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#help-13
fair fox
Idk if i can ask here but "I usually dont study so idk how to focus and that stuff , but now i really need a good grade so, can anyone explain me combinatorics pls"
fair fox
Idk if that helps but i am in 12 grade
dire geode
green coral
as riemann said
if you need help with the task of studying #study-discussion
if you need help with combinatorics as a topic #study-discussion
if you need help with specific problems of combinatorics, you are in the right place, ask a few problems, helpers will try to help you understand them
cedar kilnBOT
@fair fox Has your question been resolved?
austere hull
hi
austere hull
there was a question said, solve for $8\mu\text{A} +5\text{mA}+ 24\text{mV}=0$
wraith daggerBOT
Aκιρɑ
hollow trail
can you show the full context here?
austere hull
that was the full question
hollow trail
do you have a picture of it?
austere hull
i dont unfortunately since it was a question from midterm i have done this morning
it said like this
hollow trail
what are μ, A, m and V?
austere hull
mirco, amps and voltage
sonic thistle
you mean microampers and microvolts?
wait no
microampers, miliampers and milivolts
austere hull
yep
sonic thistle
and what am i supposed to find
austere hull
i was supposed to calculate the whole thing
hollow trail
so you aren't setting it equal to 0, you are trying to add them up?
austere hull
yea
hollow trail
you can't add voltages and currents, they're not compatible units
austere hull
thats what i thought too
hollow trail
there needs to be some conversion factor (probably a resistance)
sonic thistle
the question is like asking:
8 bananas + 5 banana trees + 25 lemon trees = 0
are you sure that it's the full question?
austere hull
yea it was a question i had in midterm
ill close this bc it literally didn't makes sense
.close
cedar kilnBOT
hollow trail
there may be some context you are forgetting to include. but we can't really know without a picture of the midterm
austere hull
im 100% it was like this
but ill wait until results come out to see if i missed something
cedar kilnBOT
Available help channel!
thorny frigate
In axler linear algebra he said a polynomial function p \in P(F) and he defined earlier P(F) to be set of all polynomial functions from F to F .. now later he took a polynomial function and he put T ... An operator as an input.. how can he do that!!! Input has to come from a field
split ice
do you have a screenshot/picture of the relevant page?
thorny frigate
abstract breach
he defines it like this
dawn junco
axler does say it is somewhat of a notation abuse just after the definition of P(T)
thorny frigate
I think there is a connection or more formally some isomorphism between algebra of polynomial and polynomial functions set ig
For infinite fields
abstract breach
yes
thorny frigate
But I don't get my own sentence very clearly 🙂 what does it actually mean
abstract breach
think about F_p (also known as Z/pZ or Z_p)
the function that maps x to x^p is equal to the identity at all points of Fp
but the polynomials X^p and X are not the same
however in an infinite field, you will always be able to map the polynomial to its corresponding function (it's an isomorphism)
hollow trail
since in LADR you pretty much exclusively work with R and C you don't really have to worry about cases where the isomorphism fails
thorny frigate
Like if a polynomial function p : F \to F is defined as p(z) = a + bz so it's isom to polynomial expression a+bz?
For infinite field
Basically it determines the ordered coefficients? Uniquely
Right?
abstract breach
yes
thorny frigate
And can we prove a+bz won't ever be equal to some z³ or something any other .. for infinite fields
Isomorphic*
abstract breach
I would say equal rather than isomorphic
thorny frigate
Oh yes it has exactly 1 roots
It can't have more something like that we will use
And it can't hage infinite roots
abstract breach
basically yes
cedar kilnBOT
hollow trail
And can we prove a+bz won't ever be equal to some z³ or something any other .. f...
i think that axler proves this somewhere
cedar kilnBOT
Available help channel!
ivory cedar
if asked to find/sketch traces, how do I determine whether to set the variable to be 0 or k? Or is that arbitrary?
Also, when sketching traces in 3D plane individually, how do I determine orientation? I’m having some trouble with the hyperbolas
cedar kilnBOT
if asked to find/sketch traces, how do I determine whether to set the variable t...
@ivory cedar Has your question been resolved?
split ice
the equation of an arbitrary trace is always z=k, x=k, or y=k, because 0 gives you one specific trace
when you're actually sketching the traces, though, you pick a few specific ones to give you the idea of the shape. usually, you want to pick 0 as one of these "specific ones," so you can start near the axis
i like to do 1, 0, -1 to start, then 2 and -2 if needed
so 3-5 traces per direction
sly schooner
idk if im being stupid but idk how to do this
cedar kilnBOT
idk if im being stupid but idk how to do this
mental trail
idk if im being stupid but idk how to do this
Can you do the forward implication?
sly schooner
i can only prove the only if part
mental trail
Really? How did you do it
sly schooner
I mean idk if it’s valid but
Ignore the bottom part
i think i mightve assumed that the range of h is the domain of X
mental trail
I mean idk if it’s valid but
First of all "forall x in X there is a unique y such that h(x) = y" is the definition of a function... not bijectiveness
The statement after that is all you need
mental trail
i think i mightve assumed that the range of h is the domain of X
And what you wrote here is weird. the range of h is subsey of its codomain, not its domain
mental trail
I mean idk if it’s valid but
Also this isn't the only if part, it's the if part
And you haven't really proven the assertion with the "proof" you wrote
to prove "g ○ h ≠ f", you have to show that there is some x such that g(h(x)) ≠ f(x)
sly schooner
Also this isn't the only if part, it's the if part
Ik the proof is wrong but surely since I’m saying that if the range of f and g r different then goh isn’t f, contradicting the friends definition, then im saying the range must be the same for g and f to be friends but not necessarily that the range being the same means they are friends
mental trail
Ik the proof is wrong but surely since I’m saying that if the range of f and g r...
I hope I'm recapping what you're trying to prove correctly
Say A is the proposition "f and g are friends"
And B is "f and g have the same range"
You've tried to prove that not(B) implies not(A)
And so that implies [A implies B]
This is normal, it's the contrapositive
I have no problem with this line of reasoning
mental trail
You've tried to prove that not(B) implies not(A)
I have a problem with the proof you gave for this statement
sly schooner
Yeah ngl I was just tired during the session and wrote smth wrong down sry abt that lol
Do u mind telling me how I’m supposed to prove the question?
mental trail
Well I would've just gone for a direct proof of "A implies B"
Suppose f and g are friends, which tells us f = g○h for some bijective h
To show the ranges of f and g are equal, just do double inclusion
Take z = f(x) for some x in X
Then z = g[h(x)], so z is also in the range of g
Vice versa, it's easy with the property that h is bijective
First try to write that down properly
And then we'll talk about "B implies A"
sly schooner
Would this do?
ok i kinda rushed the explanation where if z is in the range of f its also in the range of g
but i do need to sleep soon
mental trail
ok i kinda rushed the explanation where if z is in the range of f its also in th...
