when you do calculus with polar coordinates, sometimes you want to find the point that is parallel to the initial line (theta = 0)
#help-4
wanton ruin
marble lark
"Find dw/dt if w = tanx and x = 4t^3 + t"
marble lark
when you do calculus with polar coordinates, sometimes you want to find the poin...
i dont really understand it ? maybe its too complicated for me to understand without prior stuff idk
wanton ruin
i dont really understand it ? maybe its too complicated for me to understand wit...
ok are you aware of the form x = rcos(theta) and y=rsin(theta)?
marble lark
ok are you aware of the form x = rcos(theta) and y=rsin(theta)?
yes
wanton ruin
yes
when you want to find dy/dx of a polar curve, what you can do is convert it into (dy/dtheta) / (dx/dtheta)
and then convert y and x to rsin and rcos respectively
(sorry if my explanation is kinda bad, i'm rusty at calc with polar coordinates)
marble lark
yea i think that makes sense
but i just dont really know how to relate that back
to like chain rule and stuff
marble lark
"Find dw/dt if w = tanx and x = 4t^3 + t"
Also is this what you do then?
wanton ruin
Also is this what you do then?
yep, the dxs cancel each other out (similar to what we did in the polar example with dtheta)
wanton ruin
i know this test about to be hard af
what class are you doing?
marble lark
what class are you doing?
AP precalc
wanton ruin
so is like d/dx different from dy/dx?
d/dx usually is not used as much
it essentially means the same thing though
marble lark
idk ive seen that
i think from watching a vid
is it like the operation?
like u do d/dx or someting on the function and that gives u dy/dx?
or am i wrong and they just mean the same thing
wanton ruin
is it like the operation?
yep
marble lark
ok
wanton ruin
if you think of y=x^2, you can substitute that into d/dx(x^2) to rewrite it as dy/dx
marble lark
if you think of y=x^2, you can substitute that into d/dx(x^2) to rewrite it as d...
yea ok makes sense
is there anything else I should look into or vids to watch if i really want to understand or be able to explain stuff for chain rule or implicit differentiation?
wanton ruin
is there anything else I should look into or vids to watch if i really want to u...
i recommend 3blue1brown's essence of calculus playlist if you haven't watched that already
marble lark
because my teacher was saying like the dw/dt stuff is just showing that we've been doing chain rule the whole time
but i didnt understand it too much can u explain?
marble lark
i recommend 3blue1brown's essence of calculus playlist if you haven't watched th...
alright
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warped oracle
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warped oracle
Need help solving this
muted berry
$13-18 \neq -31$
rocky lotusBOT
Gizmic
warped oracle
$13-18 \neq -31$
Only can use the numbers below btw
muted berry
I mean it would be -13 which you seem to have crossed out already
rough talon
from the options the only thing thats a multiple of -13 is -39=3×-13
kindred sapphire
stiff fossil
<@&286206848099549185> were very stuck :(
Try doing 3 + x = y on the top right and see if any number matches
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vague gulch
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vague gulch
I got answer C, how is it supposed to be answer E? Am I just wrong?
stark wedge
that root is a, not -a.
it just so happens that the letter a stands for a negative number.
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storm ferry
how do i do this
vale dockBOT
how do i do this
storm ferry
i thought this was asking for height of the parallelopiped
so i used vector projection to solve
stiff fossil
how do i do this
Dyk what a parallelepiped is?
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spiral needle
hello can someone help me with my pre calc
vale dockBOT
hello can someone help me with my pre calc
spiral needle
I know to multiply denominator by 2(x-5) but im not sure what exactly the product would be or anything
glass kelp
,w simplify (x-8)/(x-5) - 5/2
spiral needle
I dont understand
rocky lotusBOT
spiral needle
I'm not in calculus im only in pre calc
rocky lotusBOT
k
glass kelp
Maybe some factoring from the numerator might do something
spiral needle
but im really confused with this part bc how does multiplying the denominator by 2(x-5) result in that as the denominator
rocky lotusBOT
k
spiral needle
cuz i got the denominator as (x-8)-5
glass kelp
So if I multiply 2(x-5) on top an bottom
${\frac{3x - 9}{\frac{-3(x-3)}{2(x-5)}} = \frac{3x-9 \times 2(x-5))}{\frac{-3(x-3)}{2(x-5)} \times 2(x-5)} = \frac{(3x-9)(2)(x-5)}{-3(x-3)}}$
rocky lotusBOT
k
spiral needle
kk rn i have num 6(x-5)(x-3) but for den i have (x-8)-5
the fractions are totally tripping me up
glass kelp
[ \frac{6(x-5)(x-3)}{-3(x-3)} = -2(x-5) ]
rocky lotusBOT
k
spiral needle
how did you get the denominator as -3(x-3)
spiral needle
sorry im not registering it at all
glass kelp
ok
so
the initial expression
simplifies to
[ \frac{3x-9}{\left( -\frac{3(x-3)}{2(x-5)} \right)}]
rocky lotusBOT
k
glass kelp
yes?
