i keep forgetting about that my bad
#help-13
viral kiln
violet flume
so you need to apply some rules
but just do it in order and go as slow as you need to keep track of things
violet flume
,rotate -90
wraith daggerBOT
violet flume
,w D[x^3 cos(1/x), x]
wraith daggerBOT
wraith daggerBOT
viral kiln
oh should be + because of - sinx
violet flume
oh should be + because of - sinx
you lost the x^3
you should do this problem more slowly 
violet flume
its less time to do just do it right the first time
its harder to find mistakes than avoid them
FWIW
viral kiln
yeaa my math teacher always says to slow it down
violet flume
this is a good one to practice on maybe
but ur perogative
oh its spelled prerogative 
violet flume
,rotate -90
wraith daggerBOT
wraith daggerBOT
jan Niku
$y' = x^3 \dv x \csc 6x + \csc 6x \dv x x^3$
viral kiln
did the first step
violet flume
$y' = x^3 \qty(\dv t \csc t)\bigg \vert _{t=6x}\qty(\dv x 6x) + \csc 6x \qty(\dv x x^3)$
still havent applied any derivatives
do you know all of the derivatives here?
hmm lemme edit here
viral kiln
cscx is -cscx*cotx
violet flume
maybe this is more clear
wraith daggerBOT
jan Niku
$y' = x^3 \qty(\dv t \csc t)\bigg \vert _{t=6x}\qty(\dv x 6x) + \csc 6x \qty(\dv x x^3)$
violet flume
im just trying to distinguish between the derivative of csc(6x), and after we've applied the chain rule
once we apply the chain rule, were free to just differentiate csc t
but its still evaluated at t=6x
viral kiln
ohhh okay
violet flume
(6x remains the argument of the derivative)
viral kiln
yeah yeah
violet flume
so if you know the derivative of csc t off teh top of your head
violet flume
lets do more steps
maybe we'll break it out
$\dv t \csc t = \dv t \qty( \qty( \sin t) ^{-1} )$
viral kiln
would it be -csc t * cot t
wraith daggerBOT
jan Niku
$\dv t \csc t = \dv t \qty( \qty( \sin t) ^{-1} )$
violet flume
$\dv t \csc t = \dv t \qty( \qty( \sin t) ^{-1} ) = \dv t (\sin t) \cdot \qty( \dv s \frac{1}{s} ) \bigg \vert _{s=\sin t}$
wraith daggerBOT
jan Niku
viral kiln
hmmm i think im getting it
wraith daggerBOT
viral kiln
couldnt we just do this then
violet flume
you can use the quotient rule here
viral kiln
lemme send it
violet flume
if you like it
viral kiln
i do like quotient
violet flume
$y' = x^3 \qty(\dv t \csc t)\bigg \vert _{t=6x}\qty(\dv x 6x) + \csc 6x \qty(\dv x x^3)$
wraith daggerBOT
jan Niku
violet flume
were back here
violet flume
i do like quotient
yea so just hit (1/sinx) with quotient rule
maybe thats what u did
viral kiln
yea we learnt the rules on how to find the derivatives i just wasn’t sure what i would do with the 6x
violet flume
hopefully the way i wrote it makes it make sense 🙏
and isnt just more confusing
in a way you ignore it
but you arent allowed to forget it entirely
,w D[ csc(6x) ]
wraith daggerBOT
viral kiln
because we learnt if we have y=cos(f(x)) then d’y/dx is -f’(x)sin(f(x))
sorry it takes a bit to type out haha
violet flume
because we learnt if we have y=cos(f(x)) then d’y/dx is -f’(x)sin(f(x))
sure, yea
viral kiln
i was just kinda wondering what that would be for csc and those
violet flume
well, if you apply quotient rule, you'd get to use this, right?
viral kiln
in a way you ignore it
not ignoring it don’t worry, it’s helping a lot!!!
viral kiln
well, if you apply quotient rule, you'd get to use this, right?
ohhh yeah
violet flume
$\dv x \frac{1}{\sin 6x} = \frac{ \sin 6x \cdot \dv x 1 - 1 \cdot \dv x \sin 6x }{ (\sin 6x)^2 }$
wraith daggerBOT
jan Niku
violet flume
something like this?
violet flume
because we learnt if we have y=cos(f(x)) then d’y/dx is -f’(x)sin(f(x))
then you can apply this rule right in-place
viral kiln
OHHHH
viral kiln
something like this?