And you haven't proved "if z is in the range of g then it is also in the range of f"
So you only have proved $range(f) \subseteq range(g)$ for now
wraith daggerBOT
Raphaelisius Maximus MMIII
sly schooner
Consider z=g(h(x))
Since gOh=f,
z=f(x)
thus if z is in the range of gOh, it is in the range of f
is that correct?
mental trail
If z is in the range of g, what gives you the right to say "z = g(h(x))"?
sly schooner
oh yeah
mental trail
You only know z = g(y) for some y in Y
But you don't know if y = h(x)... or do you?
mental trail
so it outputs all values in Y?
Look once more as the definition of bijectivity of h (surjectivity could have been enough but whatever)
For every y in Y, there is a unique x in X
sly schooner
it also takes all inputs of x
mental trail
Such that h(x) = y
cedar kilnBOT
@sly schooner Has your question been resolved?
hidden prawn
Yo can someone please help me with this inequality question I was thinking to expand the stuff in the brackets so I end up with a quadratic or some but like there’s a lot of roots and stuff and I don’t think it’s finna work out
cedar kilnBOT
Yo can someone please help me with this inequality question I was thinking to ex...
@hidden prawn Has your question been resolved?
ancient nova
Yo can someone please help me with this inequality question I was thinking to ex...
Go another way and conjugate the lhs
Also don't forget about the bound,x has to be more than or equal 1
hidden prawn
Also don't forget about the bound,x has to be more than or equal 1
oh ok ty i got it
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
delicate palm
i found this image online, and i’m wondering what are the angles of triangle b.
i’ve found
\begin{align*}
\angle 1 &= 240^\circ \
\angle 2 &= 60^\circ \
\angle 3 &= 240^\circ
\end{align*}
i wonder whether that’s right.
wraith daggerBOT
@delicate palm
cedar kilnBOT
@delicate palm Has your question been resolved?
cedar kilnBOT
@delicate palm Has your question been resolved?
cedar kilnBOT
@delicate palm Has your question been resolved?
floral arrow
Are these all semicircles? If so they just add or subtract 90º on each side, so you are correct. Calling b an equilateral triangle is an enormous stretch though.
cedar kilnBOT
@delicate palm Has your question been resolved?
delicate palm
Are these all semicircles? If so they just add or subtract 90º on each side, so ...
equilateral, not equiangular =)
floral arrow
equilateral, not equiangular =)
. Calling b a triangle is an enormous stretch. You can argue all you want about the "sides" being of equal length, you may even argue about the underlying space being non-Euclidean so that these "sides" would in fact be straight lines, but nothing like that is mentioned so this cannot be seen as a triangle. An equilateral triangle is a polygon (planar geometric figure made up of straight line segments) with three sides of equal length, which inevitably leads to its angles being equal as well.
surreal snow
I'm working on 5 d) now, I know that we can write the directional derivative of F at a point q in direction v as $v^i\frac{\partial f}{\partial q^i}$.
(as it's for an assignment i don't want to be given the exact answer, just guidance on if i'm on the right track)
surreal snow
I've already gotten that $\overline F$ is $(x^2+y^2)(x^2+y^2+1)$, and q is $(x,y,x^2+y^2)$ as an element of X. I don't think i can derivate wrt $q^3$, but i might be able to do it with leaving q3 as z and then adding in the restraint that $z - x^2 -y^2 = 0$
wraith daggerBOT
Frank's Sriracha
surreal snow
I'm just not sure how to go about it properly
hidden mural
@surreal snow do u see that X is diffeomorphic to R^2
surreal snow
👍
hidden mural
how did you get overline{F} btw
i'm think about approaching this slightly differently
surreal snow
i got it as restricting F to X by setting z = x^2+y^2
hidden mural
i got it as restricting F to X by setting z = x^2+y^2
oh i see
you can also replace x^2+y^2 with z to get z + z^2
so pi: X --> R^2 given by pi(x,y,z) = (x,y) is a diffeo and gives u a global chart
surreal snow
I've done that in the working out, i left it as x and y to make the partial derivatives easier
hidden mural
i think of tangent vectors as diff ops that u get from curves
so i would consider an arbitrary curve gamma on X
in global coords u can write it as t |--> (x(t), y(t))
then find \overline{F} (gamma(t))
surreal snow
atleast to me that seems like extra steps that would need more proofs
I get how that comes up and works, though
I've ended up with $v^1(2x+x^3+4xy^2)+v^2(2y+4x^2y+4y^3)+v^3(2(x^2+y^2)+1)$ using z substitution
wraith daggerBOT
Frank's Sriracha
surreal snow
Does that make any sense to work?
hidden mural
ru thinking of v as a vector in R^3
surreal snow
👍
i did define the tangent space before, so that might be wrong
I got it as span{(1,0,2x),(0,1,2y)}
would i have to write v as (a,b,2ax+2by)?
i would have to do that at the end though
To sum up my process through the whole question, i set psi (localisation) as (x,y,x^2+y^2), then found the rank of Dpsiv, that left me with a matrix {{1,0},{0,1},{2x,2y}} which i used the span of the column space for to find the the tangent space at q, then the directional derivative operator to get to where i'm at now
We haven't really done anything like it before so i'm just stuck on if my process is actually right
cedar kilnBOT
@surreal snow Has your question been resolved?
strong stirrup
How does multiplying by the conjugate cancel out and get same denominator when you have to use it in f(x+h) -f(x) /h
strong stirrup
Alg 2 last year was in one ear out the other and i have first test over derivatives in but
fossil dawn
!original, please
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.
stiff brook
How does multiplying by the conjugate cancel out and get same denominator when y...
this doesnt always work. we use it with radicals. the reasoning is the difference of squares
(a-b)*(a+b) = a^2 - b^2
so it simplifies nicely, for example, when you have square roots in the form of sqrt(x) ± b
maiden rover
Hi guys
stiff brook
hello
cedar kilnBOT
@strong stirrup Has your question been resolved?
naive bough
time to get better at math
clever frigate
I have doubt in logarithm questions
cedar kilnBOT
I have doubt in logarithm questions
frosty creek
I have doubt in logarithm questions
Yeah whats the question?
clever frigate
When I get lnx while solving integration questions , idk what to do next
fossil dawn
!original, please.
