just characterized by the cross product of two vectors, so I made this crazy solution with vector projections and it worked
ionic nest
i cant wait to hear u complain about uni
pulsar crest
i rllygotta friend u man
OMG YES
pulsar crest
i cant wait to hear u complain about uni
I complain enough abt hs
My friends get mad abt my yapping
ionic nest
I complain enough abt hs
truly
oak quartz
but my answer wasn't written exactly in the right form, so the grader marked it wrong, but I got my points back from the professor
ionic nest
if theres one advice i can give
ionic nest
rlly enjoy ur time in hs
pulsar crest
Pfft thatβs impossible
ionic nest
trust me
ionic nest
I do too many extracurricular and scjool stuff
i read way too much in hs
ionic nest
I love reading omg
comic
pulsar crest
Oh
ionic nest
not novels
pulsar crest
Iβve only read loke
ionic nest
i only got a few hundred novels i read
oak quartz
honestly, if i could tell one thing to my high school self, it would be "START READING UNDERSTANDING ANALYSIS BY ABBOTT AND TOPICS IN ALGEBRA BY HERSTEIN BECAUSE MATH IS ACTUALLY GOOD BUT U WONT SEE IT UNTIL U READ THOSE BOOKS"
ionic nest
its mainly comics lol
ionic nest
Should I sleep until 5 am
i havent slept in two days
pulsar crest
Thats in four hours π
ionic nest
dont even sweat it
pulsar crest
Actually?
ionic nest
it gets better
pulsar crest
winter break is almost here
pulsar crest
Iβm so tired
ionic nest
drink some cold water
oak quartz
lmao
pulsar crest
Well Ik the sine law
oak quartz
ngl
ionic nest
i cant lose my time passer like this
pulsar crest
And cosine law snd stuff
pulsar crest
were so getting in trouble
ionic nest
yea
pulsar crest
Ermmmm
ionic nest
i mean another gc is always fun
pulsar crest
π€
pulsar crest
R u sure?
ionic nest
@pulsar crest
amber waspBOT
amber waspBOT
Available help channel!
steep fern
this is the equation
amber waspBOT
this is the equation
steep fern
outer flame
so, you want to find the y' or what?
grim forge
so, you want to find the y' or what?
I figure that's what they want
steep fern
i have to find the slope
grim forge
The slope at what point?
grim forge
So just the derivative
steep fern
oh wait
grim forge
Didn't you get this here
outer flame
it give slope of any point (t, y(t))
grim forge
π
steep fern
finals got me messed up π
amber waspBOT
amber waspBOT
Available help channel!
split sail
Can someone explain the idea behind the Bolzano-Weierstrass theorem?
split sail
Based on the definition from wikipedia, "Every bounded sequence of real numbers has a convergent subsequence."
If the bounded sequence here refers to a finite set of numbers, how does the nested interval proof for said theorem even work?
indigo cloud
a sequence is infinite
split sail
huh
indigo cloud
bounded means that all your terms are within some finite interval
for example in [0,17]
split sail
can't a sequence be something like (a_n)_{n=1}^{10}
indigo cloud
no
indigo cloud
I wouldnt call it that
split sail
wat
indigo cloud
if your course does, then just imagine bolzano weierstrass has the modifier infinite before the word sequence
like any theorem concerning convergence of sequences
split sail
split sail
if your course does, then just imagine bolzano weierstrass has the modifier infi...
nah I'm self-studying
haven't reached that part yet
indigo cloud
we are in the context of real analysis
indigo cloud
a function N->R
split sail
right
but wait
waiiiiit
my brain is fried rn
so lets say, we have a subsequence that does not converge
wait, a sequence has order, so it may be something like (2, 4, 3, 1, 2...)
assuming there's a function that produces such an output
then the bolzano-weierstrass theorem states that we must be able to find a convergent subsequence, so is this subsequence finite or not?
how would you even define "convergent" here?
indigo cloud
wdym, have you not seen the definition of convergence for a sequence?
split sail
well yes
I've proved the monotone convergence theorem before
at least thats what my idea of a converging sequence is
indigo cloud
any sequence in real analysis is infinite
there are sequences which arent monotone and which converge
split sail
yep
i approaches infinity, the values of the consecutive terms are very close to some real number
that I understand
but what does all these have to do with the theorem?
indigo cloud
the theorem states that a subsequence of your original sequence is converging
split sail
the theorem states that a subsequence of your original sequence is converging
so lets say its a infinite sequence of random numbers that are bounded by the interval say [0, 100]
there's going to be a subsequence within this interval that converges?
say, it will definitely converge to 2?