yes yes that looks right
violet flume
its really whatever is easiest for you
$y' = x^3 \qty(\dv x \csc 6x) + \qty(\csc 6x) \dv x x^3$
wraith daggerBOT
jan Niku
violet flume
maybe you get to here and just go oh man that csc6x derivative is gonna be hairy or whatever
ill do it on the side
violet flume
why is there a cosx on the bottom
violet flume
**jan Niku**
you were working on this right?
viral kiln
oh!!
violet flume
yea this looks better
viral kiln
sorry about all the questions by the way we just started the unit on wednesday 😭
violet flume
do you see how to group this all out?
violet flume
sorry about all the questions by the way we just started the unit on wednesday �...
no worries if you can master derivatives your life will be easy
at least mathematically
viral kiln
no worries if you can master derivatives your life will be easy <:happy:90855810...
that’s all i need!!
violet flume
cos/sin would be cot
yea
then you leave behind a 1/sin6x
you do have a constant floating around
viral kiln
wouldn’t it be 1/sin6x
violet flume
ye
viral kiln
oh a plus or minus
violet flume
go back here
wraith daggerBOT
jan Niku
violet flume
this is $\dots - 1 \cdot \qty( 6 \cos (6x) )$
wraith daggerBOT
jan Niku
viral kiln
ohhhh okay
OHHH OKAU oops
thank you
just forgot it i went a bit too fast again
ORETTY SURE
viral kiln
oh yeah 😅
violet flume
,w D[x^3 * csc(6x) ]
wraith daggerBOT
violet flume
yea up to your prof but conventionally
factor out as much as you can
dont right factor like wolfram did here
lol
just my own personal taste
viral kiln
okay yeah
violet flume
maybe its trying to keep all the trig functions close together idk
viral kiln
lemme do it rn and i’ll take another pic
probably
idk this is just tough because we started the unit wednesday and we have a test wednesday
violet flume
it is a test about being careful
viral kiln
1 week to learn it all including eulers number haha
viral kiln
it is a test about being careful <:happy:908558103992225822>
if it was i would get a 60 hahaha
violet flume
i have one week to write a 10 page paper 
do not pay any attention it was assigned in january
that is not important
viral kiln
oh gotta get that started soon then right
violet flume
these trig problems are good
you know you can generalize these if you wanted but idk how good practice it is
violet flume
trig ones are good because you really have to know quotient and not lose signs
viral kiln
yeaaa i know quotient good i just forget signs sometimes
violet flume
just solve $\dv x \qty( f(x) \cdot g\qty(h(x)) )$
wraith daggerBOT
jan Niku
violet flume
or something like this
viral kiln
my last calc test went great though!
violet flume
i dont think its helpful
but possible 
dont let me waste a bunch of your time prattling about nothing
viral kiln
haha i’m not don’t worry
applications in calc was fun though, just wished we got more time to practice for this unit
mind if i try the last question and send you what i got?
violet flume
okay
viral kiln
my calc exam is next tuesday 
violet flume
I believe in you
viral kiln
i’ll do my best!
hopefully it’ll raise my grade
starting the problem now just had to grab a snack
violet flume
no problem feel free to ping
viral kiln
is this as simple as this looks
SORRY FOR ALL THE WUESTIONS but also
how do i find where sinx and cosx are equal to 0? or am i just supposed to memorized?
violet flume
you should have pinged me in channel haha
viral kiln
ah i feel bad!
viral kiln
a cat… 😭😭
violet flume
oh
wraith daggerBOT
jan Niku
violet flume
why do you need to solve where things are = 0?
violet flume
,rotate -90
wraith daggerBOT
violet flume
lol
it helps to know identities but its in a week so who cares
you should know some
$2 \sin x \cos x = \sin 2x$
wraith daggerBOT
jan Niku
violet flume
BUT you dont have to know this
viral kiln
and cos is like
i know this
i don’t remember how to like word it but it’s like kpi/2 where k is an odd number
violet flume
i don’t remember how to like word it but it’s like kpi/2 where k is an odd numbe...