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.
bleak orbit
ok so what have you done so far
bleak orbit
ok do you know what is work formula
@clever frigate ?
Basically the formula is dW=Fdx
Where W is work, F is force and x is displacement
To find total work, you can just integrate this over the limits given, x=1 and x=e
cedar kilnBOT
@clever frigate Has your question been resolved?
clever frigate
To find total work, you can just integrate this over the limits given, x=1 and x...
Okay , I can integrate it but what does lnx translate to ?
cedar kilnBOT
Okay , I can integrate it but what does lnx translate to ?
clever frigate
If I put in in definite integration what’s the next step , like if it was 1/x I would have converted it into lnx but what happens to lnx
<@&286206848099549185>
scenic narwhal
!15min
cedar kilnBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
bleak orbit
If I put in in definite integration what’s the next step , like if it was 1/x I ...
Are you asking what the integration of lnx is?
You can use integration by parts if so
fallen hollow
If I put in in definite integration what’s the next step , like if it was 1/x I ...
Do you know the First Fundamental Theorem Of Calculus?
cedar kilnBOT
@clever frigate Has your question been resolved?
tawdry terrace
Hi!
tawdry terrace
Prove that 101010.....01 is always composite except for 101.
wraith daggerBOT
tawdry terrace
so like 10101 is part opf this
ah yes
mighty shuttle
,w is 1010101 prime
okay is this is true, I can't help
tawdry terrace
no problem my g
sacred iron
Do you still need help with your question?
sacred iron
I see…
vivid valley
can someone explain how I get to the solution of simplification : b-1 / b+1 ?
tawdry terrace
wth
vivid valley
tawdry terrace
!help
cedar kilnBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
tawdry terrace
!occupied
cedar kilnBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
vivid valley
sorry I will open a channel!
tawdry terrace
np
The number always has an odd number of digits. Let the number of digits be 2n + 1, where n >= 2.
10101010.....01 with 2n + 1 total digits = 10^(2n) + 10^(2n-2) + 10^(2n-4) + ..... + 10^2 + 1 = 1 + 10^2 + 10^4 + ..... + 10^(2n-2) + 10^(2n) = 1 + (100)^1 + (100)^2 + ...... + 100^(n-1) + 100^n =
Now if n + 1 is composite, (n+1)/f groups of f consecutive terms can be can made and the expression can be factorized, proving that the expression is composite for n + 1 = composite. Now consider the case that n + 1 is prime and n + 1 ≠ 2
(100^(n+1) - 1)/99 = (10^(2n + 2) - 1)/99 = ((10^(n+1))^2 - 1)/99 = (10^(n+1) - 1^(n+1))/9 * (10^(n+1) + 1^(n+1))/11
The numertaor of the first factor is always divisible by 9. For n >= 2, n + 1 >= 3. We conclude that the first factor is always an integer greater than 1.
Now since n + 1 is prime, n + 1 is odd (since n + 1 ≠ 2). Since the he numerator of the second factor is divisible by 11 and n + 1 >= 3, the second factor is an integer greater than 1.
Hence our original number is a product of two beautiful numbers; it's composite.
How is my proof?
<@&286206848099549185>
cedar kilnBOT
@tawdry terrace Has your question been resolved?
tawdry terrace
<@&286206848099549185>
thick arch
What's the problem?
tawdry terrace
How is my proof?
...
whole nexus
I mean, any number after 101 would just be divisibile by 101 itself
thick arch
Yeah
tawdry terrace
,w factor 10101
wraith daggerBOT
whole nexus
Like (11, 111, 1111, 11111)*101 gives 10101, 1010101, 101010101, 10101010101
Don't know though, let me check with calculator too
neon egret
it doesnt
whole nexus
Nope, that ain't correct
neon egret
101*11 is 1111
tawdry terrace
11 * 101 is not equal to 10101
whole nexus
Alright my bad
cedar kilnBOT
@tawdry terrace Has your question been resolved?
normal hedge
hi sir
thick arch
I borrrowed this phone, answer is 5
tawdry terrace
what
cedar kilnBOT
cedar kilnBOT
Available help channel!
cerulean maple
Hello, I'm trying to program my own character rigging system like the one seen here: https://youtu.be/vTTdchYmzJM?si=WE7Frj8iWiU2bynP&t=14 but I am struggling to understand how to do the rotations.
If you visualise the skeleton as a bunch of nodes, you can see, for example, red = left shoulder, left arm, left hand, blue = right shoulder, right arm, right hand, and purple = torso. In the video, you can see that the nodes rotate 45 degrees around a horizontal axis to give it a flat rotation effect. What is the math behind this?
hot cipher
This server is probably the wrong place to ask for
For this particular case, i dont think this is result of real math about rotations, more like prefabs of different positions
cerulean maple
Just to clarify, I'm not asking for programming help... just the math behind it.
hot cipher
If you wanna do bone rigging, you can define a point at a fixed distance from another in sort of dependency manner
and associate rotation values as fixed numbers that are then applied depending on the prefab youre using
cerulean maple
You can ignore the sprites and things (I've already figured out how I'm going to do that). What I'm interested in is the position of the nodes (e.g, how do the blue nodes rotate around the horizontal axis in 45 degree increments).
cerulean maple
Hello, I'm trying to program my own character rigging system like the one seen h...