spiral needle
wait do you think u can explain to me how to multiply the denominator by 2(x-5)
cuz thats what im struggling with
im not sure how you got those numbers for the denominator
neon summit
$\frac{(x-8)}{(x-5)} - \frac{5}{2} = \frac{2(x-8) - 5(x-5)}{2(x-5)}$
rocky lotusBOT
Astar777
spiral needle
thank you
rocky lotusBOT
Astar777
spiral needle
ok so basically when i did this earlier i got (x-8)-5 and im not sure how i got that
bc dont u cancel out the x-5 in den and 2
neon summit
**Astar777**
here?
glass kelp
yes we removed that by muliplying top and bottom by x-5
spiral needle
**Astar777**
in the denominator here since i cancelled out the x-5 and the 2
yes
thats what i did
neon summit
not how it works
glass kelp
😭
glass kelp
thats not how cancelling works
the logic behind it is that u can factor something out
and that the thing u factored out is equivalent to 1
say
For ${c \neq 0}$
[\frac{cb - ac}{c} = \frac{c(b-a)}{c} = \frac{(c)(b-a)}{c} = \frac{c}{c} \cdot (b-a) = 1 \cdot (b-a) = b-a]
rocky lotusBOT
k
glass kelp
this is how cancelling works
spiral needle
ah
glass kelp
whyy
spiral needle
basically
hold on
so what if you just try to get the same denominator right, u multiply the x-8 by 2 and then the 5 by x-5
2(x--8) over 2(x-5)
and then 5(x-5) over 2(x-5)
then u have 2(x-8) - 5(x-5)
which is (2x-16) - (5x-25)
OH I GET IT NOW
-3x +9
glass kelp
Yup
spiral needle
ayyy
and then
factor that out so 3(x-3) over -3(x-3)
cancel out, so its -1
ah
wait but
then theres no x letter
spiral needle
it doesnt let me click on image
but why cant u cancel out now?
its a multiplication term over a mulitplcation term so its not just -3/3?
omg
i forgot the 2(x-5) on top help
glass kelp
Ye
stark wedge
do we have access to derivatives
stark wedge
RIP
karmic yacht
Arent limits besically start of calc
devout tinsel
what precalc class teaches limits? 
glass kelp
Maybe like last chapter?
karmic yacht
what precalc class teaches limits? <:catthink:526983414226747393>
Maybe there learning continuity
devout tinsel
how are these presented to you, do you learn delta epsilon proofs, or is it just "intuition" ?
karmic yacht
Smooth curves and RHL LHL
glass kelp
Prolly intuition 😭
spiral needle
im not sure, she gives us ap calc ab practice
i love my pre calc teacher but she told me i was pathetic
devout tinsel
yay lets do another
with the big denominator, bring the small fractions within the denominator to a common denominator
what??
spiral needle
kk rn i have num x-9 and denominator x-9 / 2(x+3)
eee what am i doing wrong
x+9* not x-9 for denom
wait x-9
opos
ah i know
factor x-9 out?
glass kelp
,w simplify 3/2 - (x+9)/(x+3)
rocky lotusBOT
glass kelp
Yup
glass kelp
Didn’t we cancel x-9
devout tinsel
Didn’t we cancel x-9
that doesn't seem right
glass kelp
Here?
devout tinsel
oh nm
rocky lotusBOT
devout tinsel
this one is actually easier than the other ones
it's not even an indeterminate form, so what can you do?
lyric sundial
Yeah
spiral needle
omg yay!
devout tinsel
yeah, no need for simplification in this one, can just plug in
spiral needle
tysm everyone for helping me today
its my birthday today i so happy i can sleep now
good night!
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cobalt crow
its my birthday today i so happy i can sleep now
happy b-day
karmic yacht
Happy Birthday
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unborn depot
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unborn depot
Am i doing something wrong trying to find the upper bound in exercise 3?
oh wait nvm i got it now
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gritty rock
anotner !!
Use l'Hôpital
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fallen tartan
Hello
fallen tartan
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analog schooner
For this limit $\frac{1 + \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n}}{ln(n + 2)}$ as n -> infinity, can I substitute the numerator to be ln(n) + γ and then use the L'Hopital rule?
rocky lotusBOT
Dhruv
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
analog schooner
**Dhruv**
Compile Error! Click the <:errors:504266556054962196> reaction for mor...
