lol im still mentioning my graph FUCK
#help-13
ivory finch
ivory finch
all x in the domain map to only ONE y in the codomain = injective
rain drift
the function f(x) = -x^3 takes negative real numbers, cubes them, and then multiplies that value by -1. So no matter what, we will always have have a postiive output
rain drift
now logically are there any values that don't have a mapping in the codomain?
rain drift
bingo!
ivory finch
And by logic
injective
we can say
x^3 is always unique even normally
so suffice to say -x^3 injective too
rain drift
yep!
rain drift
another way of thinking about it is this
ivory finch
odd powers ALWAYS unique right
rain drift
-x^3 from (-inf, 0) is always decreasing for x < 0. Since it's monotonically decreasing (meaning it doesn't change as you approach 0), then our function will have unique mappings from the negative reals to the positive reals
now in proof world, this wouldn't suffice, but again we're just thinking through this 🙂
ivory finch
agreed
rain drift
Another example: Let $g : \mathbb{Z} \mapsto 2\mathbb{Z}$ (aka it maps from the integers to the even integers) and let $f(x) = \frac{x + 1}{2}$ for $x \in \mathbb{Z}$? Would our function be injective, surjective, bijective, or neither?
wraith daggerBOT
MellowDramaLlama
ivory finch
am i allowed to graphj this on desmos?
rain drift
so now our domain looks like this: {..., -4, -2, 0, 2, 4, ...} and our codomain looks like this: {0, 2, 4, 6, ...}
nope lol
ivory finch
also isnt this not even a function
cuz what if x = 2
then y = 3/2
but it not in 2Z
rain drift
very good logic!
rain drift
yep! the codomain has to be possible. If you get an erroneous value like f(2) = 3/2, that's not even in the codomain
and functions have have to map values to the codomain. Not everything in the codomain has to be mapped for injectivity, but with functions:
- all elements of the domain have to be mapped
- all elements of the comain have to map to something in the codomain
so this would be an invalid function
ivory finch
dope
rain drift
(My intention was to make an injective function from a set of integers to a subset of integers and in my head I got it wrong. It's hard to think of examples, lol)
but nice reasoning!
Let $g : \mathbb{Z} \mapsto \mathbb{R}$ (aka it maps from the integers to the reals) and let $f(x) = \frac{x + 1}{2}$ for $x \in \mathbb{Z}$? Would our function be injective, surjective, bijective, or neither?
there that's valid 🙂
wraith daggerBOT
MellowDramaLlama
rain drift
bingo!
rain drift
very good!
ivory finch
i am more visual person
so basically
lets go back to here
if i want to reduce confusion
can i just turn the LHS into y
so i go back to baby school
y=x
i rly dont like that IA(X) thingy
rain drift
no worries! These are great visual tools to use
rain drift
i rly dont like that IA(X) thingy
You'll get more used to it. An identity function is a really really useful tool in a lot of fields. You'll see I_A(x) more often than not so I would jsut get used to it
rain drift
lol sure if it helps you
ivory finch
what in the hell
i think
actually
its deffo not injective
but
i think its surjective?
NI cuz sine is a string
so repeats vals
but SJ cuz every R can be covered?
rain drift
right but how would that (x^3 + 2) effect it?
rain drift
correct
ivory finch
what do u think
rain drift
now you are correct that it's not injective
ivory finch
u sure ?
rain drift
but there's a very pariticular reason why
ivory finch
sin
rain drift
sin(y) is cyclic and there's one value we hit over and over that'll map values of y to this same value
it's when sin(y) = 0
rain drift
so anytime y = pi/2 + pi * n for an integer N, then it maps to f(x, y) = 0
so things like sin(pi/2), sin(3pi/2)
otherwise (x^3 + 2) is monotonically increasing from (-inf, inf)
but the fact that we keep getting f(x, y) = 0 means that we have multiple pairs of points (x, y) that hit the same number, thus not injective
but yes you are totally right about the surjective part 🙂
there might be other reasons but that one is blatently obvious to me
ivory finch
oh cuz even though its cyclic, as x increase it will be like
rain drift
yes correct, however it won't quite look like that since it's in terms of f(x, y)
our graph here would be more 3S
*3D
it would look like this, which is where graphing can get confusing
ivory finch
interesting
rain drift
have you taken calc3 or are you going to?
ivory finch
taking calc3, diffeq, proofs
tbh
everything except proofs is fine
the rest is just mindlessly chugging numbs
diffeq esp
like
the diff is actually insane
rain drift
yeah I see what you mean. Diff EQ gave me some trouble but that's because of the things like Wronskian
proofs are like learning another language
you gotta learn syntax, reasoning, new notation
it's a whole other beast
ivory finch
diffeq and calc3 im deffo gonna pass and probably ace
proofs i got like a 55 on my first midterm LOL
rain drift
when you get into things like abstract algebra or topology and numbers just flat out disappear
shit gets weird haha
ivory finch
shit
im gonna take like 2 abstract algebra courses this yr
are those the only truly proofy ones? or will there be more?
i want to get those over with asap
i'll be doing discrete maths class too not sure if thats as similkar
rain drift
proofs i got like a 55 on my first midterm LOL
Proofs are hard, so don't beat yourself up. For some people it's incredibly intuitive.
