Yeah haha you also?
#help-38
charred trail
charred trail
Oh nice, I’m from Mumbai
charred trail
U sub kar, u = cos(x)
Actually it’s an odd function
So can just use symmetry argument
lean kraken
How you check its odd?
charred trail
f(-x) = -f(x)
lean kraken
Ohh yeah
summer haven
How you check its odd?
cause cos is odd
trim joltBOT
charred trail
Nws
trim joltBOT
Available help channel!
grizzled pendant
I want to model Y ~ X where Y is a proportion of groups (17 in total) that an observation belongs to. 2/17, 5/17 8/17, etc.
So it goes from 0-1 in steps of 0.06.
X is a normally distributed continuous variable.
Two questions
- Would it be incorrect to multiply the proportion by 17 to get the group count and do Poisson regression, given it it bounded on the right hand side of the distribution to 17?
- What would be the most appropriate way to model Y scaled as a proportion, given it isn't a continuous proportion?
trim joltBOT
I want to model Y ~ X where Y is a proportion of groups (17 in total) that an ob...
@grizzled pendant Has your question been resolved?
grizzled pendant
<@&286206848099549185>
trim joltBOT
@grizzled pendant Has your question been resolved?
verbal gulch
what do you mean by model? what parameters are you estimating? the mean/std of the normal random variable?
do you observe X or Y?
grizzled pendant
what do you mean by model? what parameters are you estimating? the mean/std of t...
Regression model.
grizzled pendant
do you observe X or Y?
Y ~ X = Y independent variable, X dependent variable.
verbal gulch
so you observe both?
grizzled pendant
Yes - I have Y and X values for each observation
grizzled pendant
then what is there to estimate?
The regression coefficient, and P-value, for the X variable
verbal gulch
regression coefficient of what?
you're saying that Y is some discretized version of the quantiles of X
but there's nothing random about Y from X
grizzled pendant
I'm not sure you understand what I'm asking
verbal gulch
I don't
grizzled pendant
Y ~ X doesn't mean Y is 'a discretized version of the quantiles of X'
Y ~ X means you are regressing Y against X. As in performing regression to see how X predicts Y (if at all)
verbal gulch
I know that
but then what is all of this stuff about "proportion of groups" an observation belongs to? seems like you're saying that Y is some binned version of F(X), where F is the normal cdf
grizzled pendant
No?
My Y variable is the number of outcome groups for each observation, where the maximum number of outcomes is 17. Essentially it's a score out of 17 as the Y variable.
X is a different continuous normally distributed variable that goes from -1 to 1
verbal gulch
you just said that X is normally distributed...
but okay
so you have 17 subsets of [-1, 1], and Y is the count of the number of subsets X falls into?
grizzled pendant
What???
Y is a score out of 17
X is a continuous variable that can be between -1 and 1
I want to know which is the best regression method for finding the association between Y and X (coefficients and P-values)
From what I understand Poisson regression would be incorrect because it assumes there is no upperband for the number of counts. In this case there is an upper band of 17/17
So I'm trying to figure out if using Y as a proportion (count/17) and using something like Beta regression would be more appropriate (with adjustment to deal with 0s and 1s)
grizzled pendant
It seems Binomial regression would be the most appropriate
trim joltBOT
@grizzled pendant Has your question been resolved?
trim joltBOT
@grizzled pendant Has your question been resolved?
grizzled pendant
<@&286206848099549185>
My current solution has been to use a Binomial model, where I give the Y variable as number of successes & number of failures. I'm still not certain if that is the most sound method though.
(interestingly, doing Poisson regression Y ~ X, and then Poisson regression of (Y*17) ~ X gives the exact same coefficients but completely different P-values. I didn't expect that)
trim joltBOT
@grizzled pendant Has your question been resolved?
trim joltBOT
@grizzled pendant Has your question been resolved?
calm breach
Help please
fierce lake
!occupied
trim joltBOT
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).
dire glacier
Help please
Hi! what exactly is it youre struggling with here?
calm breach
Yes
dusty sleet
And what is the radius in your picture?
calm breach
10CM
calm breach
5cm sorry
calm breach
So 10 x 5 =50 and i must square it so it much be 250?
dire glacier
why 10x?
calm breach
No 25 because 5 squared is 25
dire glacier
how many sides does your box have
pseudo goblet
how many sides does your box have
"faces" *, not "sides"
(only because in this case "sides" is ambiguous)
dire glacier
My bad english is not my native language and this is my first time coming into contact with it in regards to math terminology
couldnt even remember what the shape is called
pseudo goblet
(I mean "cuboid" is in the question itself lol)
trim joltBOT
@grizzled pendant Has your question been resolved?
fair forge
how do i prove: T:V->V linear trans.
0 is not an eigenvalue of T => T is invertible
thorn bay
how do i prove: T:V->V linear trans.