For example, if you rotate 180 degrees, the blue nodes will be where the red nodes are and vice versa.
cerulean maple
And the side would be like this.
hot cipher
All the left-rotations are just mirrored versions of the previous
If you have defined values for the bone rigging, how to aplly falls pretty easily
cerulean maple
Would I not only need 4? Couldn't the back also be a mirrored version of the front?
hot cipher
You still would have to draw the sprites for the back side of the body
with red and blue switched
cerulean maple
Ah, I see.
hot cipher
And rotations would apply backwards
imagine from the front, lets say a pi/2 angle means its moving its whole arm towards the camera
then in backside that same pi/2 means that its arm is moving against the camera
Thats what i meant with prefabs
it stands for "pre-fabricated"
Its not math on the fly, you just simply set it as a particular option in your rigging system
Mostly cause true 2d models dont go well with rotations around the xz plane
cerulean maple
So you're saying I would be better off just using a matrix of hardcoded angles [-180, -90, -45, 0, 45, 90, 180] etc. and then just move them? Sorry, my English isn't very good.
hot cipher
Imagine that your "default rotation" is front
You would have to hardcode every rotation around the horizontal and create specific sprites for each one
Then assign some value for each one, and let the user choose from it
But they wouldnt work like rotations
Just like entirely different models
One that faces front
One that faces right 45
One that faces right entirely
One that faces back 45 from right
One that faces back
And so on for the left side
cerulean maple
Then assign _some_ value for each one, and let the user choose from it
What do you mean by a value? Like an index?
hot cipher
yeah
0,1,2,3,4,5,6,7 would probably best suited
Then have a function which reads from it
and display the correct model
Thats mostly why i said this is not really suited for a math server
cerulean maple
And model is just the image of the part?
hot cipher
And model is just the image of the part?
You would probably need to re-do every meaningful sprite part for all rotations
sooo
8 torsos
8 heads
maybe you can get away by using 2 sprites for each arm
8 for each foot
cerulean maple
Oh okay, I will try this.
cerulean maple
Thats mostly why i said this is not really suited for a math server
Yes, I understand now, sorry. I thought it would be a math problem but I guess it's just a programming issue. I will play around with it and see how it goes, thank you so much for the help :)
hot cipher
np
cerulean maple
Probably unlikely but I don't suppose you would be interested in creating a prototype of this system? Would pay money, of course.
hot cipher
Probably unlikely but I don't suppose you would be interested in creating a prot...
I dont know shit for programming, lmao
cedar kilnBOT
cedar kilnBOT
Available help channel!
gleaming oar
yo
gleaming oar
is anyone expiereced with data managment
wicked mantle
What are you looking for?
sacred iron
yo
Just for future reference, do you mind posting the image/question as your first message so the bot doesn’t pin greetings or requests for help? This way, if the conversation continues for long, helpers don’t have to dig.
I’m sure many people here are experienced with data management. However, does your problem correlate to math? If so how?
gleaming oar
Just for future reference, do you mind posting the image/question as your first ...
Sorry, ill send the question now
In a tree diagram, you have 4 ways to do the first event, 3 ways to do the second event, 5 ways to do the third and 4 ways to do the fourth. For each of the following, state whether it is true or false and explain why.
You can add the numbers to get n(S). False
You can use the fundamental counting principle to get n(S). True
There are 240 different pathways through the tree. True
There are 16 total pathways for n(S). False
gleaming oar
i first want to confirm if these are correct
cedar kilnBOT
@gleaming oar Has your question been resolved?
gleaming oar
bruh
sacred iron
That's a user lmao
Made that mistake once… 
cedar kilnBOT
@gleaming oar Has your question been resolved?
sacred tusk
There are 49 marbles in a box. 6 of them are red marbles and the rest are blue marbles. You randomly pick 6 marbles from the box. What is the probability that you either pick 3 or 4 red marbles?
gleaming oar
oh i did lottery 6/49 lol
gleaming oar
There are 49 marbles in a box. 6 of them are red marbles and the rest are blue m...
this is the answer i came up with
sacred tusk
ohh
cedar kilnBOT
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small wing
does anybody know how to manipulate leslie matrixes so that the eigen value becomes 1 for example this matrix has an eigen value of 1.05306 how would i manipulate the matrix so that its 1
cedar kilnBOT
does anybody know how to manipulate leslie matrixes so that the eigen value beco...
@small wing Has your question been resolved?
cedar kilnBOT
@small wing Has your question been resolved?
lament epoch
o/
twilit escarp
Need help with maths ?
past glacier
cedar kilnBOT
@lament epoch Has your question been resolved?
charred wharf
Can anyone help me w fractional indices ion really understand it
charred wharf
Ya those are pretty basic I think it’s js that when like brackets n stuff come into play ion rlly understand
charred wharf
Ya
tropic oxide
aight, good
let's see: do you also understand index laws?
in particular $a^{m+n} = a^m \cdot a^n$ and $a^{mn} = (a^m)^n$
wraith daggerBOT
Ann
charred wharf
Yup
tropic oxide
wonderful
so the idea behind extending the defn of exponentiation to allow the index to be fractional is going to be based entirely upon the desire to keep these index laws working.
for example, whatever $x^{1/2}$ should be, we definitely want to have $$x^{1/2} \cdot x^{1/2} = x^{\frac{1}{2} + \frac{1}{2}} = x^1 = x$$
wraith daggerBOT
Ann
charred wharf
Yup
tropic oxide
the big reveal is that that's exactly what the square root of x does.
and this is why $\sqrt{x} = x^{1/2}$
wraith daggerBOT
Ann
tropic oxide
you can see similarly why $\sqrt[3]{x} = x^{1/3}$ and generally why $\sqrt[n]{x} = x^{1/n}$
wraith daggerBOT
Ann
charred wharf
Ya okay
tropic oxide
that's basically all there is to it
charred wharf
Like for example
27 over 8 powered to 2/3 how do we solve smth like this
tropic oxide
aight you're gonna need to post a picture
charred wharf
Alr one sec
tropic oxide
\verb|27 over 8 powered to 2/3| is ambiguous: $$\frac{27}{8^{2/3}} \quad\mbox{or}\quad \paren{\frac{27}{8}}^{2/3}?$$
wraith daggerBOT
Ann
charred wharf
The one on the right
tropic oxide
ok then you need brackets
(27/8)^(2/3)
would you know what to do if the 2/3 index were some integer instead
charred wharf
What is it
tropic oxide
... this isn't a clear "yes"/"no" and so doesn't answer my question
let's imagine that instead of 2/3 there is some whole number instead; would you know what to do, yes or no?
charred wharf
Oh ya ya
tropic oxide
ok, what would you do?