Just refer to this image
Its almost correct
odd jackal
$\lim_{n \to \infty} \frac{ \sum_{i=1}^{n} \frac{1}{n}}{\ln(n+2)}$
rocky lotusBOT
wai
odd jackal
this?
analog schooner
lhop on a function of a discrete variable is mega sus
Damn
You're right
I thought I did something
odd garnet
It's just the gamma symbol at the end that's not there
i mean you can, but i think it's a bit of a cheat to go numerator is ~logn
gritty juniper
odd garnet
i mean you can, but i think it's a bit of a cheat to go numerator is ~logn
if you know the numerator is asymptotically log n then it follows immediately that the limit is 1
odd jackal
i mean you can, but i think it's a bit of a cheat to go numerator is ~logn
That only works if the limit goes to ||0||
analog schooner
if you know the numerator is asymptotically log n then it follows immediately th...
Why
odd garnet
logn/logn = 1
odd garnet
i mean it's not quite that but like yeah
stark wedge
That only works if the limit goes to ||0||
what does
analog schooner
i mean it's not quite that but like yeah
Or I could use the Taylor series of ln(1 + x)
odd jackal
what does
nvm, I thought the appoximation only made sense if the limit were 1
I mean 0
odd garnet
anyway i think the point of the question is to show that the numerator is ~logn rather than to just claim it
analog schooner
anyway i think the point of the question is to show that the numerator is ~logn ...
I want to know if this method is correct
Because this feels like a trick
odd garnet
I want to know if this method is correct
i mean ur method does work yh
odd garnet
The normal solution is much more difficult
...that's because 1/1 + ... + 1/n ~ logn + gamma is not an obvious fact...
analog schooner
True
drifting hornet
lhop on a function of a discrete variable is mega sus
would discrete derivatives work btw?
analog schooner
So can I substitute the summation to be lnx + γ whenever n tends to infinity?
drifting hornet
would be kinda nice if it worked
you could also use this
apparently discrete lhop works
odd garnet
So can I substitute the summation to be lnx + γ whenever n tends to infinity?
i mean again, yes that works but like it's definitely not a quotable fact
if you know how to prove that the summand is asymptotically logx, then you can use that to evaluate the limit by hand anyway
analog schooner
What if after the substitution, I write n = floor(x) where x tends to infinity, and now the limit is discrete so I can use the LH rule
stark wedge
no then your numerator fails to be differentiable too often i think
odd garnet
if you don't know how to do that, ur basically pulling a rabbit out of a hat anyway so it's not really something i'd advise u to do
drifting hornet
https://en.wikipedia.org/wiki/Stolz–Cesàro_theorem
but there is actually a pretty cool analogue of lhop for discrete sequences
odd garnet
What if after the substitution, I write n = floor(x) where x tends to infinity, ...
you can then use partial summation & convert that into logn + gamma + error term
analog schooner
i mean again, yes that works but like it's definitely not a quotable fact
I don't need to use it in a subjective proof
The question is an MCQ
odd garnet
oh ok lol
odd jackal
Was this a jee question perchance?
analog schooner
Was this a jee question perchance?
Yes
odd jackal
ofcourse it was 😭
analog schooner
Idk if it was a question of jee, but it is probably a practice question designed for jee
analog schooner
no then your numerator fails to be differentiable too often i think
True
Thank you
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drifting hornet
True
The derivative would also be 0 pretty much everywhere, resulting in 0/0. You can use the discrete lhop though. The limit would simplify to (1/n) / (ln(n+3) - ln(n+2))
analog schooner
Was this a jee question perchance?
That's actually why I wanted to confirm whether my solution was correct
Because this method is not at all in the syllabus for jee
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livid pier
Calculate the convolution of functions $f(x)=\max(0,1-|x|)$ and $g(x)=\sin(x)$
rocky lotusBOT
Aruseq
livid pier
What did I wrong? I probably should get 2cos(x)[sin(1)-1]
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@livid pier Has your question been resolved?
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@livid pier Has your question been resolved?
livid pier
<@&286206848099549185>
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@livid pier Has your question been resolved?
wraith heart
What did I wrong? I probably should get 2cos(x)[sin(1)-1]
why do you think this
livid pier
that's the answer I saw on my group conversation and I thought it was the right one
but can't find any mistake in mine
wraith heart
try calculating g * f instead
and / or plot each one of your steps in desmos to see where it differs
livid pier
and / or plot each one of your steps in desmos to see where it differs
yeah, it was smart advise xd
now I know there is no mistake here
livid pier
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obsidian ginkgo
hey there i have physics questions about free body diagrams and how they look when representing a walking motion (im not sure how to use friction as the object isnt being dragged)
obsidian ginkgo
im realising physics falls under science so im not sure im in the correct place but if anyone has knowledge to share im happy to hear it
verbal badger
Show the original problem & what you've tried so far
verbal badger
hey there i have physics questions about free body diagrams and how they look wh...