0 is not an eigenvalue of T => T is invert...
finite dimensions?
marble wharf
do you see a relation to the kernel of T?
fair forge
finite dimensions?
i want to prove without the limitation but if u can with then tell me how
fair forge
do you see a relation to the kernel of T?
i did that for the oppsite direction but i dont see how here
marble wharf
you need finite dim
lilac flame
i did that for the oppsite direction but i dont see how here
what was the relation
fair forge
you need finite dim
then tell me how with it
fair forge
what was the relation
what u see
lilac flame
huh
0 eigenspace = kernel
Tv = 0v = 0
so 0 not an eigenvalue means kernel = 0eigenspace = {0}
fair forge
that only proves 1-to-1
marble wharf
in infinite dims there are injective linear maps which are not invertible
fair forge
in infinite dims there are injective linear maps which are not invertible
what i meant
marble wharf
in other words in infinite dims the claim is false
thorn bay
so you have if and only if in finite dimensions and in infinite dimensions you only have
L is invertible implies 0 is not an eigenvalue
marble wharf
it only works in finite dims
lilac flame
can i take if T's V is finite then injective => surejective?
um yes this is true
but how do u prove it
thorn bay
example of a linear transformation that's injective and not invertible:
Consider the space of infinite sequences in R
(x1,x2,x3,...)
and the map
(x1,x2,x3,...) maps to (0,x1,x2,...)
thorn bay
but how do u prove it
try proving it using the rank-nullity theorem
lilac flame
yes
lilac flame
use rank-nullity
^
fair forge
great, ty guys
manic lagoon
<@&268886789983436800>
trim joltBOT
@fair forge Has your question been resolved?
solemn pike
I need help please someone (preferably French) but I really need someone to help me with a test that I have tomorrow
whole coral
If you post your questions, someone will likely help (not me, but there are some French speaking people in the server)
cedar adder
I need help please someone (preferably French) but I really need someone to help...
Did you open a channel to ask about tomorrow?
Do you do some kind of pre-booking
stoic garden
Do you do some kind of pre-booking
I assume his test is tomorrow, which is why he's studying for it today.
trim joltBOT
@solemn pike Has your question been resolved?
trim joltBOT
trim joltBOT
Available help channel!
vapid pawn
I'm trynna show that this is not differentiable:
[
f(z) =
\begin{cases}
\frac{z^5}{|z|^4}, & \text{if } z \neq 0, \
0, & \text{if } z = 0.
\end{cases}
]
Can anyone think of a path I can take where this doesn't go to 0?
solid kilnBOT
theaveragejoe6029
rain zenith
take the limits
trim joltBOT
@vapid pawn Has your question been resolved?
austere cedar
It does go to 0, but it doesn't do so in a smooth way
You'll want to apply the definition of the derivative at x = 0
dusk summit
trim joltBOT
dusk summit
so im on part D right now
i have to make another vector that has the same relationship to t and u which was neither in part C
this is what i wrote so far
but i think i messed up
dusk summit
i have to make another vector that has the same relationship to t and u which wa...
is this neither or parallel
i just doubled the values from t
@stoic garden are you still active
dusk summit
<@&286206848099549185>
brittle light
If you do that
fierce lake
i just doubled the values from t
Why did you double it?
fierce lake
You just want a vector w such that w.t = u.t
fierce lake
Try doubling u instead
No what???
brittle light
He can
He just has to preserve the non-parallel / non-orthogonal relationship between the vectors
minor cipher
w cannot be a scalar multiple of t, that makes it parallel
fierce lake
Same relationship to t must surely mean that dot products must also be equal
brittle light
Same relationship to t must surely mean that dot products must also be equal
Not necessarily according to the way the question is phrased in C
fierce lake
Not necessarily according to the way the question is phrased in C
"Same relationship to t as it has with u"
brittle light
Read C
I mean, your answer is right too, but mine just goes with the minimal effort possible
I interpret the relationship as the possibility of being parallel, orthogonal or neither as defined in C
fierce lake
I interpret the relationship as the possibility of being parallel, orthogonal or...
Yes i understand that
brittle light
As they're neither, making w=2u preserves that wrt t
fierce lake
They haven't mentioned what same relation implies
brittle light
They haven't mentioned what same relation implies
True, but that's a semantics problem. Not a mathematical one
fierce lake
True, but that's a semantics problem. Not a mathematical one
Also going by that logic, w doesn't have to be parallel to u, we'll get a locus for that
brittle light
Also going by that logic, w doesn't have to be parallel to u, we'll get a locus ...
True, as I said, just making it parallel is the fastest answer
So basically, @dusk summit if you're sure that relationship merely means being parallel, orthogonal or neither, my solution is the fastest.
If according to your teacher it implies preserving another property, then go with Rudy's to be sure.
fierce lake
True, as I said, just making it parallel is the fastest answer
But i don't think a question like that is to be graded for 5 marks
brittle light
But i don't think a question like that is to be graded for 5 marks
Once again you're assuming semantics
fierce lake
Once again you're assuming semantics
true
fierce lake
But looking at a problem also means understanding every aspect of it whether it be linguistic or psychological or mathematical
dusk summit
i got 3168.20
brittle light
My advice is above. If "relationship" merely a condition, go with my solution. If it's something more specific, go with yours
brittle light
But looking at a problem also means understanding every aspect of it whether it ...