i mean its periodicity
violet flume
because $\cos(x) = \cos(x+\pi)$
wraith daggerBOT
jan Niku
violet flume
so if $0 = \cos \frac \pi 2 = \cos \qty( \frac \pi 2 + \pi) = \dots$
wraith daggerBOT
jan Niku
viral kiln
perfect okay, is there any way to like show that though
violet flume
it gives you infinitely many solutions
then, use the constraints of the problem to pick some out
violet flume
yeah, problem is between 0 and 2pi though so it works out
inclusive, yea
so, you want either cosx =0 or sinx = 0
since that makes the product 0
and then the derivative 0
you have a formula for where these happen
or you remember your unit circle
violet flume
yea
violet flume
I wouldnt give too much ceremony about it unless your professor is especially picky
violet flume
nice
viral kiln
thank you very much for all of your help
viral kiln
and sorry if i distracted you from other work
violet flume
i dont wanna work today lol
copper sky
cedar kilnBOT
upper abyss
Well, one could say f is approximated by 2(x-1)⁴/4!
Tbh, isn't "local extremum" just f'(1) = 0 though? We already have that.
But the approximation should make the function's behavior pretty clear
@copper sky
copper sky
Tbh, isn't "local extremum" just f'(1) = 0 though? We already have that.
we are looking for local min or local max or neither
so the derivatives dont give us that directly i believe
upper abyss
Luckily we can approximate with Taylor's theorem
copper sky
yes
but in taylors theorem we have the fourth derivative at some point c
so i dont see what to do with that
on nvm got it
.close
vital mason
I believe I made a mistake but I can’t seem to find it.
cedar kilnBOT
I believe I made a mistake but I can’t seem to find it.
bleak viper
its correct
vital mason
Would I leave it as cosx/1 or is just cosx?
slate lintel
i'd write cosx
cedar kilnBOT
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orchid moat
cedar kilnBOT
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@orchid moat Has your question been resolved?
wicked jetty
Hey could someone teach me how to graph these?
cedar kilnBOT
Hey could someone teach me how to **graph** these?
bleak viper
do you know about curve sketching?
bleak viper
using differentiation to sketch graphs
wicked jetty
I do not know how to do that
bleak viper
then plot the graph
put values of x solve for y and vice versa and get coordinates
then plot it
silver oxide
isnt this just asking for when f(x)=0?
silver oxide
have u already solved it algebraically?
wicked jetty
silver oxide
aight guess that works
wicked jetty
I got some weird decimal numbers so I just drew a rough sketch using them
How to do these 2?
@silver oxide
silver oxide
at that rate just sub in values and plot the points
wicked jetty
at that rate just sub in values and plot the points
How do I do the bottom 2?
D and e?
@silver oxide
Pls teach me how to do the bottom 2
@silver oxide
@silver oxide
royal loom
<@300086056378695691>
!noping
cedar kilnBOT
<@300086056378695691>
Please do not ping individual helpers unprompted.
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obtuse mantle
how would I go about solving this?
cedar kilnBOT
how would I go about solving this?
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cedar kilnBOT
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hearty mountain
cedar kilnBOT
hearty mountain
I understood the first part
But I didn't like using manual counting to find all the sample space
Is there any other intuitive way to find the answer
cedar kilnBOT
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quaint sun
What is the minimum number of books required to ensure that we have at least 18 books of the same genre (all 18 books being from one genre), if there are a total of 31 genres?
fair geyser
31*18 is nothing
crimson sedge
not sure tho
fair geyser
it's 31*17+1
bleak viper
because we ensure atleast 1 genre is repeated atleast 18 times
not -17
should be 528 (558-30)
quaint sun
it's 31*17+1
that's the right answer. But i don't know what's the thought process to get it
bleak viper
that's the right answer. But i don't know what's the thought process to get it
basically 31*17 is for 17 books for all genres
now it says you should have atleast 1 genre with 18 books
so if you pick a book of any genre you'll fulfill the condition
so you add +1
bleak viper
yeah
crimson sedge
I counted the books it seems
quaint sun
can we start from the beginning? I don't even understand the question. What do they mean by "ensure that we have at least 18 books of the same genre"?
bleak viper
okay, so
there are 31 genres
now it asking you the minimum number of books you must have so that at least one genre out of 31 has 18 books in it
got it?
quaint sun
but they never tell us how many books are in each genre or how many books are there total
im still confused, sorry
bleak viper
but they never tell us how many books are in each genre or how many books are th...