If you're walking at a constant velocity the fbd would look no different than that of a standing person's, but need more detail
obsidian ginkgo
my actual notes are on an ipad so i cannot send them but i can send the question and graph
so i know on the free body diagram youd havew the normal force shown and another arrow when he starts walking fowards but how is air resistance or friction shown?
my gut tells me there must be some opposing force
verbal badger
Are you sure a free body diagram is even appropraite here?
obsidian ginkgo
current diagram is just a box with a upward arrow and downward to represent normal force
verbal badger
we're not directly modeling forces, we're modeling motion
obsidian ginkgo
sorry i forgot to include part 3 in the ss
a free body diagram is asked for all 5 parts
thats my mistake apologies
verbal badger
alright
obsidian ginkgo
verbal badger
so i know on the free body diagram youd havew the normal force shown and another...
generally you can disregard friction/air resistance here
they don't play a significant role in the dynamics- the guy's motion is mainly driven by him walking forward or back, not the impact of the friction on his shoes
obsidian ginkgo
okay so just the normal force and an arrow to represent the forward motion would be sufficent?
verbal badger
A downwards arrow for gravity and upwards for normal force is akways going to present, obviously
when the guy is accelerating forward (ie. his velocity is increasing), there's a forward arrow
and when hes decelerating, backwards arrow
Because F = ma
obsidian ginkgo
okay thank you, suppose im over thinking it lol, this was very helpfull thanks again
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oak herald
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oak herald
just a quick question
How do I know which number I should add pi n
For the two number
Cuz the book said is 2.84
I always thought both number work
Kinda getting confuse on this
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oak herald
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torn fox
I dont quite understand what youre asking here
Like how to get the second solution after get one?
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ebon gulch
I have many questions
vale dockBOT
I have many questions
midnight pier
I think it’s 4
ebon gulch
i got 3 and my friend got 2
ebon gulch
I think it’s 4
it asks which is false
shadow moss
why do you say 3?
shadow moss
why would people be compelled to call a number?
ebon gulch
you can argue multiple things
shadow moss
no
shadow moss
if the possibility of being polled is out of cobtrol of respondents, it is unlikely for a bias to appear
midnight pier
3 then
ebon gulch
moving onto # 12, arent both 3 and 4 true
shadow moss
so do you understand why it is 3 for problem 9
ebon gulch
yea
shadow moss
majority means larger than 50%
but if the spinner was fair, do you know how to calculate probability of winning?
ebon gulch
1/6 x 10?
shadow moss
the probability of winning is 1.667?
shadow moss
what is the probability of losing two spins in a row?
ebon gulch
what is the probability of losing two spins in a row?
5/6 x 5/6
shadow moss
what is the probability of losing ten times in a row?
shadow moss
so the probability of winning is what?
shadow moss
it seems reasonable to say 3 or 4
but id go with 4
since the expected number of wins per run is when you would use (1/6)*10
or about 1.667 wins per run
so 4 seems better
shadow moss
do you know where to start?
ebon gulch
all i got is( 679 - x) / 100 = Z
ebon gulch
nah thats why im confused
shadow moss
so we need to find the set of people that are in the 90th percentile
or we need a zscore such that on the table we get .9000 or close enough
you have a z table right?
ebon gulch
no
shadow moss
you should
ebon gulch
is it in a calc?
shadow moss
pick the closest to .9000
ebon gulch
1,28
shadow moss
yes
ok i asked a friend and they said that there might be an inverse cumulative distribution function button on your calculator
but i wouldnt know
i would ask your teacher how they would solve this
ebon gulch
ill figure it out thanks for all help
shadow moss
youre welcome!