With the information provided, I'd say the onus is more on a poorly formulated question
fierce lake
Let us focus first on helping the guy then we can go on about our arguement
brittle light
I'm about to sleep, that's the issue 😅
fierce lake
no worries
brittle light
Do not merely multiply t by a scalar @dusk summit
That will make it parallel
I think Rudy and I agree on this one
dusk summit
Do not merely multiply t by a scalar <@563472377426477076>
wait is this good then
brittle light
Has your teacher explained abput what "relationship" means before?
brittle light
wait is this good then
That's multiplying t by 2, so no, it's wrong.
brittle light
Wrong arithmetics probably
brittle light
But you're going into a dead end
Any vector multiplied by a scalar (a number) not equal to 0 produces a parallel vector
dusk summit
Any vector multiplied by a scalar (a number) not equal to 0 produces a parallel ...
so what values shouild i use for w
brittle light
True, as I said, just making it parallel is the fastest answer
Read this
And the message after that one
And the previous ones
dusk summit
So basically, <@563472377426477076> if you're sure that relationship merely mean...
yeah relationship does mean parallel, orthogonal or neither
trim joltBOT
@dusk summit Has your question been resolved?
trim joltBOT
trim joltBOT
Available help channel!
cedar adder
$\int -\frac{e^{-2x}}{e^{-x}+1}\ dx$
trim joltBOT
$\int -\frac{e^{-2x}}{e^{-x}+1}\ dx$
solid kilnBOT
SELVATOR
empty prairie
!status
trim joltBOT
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
I can't solve it
empty prairie
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
which step?
cedar adder
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
U can say 1
cedar adder
fierce lake
Howd y9u get the first term?
cedar adder
Howd y9u get the first term?
By Factorise
fierce lake
No are y9u perhaps showing different questions here ?
Original one had e^-2x in the numerator, this one has e^x + e^-x
cedar adder
No are y9u perhaps showing different questions here ?
Original one had e^-2x in...
Look at last sentence
fierce lake
Oh sorry my bad 
cedar adder
@empty prairie
fierce lake
Use u sub here
cedar adder
It would be x/(e^x + e^-2x)²
fierce lake
Where'd the square come from now...
empty prairie
<@946379454056386560>
I mean have you tried simplifying the fraction by resolving the negative powers?
empty prairie
Is this your original question or is the question posted original?
cedar adder
**SELVATOR**
.
clear cloud
U sub seems quite forward
cedar adder
Yea have you tried to resolve the negative powers?
1/(e^x + e^{-2x})
cedar adder
U sub seems quite forward
What would U be and V' be
clear cloud
u-sub ce nest pas integration par parties
Changement de variable
u = e^x
du = e^x dx donc du/u = dx
cedar adder
Changement de variable
Idk how to use it
clear cloud
Ok so lets not to it then
empty prairie
$\frac{e^{-2x}}{e^{-x} + 1} = \frac{1}{e^{2x}} \cdot \frac{1 + e^x}{e^x}$
solid kilnBOT
@empty prairie
fierce lake
<@946379454056386560>
???
cedar adder
<@946379454056386560>
empty prairie
$\frac{1 + e^x}{e^{3x}} = e^{-3x}(1 + e^x) = e^{-3x} + e^{-2x}$
solid kilnBOT
@empty prairie
limpid dawn
cedar adder
<@946379454056386560>
Any steps?
empty prairie
<@946379454056386560>
What this is literally just re-writing $a^{-b} = \frac{1}{a^b}$ and then reciprocating and multiplying
solid kilnBOT
@empty prairie
cedar adder
+1 was in the denominator
cedar adder
<@946379454056386560>
$\frac{1}{e^{2x}} \cdot \frac{e^{x}}{1 + e^x}$
empty prairie
Hold on lemme get some pen and paper
solid kilnBOT
SELVATOR
cedar adder
$\frac{1}{e^x + e^{2x}}$
solid kilnBOT
SELVATOR
empty prairie
Oh shit mb lol
cedar adder
U mean add e^x + e^2x and minus it?
fierce lake
First of all
Which integral do you wanna do
cedar adder
**SELVATOR**
@fierce lake
fierce rain
Can u not just write this as some hyperbolic function
cedar adder
Idk how to use it
@fierce lake @fierce rain
fierce lake
<@1356904580633596075> <@584433588825620481>
e^-x = t
-e^-xdx = dt
stable crescent
whats the question,
fierce lake
fierce lake
**SELVATOR**
@stable crescent
trim joltBOT
@cedar adder Has your question been resolved?
trim joltBOT
trim joltBOT
Available help channel!
timid bear
anyone know fast multiplication algorithm for medium size number? Karasuba seems to be only good for big size one, so Karasuba is no go to me
boreal apex
anyone know fast multiplication algorithm for medium size number? Karasuba seems...
why not just like, schoolbook multiplication
do word-wise multiplication with carry propogation
it works fine if you are not using too many bits
it is asymptotically slower than Karatsuba, but overhead matters a lot more for not-so-large numbers i reckon
summer tapir
how many digits?
timid bear
how many digits?
36 digits
timid bear
why not just like, schoolbook multiplication
because I want something faster
summer tapir
by hand or by computer?
summer tapir
well, for hand i would reccomend karatsubaing until 3-4 digits and the school multiplication
timid bear
hmm...
summer tapir
for computer, i dont think 36 digit multiplication takes enough time to be non-negligible? 36 bits or digits? cause 36 digits is like 120 bits, and then tom-cook seems nice, or maybe even the fft one, idk ehich is faster tho, i would reccomend just trying them both out, tom-cook is a safer bet ig tho
timid bear
aight thx
next vapor
given the equacion x^2+y^2=a^2 we need to integrate the area using a closed line integral
sudden mist
What is the integrand?
next vapor
x^2+y^2 =a^2
carmine spade
given the equacion x^2+y^2=a^2 we need to integrate the area using a closed line...
do you mean to say you want to find the area of a circle with integration?
sudden mist
Oh I see
Well what’s a parametric description of that region?