there arent any books in total
you need to find the number of books
lets say you're building a library, you can fill in books with 3 genres
now u have to find the minimum number of books you must fill so that atleast 1 genre has 2 books
now in this case you take the worst possible scenario
that you get 1 book of each genre first
now since you need atleast 1 genre with 2 books in it and the total number of books should be minimum
so you just get 1 more book now, regardless of its genre you'll have 1 genre with 2 books in it
fulfilling the condition
now just repeat this but with 31 genres and 18 books in atleast 1 genre
quaint sun
is this what u mean by your library example:
bleak viper
yes
so the minimum number of books required to ensure that we have at least 2 books of the same genre, if there are 3 genres, is 4
now repeat this thought process for 18 books of same genre if there are 31 genres
quaint sun
i think we going too far ahead. what do we add or multiply in the library example
bleak viper
wdym
quaint sun
assuming we add or multiply to get 4, what numbers do we add or multiply and why?
bleak viper
3*1 + 1
3 for the 3 genres multiplied by 1 for the first book in all three of them and then add +1 to fulfill the condition of having atleast 2 books of the same genre
quaint sun
so 3*1 because there's 1 book for 3 genres each, and then that 1 is added so that one of the genres has 2 books?
bleak viper
yes
fair geyser
@quaint sunthere's 31 genres in existence, like any book at all is definitely one of those, and no book is 2 genres
that's the assumption
there's some magical number of books that you can be sure you have 18 of the same genre in them (and it's the smallest such number)
it would be impossible if for example we wanted 2 genres at the same time, 18+18
take a million books, they could all be from genre 1, so we don't have 2 times 18, so we can never be sure
but if we only want one genre there's no problem
527 books could be not enough (31×17) but one more book makes it certain
quaint sun
"it would be impossible if for example we wanted 2 genres at the same time, 18+18"
i like this counterexample, it really makes the problem clearer.
"take a million books, they could all be from genre 1, so we don't have 2 times 18, so we can never be sure"
I don't understand this though
Re-thinking this problem on my own. I've arrived at a different answer (but its not the right answer).
Since there are 31 genres. Since one of them has 18 books, then the minimum book case is where 30 genres have 1 book each: 30*1 = 30 books. Then add 18 books from that 31st genre: 30 + 18 = 48.
Why is this wrong??
cedar kilnBOT
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quaint sun
<@&286206848099549185>
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cloud jay
What happened to the -1/j from the second line to the third line? My answer is the same with the third line except with a -1/j multiplied to it
cloud jay
Is it just a typo or am I missing a rule or smth
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wary wasp
Given a vertical prism ABCD.A'B'C'D' with B'D = 3a, the base of ABCD is a rhombus with AB = a, BAD=60⁰
a) What is the volume of prism ABCD.A'B'C'D'?
b) Let d be the measure of the dihedral plane angle [A', BD, C]. Calculate d?
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Given a vertical prism ABCD.A'B'C'D' with B'D = 3a, the base of ABCD is a rhombu...
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indigo cove
A wagon with a mass of 120 kg moves at a speed of 6 m/s. After a person with a mass of 80 kg jumped from it at an angle of 60° to the direction of movement, the speed of the wagon became 5 m/s. Find the speed of the person during the jump.
cedar kilnBOT
A wagon with a mass of 120 kg moves at a speed of 6 m/s. After a person with a ...
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real forge
That i pinged twice
n p
oh sorry
i dont have enough time rn to correct this
anyway, I wish you good luck in your search for help.
it makes me feel bad that I can't help you, I'm really sorry.
cedar kilnBOT
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fallen shadow
cedar kilnBOT
fallen shadow
this question is driving me crazy idk how to do it
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spice phoenix
Can someone help?
cedar kilnBOT
Can someone help?
spice phoenix
livid hound
open () not []
spice phoenix
Why are the others []?
livid hound
inf aren't numbers, there is no bound
and tan(x) is undefined at pi/2,-pi/2
astral steppe
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sharp surge
hi i know its very simple but i have a test tomorrow and this is one of the only questions im confused on im just stuck on what the other angles are
neon void
i think if the quadrilateral is circumscribed then opposite angles are supplementary
sharp surge
i think if the quadrilateral is circumscribed then opposite angles are supplemen...
ooohhhhh
that makes so much more sense
so just do 91-180 and i have my answer for W?
ok i got it tysm
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light temple
light temple
<@&286206848099549185>
static cloak
@light temple Based on that table we need to answer.Right?