verbal badger
You use the invnorm function on the ti-84 https://www.statology.org/invnorm-ti-84/
verbal badger
is ther a z table on a ti-84
Assuming you're not given that table (you probably will be?), goal is to get the z score that corresponds to the 90th percentile, which you do via the invnorm function
Once you get the z score, you just do mu = X - z*std
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tropic mountain
is this right
vale dockBOT
is this right
tropic mountain
,tex
\begin{enumerate}
\item Given $B_i = {{x \in \mathbb{R} : |x| < i}}$:
\begin{enumerate}
\item $\bigcup_{i \in \mathbb{Z}^+} B_i = (-\infty, \infty)$
\item $\bigcup_{i \in \mathbb{R}^+} B_i = (-\infty, \infty)$
\item $\bigcap_{i \in \mathbb{Z}^+} B_i = (-1, 1)$
\item $\bigcap_{i \in \mathbb{R}^+} B_i = \emptyset$
\end{enumerate}
\end{enumerate}
rocky lotusBOT
licentia
next vortex
looks right to me 
earnest summit
onyx bluff
can someone check these answers
vale dockBOT
can someone check these answers
shrewd hinge
can someone check these answers
Maybe use Desmos for checking these!
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forest skiff
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forest skiff
Hi. My prifessor solved like it is solved above
But i think that the highlighted part should have been calculated diffrently
Like that:
manic igloo
Before the highlighted step, it would be much easier to simplify to (x - ln(x+1)) / x^2 and use l'Hôpital's rule.
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ivory arch
hey i have a little verbal test tomorrow on mainaxistransformation and i have found a perfect video for it in 2d but i cant find anything in 3d so if someone could send me link for a video or a book where they explain it using a matrix
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hey i have a little verbal test tomorrow on mainaxistransformation and i have fo...
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ivory arch
<@&286206848099549185>
midnight pier
Can someone tell me why he solved it like that?
He was using the L’Hospital’s rule
midnight pier
hey i have a little verbal test tomorrow on mainaxistransformation and i have fo...
Hm
ivory arch
is that short for smthg or are you thinking
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wraith heart
hey i have a little verbal test tomorrow on mainaxistransformation and i have fo...
Why can't you just google this
harsh wraith
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shadow moss
yes theyre the same
harsh wraith
HOW
shadow moss
you can pull out a x^(1/2) and distribute that into the sqrt
shadow moss
all good
wanton jasper
1 + 1/x = (x+1)/x
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untold crescent
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golden gate
!showyourwork
vale dockBOT
Show your work, and if possible, explain where you are stuck.
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untold crescent
!showyourwork
the only thing i wrote was v^2=n^2(a^2-x^2) i dont get how to find the n, a or x
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eager ocean
why are people obsessed with trying to create categories for similar stuff in math
sleek nebula
wdym
sleek nebula
why are people obsessed with trying to create categories for similar stuff in ma...
mathematicians think mysteriously
eager ocean
we call every equation that looks like $$a^n+b^n=c^n$$ a diophotian equation
rocky lotusBOT
wololo
ebon glade
oh no we have words for stuff
novel canyon
**wololo**
what in the fermats last theorem
ebon glade
oh god
eager ocean
decided to put names in there
shadow moss
because words that explain certain things are helpful then having to descrive it every time
ebon glade
also we dont call any equation like that a diophantine equation. we call an equation a diophantine equation if we are interested in integer solutions of that equation
shadow moss
also diophantine equations are any equation in which you solve gfor variables in the integers
ebon glade
we call functions morphisms if they respect some structure that we care about
sleek nebula
i can tell
ebon glade
and no one was surprised
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sleek nebula
ig
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zenith mesa
can anyone help me with this?
vale dockBOT
can anyone help me with this?
lost marlin
What have you tried
zenith mesa
im assuming its supposed to go like this
lost marlin
Yes
zenith mesa
and im stuck there
zenith mesa
what do you mean
lost marlin
In the first image it is 3x-2x³
In the second 3x³-2x
zenith mesa
oh thats my bad i wrote it wrong
i just realized
the coefficient is supposed to be on-2x
lost marlin
So the second image ???
zenith mesa
no the first
zenith mesa
lost marlin
It is -2x²
zenith mesa
okay
lost marlin
And get x(3-2x²)
After factoring this it will be a simpler rational inequality
zenith mesa
what do i do now
zenith mesa
so a is 1 b is 3 and c is 2?
lost marlin
What are a b and c here
zenith mesa
x is 1, b is 3 and c is -2?
lost marlin
???
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tropic mountain
Hey, how can I solve the following
vale dockBOT
Hey, how can I solve the following
tropic mountain
$\bigcup_{x \in [-1,1]} [x,1] \times [x^2,1]$
rocky lotusBOT
licentia
ivory valley
I would consider drawing a picture and do some examples like for x=0 or x=±1.
vale dockBOT
@tropic mountain Has your question been resolved?
grand parcel
how to compute 2^(3^n) % 5 with large n?
vale dockBOT
how to compute 2^(3^n) % 5 with large n?
tidal terrace
!original
vale dockBOT
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.
ivory valley
,w 2^(3^n) mod 5
rocky lotusBOT
stark wedge
a question in a programming contest
start with the value for n=0 (which is just 2) and then repeatedly raise to the third power and reduce mod 5
vale dockBOT
vale dockBOT
Available help channel!
wind harness
How do I Solve linear systems of equations graphically? Stuff like I x-2y=0 and II -3x +2y = -8
stray moat
Every point on a graph describes a pair of x and y where the equation is true right?
wind harness
Every point on a graph describes a pair of x and y where the equation is true ri...