If you can do that, then you can find it’s area using a closed line integral
(Due to Greens theorem)
next vapor
huh?
cedar adder
To give you an idea, it's a sphere with center (0,0) and radius r.
sudden mist
I’m not integrating it any other way, I’m doing it by a closed line integral. I’m not trying to avoid it
It seems like you assumed I’m trying to to it without a closed line integral
next vapor
ummm ok so your way then i will shut up
next vapor
so what should i do first
sudden mist
Well what’s a parametric description of that region?
.
Find a parametric description of the boundary of ur region
That’s how u start when calculating a closed line integral
next vapor
x=t^2.y= -+root(a^2-t^2)
sudden mist
How do we know when to switch sign?
There’s a better way to describe it
Hint: ||trigonometry||
next vapor
hmmm sin^2t+cos^2(t)
next vapor
asin^2t+acos^2(t)
sudden mist
Yes, I’m assuming you have ^2 around all of a*sint, right?
next vapor
yes
next vapor
sin^2,cos^2
sudden mist
Not quite
next vapor
cos^2,sin^2?
sudden mist
x^2 + y^2 = a^2 described our boundary
next vapor
cos,sin
next vapor
acos(t).asin(t)
sudden mist
Yea!
Let us assume t varies between 0 and 2pi
Now we have a parametric description of the boundary of the region you want to find the area of
Denote ur region by $D$
solid kilnBOT
Aslan
sudden mist
Then $\iint_D , dx dy = \text{Area}(D)$
solid kilnBOT
Aslan
sudden mist
But by Greens theorem we then have that, say $\int_{\partial D} x, dy = \iint_D, dxdy = \text{Area}(D)$
solid kilnBOT
Aslan
sudden mist
So if you can calculate the closed line integral $\int_{\partial D} x, dy$ then you’ve calculated the area of D, ur region.
solid kilnBOT
Aslan
sudden mist
And now since you’ve got a parametric description of $\partial D$ then it’s straightforward
solid kilnBOT
Aslan
sudden mist
Do you know how to proceed with the line integral?
sudden mist
Are you familiar with a line integral of the form $\int_{\gamma} P, dx + Q, dy$ ?
solid kilnBOT
Aslan
sudden mist
i lost you in the Green's Theorem
I showed that for completeness, you only now have to compute a certain closed line integral.
next vapor
so you are saying in order to do a line integral for the function y= f(x)
we need two functions for y and x in terms of variable t
and then apply Green's Theorem
sudden mist
?
sudden mist
so you are saying in order to do a line integral for the function y= f(x)
we ne...
What do u mean by this
next vapor
parametrization as you called it
sudden mist
i am trying to understand you
I’m assuming you know how to compute line integrals
Is this ur first time?
next vapor
first time for what?
next vapor
ohhh no you did great
sudden mist
Let’s start over and go back to ur problem about the area later when we’ve gone through how to compute line integrals
next vapor
yes
sudden mist
Could u give me a definition or a short description of it?
sudden mist
Contrary to what the word may suggest, a curve can certainly be a straight line
An n-dimensional (real) curve, say gamma, is a continuous function from some interval I to R^n
next vapor
well some function not in the form y=mx+b
sudden mist
An n-dimensional (real) curve, say gamma, is a continuous function from some int...
Does this make sense?
sudden mist
So for example, if n = 2
Then $\gamma : [0,1] \to \mathbb{R}^2, , \gamma(t) = (t, t + 1)$ is a curve
solid kilnBOT
Aslan
next vapor
yeah i checked it
sudden mist
So suppose you were only given the graph y = x + 1
Then working backwards, gamma above is a curve that parametrizes the graph y = x + 1
Makes sense?
next vapor
yes
sudden mist
So why do we care about parametrizing an equation or curve?
Well because line integrals are defined in terms of a parametric description of a given curve!
Let’s go over that definition
next vapor
hmmm
next vapor
ohh yes i get it
sudden mist
This is just a definition
next vapor
yeah yeah gama prime is dx,dy
next vapor
ok
sudden mist
That relates this notion of a line integral with the usual double integral
And that’s how you can calculate the area of a region using a closed line integral
next vapor
one question what if the line is not closed does the theorem break
sudden mist
It breaks in the sense that we don’t know what the “region” means in that case
The way the theorem is setup, is that we start with a region
Then take its boundary
This must be a closed curve/line
So going backwards is undefined if the curve is not closed
I.e it doesn’t enclose a region
next vapor
ok got it
sudden mist
**Aslan**
This is basically a formula
U can now use this to calculate ur area from before
Ur gamma is (a cos t, a sin t) with 0 <= t <= 2pi
While P = 0, Q = x
next vapor
ohh right
trim joltBOT
@next vapor Has your question been resolved?
trim joltBOT
@next vapor Has your question been resolved?
trim joltBOT
Available help channel!
marsh forum
Let $G'$ be the group of real matrices of the form$\begin{bmatrix}
1 & x \
& 1
\end{bmatrix}$. Is the map $R^{+} \to G'$ that sends $x$ to this matrix an isomorphism?
marsh forum
shit, sorry
solid kilnBOT
What a wonderful world !
marsh forum
So can I interpret the blank as an arbitrary constant
?