for example if we were looking at $\paren{\frac{27}{8}}^{4}$
wraith daggerBOT
Ann
charred wharf
U power the 27 by 4 and 8 by 4
tropic oxide
just tell me what one next step you'd take
tropic oxide
U power the 27 by 4 and 8 by 4
ok good
you distribute the index to the top and bottom
and are left with 27^4 / 8^4
wonderful
now im gonna tell you to go do the EXACT SAME THING in your question!
charred wharf
So multiply the 27 by 2over 3 n same thing for 8
wraith daggerBOT
Ann
tropic oxide
that doesn't look right to me
in fact it doesn't look right at all
it looks like you "timesed" 27 by 2/3 after me telling you that was wrong
so what's up w that?
charred wharf
How else could u solve that besides multiplying it by 2 and dividing it by 3 tbo
tropic oxide
i mean uhhhhhh
we... went over the meaning of fractional indices just now, didn't we...
raising to the power of 1/3 means the cube root...
like. mate, you kept telling me "yes" when i asked if it made sense to you
are you now telling me that the explanation you heard just now was in one ear and out the other
yknow what i think i need to go
charred wharf
.close
cedar kilnBOT
ancient nova
<@&268886789983436800>
timid basin
If:
timid basin
then whats the maximum value of this?
cedar kilnBOT
@timid basin Has your question been resolved?
jade blaze
then whats the maximum value of this?
i think u need to make it a quadratic equation and then solve for roots
cedar kilnBOT
@timid basin Has your question been resolved?
cedar kilnBOT
@timid basin Has your question been resolved?
zealous plinth
is this from a vector calc class?
have you learned lagrange multipliers
since that's what im thinking would be used for this problem
crimson sedge
is anyone here
zealous plinth
yes there's an open problem here but there's several open help channels if you need help
zealous plinth
guys please i have no idea
may I please ask which class this is from? or where it is from if not from a class?
timid basin
may I please ask which class this is from? or where it is from if not from a cla...
uhh
i know some high school calculus
im def not in a vector class
zealous plinth
this seems like a hard problem without the tools of vector calc 😭 I'll try to see if I can find a suitable way to do this like calc 2 style
i couldn't figure out a good way to write the first equation in terms of one variable which is why I'm thinking this would be like a vector calc type question
okay ngl i can't seem to find anything like that, i can only find vector calc methods
i could i guess write out an overview of how you would do the problem using vector calc, if you'd like?
timid basin
i could i guess write out an overview of how you would do the problem using vect...
go ahead
i kinda understand what the concept of that method
from what ive read, these type of problems will have a boundary (in this case its that 9x + 9y = thing)
and the actual function to calculate the min max
cedar kilnBOT
slender atlas
,rccw
safe nest
slender atlas
,rccw
wraith daggerBOT
chrome elk
,rotate
wraith daggerBOT
clever venture
4 quadrillion rotations
chrome elk
Okay so he starts at x
Then goes up to 1.05x
Then goes up to 1.07*1.05x
,calc 1.07*1.05
wraith daggerBOT
Result:
1.1235
Okay uh
Why is there a y
What is the x then
And what is x then?
...no
x and y are the same thing
sacred iron
!noans
cedar kilnBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
Available help channel!
vernal kite
how do i do this q?
cedar kilnBOT
how do i do this q?
floral arrow
This is a quadratic, it has two roots. You should know something about complex roots of polynomials
vernal kite
This is a quadratic, it has two roots. You should know something about complex r...
the two roots should be both complex?
last apex
Something a bit more specific
vernal kite
conjugate complex pairs?
last apex
Yes
vernal kite
so the roots are i and -i
crimson delta
vernal kite
oh right
vernal kite
yea thats what i thought originally
last apex
vernal kite
.close
vestal horizon
i would like some help on algebra
cedar kilnBOT
i would like some help on algebra
sacred iron
Just for future reference, do you mind posting the image/question as your first message so the bot doesn’t pin greetings or requests for help? This way, if the conversation continues for long, helpers don’t have to dig. 
Do you have a specific question?
vestal horizon
no i just need help for my finals
last apex
What about them
sacred iron
What do you need help with about your finals?
jade blaze
Just for future reference, do you mind posting the image/question as your first ...
do u have this thing copy pasted in your clipboard 😭
vestal horizon
What do you need help with about your finals?
perpandicular lines and standard form
sacred anchor
perpandicular lines and standard form
do you have a specific question that you're struggling with?
sacred iron
do u have this thing copy pasted in your clipboard 😭
I do. It’s like a factoid but kinder. It’s an autocorrect feature
vestal horizon
do you have a specific question that you're struggling with?
no i just dont understand the concept
ok
my as well close this then
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
knotty kernel
Can someone verify my work and tell me what I did wrong, my buddies are saying the integration by parts is right but I might’ve made an algebra mistake but I don’t see one
rain idol
Can someone verify my work and tell me what I did wrong, my buddies are saying t...
,rccw
wraith daggerBOT
oak anchor
Can someone verify my work and tell me what I did wrong, my buddies are saying t...
you forgot the - - on the last part
- - = +
knotty kernel
you forgot the - - on the last part
but where does that second - come from
oak anchor
$\int u'' v = u'v - ( \int u' v' ) = u'v - (u v' - \int u v'')$
wraith daggerBOT
Médicis
oak anchor
the two negative signs cancel out
oak anchor
you're welcome
knotty kernel
.close
pale lake
i need some help plz answering the first part
cedar kilnBOT
i need some help plz answering the first part
cedar kilnBOT
@pale lake Has your question been resolved?
pale lake
<@&286206848099549185>
dawn junco
well A*v(mu) is a linear map R^3 -> R
if you know what it does to some basis of R^3, you know what it does to all of R^3 (i.e. "finding" the map)
dawn junco
sure
pale lake
where did you pull that from ?
dawn junco
right ok
dawn junco
I'm looking at the second part rn
pale lake
I'm looking at the second part rn
any luck?
dawn junco
any luck?
I think your answer's good, but it's prolly better if some other eyes check your thing also
pale lake
I think your answer's good, but it's prolly better if some other eyes check your...
ok, thanks a lot for checking
appreicate it
.close
wild belfry
Can I say f(x) = x - 1?
cedar kilnBOT
Can I say f(x) = x - 1?
flint plinth
does it map every number in N to a number in N?
wild belfry
does it map every number in N to a number in N?