See the table if one person is voted in the last election the probability will be 0.23 and so on.
light temple
oh yea I got that but I have another question
static cloak
Tell
light temple
for this question
The 5% on the graph should be shaded right
But idk how to determine if it’s on the left or the right
wraith daggerBOT
KingDanger
static cloak
What these three things means here? @light temple
cedar kilnBOT
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ripe valve
(dont actually need to solve) but i want to know how would i go about checking if they collide at the same time?
ripe valve
is it just comparing to see if t and u are the same?
in this case they are not the same so they dont collide?
main needle
like if the u and t are the same at (1,5,0)? yea it's not simultaneous since you can just check it doesn't work for x=1
ripe valve
so in the future if i get a problem about asking if they intersect at the same time, i just compare t and u?
im a bit confused by the differing notation
yeah im just a bit confused why it's u
so u also denotes time
alright thanks
so both systems are still time
i thought u meant something different
the t and u variable
uh
calculus 3
lines and planes
yeah variables not i j or k
i just wasnt sure if u also denoted time
autumn tusk
hello!
autumn tusk
i am struggling with tle last part.
the last espression we have is (r/k +c_2)delta(t)
but that is zero on 0+ and 0-
so the solution would be just 0 and r
I don't understand what should i compare
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autumn tusk
<@&286206848099549185> someone knows this stuff? it's Unit Step and Unit Impulse Response for differential equations
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empty rain
hi I need a counterexample of Barrow's Proof of the Fundamental Theorem of Calculus when function f is not continuos
empty rain
As continuity in [a,b] for f: [a,b] --->R is required
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<@&286206848099549185>
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upper kraken
I’m having trouble proving this identity, it seems true but I can’t find a path to proving it. I’ve tried looking at its relation to Pascal’s triangle and some algebra but nothing really jumps out to me
cedar kilnBOT
I’m having trouble proving this identity, it seems true but I can’t find a path ...
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narrow lantern
Help
narrow lantern
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narrow lantern
Yes could you provide me with an answer plz
narrow lantern
Ok thanks
narrow lantern
Ur supposed to find d^2y/dx^2 at the point (1,-3)
glossy sierra
So the fraction
narrow lantern
Yes
narrow lantern
Np
upper abyss
Hopefully you're good with finding the first derivative. If not, we can focus on that instead
Once you have the first derivative, solve for it. Then take the derivative in terms of x again.
It's lengthy, sadly.
narrow lantern
Once you have the first derivative, solve for it. Then take the derivative in te...
I believe the first derivative is 2 could u help me answer the other half
upper abyss
Sorry I don't mean the first derivative at that point
You'll need the general first derivative
narrow lantern
You'll need the general first derivative
So -1/x-y/x that doesn’t seem right to me
upper abyss
That's right
narrow lantern
Can u answer the rest of the problem and show the work so I can see how to do the rest
upper abyss
Not my style sorry. Hopefully someone else can help
narrow lantern
Ok can u atleast help me
What do I do after I have the first derivative
@glossy sierra did u get an answer?
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cedar kilnBOT
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languid oriole
cedar kilnBOT
languid oriole
how to solve
languid oriole
partial fractions
should telescope
i don't see it telescope
languid oriole
i didn't find a way to express it in a general expression for nth term
or i'm high
chrome delta
i didn't find a way to express it in a general expression for nth term
the denominators increase by 5 for each term
languid oriole
yeah
chrome delta
that should be enough for you to get started
unique valley
add 5 to the 4 and add 5 to the 9 right?
languid oriole
i was curious, you supposed to answer this in 10s?
yes
i mean i thought of a way already
but i don't think it's right bcs it's 10 seconds
languid oriole
take time to learn
i fucking hate orals0
unique valley
i get you man, but trying to do every question as fast as you can is not a good way to learn it
some question youd get faster some slower
unique valley
add 5 to the 4 and add 5 to the 9 right?
coming back, i can write this as 1/(4+5)(9+5)
from second to third it would be 1/(4+5+5)(9+5+5)=1/(4+2* 5)(9+2* 5)
languid oriole
coming back, i can write this as 1/(4+5)(9+5)
how can i express it as n?
unique valley
do you see the pattern?
languid oriole
a
unique valley
you still dont see how to express it?
languid oriole
i see now
unique valley
and you can obv simplify this afterwards
unique valley
what you got brother?