Let $G'$ be the group of real matrices of the form$\begin{bmatrix}
1 & x \
& 1
\end{bmatrix}$. Is the map $R^{+} \to G'$ that sends $x$ to this matrix an isomorphism?
solid kilnBOT
What a wonderful world !
urban copper
trim joltBOT
@urban copper Has your question been resolved?
whole granite
Hi what's the question
trim joltBOT
@urban copper Has your question been resolved?
willow urchin
pls translate
urban copper
red loom
well question 1 is analogous to solving ([\vec{v}]{B}=[\vec{v}]{B'}), or:
[\begin{bmatrix}1 & -2 & -2 \ 1 & 1 & 2 \ 0 & 1 & 3\end{bmatrix} \begin{bmatrix}x \ y \ z\end{bmatrix} = \begin{bmatrix}2 & 1 & -1 \ 2 & 2 & 1 \ 2 & 3 & 1\end{bmatrix} \begin{bmatrix}x \ y \ z\end{bmatrix}]
solid kilnBOT
PajamaMamaLlama
urban copper
**PajamaMamaLlama**
yes but instead of x,y,z its a,b,c if you will because is coordinates, do not confuse with a vector, right?
also is this valid?
urban copper
well question 1 is analogous to solving \([\vec{v}]_{B}=[\vec{v}]_{B'}\), or:
\...
either you or me made a mistake mate
red loom
yes but instead of x,y,z its a,b,c if you will because is coordinates, do not c...
ig if your teacher specified but they're just letters 😅
red loom
yes that's just rearranged
(\begin{bmatrix}1 & -2 & -2 \ 1 & 1 & 2 \ 0 & 1 & 3\end{bmatrix} \begin{bmatrix}a \ b \ c\end{bmatrix} = \begin{bmatrix}2 & 1 & -1 \ 2 & 2 & 1 \ 2 & 3 & 1\end{bmatrix} \begin{bmatrix}a \ b \ c\end{bmatrix}\implies\left(\begin{bmatrix}1 & -2 & -2 \ 1 & 1 & 2 \ 0 & 1 & 3\end{bmatrix}-\begin{bmatrix}2 & 1 & -1 \ 2 & 2 & 1 \ 2 & 3 & 1\end{bmatrix}\right)\begin{bmatrix}a \ b \ c\end{bmatrix}=\begin{bmatrix}0 \ 0 \ 0\end{bmatrix})
urban copper
we get different matrices mate
solid kilnBOT
PajamaMamaLlama
urban copper
either you or me made an oopsie
red loom
we get different matrices mate
we do? 🤔
urban copper
subtract
urban copper
well question 1 is analogous to solving \([\vec{v}]_{B}=[\vec{v}]_{B'}\), or:
\...
also we haven't covered change of basis matrices
red loom
🤔
solid kilnBOT
red loom
, w nullspace {{-1,-3,-1},{-1,-1,1},{-2,-2,2}}
solid kilnBOT
red loom
entry a_23 was incorrect
and indeed now notice R3=2R2
thus we expect the dimension of the nullspace to be 1
which is what was returned
urban copper
\(\begin{bmatrix}1 & -2 & -2 \\ 1 & 1 & 2 \\ 0 & 1 & 3\end{bmatrix} \begin{bmatr...
i think it should be x,y,z, not a,b,c
or no?
i am already confused
red loom
(v)B = (v)B'
well no, we have:
[
\begin{bmatrix}
-1 & -3 & -1 \
-1 & -1 & 1 \
-2 & -2 & 2 \
\end{bmatrix}\overset{G}{\longrightarrow}
\begin{bmatrix}
1 & 0 & -2 \
0 & 1 & 1 \
0 & 0 & 0 \
\end{bmatrix}
]
urban copper
G?
red loom
gaussian elimination/row reduction
red loom
i think it should be x,y,z, not a,b,c
they're just letters, I could've chosen n,b,p and it wouldn't matter
urban copper
when we got the nullspace what did we find
urban copper
they're just letters, I could've chosen n,b,p and it wouldn't matter
the meaning of the letters
solid kilnBOT
PajamaMamaLlama
red loom
the meaning of the letters
wdym? the letters don't inherently mean anything
urban copper
when we got the nullspace what did we find
red loom
the vector (or family of vectors) (\mathbf{v}) such that ((B-B')\mathbf{v}=\mathbf{0})
solid kilnBOT
PajamaMamaLlama
urban copper
in other words we found all v such that (v)B = (v)B'
is a line that passes through the origin, infinitely many v such that (v)B = (v)B'
red loom
it appear to be so, yes
vestal token
OD is the bisector of AOC,OE is the bisector of angle BOC and OD is perdecular to OE
prove A O B are collinear
trim joltBOT
@urban copper Has your question been resolved?
trim joltBOT
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).
trim joltBOT
@urban copper Has your question been resolved?
urban copper
but I distrust it
why would they have no intersection?
most likely I made a mistake
lime sphinx
I went through the previous discussion and the method and i arrived at the same results doing the computations
lime sphinx
why would they have no intersection?
the solution space to this matrix is a line passing by 0 and there is no intersection between the plane S and this line
except 0 of course
urban copper
I went through the previous discussion and the method and i arrived at the same ...
is strange, when we found the nullspace, would u have used a,b,c or x,y,z
lime sphinx
either a,b,c or x,y,z are fine on my part, the important thing is that you know what these represent in the problem i.e. the coords in both base of a vector with the property we want
it’s just notation imo, pick the one that makes the most sense to you, or the one imposed to you
urban copper
sure but when we were doing the equality vB = vB'
a,b,c made more sense
but the result of the nullspace is a vector
like multiples of a vector
is confusing, I got lost
urban copper
either a,b,c or x,y,z are fine on my part, the important thing is that you know ...
yes, but when we found the nullspace we got a subspace
lime sphinx
wait up you might be right
the a,b,c are coords, scaling factor in a linear combination of vector from either base A or base B
urban copper
the a,b,c are coords, scaling factor in a linear combination of vector from eith...
yes
lime sphinx
so computing the linear combination in both base should gets you the actual vector generating the line of sol in R^3
ngl this is a bit wacko
urban copper
so computing the linear combination in both base should gets you the actual vect...
oh OK
so the subspace we got are the coordinates or the vector?