Especially when you look at a proof that looks concise and nicely put together, that often takes a long time and a lot of work to make it look that good.
Kind of like a marble statue. You gotta chip away for a while until your sculpture looks good
rain drift
are those the only truly proofy ones? or will there be more?
Oh there are proofs everywhere. Your "plug and chug" courses are built up on Real Analysis and Numerical Analysis which are chalk full of proofs
so the reason that you can use tools like derivatives, integrals, vectors, etc is because they've been rigorously proofed in real analysis, linear algebra, etc.
ivory finch
thank god for those saviors
thankfully i dont need to take real analysis afaik but its an elective choice
pretty sure 99% of people would decided not to take it
brb15
rain drift
no it's a hard course
I'm re-learning it post graduation because I think I missed out on some stuff that I might not have had the technical understanding for at the time.
hardy minnow
some one hel;p me with multiple choice grade 7 questions
cedar kilnBOT
some one hel;p me with multiple choice grade 7 questions
hollow minnow
Just post it
cedar kilnBOT
@hardy minnow Has your question been resolved?
abstract furnace
0<0<2pi for cos^2=sincos
cedar kilnBOT
0<0<2pi for cos^2=sincos
abstract furnace
I did
1-sin^2=sincos
sin^2+sincos-1=0
sin^2+sincos-sin^2xcos^2
cos(sin cos)=0
so get two solutions pi/2 and 3pi/2 but i’m missing two
for whatever reason
digital cliff
why have you said 1=sin^2 x cos^2
assuming that was a typo
sincos-cos^2=0
cos(sin - cos)=0 fine
youve only solved the case of cos=0
and havent done sin-cos=0
abstract furnace
but how do i put that in a calculator
digital cliff
sin=cos, cos and sin cant be 0 simultaneously so cos!=0 here
then tan=0
abstract furnace
i don’t get it
cedar kilnBOT
@abstract furnace Has your question been resolved?
hollow trail
sin θ = cos θ
sin θ/cos θ = cos θ / cos θ
(assuming cos θ ≠ 0)
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Occupied
crimson sedge
Prove that f(x) is a fractal iff it is nowhere differentiable
idle tusk
Prove that f(x) is a fractal iff it is nowhere differentiable
define fractal
cedar kilnBOT
@crimson sedge Has your question been resolved?
graceful ridge
We consider a private student loan at 6.49%, but the rate for such a loan could be as high as 12.99%. With $10,000 principal, interest-only repayment, and at the higher rate, how much interest would you pay over 59 months of deferred payments on the principal?
I did this type of problem with the 59 months switched for 55 months once before but I'm not quite sure what the formula is to do it again as I didnt write it down, and I dont have any frame of reference for how to do it since my prof didnt put down any equations for this
crimson olive
any ideas what i did wrong here?
cedar kilnBOT
any ideas what i did wrong here?
crimson olive
ik if it is a single tree then its a forest
but it says what i have is wrong
im fairly certain bottom left is a forest as the node by itself is acyclic
rare vault
the second box doesnt look like a tree to me
rare vault
GHK
crimson olive
?
rare vault
GHK forms a loop
crimson olive
oh, so if it has a loop it is considered a cycle?
rare vault
a cycle is just a (non-empty) route that only the first and last vertices are equal
rare vault
also im pretty sure the definition of a forest includes that all the connected components are trees
crimson olive
yep
rare vault
so why does the loop matter if it isnt a cycle?
it is a cycle
rare vault
yes
rare vault
yes
ebon tangle
cant seem to figure this one out. I do n=1, n=k, n=k+1 but i cant manage to simplify correctly
olive crescent
so where did you get to
ebon tangle
sorry two seconds im having problems sending the picture
i think the main problem is i might be using th einductive hypothesis wrong?