unique valley
hmm, i dont have time so cant really help you
unique valley
thx
crimson sedge
cedar kilnBOT
crimson sedge
<@&286206848099549185>
dreamy void
what is it that you struggle with
dreamy void
you need to construct a linear function
the input is t and output is d
imagine t was time and d distance
for every 5 minutes you travel 2km for example
crimson sedge
ok
dreamy void
now you want to know how much you travelled after 10min for example
or basically want to always know how much you travelled
crimson sedge
that would be 4km?
dreamy void
yea how did you do that?
crimson sedge
times 5 by 2 to get 10 which represents 10 mins then got 4 and multiplyed it by 2
dreamy void
you basically just did
what your function line would do for you
so basically
a multiply of 5 minutes gives us a multiply of 2km
we can also say
dreamy void
basically you have
crimson sedge
i have it like this
dreamy void
d/2 = t/5
crimson sedge
ok
crimson sedge
so like this?
dreamy void
not quite
think
this functions says
at 5 minutes i travelled 0km
and at 10 you would be in the negative
but it's the opposite
as time progresses your distance increases
so it goes up
dreamy void
not it's worse
it still goes down
from left to right
it has to go through your points
(5,2) and (10,4)
ok 10 is not on the axis
but it goes through (0,0) the origin
at 0 minutes you travelled 0 km
crimson sedge
dreamy void
nope
crimson sedge
im stupid frfr
dreamy void
this line means you didn't travel for example
at 5 minutes you are at 2km
and after 8min you are still at 2km
it has to go through (0,0) and (5,2)
crimson sedge
im so lost
dreamy void
what is the problem
crimson sedge
so make it like this?
dreamy void
To explain how we came up with the function:
For some time you traveled some distance.
5min -> 2km
10min -> 4km
So for every 5 minutes your km increases by 2.
You have a ratio of 2/5 which describes you rate of change
2km per 5 minutes
dreamy void
so make it like this?
not quiet
crimson sedge
i suck at this
dreamy void
your two points
crimson sedge
dreamy void
now draw the line through thes
dreamy void
it says for one unit
crimson sedge
oh okay lol tysm and im sorry
crimson sedge
no ig not
dreamy void
haha
crimson sedge
i wasted ur time though lol
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lean skiff
You have 6
identical dice. What are the total number of outcomes?
Note that cases like (1,5,5,2,3)
and (3,5,2,1,5)
are considered the same outcomes since the dice are identical.
cedar kilnBOT
You have 6
identical dice. What are the total number of outcomes?
Note that cas...
@lean skiff Has your question been resolved?
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@lean skiff Has your question been resolved?
nimble juniper
I've been having this problem for a long time.
Translation: Problem 3. How many subsets of S = {1, 2, 3, ..., 33} have the property that the sum of their elements is greater than 280?
limber willow
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cedar kilnBOT
I've been having this problem for a long time.
Translation: Problem 3. How many...
Show your work, and if possible, explain where you are stuck.
nimble juniper
I achieved basically nothing. I know it's a combinatorial problem. From subsets that add up to 561 to 528 I had gotten the number of possibilities, but I realized that the method was humanly impossible later.
I noticed that the difference between the sum of all the elements is 561, which divided by two basically gives 280.
raven shard
I achieved basically nothing. I know it's a combinatorial problem. From subsets ...
the sum being 561 is not a coincidence btw
nimble juniper
the sum being 561 is not a coincidence btw
definitely
raven shard
but ur pretty much done once u realize that
nimble juniper
but ur pretty much done once u realize that
honestly i dont know how to proceed
raven shard
number of subsets that sum to 0 = number of subsets that sum to 561
number of subsets that sum to 1 = number of subsets that sum to 560
...
etc
nimble juniper
i cant prove it, but i think that the number of subsets that sum to a number has a pattern
sum to 561 = 1 probability
sum to 560 = 1
sum to 559 = 1
sum to 558 = 2
sum to 557 = 2
sum to 556 = 3
sum to 555 = 3
and this will continue at least until 528
but this should go half
but I can't really prove this, and for the exercise in question, I would actually need to prove
cedar kilnBOT
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soft lark
cedar kilnBOT
tardy oasis
This is 1/4^3
tardy oasis
Yes
soft lark
nice
soft lark
You can write in general
for this example since you have the negitive in brackets
it means that you do the 6th power
with it in brackets
but if the negitive was on the outside you would just ignor the negitive and add it back on in the end right?
tardy oasis
Yes
You can just replace the minus sign by multiplying by -1
It is really just shorthand for that
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crimson sedge
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crimson sedge
how do I start 5a (ii)
crimson sedge
how do I start 5a (ii)
so do you know what you are trying to find exactly?
ratios for sin cos and tan
yeah
how☹️
so the 15 degrees angle is what you call a reference angle. Are you familiar with those
i think so ya !