XD
lime sphinx
case and point when solving the system we found the set of coords for which vector expressed in each base have the same coords, but the coords are not the og vectors
urban copper
case and point when solving the system we found the set of coords for which vect...
yes!
its the coords
urban copper
(a,b,c)=(2,-1,1)
this is why insisted on the a,b,c vs x,y,z thingy
it gets confusing
yeah sure, you can use x,y,z
but then you end up believing other thing that is not
urban copper
case and point when solving the system we found the set of coords for which vect...
what are the possible Vs?
solid kilnBOT
urban copper
,w 2{2,2,2}-{1,2,3}+{-1,1,1}
solid kilnBOT
lime sphinx
the coords that works are scalar multiple of (2,-1,1), then i think this means that doing the last computation here gives you the vector that spans the line of vector in the actual R^3 which have the same representation in both bases
urban copper
the coords that works are scalar multiple of (2,-1,1), then i think this means t...
all the possible vs is this <(2,3,2)> i guess
lime sphinx
and it’s in S
urban copper
crazy mate
lime sphinx
a yeah what a tricky one
really good exercise though, it really checks if you understand what a basis is
by confusing you between the vectors of coords and the actuarial R^3 where the basis vector are
urban copper
really good exercise though, it really checks if you understand what a basis is
you mean that in a basis {x1,x2,x3}
ax1 + bx2 + cx3 = 0
if and only if (a,b,c)=(0,0,0)
or somrthing like that?
where x1,x2,x3 are vectors tho
lime sphinx
idk when we solved the system we got out a vector of coords which was ‘disconected’ from the R^3 where the basis were
urban copper
yeah
lime sphinx
ima go get chips and a coke
urban copper
by confusing you between the vectors of coords and the actuarial R^3 where the b...
yes mate, I appreciate the clarification
urban copper
idk when we solved the system we got out a vector of coords which was ‘disconect...
its related but not disconnected I think, like when we solved the nulspace we got all the scalar multiples of (a,b,c)
lime sphinx
that choice of words is just my limited english
urban copper
you are not from the states? oh
lime sphinx
i’m from québec, it’s a french speaking province in canada
it’s funny because imo french and spanish are closer from each other than they are from english, so when you send your problems it’s close enough i can make a rough translation that works
lime sphinx
no you did this time but it’s way back up
urban copper
well I just used the inbuilt translation from the phone haha, didn't even checked if its correct translation
lime sphinx
was ok imo
urban copper
what about 2) though? are you still getting chips? can u maybe help me a bit more 🥺
urban copper
well
(-3,1,5) = -2(2,1,1) + v2 + 3v3
(8,5,9) = 3(2,1,1) + 2v2 + 2v3
this is way more simplistic compared to the first one, I think
but lets see
,, \begin{cases} (-3,1,5) + 2(2,1,1) = v_2 + 3v_3 \ (8,5,9) - 3(2,1,1) = 2v_2 + 2v_3 \end{cases}
solid kilnBOT
renato
urban copper
,w {-3,1,5}+2{2,1,1}
solid kilnBOT
urban copper
,w {8,5,9}-3{2,1,1}
solid kilnBOT
urban copper
,, \begin{cases} (-3,1,5) + 2(2,1,1) = v_2 + 3v_3 \ (8,5,9) - 3(2,1,1) = 2v_2 + 2v_3 \end{cases} \ \begin{cases} (1,3,7) = v_2 + 3v_3 \ (2,2,6) = 2v_2 + 2v_3 \end{cases}
solid kilnBOT
renato
urban copper
(2,6,14) = 2v2 + 6v3
(2,2,6) = 2v2 + 2v3
(2,2,6)-(2,6,14) = 4v3
no I made a mistake
-4v3
(2,2,6)-(2,6,14) = -4v3
lime sphinx
no I made a mistake
idea is good though
solid kilnBOT
solid kilnBOT
solid kilnBOT
urban copper
(1,0,1) = v2
(0,1,2) = v3
B = {(2,1,1); (1,0,1); (0,1,2)}
(-4,1,1) = a(2,1,1) + b(1,0,1) + c(0,1,2)
,, \begin{amatrix}{3} 2 & 1 & 0 & -4 \ 1 & 0 & 1 & 1 \ 1 & 1 & 2 & 1 \end{amatrix}
solid kilnBOT
renato
urban copper
,w rref {{2,1,0,-4},{1,0,1,1},{1,1,2,1}}
solid kilnBOT
urban copper
idea is good though
first exercise was way more difficult, this one is entirely mechanical
urban copper
yep, I appreciate it mate
lime sphinx
!rats
trim joltBOT
urban copper
hopefully my exam contains exercises like first one or harder
I have prepared a lot, it would be a pity if it contains only mechanical exercises
ty for the help
.close
trim joltBOT
trim joltBOT
Available help channel!
wraith hinge
what will the domain of gof be?
trim joltBOT
what will the domain of gof be?
wraith hinge
(-Infinity,4] or R?
zenith bane
Should be all real number
marsh forum
Should be all real number
pretty sure it's $( -\infty, 4]$
solid kilnBOT
What a wonderful world !
marsh forum
When you compose functions, the function's domain is at most the domain of the innner function
zenith bane
Is g(fx) right
wraith hinge
When you compose functions, the function's domain is at most the domain of the ...