I think so thats what I want to know
Im not 100% familiar with this topic so I want someone to confirm haha
flint plinth
what's the smallest number in N?
flint plinth
and what is f(1)?
formal glacier
Can I say f(x) = x - 1?
ye i think so
wild belfry
0
flint plinth
is 0 in N?
wild belfry
no (in our course)
flint plinth
so f doesn't map N to N
flint plinth
wait
wild belfry
.close
cedar kilnBOT
formal glacier
lol
wild belfry
.reopen
flint plinth
why are you saying awesome
cedar kilnBOT
✅ Original question: #help-13 message
wild belfry
Oh?
flint plinth
your answer doesn't work, for that reason
wild belfry
Oh
formal glacier
your answer doesn't work, for that reason
no we need that to happen
its not surjective
flint plinth
it's not even a function from N to N, so it can't be an injective function from N to N
wild belfry
Ahhhh I see
formal glacier
it's not even a function from N to N, so it can't be an injective function from ...
hmm
flint plinth
yea see if that works
wild belfry
Well nothing maps to 1
flint plinth
right
wild belfry
So it should be good right?
flint plinth
so it's not surjective
formal glacier
wait wait
flint plinth
and it does map every element of N to an element of N
so just check whether it's injective
wild belfry
Well 1 maps to 2
And every number greater than 2 maps to itself +1
So thats all of them right?
wild belfry
Everything in the codomain maps to something in the domain
formal glacier
Everything in the codomain maps to something in the domain
yes
and we need that to not happen
cedar kilnBOT
cedar kilnBOT
Available help channel!
opaque narwhal
Im completely stuck on this real analysis question. From my understanding so far, f is discontinuous at every single point such that at least one of the digits in a square index is non zero, but it is continuous at between some points where all of those digits are zero. As im writing this, im beginning to think its just discontinuous everywhere. Anyone have any idea? Been trying to wrap my head around this for 3 hours now
cedar kilnBOT
@opaque narwhal Has your question been resolved?
opaque narwhal
<@&286206848099549185> anyone?
hot mauve
this function isn't technically well-defined: f(1.000...) = 1.000..., but f(0.999...) = 0.099099...
but I guess you're supposed to use the digit representation with trailing zeros instead of trailing 9s, then I think it's well-defined
opaque narwhal
Thats what ive been working with, and trying to extend it generally to prove that every point is discontinuous, as there will always be a jump if you go far enough right if that makes sense. I just cant seem to put it on paper
hot mauve
no no, a function being well-defined has nothing to do with it being continuous. I'm saying that since a real number doesn't necessarily have a unique digit representation, you can't just define the function based on its digit representation - some numbers can be written two different ways, so the function takes on two different values depending on which representation you choose
you're familiar with the fact that 0.999.... = 1?
opaque narwhal
No lmao
I mean ive seen it, but never fully undestood it
What im trying to show is that the limit from the right will always be f(a) but the limit from the left can never be f(a), because there will always be some sort of gap at the square index
hot mauve
it's being comfortable with the fact that 0.999 = 1, but you can do that later, just bookmark https://en.wikipedia.org/wiki/0.999 for example
anyways, I don't think the function is discontinuous everywhere - there are some points where it's continuous
which definition of continuity are you using? epsilon-delta?
opaque narwhal
yeah
hot mauve
oh wait, you might be right actually, I didn't think about the limit from the left side 🤔
opaque narwhal
Yeah what im working with is the example of the limit at x goes to 100. From the right its 100, but from the left its just 0.0990999 and so on. Then Im trying to generalize it to show that those kinds of gaps will exist at any square index, and then show that between every 2 real numbers there will always be a number with at least one of those gaps
viral sundial
There should be a definition for “decimal expansion” in the book, removing the ambiguity. Let's assume that decimal expansion does include the form ending with infinite 9's.
opaque narwhal
yeah were not using a book
viral sundial
Let's first consider irrational number x0. For any epsilon, we can find 10^{-n} < epsilon, where the digit on 10^{-(n+1)} is not 0. Then take delta to be 10^{-(n+2)}. The decimal representation for any number x in the range (x0-delta, x0+delta) should have the same decimal representation until 10^{-n}, and f(x) also have the same decimal representation. |f(x)-f(x)| should be less then 10^{-n} < epsilon.
For rational number x0, there must be a lot of 0's at the end. We can find a square numbers n^2 , the decimal representation are all 0's after n^2-1. For epsilon < 10^{-(n^2 + 1)}, for any delta for any x in the range (x0-delta,x0), f(x) - f(x0) > 8*10^{n^2} > epsilon.
hot mauve
For rational number x0, there must be a lot of 0's at the end. We can find a squ...
For rational number x0, there must be a lot of 0's at the end
Not necessarily, consider 1/3 for example
Wouldn't f be continuous at 1.111... for example? I'm starting to think it's only discontinuous at points that have 0s on square indices, because then the left side limit of f(x) wouldn't equal f(a)
viral sundial
Oh, my bad. Then it should be number with a finite represent and numbers without a finite representation.
cedar kilnBOT
@opaque narwhal Has your question been resolved?
opaque narwhal
Wouldn't f be continuous at 1.111... for example? I'm starting to think it's onl...
The limit from the left would end up being 0.0110....some pattern... eventually hitting a point where you have to get some sort of 999 to reach a 1, and the limit from the right would just be 0.011011..pattern repeats... from my understanding
I really dont understand it at all
hot mauve
The limit from the left would end up being 0.0110....some pattern... eventually ...
To determine the limit of f(x) as x -> 1.111... we look at x arbitrarily close to 1.111... So for example, we can assume without loss of generality that x is between 1.1110 and 1.1112, so lim_{x -> 1.111...} f(x) cannot be 0.0110 for one. I'm pretty sure lim_{x -> 1.111...} f(x) would just be 1.111... (from both sides)
oops, I mean lim_{x -> 1.111...} f(x) would be f(1.111...)
which is 0.0110, which is the same as the right sided limit
Sorry, I'm not quite awake enough to give a proof right now, but the idea is that you can choose a delta small enough such that all x such that |x - a| < delta have the same n first decimal digits as a, but only if a doesn't end in repeating 0s
viral sundial
for any N, we can find a neighborhood of 1.1111111....., where the first N digits for x in the neighborhood does not change, so the first N digits for f(x) does not change either. So f(x) is close to f(1.11111), and the difference would be less than around 10^N.