,,, right so your first objective is to find
\e{align*}{
\6\sin{\0b\theta} &= \0r{{???}} \
\6\cos{\0b\theta} &= \0r{{???}} \
\6\tan{\0b\theta} &= \0r{{???}}
}
wraith daggerBOT
crimson sedge
ooooo ya (wait that’s texit thing so cool)
hope the colour coding helps. What im trying to say is can you represent the blue theta angle trig ratios in terms of the red (15 degrees) trig ratios?
um um um I don’t know😭
,,,
\e{align*}{
\6\sin{\0b\theta} &= {???}(\0r{15\degrees}) \
\6\cos{\0b\theta} &= {???}(\0r{15\degrees}) \
\6\tan{\0b\theta} &= {???}(\0r{15\degrees})
}
wraith daggerBOT
crimson sedge
hopefully this is better?
the ???s can be sin, cos, tan, -sin, -cos, or -tan
so do I just solve for theta using the inverse(15)?
no haha i think you are overcomplicating things
so basically like how reference angles work is like
in all of those situations you can have a reference angle, and that reference angle has a very nice property
the trig ratios of the green theta (the main angle in the picture) are equal to the trig ratios of the red theta (the reference angle) BUT with a small catch that they might have a - attached next to them
to know if they have a - attached, just remember that cos is negative in the 2nd and 3rd quadrant, and sin is negative in the 3rd and 4th quadrant
oh the CAST rule?
as an example
[
\cos(120 \degrees) = -\cos(60\degrees)
]
wraith daggerBOT
crimson sedge
oh the CAST rule?
yeah!
crimson sedge
so here 120 degrees is in the second quadrant and cos is negative there
the reference angle to 120 degrees is 60 degrees from the negative x axis
so the two are equal with a -
hope this is understandable in some way?
yaaaaa that makes sense ty
crimson sedge
oki so going back to this
first; what quadrant is the blue theta angle in?
q2
yeahh
is it also in q1
nop! can only be in one at a time
so cos is negative and so is tan right?
oh oh sorry ignore what I’m saying lol
yaaaa
yeyeyey so now, the reference angle is 15 degrees
ya ya
crimson sedge
so knowing all of this what are the ???
165
the ??? can be sin, cos, tan with a potential - attached
oh wait the theta is 165 right then the ??? is sin, -cos, -tan
YESSSS! good job!
ok so
,,,
\e{align*}{
\6\sin{\0b\theta} &= \sin(\0r{15\degrees}) \
\6\cos{\0b\theta} &= -\cos(\0r{15\degrees}) \
\6\tan{\0b\theta} &= -\tan(\0r{15\degrees})
}
wraith daggerBOT
crimson sedge
yaaaaaaa!
now we wanna calculate those on the right
do u have any ideas on how to calculate something like sin(15 degrees)
do i take the inverse of sin then multiply it by that
no haha that doesn't work
aw☹️
as a hint, think of sin(a + b) for example
can i just plug in sin(15) into my calculator lol
idk ur teacher but i dont think they want u to do that 😅
,align
\6\sin{a\pm b} &= \6\sin a \6\cos b \pm \6\sin b \6\cos a \
\6\cos{a\pm b} &= \6\cos a \6\cos b \mp \6\sin a \6\sin b
oh☹️
wraith daggerBOT
crimson sedge
you can use this here tho
do u know about this
no this is my first time seeing this
mmmm
tytho
what trig identities do yk
we didn’t learn trig identities yet
i think we start that next monday
hmmm okii i guess u cant do this one manually then
you can use a calculator then
ooooooo yay ok !!
TYSM for the help 😊
no worries good luck!
sorry I’m like terrible at math lol
tyyy
.close
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crimson sedge
nah it's ok
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polar flame
for a, do i just take the f_x (x - x0) + f_y(y - y0) equation and do it s and t?
for b, i assume I take an integral, but how to set it up I'm a bit lost
cedar kilnBOT
for a, do i just take the f_x (x - x0) + f_y(y - y0) equation and do it s and t?...