Alright
Thankyou!
.close
trim joltBOT
trim joltBOT
Available help channel!
mystic pilot
trim joltBOT
dense breach
- resolved (I think)
trim joltBOT
trim joltBOT
Available help channel!
sharp rampart
trim joltBOT
sharp rampart
i ended up with r= lambda but idk what to do now
i know
2pirh = 150
V(r,h) = pir^2h
then we have
Vr=lambdaSr
and
Vh=lambdaSh
did i do it right
.close
trim joltBOT
trim joltBOT
Available help channel!
gusty valley
The question: Generally if p is evidence for q, and q for r, then p is evidence for r. But this is not necessarily so. For, p might also be evidence for some 'cancelling event' c, which is evidence against r such that all-things-considered p is neither evidence for nor against r, i.e., such that P(p | r) = P(p). In that case, p's positive influence on r through q gets perfectly cancelled by p's negative influence on r through c. What I call 'premise 3' prevents there being such a c, which seems to make the transitivity inference valid, assuming we know that p is not evidence against r.
The intuitiveness of this piece of informal reasoning suggests that the following inference is valid:
- Premise 1: P(q | p) > P(q)
- Premise 2: P(r | q) > P(r)
- Premise 3: 'There is no such c.'
- Premise 4: P(p | r) ≥ P(r)
- Conclusion: P(r | p) > P(r)
The validity of this inference can be proven if P3 was P(r ∩ p | q) = P(r | q) and P(r ∩ p | ¬q) = P(r | ¬q), i.e., if the only way p influences r is through q. But that's a much stronger assumption then saying that there is no such c. In fact, it's so strong that it makes P4 superfluous. I am looking for a formalization of the informal thought expressed P3 that does not make any of the premises superfluous but still makes the inference valid. I am super stuck on this problem... Hence, I am very curious to hear your thoughts :)
thorn bay
The question: *Generally* if p is evidence for q, and q for r, then p is evidenc...
I mean P1 is false right away
gusty valley
I mean P1 is false right away
can you prove that?
thorn bay
take p = ¬q
thorn bay
oh P is premise
gusty valley
Hence, there's no inconsistency
gusty valley
I don't get what "c" is
It's an event.
It's supposed to be an event such that p influences r through c.
in such a way that this influence exactly cancels against p's influence on r through q.
does that help @thorn bay ?
lost bane
trim joltBOT
@gusty valley Has your question been resolved?
summer tapir
why are you using premise 4?
would you want probability of p given r is greater than probability of r?
gusty valley
why are you using premise 4?
well otherwise outweighing propositions would also be counterexamples to the validity of the inference. That is, otherwise it wouldn't be the case that the only type of counterexamples to the validity of this inference would be cancelling propositions. More formally, the following type of proposition would also consistute a counterexample to the validity of the inference: a proposition o such that p is evidence for o, while o is strong evidence against r such that all-things-considered, p is actually evidence against r, i.e., such that P(r | p) < P(r).
I am interested in a formalisation of the informal thought expressed by premise 3 and not in something much strong that would obviously make the inference valid.
summer tapir
well otherwise outweighing propositions would also be counterexamples to the val...
i think you mean P(R|P) < p(R)
gusty valley
would you want probability of p given r is greater than probability of r?
well, what I want is a formalisation of the informal thought expressed by premise 3 such that one can validly infer the conclusion from premise 1-4.
gusty valley
i think you mean P(R|P) < p(R)
yes sry
Would be curious to hear your thoughts :) @summer tapir
summer tapir
yes sry
well, premise 4 is:P( r|p) >= P(r)
so the conclusion is basically P(r|p) is not = P(r)
gusty valley
well, premise 4 is:P( r|p) >= P(r)
so the conclusion is basically P(r|p) is not ...
yes
summer tapir
well so you eant P(r and p)=\= P(r)P(p)
gusty valley
well so you eant P(r and p)=\\= P(r)P(p)
yes
i.e., r and p are no independent.
right?
gusty valley
BTW: I am confident that this cannot be done without using premise 3. That is, without using a formalisation of the informal thought expressed by premise 3.
summer tapir
BTW: I am confident that this cannot be done without using premise 3. That is, w...
so you want a neat version of Premise 3
gusty valley
yes!
gusty valley
so you want a neat version of Premise 3
and once we have that, I don't think the proof will be too difficult
summer tapir
hm
P(r|p) = P(r|qp)*P(q|p) + P(r|-qp)*P(-q|p)
well
cant you just say P3 is P(r|p) =\= P(r)
gusty valley
cant you just say P3 is P(r|p) =\\= P(r)
haha
that would be easy right
but that is not at all a formalization of the informal thought expressed by premise 3
summer tapir
the issue is although p affects q and q affects r, the part of q that p affects is not neccessarily of part of q that affects r
gusty valley
Like I said, what I need is a formalization of the informal thought expressed by premise such that none of the premises become superfluous. This definition of premise 3 makes premise 1 and 2 superfluous
summer tapir
lemme give you an example of what i mean
gusty valley
the issue is although p affects q and q affects r, the part of q that p affects ...