Yes
polar oxide
How do I Solve linear systems of equations graphically? Stuff like I x-2y=0 and ...
wdym by solve it
wind harness
I just dont get how I would draw the points
wind harness
So I always would do in the example y=x/2 and y=1,5x-4
stray moat
That's right, but it's not something you have to do, it's just so you can see that it's a line better
To plot a line graph you find two points on the line and connect them
For example, if you pick x=0, then y = 0/2 = 0 for the first line
Then you can pick x=2 and then y = 2/2 = 1
stray moat
For example, if you pick x=0, then y = 0/2 = 0 for the first line
Draw the two points (0;0) and (2;1) and then connect them with a ruler
And then you repeat this process for the other line to draw it
Once you have both graphs you can solve the system
wind harness
Once you have both graphs you can solve the system
When I calculate it so -2x=-8 :-2= x=4 and y=2
wind harness
x=4 and y=2 is a solution yes
But when I do it graphically, it would be (1/-1)
stray moat
Send a picture of the graphs
wind harness
wind harness
Wdym?
stray moat
Walk me through how you drew the two lines
They are drawn incorrectly but we need to know what went wrong
wind harness
So I took the first equation and did -x and the second equation +3x. That equals to I 2y=0-x and II 2y=-8+3x. Then 1 divided by two so: I y=0/2 and x/2 and II y=-4+1,5x. Then I did -4 and always went one to the side and 1,5 up
wind harness
Walk me through how you drew the two lines
For the other one the same\
stray moat
Okay so you're saying you started at x=0 and y=-4
And went up by 1.5 for every x=1 right?
wind harness
And went up by 1.5 for every x=1 right?
Yes, I think so
stray moat
However, you didn't actually do that
What is your y value at x=0
And compare it to your y-value at x=1
stray moat
Look at your graph
when x=0 what value does y have
This part is correct for now, just tell me
wind harness
This part is correct for now, just tell me
-0.5
stray moat
This is x=0, y=-0.5?
wind harness
This is x=0, y=-0.5?
ohh no, Its x=0 and y=-4, but isnt that 2 different lines?
stray moat
We're focusing on this line for now
wind harness
ok
stray moat
Ok now, for x=1 on the same line, what did you draw y to be?
wind harness
Ok now, for x=1 on the same line, what did you draw y to be?
1 to the side and 1.5 up
stray moat
Yeah but in your drawing what value does it have
wind harness
Yeah but in your drawing what value does it have
oh x only 0,5, right?
stray moat
What I'm trying to get you to see, is that you did not go up by 1.5
You went up by 3!
At x=0, y is -4
but at x=1, y is -1, not -2.5
wind harness
You went up by 3!
But isnt one of those blocks 0.5 because 2 are 1
stray moat
You yourself got it in the form
y = 1.5x - 4
For every 1 x, y goes up by 1.5
You can't use this "one to the right, slope upwards" method unless your y is completely alone
What I think you accidentally did was leave it as
2y = 3x - 4
You can't draw using the slope here, y must be alone
wind harness
If I divide by 2 it would be y= 1.5x-4 because origanally it was 3x-8
stray moat
Yes, and that's the line equation you work with
If you use that, you'll draw it correctly.
wind harness
So I start from -4 and then?
stray moat
But also if you'll humour me, let's try to draw the second one using a different quicker method
wind harness
But what do I do with the other equation?
wind harness
But also if you'll humour me, let's try to draw the second one using a different...
ohoh Im scared
stray moat
But what do I do with the other equation?
You draw it in the same way, once again you made a mistake and drew it without y being alone
But let's just try another method
x - 2y = 0 right?
wind harness
You draw it in the same way, once again you made a mistake and drew it without y...