@polar flame Has your question been resolved?
polar flame
<@&286206848099549185>
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@polar flame Has your question been resolved?
frozen spoke
for a, do i just take the f_x (x - x0) + f_y(y - y0) equation and do it s and t?...
for a
r(2,3,1) + gradient of r(3,2,1) • <x-2, y-3, z-1>
for b
geometrically, what shape does the restriction make? if you understand that, it will help with setting up the bounds
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torpid fern
would P(1-r/100)^n be the same as P-P(r)^n in exponential decay when p is decreased by r%, n times
plain ridge
are you asking if P(1-r/100)^n = P-Pr^n? if so, no
the second one factors as P(1-r^n) with the ^n inside the brackets
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halcyon junco
i was doing an exercise related with find and draw the domain and from log(y-x^2+4) which they give us the value of 1 (idk in english how its call but in the question we say cotes), the thing is why from y-x^2+4 = 1 it changes to y-x^2+4=10
raw sky
Guys what's 1+1
undone halo
2, broken window, 11, window
halcyon junco
?
peak minnow
i was doing an exercise related with find and draw the domain and from log(y-x^2...
$$\log (y-x^2 + 4) = 1 \cdot 1$$
i think here the base of log is 10 , so the question becomes
$$ \log_{10} (y-x^2+4) = 1 \cdot log_{10} 10$$
if u didnt know then $log_{a}a = 1$
Taking anit log u get
$$ y-x^2+4 = 10$$
wraith daggerBOT
JustToPro
halcyon junco
$$\log (y-x^2 + 4) = 1 \cdot 1$$
i think here the base of log is 10 , so the que...
i see, in the question is like this
peak minnow
yeah usually log written like that has base 10
peak minnow
unless if base is different , then base is mentioned
halcyon junco
if doesnt says anything more
peak minnow
yeah log has base 10 , ln has base e and if base is different then its mentioned
halcyon junco
if the exercise was with ln
plain ridge
usually yeah
but in this case it doesn't rlly matter
you'd just get 1*log_e(e) or whatever
peak minnow
!done
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halcyon junco
.close
cedar kilnBOT
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random raptor
cedar kilnBOT
random raptor
Help with d pls
plain ridge
,rotate
wraith daggerBOT
atomic chasm
Help with d pls
There is an interesting number theory result that if u add up the digits of a number and the sum is divisible by three, then the number is also divisible by three
Might be helpful
Oh wait, my bad, I was looking at e not d.
atomic chasm
Help with d pls
Well, for it to be greater than 3000, you know that the first digit has to be either 3 or 4 and the last digit has to be either 1 or 3. So how many numbers work with those restrictions. It should just be counting 😭 after this.
cedar kilnBOT
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random raptor
Well, for it to be greater than 3000, you know that the first digit has to be ei...
Yea I did 2 x 2 x 1 x 2 over total amount
Is that right?
atomic chasm
Yea I did 2 x 2 x 1 x 2 over total amount
Pretty sure the answer is 6.
Consider 2 case
Case 1 ( first digit is 3):
Then the last digit is 1. So the middle digits are either 2 or 4.
So case 1 has 2 options
Case 2 ( first digit is 4):
Then the last digit is either 3 or 1
So between the last 3 digits there are 2x2 so 4
So 6 total
atomic chasm
Yea I did 2 x 2 x 1 x 2 over total amount
I think where u went wrong is u multiplied the first 2 rather than adding them
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half quail
Ive factored the bottom to (x+1)(x-1), i've got a feeling i need to use substitution, but as x approaches 1, i cant use a standard limit, and so i dont know where to go
half quail
I also can't use Lhopitals and only standard limits
crimson sedge
can you use the series
half quail
You mean taylor series? I believe so but i've had a little trouble understanding it
crimson sedge
i cant find other ways of solving it rn, sry
crimson sedge
f(x) can't be increasing if f'(x) = 0 right
it just isn't doing either
crimson sedge
i'm so fucking confused
bleak viper
it can be
crimson sedge
bleak viper
if f'(x) is 0 at point c
crimson sedge
it can be
how does that make sense intuitively
if the rate of change at c is 0, how can it be increasing