or maybe idk when to use it or how to use it here
olive crescent
assume
f_k-1 + f_k+1 = l_k
f_k + f_k+2 = l_k+1
then we need to prove f_k+1 + f_k+3 = l_k+2
we can write l_k+2 in terms of k and k+1
similarly we can rewrite f_k+3 in terms of k+2 and k+1
olive crescent
so with the inductive step where we assume it holds for k, we can assume it holds for k-1 too
olive crescent
prove the base case: n=1
assume the inductive case: n=k
prove it holds for n=k+1 (reduce it to the n=k case)
then it must hold for all n >= 1
however if we instead
prove the base caseS: n=1, n=2
assume the inductive caseS: n=k, n=k-1
prove it holds for n=k+1 (reduce it to the n=k and n=k-1 cases)
then it must hold for all n >= 1
if you can prove n=k+1 holds assuming n=k, then you can say okay k=1, so it must hold for n=1+1=2. now we can say well k=2 works, so n=2+1=3 works too. and so on
ebon tangle
ohh okay
olive crescent
the second one is a slightly weaker form of strong induction, where you can use all the n=k-1, n=k-2, n=k-3...etc as part of the proof
ebon tangle
Im still slightly confused on how id have to know to use both n=k and n=k-1
olive crescent
well let's try it with just n=k
assume
f_k + f_k+2 = l_k+1
then we need to prove f_k+1 + f_k+3 = l_k+2
we can write l_k+2 in terms of k and k+1
similarly we can rewrite f_k+3 in terms of k+2 and k+1
so now we have terms of l_k, l_k+1 and f_k+2 and f _k+1
but we don't have any way to do things with f_k+1 or with l_k
ebon tangle
oh okay yeah i understand that
olive crescent
so it's sort of...okay well clearly I don't have enough info to prove just with these terms, but I should know things about those smaller terms
olive crescent
induction problems are almost all practice and then you get the hang of how to approach them
cedar kilnBOT
@ebon tangle Has your question been resolved?
plush wharf
cedar kilnBOT
hollow minnow
- thats not a graph of sqrt(x)
tepid sail
you were unable to read the question
and made a critical mistake
explain how g(x) is obtained from f(x)
hollow minnow
?
rare vault
okay like the answer is clearly wrong because they dont know what sqrt(x) looks like but i feel like they still answered the spirit of the question
id surely give partial pts if i was the teacher
plush wharf
okay like the answer is clearly wrong because they dont know what sqrt(x) looks ...
Oh damn I was thinking of |x| for the graph I just realized
tepid sail
okay like the answer is clearly wrong because they dont know what sqrt(x) looks ...
I think like where they made the biggest mistake imo is not reading the question
it's like how do you get from g(x) from f(x)
not how are they similiar
plush wharf
What about 10
rare vault
i mean "flip and raise 3" is pretty much what the answer is saying
hollow minnow
okay @plush wharf you have the right idea you just need to use precise language here. -sqrt(x) means f(x) is reflected in the x-axis (what you said goes downwards), and +3 translates it by 3 units.
cedar kilnBOT
@plush wharf Has your question been resolved?
hearty fjord
Hi there I'm studying axiomatic properties of probability functions
hearty fjord
I came across this and was confused
So we have our set S with subsets s_i and B is our sigma algebra and is subsets of S. I'm having trouble discerning p_i
I get that they are non-negative values and their sum is 1 (telling me these are probability values), but I don't get how they're coupled with the s_i in teh summation
is it that s_i has probability of p_i?
dawn junco
is it that s_i has probability of p_i?
yes
hearty fjord
oh ok. I feel like they could've made that more clear lol
Ok so basically this is all elements of our sigma algebra added up equal 1 which satisfies the axiom.
I think I get confused with the sigma algebra. So the sigma algebra is defined to basically be the powerset of sample space S as well as a subset of S
wait...
no that doesn't make sense
dawn junco
that's a sigma algebra
dawn junco
no
hearty fjord
(sorry this is hard for me to visualize)
dawn junco
what do you think P(S) is ?
hearty fjord
oh right
P(S) = 1
sorry one moment I'm thinking through something
Ok so we have our definition of a sigma-algebra here:
and our definition of a probability function here
So B is a set of subsets of S, in which all elements of B summed up must equal 1 and the whole sample space = 1.
I guess where I'm confused is that you could have overlapping subsets, right? It doesn't say anything about them being disjoint in the defintion (other than part 3 of 1.2.4, but I'm assuming that's a special case of mutually exclusive sets)
Like if S = {1, 2, 3} as an example, then B = {empty set, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
so like what if you were looking for {1, 2} + {2, 3}?