indigo cloud
no
it will converge to some number
you dont know which
could be 2, could be 47.1947461844233...
split sail
right
but we know it will definitely converge
and how does the nested intervals proof for this theorem demonstrate that?
indigo cloud
well it even "constructs" the sequence for you
you have smaller and smaller intervals converging to some number
and in each of these intervals you pick one of your sequence terms
so that subsequence you pick converges to that number
split sail
well, the sequence isn't infinitely dense like real numbers
split sail
you have smaller and smaller intervals converging to some number
how do we ensure that each nested interval a. contains a term in the sequence b. an infinite number of terms from the sequence?
since the sequence is a function but just with an infinite number of terms, doesn't mean the terms will have the same density throughout the interval does it?
indigo cloud
I am questioning how bad the proof you saw is written
you split your first interval into two
there have to be infinitely many terms in at least one of these two subintervals
indigo cloud
because otherwise there are only finitely many in each but thats impossible cause then there are also only finitely many terms in the sequence itself
split sail
there have to be infinitely many terms in at least one of these two subintervals
infinitely many real numbers yes
ohhh wait
when we split it in half, theres bound to be one half where theres at least another infinite amount of terms
cause the sequence is infinite
then we just pick the next half (quarter) containing the infinite terms
indigo cloud
yes
split sail
yes
right, but does this connect with the fact that we will pick a subsequence thats convergent?
wait is this subsequence finite or infinite?
indigo cloud
infinite
indigo cloud
any sequence in real analysis is infinite
.
split sail
infinite
but I still dont understand how this nested interval thing demonstrate that a subsequence will be convergent though
indigo cloud
we pick one term of the sequence for each subinterval
the intervals get smaller
so the terms we pick get closer and closer together
so they converge
split sail
ok right now that makes sense
but
isn't a sequence with order?
the proof on the wikipedia page shows that its all on a number line with no regards for its order
wouldn't that contradict with the definition of a sequence?
wouldn't that be just an unordered set then
indigo cloud
no
indigo cloud
lets say yn is the subsequence we pick
split sail
mhm
indigo cloud
we pick y1 as the first term in the sequence which is in the first subinterval
then y2 as the first next term after that which is in the next subinterval
and so on
split sail
wait wait wait
so currently in this proof, we have ignored its order
otherwise how would be draw intervals?
oh wait
you can still draw an interval from (2, 3, 1) and (4, 2, 3) from (2, 3, 1, 4, 2, 3)
indigo cloud
what
indigo cloud
you can still draw an interval from (2, 3, 1) and (4, 2, 3) from (2, 3, 1, 4, 2,...
wdym by that
split sail
wdym by that
well, lets just assume we have such a sequence
(2, 3, 1, 4, 2, 3,...) repeating itself
assume a function corresponds to such a sequence
its bounded by [1, 4]
indigo cloud
well ok
split sail
right, then when we draw the nested intervals
indigo cloud
piecewise constant functions arent often that enlightening but ok
so, the first interval is [1,4] and we pick y1=2
split sail
we cant be sure that whatever thats inside the nested interval is always larger/smaller than the previous interval
indigo cloud
our next intervals are [1,2.5] and [2.5,4]
there are infinitely many in the first one of those
say we pick y2=x3=1
split sail
right, but that would be rearranging (2, 3, 1, 4, 2, 3...) into (1, 2, 2, 3, 3, 4,...
for it to work
indigo cloud
then next we have the intervals [1,1.75] and [1.75,2.5]
there are infinitely many terms in the first one
lets pick y3=x9=1
and now it becomes boring
y4=x15=1
split sail
yes I know there are infinitely many terms in [1, 2.5], but thats an interval of real numbers
split sail
we're now talking about an interval in the subsequence
aren't those different things?
indigo cloud
right, but that would be rearranging (2, 3, 1, 4, 2, 3...) into (1, 2, 2, 3, 3, ...
huh
split sail
yeah
split sail
right, let me demonstrate what my brain is currently thinking
we have a sequence (2, 3, 1, 4, 2, 3, 2, 3, ...), we chop this in half, (2, 3, 1, 4) and (2, 3, 2, 3)
indigo cloud
no
split sail
this nested half of the sequence
indigo cloud
no one said anything about chopping the sequence in half
split sail
what
well if we aren't chopping the sequence in half, then we can't ensure that the order is maintained can we?
indigo cloud
what do those things have to do with each other
split sail
if what you're saying is that, there's infinitely many terms of 1, 2, 3 and 4in [1, 4]
of course it would converge
we can just pick {1, 1, 1, 1, 1, 1, 1...} and that would converge to 1
that makes sense
split sail
but now we're talking about a sequence with order
we aren't rearranging (2, 3, 1, 4, 2, 3, 2, 3) into something thats from small to big
indigo cloud
the subsequence I picked is precisely 1,1,1,1,...