Quick question before, how would I handle 0/2
Because 0 is nothing
stray moat
You have 0 cookies and want to give 2 of your friends those cookies
how many cookies do your friends get
stray moat
sorry I meant 0 divided by anything is 0
0/2, 0/5, etc etc
Anyways let's try drawing using points on the graph
We have x-2y = 0
We can choose any two values for x that we want
Let's say x=0 and x=2
wind harness
Let's say x=0 and x=2
ok
stray moat
when x = 0, 0-2y = 0, y = 0/-2 = 0
when x=2,
2-2y = 0
2=2y
y=1
So we have two points on the graph
(0; 0) and (2; 1)
Do you follow me?
wind harness
Wait a sec, so first we do x-amount of x times y and then x=y. Or am I just stupid
stray moat
Do you mean what I just did?
wind harness
yes
stray moat
I just took two random x values, any x works
And then I put that value into the equation and solved for y
wind harness
And then I put that value into the equation and solved for y
ah ok
wind harness
Do you get it now?
got it
stray moat
Okay now we simply draw these two points on the graph
One point where x=0 and y=0
One point where x=2 and y=1
Connect these points with a ruler and you're done, you just drew the line correctly
Please send a picture to confirm haha
wind harness
Please send a picture to confirm haha
And both strats would have the same outcome but the second one is faster, right?
stray moat
That's much better let me see what still went wrong
they were supposed to meet a bit lower down
wind harness
they were supposed to meet a bit lower down
Its just a drawing skill issue on my side I think
stray moat
Yeah it is, the bottom graph goes a bit too low after the correct 1.5 jump
Like it is no longer accurate for x=2
But that's fine
stray moat
And both strats would have the same outcome but the second one is faster, right?
Ok I think the best practice would be to continue doing like you did this problem
One of them you do with the "go up by the slope" the other you do with "find two points and connect"
Both are very important to understand how they work
This is just me from a teacher POV though haha, if you want results use the second one
wind harness
I have a second one, can we do it together 1 last time plsss?
wind harness
So I have I-4x=3y=15 an II -x+y=4
stray moat
Ok do I with the slope method
wind harness
I do +4x and +x to have y alone and multiply II by 3 so I have 3y=15+4x and 3y=4=3x
WAs the second one the slope method?
stray moat
Slope is the name for the number attached to x
y = mx + n, m is called the slope
Slope method is your method, the first one
If you find it easier write down your work and send it here btw
wind harness
Then I did a mistake by multiplying 3, I divide the top one by 3 to have y
stray moat
No need to type it out
wind harness
I have y=5+4/3x so I put a point at x=0 and y=5 and other point at x=4 and y=3
stray moat
So I have I-4x=3y=15 an II -x+y=4
Did you write this correctly, I think you accidentally put an extra =
wind harness
Ah yes, it should be a plus so -4x=3y+15
stray moat
You made a small algebra mistake
wind harness
It would be other way around so y=4 and x=3, correct?
stray moat
-15 - 4x = 3y
so y = -5 -4/3x
rocky lotusBOT
🌈🌈🌈Toby
wind harness
Why a minus, Im trying to find the spot where it appears
stray moat
Did you not start with - 4x = 3y+15
wind harness
Other way around, $-4x+3y=15$
rocky lotusBOT
pinepanPM
stray moat
Oh this was what the problem gave you?
wind harness
Oh, my mistake
stray moat
Yes, what you're doing when you choose these x-values is finding two points on the graph
Because all points on the line will be solutions of the equation
so x=0;y=5 and x=3;y=1
Now draw them, and connect and this method is done
wind harness
Exactly
stray moat
Any other questions with this method?
wind harness
Now I put the 2 points in
stray moat
Send the drawn line
rocky lotusBOT
🌈🌈🌈Toby
rocky lotusBOT
🌈🌈🌈Toby
wind harness
mhm
stray moat
Ok so you draw x=0 y=5 and x=1 y= 11/3
wind harness
Ima switch to a bigger piece of paper and then after draw it in the book
wind harness
Send the graph when you're done
Wait a sec... I did the other on too with the 2nd methos, Im going to send you a picture rq, I think I did it
stray moat
Ok
wind harness
Yup, seems so
Thank you so much
stray moat
Yeah you did it well
Don't forget the slope method though, they are both equally valuable
wind harness
One last question, how do I decide which is the y for example the +5, is it just the one without the x behind it
wind harness
So in this one we had y=5+4/3x and we went up by 5 on y
rocky lotusBOT
🌈🌈🌈Toby
stray moat
"m" is called the slope and it shows us how "steep" the line is (exactly what you were doing, m shows us by how much the graph goes up every x=1)
"n" is called the y-intercept and it is the value when x=0
wind harness
"m" is called the slope and it shows us how "steep" the line is (exactly what yo...