(if that notation makes sense)
dawn junco
P({1, 2} U {2, 3}) you mean
hearty fjord
yeah sorry
dawn junco
I mean this is just some basic conditions given for the proba function
it's not exhaustive at all
hearty fjord
it's exhausting if anything lmao
dawn junco
it's the minimum set of things from which you derive everything else
dawn junco
it's exhausting if anything lmao
nice
so then you use better formulas
like inclusion-exclusion
or the famous P(A U B) + P(A n B) = P(A) + P(B)
hearty fjord
So then for example, by 1.2.4's 1st property: P(emptyset) + P({1}) + P({2}) + P({3}) + P({1} U {2}) + P({1} U {3}) + P({2} U {3}) + P({1, 2, 3}) = 1?
hearty fjord
or the famous P(A U B) + P(A n B) = P(A) + P(B)
oh. OH
OOOOH
oh duh I forgot about that, lol
hearty fjord
So then for example, by 1.2.4's 1st property: P(emptyset) + P({1}) + P({2}) + P(...
But to this question, P({1, 2, 3}) = 1 by definition since S = {1, 2, 3}. But S is also an element of B.
if the above statement is true, that is
dawn junco
So then for example, by 1.2.4's 1st property: P(emptyset) + P({1}) + P({2}) + P(...
the first property is just P(A) >= 0 for any A, did you typo ?
dawn junco
yeah but how do you get that they sum to 1 from that ?
if anything you can just say P(emptyset) + P({1}) + P({2}) + P({3}) + P({1} U {2}) + P({1} U {3}) + P({2} U {3}) + P({1, 2, 3}) >= 0 using the first property of 1.2.4
I really think you typo'd your explanation
and you weren't talking about the first property
hearty fjord
oh I guess I confused them.
from prob class I remember that all of your probabilities need to sum to 1
so I assume that all of B would have to sum up to 1 too
dawn junco
well the probabilities of your "elementary events" (i.e. the events which only have one element in it) have to sum to 1
it's the same thing as saying P(S) = 1
hearty fjord
oh they didn't mention that in the book I'm reading yet (I don't think...)
dawn junco
let's say we were flipping a coin
you wouldnt say that P(heads) + P(tails) + P(heads or tails) = 1 right
dawn junco
So then for example, by 1.2.4's 1st property: P(emptyset) + P({1}) + P({2}) + P(...
that's what you're doing here essentially
hearty fjord
oh yeah you wouldn't, would you
so elementary probabilities must sum up to 1, but any intersections or unions don't matter. They do have a value greater or equal to 0 and less than 1, but you don't count those towards the summation of 1 for the axiom
...hopefully that made sense my brain is giving out a little bit haha
hearty fjord
so {1} U {2} U {3} = {1, 2, 3} and thus P({1} U {2} U {3}) = P({1, 2, 3}) = 1?
hearty fjord
and if they're mutually exclusive then that works out of the box but if there is any overlap (aka intersections) and they're not disjoint then you would use the inclusion-exclusion principal?
dawn junco
yeah
hearty fjord
oooooook
I think where I was confused is the 1st statement I was assuming that all elements of the sigma alpha must equal up to 1
the book didn't explain that part (mabye it assumed it was common knowledge)
thank you for your help!
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
finite cape
cedar kilnBOT
plucky owl
You can apply this to $\int \left(4 - \frac{e^u}{-3}\right) du$ and integrate each term
wraith daggerBOT
CaptainNova22
wraith garnet
worthy swallow
cedar kilnBOT
cedar kilnBOT
@worthy swallow Has your question been resolved?
worthy swallow
<@&286206848099549185>
worthy swallow
.close
boreal canopy
If I post here, it opens a channel?
cedar kilnBOT
If I post here, it opens a channel?
cerulean sail
All yours 
boreal canopy
Sweet ^_^, I'll post my issue here. One moment
The lower the Y coordinate, the further to the north the point is
The higher the X coordinate, the further to the east the point is.
Here is the first main coordinate, 493.1, 366.9
Here is the second coordinate, 497.7, 410.6
Assuming that the first main coordinate is facing true north, and that in order for us to do a full 360 rotation on the X axis and face true north again it takes 3840ms, 960ms to do a 90 degree turn to face true east or true west, and 1920ms to face true south, how can we find the time in ms that it will take for us to face the second coordinate?
cedar kilnBOT
@boreal canopy Has your question been resolved?
cedar kilnBOT
@boreal canopy Has your question been resolved?
boreal canopy
@opaque goblet
boreal canopy
indeed, i have been stumped on this for hours
tried chatgpt, chatgpt couldn't give me a correct answer
opaque goblet
lol
boreal canopy
opaque goblet
okay so I think the question's wording is a little confusing
how can we find the time in ms that it will take for us to face the second coordinate?
boreal canopy
yes so like, how many milliseconds would it take for main point to face the second point I mean
opaque goblet
Assuming we take 960ms on X coordinate and 1920ms on Y coordinate to face the true directions
boreal canopy
based off how many milliseconds it takes for us to face 180 degrees
or 360
you get what i mean? reading it now, It does come off a little confusing lol
opaque goblet
yeah also the terminology of facing the second coordinate
id assume it means time to reach second coordinate
I might need more context
but can we go east and south at the same time?
or do we need to do one and then the other?