split sail
hm
I still don't understand
right, let us go through the very simple definitions
"The theorem states that each infinite bounded sequence in R n {\displaystyle \mathbb {R} ^{n}} {\displaystyle \mathbb {R} ^{n}} has a convergent subsequence."
sequence is a function with infinite terms and bounded means the values in the term doesn't go into infinity
convergent subsequence means that we can pick a mini infinite sequence within this large sequence while still maintaining the relative positions to each other
e.g. not shifting a term around the subsequence
which makes sense
we now, lets say we have a function, sin(x)
it's bounded by [-1,1]
so it the sequence would be something like (0, 0.01, 0.02, ..., 1, 0.99, 0.98, ..., 0, -0.01, ...)
and so on
indigo cloud
what
split sail
wdym
indigo cloud
nvm
indigo cloud
would it help you if I randomly wrote x1,x2,... next to those points? it just makes the picture harder to read but it doesnt change anything
s=-1,S=1
split sail
yep
so if s = -1, S = 1
that would mean that line would be the number line
and I would assume the blue dots inside to be arranged as (-1, -0.9999, -0.9998, ...., 0.9999, 1)
split sail
so it the sequence would be something like (0, 0.01, 0.02, ..., 1, 0.99, 0.98, ....
but that would mean jumbling up our original sequence
indigo cloud
the dots have names x1,x2,...
and the same dot can have different names
because the sequence gets there over and over again
split sail
right, if the dots correspond to the order of the original sequence
indigo cloud
so 0 is x1 and x200 (or whatever) and x400 and x600 and so on
split sail
yep that makes sense
then wouldn't that make s and S irrelevant?
see like, the line s clearly marks -1
then the first blue dot would be 0 already
split sail
yeah but in the context of the number line
its contradicting
let me explain
so, if s and S is meant to be bounding the blue dots, then the blue dots would have to not correspond to order
indigo cloud
what does that have to do with the order
split sail
doesn't make sense to have a number line of -1 0 0.01 0.02 ... 1 0.99 0.98 0 ... -1 ... 1
the first and last being s and S
split sail
right then what does this mean lmao
indigo cloud
take the sequence x1,x2,...
split sail
right
indigo cloud
for each of them, draw a blue dot where it is on the number line
indigo cloud
next to the dot draw the name xn
split sail
you cant maintain the order
indigo cloud
that makes your image unreadable but you dont lose order
indigo cloud
sure
split sail
oh
so we keep the order
wait but if we then draw intervals, say we know the convergent subsequence is x_180 x_130 x_40 x_1000 x_5000 ...
then the order would disappear
split sail
since you say we're picking a term from each half of the nested interval?
indigo cloud
exercise for you while I am taking a shower
split sail
right
indigo cloud
take a calculator and compute xn=sin(n) for n=1,2,3,...,15
then draw the image
on paper or paint or whereever
indigo cloud
take a calculator and compute xn=sin(n) for n=1,2,3,...,15
this sequence
split sail
exactly in this fashion
indigo cloud
so we get away from the piecewise constant stuff
split sail
sure
indigo cloud
exactly in this fashion
yes step by step and always with the name next to each dot
split sail
yes step by step and always with the name next to each dot
well since each side both have infinite number of points
lets just take the right half of the it, [0,1]
lets just say we want it to converge to 1
how does this nested interval ensure that we'll always pick say x_0, x_15, x_390, ...
and not something like x_0, x_10, x_372, x_150, x_90
split sail
and not something like x_0, x_10, x_372, x_150, x_90
although this converges, it doesn't maintain the order anymore
indigo cloud
I told you to draw a different sequence
indigo cloud
and not something like x_0, x_10, x_372, x_150, x_90
well just dont fucking pick a term with a lower index than you already have
you have infinitely many terms available
just pick one thats allowed
split sail
well just dont fucking pick a term with a lower index than you already have
ohhh
fucking hell
now I understand
ohhh god damn
alright then
steep fern
amber waspBOT
tardy dune
you can do this using kinematics equations, but i guess they want you to derive it via calculus methods
tardy dune
how π§ββοΈ
Do try to get an expression of s by double integrating d^2s/dt^2
steep fern
im not sure how to do that
tardy dune
so
steep fern
we've only been taught single integrations π
tardy dune
what is [
\int \frac{d^2s}{dt^2} \dd t = \int -5.2\dd t
]
grizzled pagodaBOT
Aero
steep fern
ds/dt = -5.2t + C ?