hot mauve
so the numbers close to 1.00 would be between 0.999 and 1.001 which don't have the first same digits, but the numbers close to 1.111 would be between 1.1110... and 1.1112, which do
yep, fefe can explain the details 💪
worldly walrus
Say you took a circle and drew a diameter and then put a point on the opposite side. Why is the measure of that angle always 90 degrees?
ancient lodge
worldly walrus
I read that and I still don’t really understand
whole nexus
Well you can prove it yourself through congruency
Draw a point opposite to the diameter
Connect centre to it
Then connect both ends of circle where the diameter touches the circumference to it
You'll have two triangles, one with vertex at centre, point and one end if diameter, the one would have at centre, point, and other end of diameter
Now prove the triangles equal by congruency
And now prove that the central angle is perpendicular
whole nexus
Ok I got it
!done?
cedar kilnBOT
Ok I got it
If you are done with this channel, please mark your problem as solved by typing .close
@worldly walrus Has your question been resolved?
weak granite
what do you MEAAAN the answer is a? (first on the right)
HOW WAS V AT P 2?!?!?!?!?!?
8V LOST IN THE 0 RESISTANCE WIRE?
hollow trail
the battery only enforces that the voltage difference between P and S is 10V
it doesn't enforce any absolute voltage value (that's dictated by the placement of the ground)
weak granite
the battery only enforces that the voltage difference between P and S is 10V
oh ig that makes sense... but what's so different about this guy then?
hollow trail
different compared to what?
weak granite
different compared to what?
to... usual circuits? we would usually say that the 4ohm will "consume" 2V , the 10ohm will consume 5V , then 6 ohm will consume 3V
(yes ik consume here is the wrong word to use but idk what's the proper word for it)
(convert energy?)
hollow trail
well yes, and that is shown in the voltage drops
the only physically meaningful measurement is a voltage difference, the actual value of voltage is just a matter of where you put your reference point
weak granite
well yes, and that is shown in the voltage drops
oooh...
so negative values
would make sense here
hollow trail
yes, there's nothing physically wrong with negative voltage
it just means it's below the reference point (ground)
weak granite
what do you MEAAAN the answer is a? (first on the right)
HOW WAS V AT P 2?!?!?!...
2--8 is indeed 10... wow.
weak granite
it just means it's below the reference point (ground)
what is a reference point
hollow trail
since only voltage drops are physically meaningful, to define a voltage you have to choose a point (a reference point) which you declare to have a specific value of voltage, usually that value is 0 (in which case we call it a ground and use the ground symbol)
weak granite
since only voltage drops are physically meaningful, to define a voltage you have...
understood!
cedar kilnBOT
Available help channel!
balmy prawn
cedar kilnBOT
tranquil oracle
!status
cedar kilnBOT
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
ik the IQR
tranquil oracle
so it's just interpreting it right
balmy prawn
yep
tranquil oracle
you know the IQR, how about try stating what it means
tranquil oracle
yeah, so interpret that with the situation
tranquil oracle
try making a statement about "the middle 50% of sale prices"
balmy prawn
but isnt that what the median do
tranquil oracle
I'm talking more of "if you sort all the sales prices, then you can use the IQR to say something about the two middle quartiles (which span 50% of all the prices)"
balmy prawn
waitt so whats the difference between median and IQR
tranquil oracle
median is Q2 right
IQR is Q3-Q1
but now you need to interpret it with words
i'm trying to motivate an answer that talks about "the sale prices that go from Q1 to Q3"
which form half of all the sale prices
cedar kilnBOT
cedar kilnBOT
Available help channel!
torn marsh
cedar kilnBOT
bold lotus
Which part dont you understand
wraith daggerBOT
(λs.ss) λx.x
torn marsh
From second line of second slide
noble granite
do you just want to understand why ln(x) d/dx = 1/x, or do you want to understand this specific proof
in other words, whats the context here, this seems like a very unnecessarily complicated proof unless its trying to do something which i think it does
torn marsh
**(λs.ss) λx.x**
Natural log of x
bold lotus
Natural log of x
okay, so we are just defining a function to assist us with finding the derivative
we dont know how to find the derivative of the natural log right
torn marsh
do you just want to understand why ln(x) d/dx = 1/x, or do you want to understan...
U are free to explain anything 🙂 I just want to deepen my understanding and be able to do calculus of logs
bold lotus
so this form is not helpful to us
but we know how to get rid of the natural log
$e^{\ln(x)} = x$
wraith daggerBOT
(λs.ss) λx.x
bold lotus
do you understand that?
torn marsh
I think we could find the derivative of a natural log
bold lotus
yes, that's what the slides are doing
torn marsh
From ln
torn marsh
**(λs.ss) λx.x**
What did u do here
bold lotus
What did u do here
nothing
that's the definition of a logarithm
do you know what logs are?
torn marsh
can you elaborate?
Well u said earlier we cannot find the derivative of a natural log in that form but I believe we can
torn marsh
do you know what logs are?
Yes
noble granite
Well u said earlier we cannot find the derivative of a natural log in that form ...
go on
torn marsh
Well the derivative of lnx is 1/x
bold lotus
Well the derivative of lnx is 1/x
how do you know that?
you cant just say this is the derivative
you need to find it
how did you go from ln(x) to 1/x
bold lotus
The slides are explaining that process right?
yes exactly
they are showing how you find that result in the first place
should we go back to explaining the slides?
torn marsh
Sure
bold lotus
**(λs.ss) λx.x**
you need me to explain this right?
torn marsh
yes
cedar kilnBOT
@torn marsh Has your question been resolved?
bold lotus
yes
okay do you know what logarithms are?
what result do you they give you?
for example what is the meaning of $\ln(2)$
wraith daggerBOT
(λs.ss) λx.x
dusk goblet
\ln
bold lotus
for example what is the meaning of $\ln(2)$
wraith daggerBOT
(λs.ss) λx.x
cedar kilnBOT
@torn marsh Has your question been resolved?
zinc quarry
Could I get some help on these? Not even sure where I’m starting
zinc quarry
I know I’m using the quantifiers but how am I supposed to express them?
drowsy rock
I know I’m using the quantifiers but how am I supposed to express them?
Wdym?
zinc quarry
Like I get the quantifiers but how do I express (for example, a) "drivers do not obey the speed limit"
as a quantifier?
drowsy rock
Like I get the quantifiers but how do I express (for example, a) "drivers do not...