I guess the facing terminology would need work for me
but its saying that to make a 90 degree transistion in any cardinal direction takes 1920ms
boreal canopy
no so like, imagine we got a person standing in one fixed spot, that is the main point right? and it takes 3840ms for that person to fully rotate around and face north again. how would we figure out how long it would take, based on the speed of the persons set rotation, to face point 2
the person always rotates at the same speed
opaque goblet
oh ok
boreal canopy
let's say they rotate going left all the time for this
If a person standing at a fixed point takes 3840ms to complete a full 360-degree rotation, with 960ms for a 90-degree turn to face east or west, and 1920ms to face south, how can we calculate the time in milliseconds for that person to face a second coordinate located at (497.7, 410.6) when initially facing true north?
opaque goblet
Is there a way we can convert the two coordinates into one?
hmm
nah
ig this is easiest way id approach problem
@boreal canopy what class are you in before I explain?
linear algebra?
opaque goblet
okay cool then
what is context you saw this problem if I can ask?
Because my solution would be to normalize both first point and second point
which means rewrite the vector as a distance 1 vector
to do that we take distance formula so as an example
$(493.1, 366.9) \cdot \frac{1}{(\sqrt{493.1^2 + 3.66.9^2})}$
wraith daggerBOT
cofe prpl
opaque goblet
do the same with the second coordinate also
then I would rewrite in polar form e^i\theta
and we know that 3840ms to rotate 360 degrees, so it takes 3840/360 per degree
i would divide that value by the difference of the modulous in polar form
boreal canopy
i've been playing around with an old 3D game for fun, and I've managed to run multiple instances of it so my characters can play with each other. I have discovered the X and Y coordinates for both characters in each instance, however, I don't have the direction the secondary client's character is facing. My goal is to make the secondary client's character look at the main game client character. Unfortunately, I only have access to the X and Y coordinates of each character and the time it takes for a full rotation
opaque goblet
I can write the whole thing out if u want
opaque goblet
i've been playing around with an old 3D game for fun, and I've managed to run mu...
toontown lol?
opaque goblet
I used to love that game as a kid
boreal canopy
same 
opaque goblet
i would get back into it if it wasn't slow paced
boreal canopy
been tinkering with it for fun
boreal canopy
I can write the whole thing out if u want
sure i would appreciate that a lot ^_^
boreal canopy
sure
cedar kilnBOT
@boreal canopy Has your question been resolved?
wary nebula
how to construct a sqrt21 segment
cedar kilnBOT
how to construct a sqrt21 segment
wary nebula
I'm having a headache
runic garnet
Find 2 numbers a and b such that when u take the sum of their squares you get 21
wary nebula
._.
runic garnet
If there aren’t exactly 2 integer values for a and b
Then break it apart even further
runic garnet
Alr, so that may potentially work
wary nebula
I think it does
wary nebula
1 and 2
wary nebula
then the hypotenuse as a leg with another leg length 4
runic garnet
Yep
cedar kilnBOT
cedar kilnBOT
Available help channel!
simple totem
confused
glacial heron
do you know the pythagorean identities?
simple totem
do you know the pythagorean identities?
the one that goes
x squared + y squared = r squared
?
wraith daggerBOT
mud ツ
wraith daggerBOT
mud ツ
simple totem
hm
glacial heron
yes
glacial heron
both sides
glacial heron
you can write $cos^2(\alpha)$ for that part
wraith daggerBOT
mud ツ
glacial heron
yup
simple totem
you can write $cos^2(\alpha)$ for that part
oh why cos squared
wouldnt that still be cos
but the left side simplifies to 1
cos/cos = 1
wraith daggerBOT
mud ツ
glacial heron
for the first step
wraith daggerBOT
Zodd
wraith daggerBOT
mud ツ
simple totem
$cos(alpha)$
wraith daggerBOT
Zodd
glacial heron
yes
glacial heron
which side do you want to work on?
simple totem
which side do you want to work on?