tardy dune
ds/dt = -5.2t + C ?
yeah exactly!
so C here is your initial velocity because ds/dt is your velocity
but the question says it was dropped from an initial point, meaning what is the initial velocity?
steep fern
wont it be negative
tardy dune
ds/dt = -5.2t + C ?
so Integrate this again, what do you get?
but now C = 0
so [
\int \frac{ds}{dt} dt = \int -5.2t dt
]
grizzled pagodaBOT
Aero
steep fern
wouldn't there just end up being another + C
tardy dune
wouldn't there just end up being another + C
yep there will
that will be ur initial position now
steep fern
-5.2 + 0 + C?
tardy dune
you messed up the integral
tardy dune
-2.6^2t + t + C
nope
steep fern
oh
amber waspBOT
@steep fern Has your question been resolved?
tardy dune
-2.6t^2 + t + C
qhy the extra t term?
steep fern
oh
steep fern
idk π
steep fern
ohh
steep fern
-2.6t^2 + t + C
-2.6t^2 +C
steep fern
0
steep fern
yuh
tardy dune
yuh
they want u to find when it hits the ground
what is "the ground" mathematically in this context?
steep fern
0 ? π
amber waspBOT
amber waspBOT
Available help channel!
fierce edge
stupid question but i'm looking to maximize the sum of the diagonals given that the product of the diagonals of a rhombus is fixed
fierce edge
but there's no maximum right?
fresh ocean
nope. very large * very small is finite, but sum is very large
fierce edge
nope. very large * very small is finite, but sum is very large
then what does calculating the local maxima do?
,w maximize x + y given xy = 4
grizzled pagodaBOT
fierce edge
for example^
fierce edge
yeah but what are those local maximas
and why do they take the minimum values
when it's written max
like what are they supposed to be in this context
amber waspBOT
@fierce edge Has your question been resolved?
fierce edge
<@&286206848099549185>
could someone help?
actually i start a new channel cuz my main question is a bit differnet
.close
amber waspBOT
amber waspBOT
Available help channel!
flat patio
amber waspBOT
true tinsel
because that's $1-x$ and not $x$
grizzled pagodaBOT
ε¦ζγγγΏγKisaragi Ayami
flat patio
not allowed to do that?
true tinsel
you are allowed to do that but it's not the final answer
the value is correct but that one is $1-x$ and you need to find $x$
grizzled pagodaBOT
ε¦ζγγγΏγKisaragi Ayami
true tinsel
so what you're dealing with is $$1-x=\frac{\log2}{\log3}$$
grizzled pagodaBOT
ε¦ζγγγΏγKisaragi Ayami
amber waspBOT
amber waspBOT
Available help channel!
flat patio
chwists sake
amber waspBOT
chwists sake
flat patio
my idea was simple
2x log(5) - x log(5) = 12
x(2log(5) - log(5) ) = log(12)
and then just divide and you get x right?
why i don't get the desired answer??Γ
split sail
no thats not how logs work
flat patio
???? what the hell
flat patio
why does same technique work here
split sail
its not the same
flat patio
oh ok i see the problem
here the exponent consists of 2
while in 7) the base consists of 2
jeez
its crazy
2x+1 ln 3
2x ln3 + ln3 is allowed
but in our case its forbidden?
split sail
in 7) u need to use the quadratic formula
amber waspBOT
@flat patio Has your question been resolved?
flat patio
in 7) u need to use the quadratic formula
sry just had a pause, how exactly should i tackle this
like the 5 has 2x in the exponent
its not x^2
split sail
its 5^2x which is equal to (5^x)Β²
flat patio
its 5^2x which is equal to (5^x)Β²
how is it a quadratic equasion though?
x is not the base
flat patio
using the quadratic formula you can find values for 5^x
yep i got it now thx
basically just substitute 5^x for y
split sail
Yes :)
flat patio
and you can work with y as if its a quadratic euqasion
split sail
Yup
flat patio
what can we get from these graphs
amber waspBOT
what can we get from these graphs
fiery moss
no idea what i am supposed to see here
how have the other graphs been transformed from the graph of y = logx?
fiery wharf
If |an|= convergent then an always is convergent too?
amber waspBOT
If |an|= convergent then an always is convergent too?
elder harbor
elder harbor
If |an|= convergent then an always is convergent too?
i think alternating series is easier
fiery wharf
Yes so if |an| converge I donβt need to test the original one anymore right
elder harbor
yes, if it absolutely converges
fiery wharf
yes, if it absolutely converges
Ok well I took the abs value and I got 0 as my answer using limit as n =0
But Iβm not sure what that even means
Does that mean it converge or diverge
fiery wharf
cuz absolute converge
But 0 doesnt tell me anything I think. Like ratio test says if my answer is less than 1 then it converges but just took the limit as n goes inf
elder harbor
But 0 doesnt tell me anything I think. Like ratio test says if my answer is less...