And y is the starting point
wind harness
"n" is called the y-intercept and it is the value when x=0
got it
stray moat
But you have to be careful
y should always be alone
$2y = mx + n$ for example won't help you too much, you have to divide by two
rocky lotusBOT
🌈🌈🌈Toby
stray moat
Glad I could help, I think we're done here
Don't forget to practice both methods, it is pretty important to understand both
wind harness
I think we are too, Thank you so much 💖
wind harness
Don't forget to practice both methods, it is pretty important to understand both
Have an exam about that in 3 days so I know what im doing in that time
stray moat
!done
vale dockBOT
If you are done with this channel, please mark your problem as solved by typing .close
wind harness
.done
stray moat
Have an exam about that in 3 days so I know what im doing in that time
Good luck!
vale dockBOT
vale dockBOT
Available help channel!
cunning peak
$\sum_{n=0}^\infty \frac{n\log^n(x)}{n!}$
vale dockBOT
$\sum_{n=0}^\infty \frac{n\log^n(x)}{n!}$
rocky lotusBOT
Miguel, Duke of Texas🌈
cunning peak
I really don't know what to do
I see an e there
e^log(x) = x
But I don't know what to do with that n
heady pawn
what's ur goal
patent crow
Does $\log^n(x)$ mean iterated log or the $n$-th power in this context?
rocky lotusBOT
spindle
patent crow
I really don't know what to do
Are you familiar with Taylor series?
frigid harbor
I think its (log x)^n
patent crow
It most likely is, yeah
patent crow
Well, obviously n cancels out and one log(x) can be factored out, leaving us with series for of e^logx
Unfortunately OP is afk rn
frigid harbor
Try derivating wrt log x
cunning peak
Are you familiar with Taylor series?
Yes
cunning peak
Does $\log^n(x)$ mean iterated log or the $n$-th power in this context?
Nth power
frigid harbor
@patent crow im getting xlogx
patent crow
That's correct
cunning peak
<@301295716066787332> im getting xlogx
That's the solution yes
But I don't know how to get it
patent crow
Try seeing taylor series in your expression
frigid harbor
Yeh
patent crow
Hint: temporarily replace log(x) with y
patent crow
that's almost all you have to see
cunning peak
Well what do I do with that annoying n?
patent crow
Now a but of rearrangement will lead you to the answer
frigid harbor
I considered that log x as y
patent crow
Well what do I do with that annoying n?
Cancel it with n from denominator
frigid harbor
And derivated it wrt y
patent crow
Differentiating is a slight overkill
frigid harbor
Yeh
cunning peak
$\sum_{n=0}^\infty \frac{\log^n(x)}{(n-1)!}$
rocky lotusBOT
Miguel, Duke of Texas🌈
patent crow
Nice
cunning peak
Oh
patent crow
Although the summation is from n=1
frigid harbor
Yeh
patent crow
Because the 0-th term was 0
cunning peak
I factor out log(x)?
patent crow
yep
storm perch
miggy?!!!?!?!?!?!??!
frigid harbor
Thats actually much more simpler
cunning peak
Okay okay okay
cunning peak
miggy?!!!?!?!?!?!??!
Y'all ignored me in the other servers see where I had to come 😔
cunning peak
Thats actually much more simpler
Okay thanks you so much you two!!!
frigid harbor
Thats sad to hear man
patent crow
gg
frigid harbor
GG indeed
cunning peak
.close
fluid acorn
vale dockBOT
fluid acorn
i need help
i have written
S
U
V
A
T
and i got U as 14.7
and T = T
A = -9.8
and i dont know how to find my 3rd unkown
waxen berry
You also know S
fluid acorn
You also know S
idk it
waxen berry
at t=T it is at A, at t=0 it is at A
vale dockBOT
vale dockBOT
Available help channel!
zinc fulcrum
is this done right
vale dockBOT
is this done right
stiff lily
yes
zinc fulcrum
so it is d
stiff lily
yes
hazy lily
wassup
stark wedge
do you know your SOH-CAH-TOA
stark wedge
can you write down the ratio in full
hazy lily
but I’m getting a different answer
stark wedge
ok show your work
hazy lily
that’s what I’m getting
stark wedge
this looks way off
stark wedge
you should have had: $$\tan(58\dg)=\frac{52.1}{x}$$
rocky lotusBOT
Ann
stark wedge
there is nothing sacred about the number 52
hazy lily
see also https://youtu.be/t2uPYYLH4Zo
this just made it 10x more confusing
stark wedge
fair
hazy lily
anytime someone tries to simplify math or science with a song it just doesn’t work
u ever notice that
stark wedge
do you understand why the correct equation for your problem is 52.1/x = 1.6
hazy lily
nope
stark wedge
52.1 is the opposite and x is the adjacent as you yourself said
hazy lily
yeah