im thinking left
glacial heron
alright
wraith daggerBOT
Zodd
simple totem
if im not mistaken?
glacial heron
that's correct
simple totem
that's correct
hm so its 1 then
glacial heron
that's interesting...
glacial heron
so it doesn't let you skip steps...
simple totem
lmao yeah i got it now in the next step it was the pythagorean identities
this software is so weird, it defines rules per question
glacial heron
that's hilarious
simple totem
sometimes itll encourage you to skip steps and round values
then other times itll ask for every lil detail and make sure u give exact value to a billion decimal places
glacial heron
that sucks
glacial heron
nice
glacial heron
$(\frac{cos{x}-1}{sinx})^2?$
wraith daggerBOT
mud ツ
glacial heron
lmao
simple totem
trying this one now
glacial heron
what software is this?
glacial heron
same question
simple totem
it never does that
glacial heron
yeah
simple totem
this is the first time
it ever did that
also it literally wants me to go STEP BY STEP
glacial heron
yeah...
glacial heron
wow
whatever you're using kinda sucks
it probably wants you to write down the squared answer
glacial heron
$cot^2(x) + 1 = csc^2(x)$
wraith daggerBOT
mud ツ
simple totem
hm
glacial heron
$tan^2(x) + 1 = sec^2(x)$ things going pretty well?
wraith daggerBOT
mud ツ
simple totem
$tan^2(x) + 1 = sec^2(x)$ things going pretty well?
im on this q fr
i finished that one w ur help
dk what they're asking for here
glacial heron
i see
simple totem
yas
simple totem
okie
glacial heron
that's a weird one
simple totem
that's a weird one
ikr
glacial heron
i think i got it?
glacial heron
$\frac{cos(\theta)+1}{sec^2(\theta)-1}=\frac{\frac{(cos(\theta) + 1) cos(\theta)}{cos(\theta)}}{(sec(\theta)-1)(sec(\theta)+1)}$
glacial heron
ahh
simple totem
glacial heron
$tan^2(\theta)=sec^2(\theta)-1$
wraith daggerBOT
mud ツ
simple totem
**mud ツ**
oh yeah no this is the next step
i already wrote that part and it was right
wraith daggerBOT
mud ツ
glacial heron
i see
glacial heron
$\frac{1}{cos^2(\theta)}-1$
wraith daggerBOT
mud ツ
glacial heron
did you forget to square?
simple totem
did you forget to square?
I did
God, I always do that shit smh
hmm
what abotu here i tried a couple idaes but ditn work
didnt*
glacial heron
what's the complex fraction?
glacial heron
$sec^2(\theta)-1$ right?
wraith daggerBOT
mud ツ
simple totem
yeps
glacial heron
since $\frac{1-cos^2(\theta)}{cos^2(\theta)}=\frac{1}{cos^2(\theta)}-\frac{cos^2(\theta)}{cos^2(\theta)}$
wraith daggerBOT
mud ツ
glacial heron
i'm getting confused by this
simple totem
us
glacial heron
can it be just $\frac{cos(\theta) + 1}{(cos(\theta) + 1)(cos(\theta)-1)(sec^2(\theta))}$
wraith daggerBOT
mud ツ
simple totem
can it be just $\frac{cos(\theta) + 1}{(cos(\theta) + 1)(cos(\theta)-1)(sec^2(\t...
thats not quite simplified tho
u gotta cancel out the costheta + 1 's
glacial heron
yes
simple totem
so it'd just be cos theta - 1 (sec^2 theta)
@glacial heron this is still somehow fcking wrong 😭 whattttttttttttttt
glacial heron
...
wraith daggerBOT
mud ツ
simple totem
does writing $(1-cos^2(\theta))(sec^2(\theta))$ not work?
what the fuck
crimson sedge
I hate trig
simple totem
😭
simple totem
I hate trig
us
simple totem
i learned that doing too much trig in one day is bad
fuck trig
uneven kelp
hello
exotic furnace
Have you heard of implicit differentiation?
uneven kelp
Have you heard of implicit differentiation?
i think so yeah
exotic furnace
You know the derivative of sec(x)?
If so, with chain, power, and product rule, you have all you need really to imp diff
uneven kelp
If so, with chain, power, and product rule, you have all you need really to imp ...
im an idiot i didnt read ur name LOL
cedar kilnBOT
@uneven kelp Has your question been resolved?
cedar kilnBOT
@uneven kelp Has your question been resolved?
small sonnet
Need help with 1.2 and 1.3
cedar kilnBOT
Need help with 1.2 and 1.3
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
silver oxide
aight so with 1.2
we see a sqaure root
so we want to try and square both sides to cancel it out
but first i'd recommend just having the square root on the left hand side as it makes it easier
small sonnet
but first i'd recommend just having the square root on the left hand side as it ...