It does
For alternating series
But not for always-positive ones
fiery wharf
For alternating series
How do I check if it is absolute or conditional convergence
elder harbor
.
elder harbor
an is the alternating series itself
|an| is the always-positive version of the alternating series
rotund oak
Yes so if |an| converge I donβt need to test the original one anymore right
yeah if the sum of |an| converges then the sum of an converges
though that information doesnt help in this example
amber waspBOT
@fiery wharf Has your question been resolved?
proud nebula
amber waspBOT
proud nebula
need help with this partial derivatives question, pls if smo could guide me thru iot
pseudo crescent
need help with this partial derivatives question, pls if smo could guide me thru...
!status
amber waspBOT
need help with this partial derivatives question, pls if smo could guide me thru...
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
pseudo crescent
where fx = 0 and wheer fy = 0
yep
try doing that then
can you find fx and fy?
oh btw the function is g
so we should say $g_x$ and $g_y$
grizzled pagodaBOT
MæthIsAlwaysRight
pseudo crescent
not fx and fy
proud nebula
1 moment
so what i struggle with is what do i do when the other varaible is attached to the one we r partially differentaiting?
like if they weere seperated by a + or -the one we r currently diffentiating would simply go to0
yk
pseudo crescent
so what i struggle with is what do i do when the other varaible is attached to t...
like in -3xy?
pseudo crescent
you basically treat the other variable like a constant
proud nebula
so whar does that mean, because deriv of consrant goews to 0
pseudo crescent
so whar does that mean, because deriv of consrant goews to 0
what would be the derivative of -3x*pi (with respect to x)
proud nebula
-3pi
proud nebula
pseudo crescent
and in pretty much the same way, derivative of -3xy wrt x is -3y
pseudo crescent
so y doesnt change
depends
you can treat it like a constant
if it helps, you could even replace it by something like pi temporarily
(actually dont do that, as it will make the notes really messy. But the result would be exactly the same)
there is one mistake here
whats the derivative of y^3 wrt x?
proud nebula
0
pseudo crescent
0
yeah
so it shouldnt be +y^3
it's just 3x^2 - 3y
so that's gx
can you find gy?
proud nebula
pseudo crescent
one small sign error
pseudo crescent
yep
-3x, right
alright, so now we set gx = 0 and gy = 0
what do you get?
you should get 2 equations with 2 variables - x and y
pseudo crescent
alright, I will give you some time to solve them and once you get the solution lmk
proud nebula
gx = 0 when x = +-y
pseudo crescent
you sure?
proud nebula
i gotta go to the washroom be back in 5mins
please dont leave i got a final in 2 hours
pseudo crescent
okay, so firstly, you should never write it like this
you had an equation gx = 3x^2 - 3y = 0
now you cant work with all of this at once
so you cant e.g. just move the -3y to the RHS and expect gx = 3x^2 = 3y
what you can do is only focus on the equation 3x^2 - 3y = 0 and write 3x^2 = 3y and so x^2 = y
this would be valid
but leave out the gx
pseudo crescent
-+rooty
oh, this is actually correct, you were only focusing on gx
anyway we want gy to be equal to 0 as well
so you should also set up the second equation
which should yield y^2 = x
so we will have
gx = 0 iff x^2 = y
gy = 0 iff y^2 = x
and those are the 2 equations we need to solve
i'd advise you to solve them simultaneously rather than one by one
pseudo crescent
try reading what I wrote and check if you understand that
proud nebula
okay
pseudo crescent
at the crtical pointss..
yeah
what are those points?
can you give me the precise coordinates?
proud nebula
pseudo crescent
that doesnt look right
let's work through it once again
so we had this:
gx = 0 iff x^2 = y
gy = 0 iff y^2 = x
do you agree?
proud nebula
yes
pseudo crescent
alright
so now we need to know when are both of these 2 true
so we need to solve the following system:
x^2 = y
y^2 = x
dont solve them as seperate equations, solve it as a system of equations
pseudo crescent
not quite
it's just a polynomial equation
your solution should be an exact number
like 1
or 3
pseudo crescent
try subtracting x from both sides and factoring e.g.
or you could just guess the solutions in this case
proud nebula
0 and 1
pseudo crescent
yeah