So it would be like "There exists driver x, x does not obey the speed limit"
zinc quarry
How would I write the second part of that sentence?
drowsy rock
In plain english?
zinc quarry
I know the first part would be the existential quantifier (backwards E), but would I just write out in english the second part?
Oh alright
drowsy rock
I know the first part would be the existential quantifier (backwards E), but wou...
Yeah
Keep in mind though, it's asking for the negation not just the proposition itself
zinc quarry
oh true
alright ill see if i can read into the textbook for the negation part
thanks!
drowsy rock
Yw
zinc quarry
.close
cedar kilnBOT
dusk goblet
,avbob_kerman
wraith daggerBOT
cedar kilnBOT
Available help channel!
zenith sedge
cedar kilnBOT
zenith sedge
the answer key says this is true but im confused how it is
because suppose if f(0.5) = 5 then for g(f(x)) we'll have g(5) but if g(5) isn't defined then it isn't continious when x = 0.5
cedar kilnBOT
@zenith sedge Has your question been resolved?
honest knoll
I would love some help with an exercice on functions and exponentiels chapter (12th grade).
the function f is defined on R by f(x) = ln(x^2 +1) + 3 - ln (2)
show that f is an even function
determine the limits of f in - infinity and in - infinity
determine the expression of f'(x)
study its variation on R and show a variation table of f in y showing the exact minimum value and its limits of - infity and + infinity
with the variation table of f give the values of K for which f(x) = K gives 2 solutions
solve for f(x) = 3 + ln 2
mighty shuttle
Define an even function for me
honest knoll
a function is even if f(x) = f(-x)
mighty shuttle
Apply that here
mighty shuttle
yes
mighty shuttle
notice that as x-> infty, ln(x^2+1)-> infty
can you do the other limit based on this
fiery violet
You've shown that f(x) is even
fiery violet
a function is even if f(x) = f(-x)
and we know that if f(x) is even, then this is true
so if the limit approaching infinity = infinity, it follows that..?
cedar kilnBOT
@honest knoll Has your question been resolved?
honest knoll
so if the limit approaching infinity = infinity, it follows that..?
so infinity = f(x) = ln((x)^2 +1) + 3 - ln (2)
fiery violet
so $lim_{x\to\infty} f(x) = \infty$
wraith daggerBOT
Hyper
upper laurel
use \lim instead of lim to get the letters to stand up and look nicer
wraith daggerBOT
Hyper
fiery violet
was wondering how to do that xD
honest knoll
still dont get it
fiery violet
okay
so if the function f is even
then, for example
what will f(5) be the same as?
honest knoll
f(-5)
fiery violet
cool, and that should hold for every number, right?
honest knoll
yes
fiery violet
so as f approaches a really large number in the positive direction
say, f(10^4)
that'll be the same as?
honest knoll
f(-(10^4))
fiery violet
which means that as f approaches infinity, that's the same as..?
honest knoll
-infinity
honest knoll
f(x)=∞+(3−ln(2))=∞
fiery violet
Yes!
cedar kilnBOT
honest knoll
.reopen
cedar kilnBOT
✅ Original question: #help-13 message
honest knoll
f'(x) for this I have to use e ?
fiery violet
yes, but u missed a step
honest knoll
ln(2) ?
fiery violet
if i take the derivative of f(u) where u = x^2, i need to..?
honest knoll
+1
fiery violet
okay
try familiarise yourself with this rule
you were on track with 1/(x^2 +1)
u just missed a step
crimson sedge
is your has done
cedar kilnBOT
Available help channel!
hot folio
is my proof correct?
cedar kilnBOT
is my proof correct?
hot folio
P
tropic oxide
this 7D is P?
hot folio
it's (not P) sorry for the hand writing hahaha
void mortar
its just not P i guess
tropic oxide
ok right..
im not sure i follow the logic of your proof
why are you supposing two things back to back
why are you supposing $P \land Q$ and also $Q \to \neg P$
wraith daggerBOT
Ann
tropic oxide
what are we even doing
hot folio
I supposed that P is true and Q is also true not the logical connective and
tropic oxide
ok then why are you supposing 3 things then
not that it would've made much of a difference
imma say your proof is not signposted enough as it stands rn
hot folio
ok then why are you supposing 3 things then
I'm clueless
what would be the proper proof for it?
tropic oxide
maybe something like:
1. P [given]
2. Assume: Q & ~~(Q -> ~P) [negation of goal]
3. Q & (Q -> ~P) [#2 + double negation]
4. ~P [#3 + modus tollens]
5. Contradiction in steps: 1, 4
6. Therefore, last assumption (step 2) is wrong.
7. Therefore, goal is true.
which isnt written the best way possible but this is all i can do without descending into bureaucratic anxiety
hot folio
in number 2 why did conditional symbol became and? The Q & ~~(Q -> ~P)
hot folio
idk know that, I'm just beginning to write proofs
oak anchor
idk know that, I'm just beginning to write proofs
$(P \rightarrow Q) \leftrightarrow (\neg Q \rightarrow \neg P)$
wraith daggerBOT
Médicis
hot folio
oh that's called contraposition
I know that but I didn't know that that's how it's called
damn you're right
thanks
oak anchor
you’re welcome c:
hot folio
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
torn marsh
cedar kilnBOT
torn marsh
Is this correct
neon egret
the integration looks correct
sacred iron
Is this the integral? $\int_0^1 e^{-4x}\di x$
wraith daggerBOT
𝙸𝚗𝚏𝚒𝚗𝚒𝚞𝚖³
elder scroll
Im wondering if it mathes here
this is a cleaner way of writing your final answer, yes
cedar kilnBOT
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zenith grail
is there an easy way to remember when to use law of cosines and when to use law of sines when solving oblique triangles?
pastel vault
is there an easy way to remember when to use law of cosines and when to use law ...
yes, law of cosines is used for SAS or SSS triangles
law of sines is used for AAS, ASA
zenith grail
so as long as i remember SAS and SSS for law of cosines, everything else is law of sines?
pastel vault
so as long as i remember SAS and SSS for law of cosines, everything else is law ...
well, there are some questions where you need to use the cosine rule first to find the 3rd side
then to find the angles you then need to use the sine rule afterwards
pastel vault
so as long as i remember SAS and SSS for law of cosines, everything else is law ...
but yes, that's correct