Sqrt5-x = 1+x?
silver oxide
yes
silver oxide
ur right hand side is correct
small sonnet
ur right hand side is correct
Lhs stays as 5-x?
silver oxide
correct
silver oxide
not yet, u want the lhs to = 0
small sonnet
not yet, u want the lhs to = 0
For that to happen u take it to the rhs?
silver oxide
correct
silver oxide
yeah
small sonnet
yeah
so i plugged it into the calculator and got a math error
for the quadratic formula
silver oxide
yeah i would avoid the quadratic formula for this one
small sonnet
yeah i would avoid the quadratic formula for this one
howcome? and should we just leave it at x=-1 or x=4?
silver oxide
where'd u get -1 and 4?
silver oxide
(x-1)(x+4)=0?
small sonnet
im doing this whilst also refering to an example i did earlier in the year
small sonnet
(x-1)(x+4)=0?
hyep
silver oxide
(x-1)(x+4)=0?
x=1, x=-4
small sonnet
aight
small sonnet
not final answer though
x=1 ?
silver oxide
correct
small sonnet
thanks so onto 1.3
silver oxide
its pretty hard to see
silver oxide
thanks so onto 1.3
.
small sonnet
its pretty hard to see
silver oxide
ah ok thats much easier to see
so first looking that we want bases that are the same.
oh well im getting off, get the bases the same and try to cancel them, also figure out how to express 15 as 2 factors
cedar kilnBOT
@small sonnet Has your question been resolved?
midnight island
cedar kilnBOT
midnight island
<@&286206848099549185>
cedar kilnBOT
@midnight island Has your question been resolved?
crimson sedge
@cedar kiln
cerulean sail
which part do you want help with? Assumedly the first part?
(If so, note that if a sequence converges to a limit l, then all subsequences also converge to l as well)
cedar kilnBOT
@midnight island Has your question been resolved?
sudden heart
cedar kilnBOT
sudden heart
I'm stuck on the actual integration part
only thing that I've done so far was make the denominator x^(1/2)
would it just be a reverse of the quotient rule of differentation
smoky idol
Splitting the fraction into 2 pieces would help you see it I think
sudden heart
ok lemme write it out on paper
smoky idol
(Also, having the square root as an exponent is a good thing :) )
smoky idol
Yup
sudden heart
or what if the first fraction becomes 2x^(-1/2)
and the second becomes x^2 * x^(-1/2)
you could take the two out of the integral in the first one to make it easier
so the first would be
4x^(1/2) right
smoky idol
Yeah
sudden heart
is there another way
wraith daggerBOT
τγρθ
smoky idol
When multiplying the same base you can add the exponents
We‘re getting the same result inthe end if you simplify your answer but still, these laws are a good thing to remember
smoky idol
I mean hey, as long as you get the answer 🤷
sudden heart
alr so the integral would then be 4sqrtx + xsqrtx^3 from 1 to 4
lemme plug this in quickly
smoky idol
I‘m on the bus so I don‘t have paper to verify, but we can use the bot here when you‘re done to check your answer
smoky idol
,w integral (2+x^2)/sqrt(x) from 1 to 4
wraith daggerBOT
sudden heart
lemme see my mistake
smoky idol
Oh you didn‘t integrate x^(3/2) maybe?
smoky idol
Yup
sudden heart
so the integral would actually be 4sqrtx + (2sqrtx^5)/5 right
smoky idol
Now you should get the /5 stuff qhen plugging in 1 and 4
sudden heart
ah ok
smoky idol
(x^3 / 3) * (x^(-1/2)) + (x^2) * 2x^(1/2)
Did you simplify this answer btw? Out of curiosity
sudden heart
nah too much work
wraith daggerBOT
sudden heart
i'm getting 72/5 for some reason
smoky idol
i'm getting 72/5 for some reason
Can you show me the sheet with your work please?
sudden heart
sure hold on
Nvm I got it
I canceled something that wasn’t supposed to be canceled
Ok I think that’s it thank you
smoky idol
Oh nice! Good job :)
cedar kilnBOT
@sudden heart Has your question been resolved?
marsh spindle
Do you know any other way than using lhopitals rule?
cedar kilnBOT
Do you know any other way than using lhopitals rule?
crimson delta
you can multiply by x/x then split into two limits
muted bear
Use conjugates
crimson delta
they will both be essentially derivatives tho
marsh spindle
you can multiply by x/x then split into two limits
could you write that down please?
glass sky
Do you know any other way than using lhopitals rule?
if you can open sin x series i think it should work
(after we multiply by conjugates)
glass sky
no conjugate of the numerator...
then opening sin3x series , taking x common
cancelling x
from wat i can imagine
marsh spindle
then opening sin3x series , taking x common
by that you mean sin(2x + x) and using formulas?
I'm not studying maths in english, so the terminology is not known for me
crimson delta
could you write that down please?
$\lim_{x\to 0} \frac{\sqrt{x+1}-1}{\sin 3x} = \lim_{x\to 0} \frac{\sqrt{x+1}-1}{x}\frac{x}{\sin 3x} = \lim_{x\to 0} \frac{\sqrt{x+1}-1}{x}\cdot \lim_{x\to 0} \frac{x}{\sin 3x}$
wraith daggerBOT
Denascite
crimson delta
and those two limits might be already known to you
glass sky
by that you mean sin(2x + x) and using formulas?
no?
cedar kilnBOT
glass sky
**Denascite**
wait but how did this solve the question
its still undertermined
.reopen
cedar kilnBOT
✅
glass sky
dont we have to open the sin 3x ( taylor series)
then take x common from numerator
and then just cancel x
cedar kilnBOT
@glass sky Has your question been resolved?
cedar kilnBOT
@glass sky Has your question been resolved?
glass sky
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
bright sorrel
is this valid? I just used a^3-b^3
cedar kilnBOT
is this valid? I just used a^3-b^3
bright sorrel
and got the same answer
dull oxide
Depends on how they wanted you to find the limit. Like if they wanted you to use a specific approach.
!xy
cedar kilnBOT
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.
bright sorrel
Depends on how they wanted you to find the limit. Like if they wanted you to use...
The original problem is shown in the picture
but without the equals to 0
and my lecturer hinted that I should use a^3-b^3
so I used it and got 0
just askign
dull oxide
Oh then yeah you're fine.
static loom
Hello
past wind
What have you done so far?
static loom
I have the answer but my tutor for maths is saying a different answer and a teacher at school is saying different and I don't understand
past wind
what answers are you told
static loom
If you have the answer gan you check if it's 16+3pi
past wind
that seems right
static loom
Can you work it out and confirm for me
past wind
i just did and it seems correct
static loom
No but my tutor who gets an incredible amount each lesson is dodging when I ask him about it
Like dang bro
Brb in 8 tho
past wind
gotchu
past wind
sorry was doing something
static loom
Allgood
past wind
radius is 2 as we can see
static loom
Alr because my teacher said it's not possible to get radius
But I re assured him it's 2
He said it's not
static loom
He said the curved arc is the radius
past wind
the curve is a part of the circumference
static loom
Exactly
past wind
idk what ur teacher means
past wind
that’s right
static loom
Brother said for 52 minutes that he can't find but then says you can
past wind
huh
static loom
Like for 52 minutes he's blabbing on that it's impossible.
Man this Is hurting my brain do I decline the call
past wind
idk
static loom
He's extended my class by 8mins
Dang bro
I'm tryna get on that fn
It's 8pm my time that's late for a tutor class ngl.
past wind
rip
cedar kilnBOT
@static loom Has your question been resolved?
neat gale
i need to prove that if M,N are complex nxn matrices MN-NM cant be the identity matrix
cedar kilnBOT
@neat gale Has your question been resolved?
cedar kilnBOT
@neat gale Has your question been resolved?
cedar kilnBOT
@neat gale Has your question been resolved?
gentle pecan
@neat gale I would suggest using properties of Trace to get the job done here
We know that Tr(A - B) = Tr (A) - Tr(B) and that Tr(AB) = Tr(BA)
so you should be able to show that the trace of MN-NM should always be zero
wise lily
I dont know how to work out logarithmic fractions is there a rule for this?
wise lily
digital cliff
if $log_{a}(b)=c$ then $a^c=b$
wraith daggerBOT
AℤØ
digital cliff
youre finding c such that 2^c=1/8
wise lily
so 2 would be the base and 1/8 is the answer so the index would be like what.
Something that would multiply to that
digital cliff
write 1/8 as an exponent of 2
wise lily
wdym
digital cliff
write 1/8 as 2^x
wise lily
but a fraction would be a fraction of a number
digital cliff
a^(-1)=1/a
digital cliff
reciprocal*
wise lily
yeah that thingy
So then if log2 1/8 = X
then you use that formula.
but would you make the 1 -1
sorry i struggle a little with logarithms because of where you substitute everything
digital cliff
you arent subbing anything