ye, no I understand why the 'makes more probable' relation isn't transitive
summer tapir
P: it was raining
Q: garden is wet
R: you poured water on plants in garden
gusty valley
but I am looking for conditions under which it's transitive
summer tapir
P: it was raining
Q: garden is wet
R: you poured water on plants in garden
can you tell me what your intuitive version of P3 would say in this case?
gusty valley
I have found very strong conditions under which it's transitive, namely P(r ∩ p | q) = P(r | q) and P(r ∩ p | ¬q) = P(r | ¬q), but I am looking for conditions that are much weaker.
summer tapir
well, the minimally weak condition is "it is transitive"
you literrally cant get weaker than that
so can you tell some place of how weak you want it?
gusty valley
P: it was raining
Q: garden is wet
R: you poured water on plants in garden
well, idk this is a difficult one because the context suggests that p is actually evidence against r, while in my example I want p to be evidence for r.
gusty valley
P: it was raining
Q: garden is wet
R: you poured water on plants in garden
but like we may stipulate that the plants are likely to be happy when the garden is wett
p: it was raining
q: garden is wet
r: plants are happy
On this set up, it suggests that it's raining makes it probable that the plants are happy
summer tapir
ok, but what would premise 3 be in this case? (intuitively speaking)
gusty valley
i.e., it was raining positively influences the probability of the plants being happy through making it probable that the garden is wet.
gusty valley
ok, but what would premise 3 be in this case? (intuitively speaking)
well, c would be some event such that c is made more probable by p, while c makes r less probable, i.e., p has a negative influence on r's probability through c.
A final condition c has to satisfy is that the positive influence p has on r's probability through q has to be exactly as big as the negative influence p has on r's probability through c such that all-things-consider p has neither a positive nor negative influence on r.
Well, we can find an intuitive example of that
summer tapir
well, c would be some event such that c is made more probable by p, while c make...
well the issue is c can intersect with q
not r, q
sry
gusty valley
p: it was raining
q: garden is wet
r: plants are happy
let's consider the example of the kids playing in the garden.
Suppose the kids like playing in the garden when the garden is wett. Then, it was raining makes probable that the kids are playing in the garden. However, the kids destroy the plant. Hence, the plants are less likely to be happy given that the kids play in the garden
Now, there might be all sorts of other things going on of course and it will be important to take that into account, but let's suppose for the moment that these are the only events influencing thing probability of the plant's being happy
summer tapir
Now, there might be all sorts of other things going on of course and it will be ...
here is the issue, how would you well define that
gusty valley
here is the issue, how would you well define that
the kids play in the garden then would qualify as a proposition c only if the effect the event of it was raining has on the plants being happy through the event of making the garden wet has exactly the same effect but in the opposite direction as the effect of it was raining has on the being the plants' being happy through the event of the kids playing in the garden
gusty valley
here is the issue, how would you well define that
that's exactly my question
summer tapir
that's exactly my question
i dont think there is a nice well definition of that?
imagine you have avenn diagram
how would you represent what you are saying on the venn diagram
gusty valley
how would you represent what you are saying on the venn diagram
let me think
@summer tapir
so P(r) = 0.5
P(p) = 0.5
summer tapir
well, you arent considering that c can intersect q?
gusty valley
P(p | r) = 0.5
gusty valley
well, you arent considering that c can intersect q?
doesn't matter for this example
you can let them intersect
summer tapir
also what would "c" be in this case?
gusty valley
gusty valley
also what would "c" be in this case?
well, the end result of there being a c is that P(p | r) = P(r)
that's impossible in what you have drawn
gusty valley
also what would "c" be in this case?
also the conclusion we want wouldn't follow here
gusty valley
but ye that's not the case here either, but that's in virtue of there being a c
alright sry
gtg
summer tapir
well, the end result of there being a c is that P(p | r) = P(r)
exactly, so even without a C, you cant get the conlcusion you want
also you mean P(r|p) = P(r), right?
gusty valley
exactly, so even without a C, you cant get the conlcusion you want
also you mean...
The question: Generally if p is evidence for q, and q for r, then p is evidence for r. But this is not necessarily so. For, p might also be evidence for some 'cancelling event' c, which is evidence against r such that all-things-considered p is neither evidence for nor against r, i.e., such that P(p | r) = P(p). In that case, p's positive influence on r through q gets perfectly cancelled by p's negative influence on r through c. What I call 'premise 3' prevents there being such a c, which seems to make the transitivity inference valid, assuming we know that p is not evidence against r.
The intuitiveness of this piece of informal reasoning suggests that the following inference is valid:
- Premise 1: P(q | p) > P(q)
- Premise 2: P(r | q) > P(r)
- Premise 3: 'There is no such c.'
- Premise 4: P(p | r) ≥ P(r)
- Conclusion: P(r | p) > P(r)
The validity of this inference can be proven if P3 was P(r ∩ p | q) = P(r | q) and P(r ∩ p | ¬q) = P(r | ¬q), i.e., if the only way p influences r is through q. But that's a much stronger assumption then saying that there is no such c. In fact, it's so strong that it makes P4 superfluous. I am looking for a formalization of the informal thought expressed P3 that does not make any of the premises superfluous but still makes the inference valid. I am super stuck on this problem... Hence, I am very curious to hear your thoughts :)
premise 4 is not satisfied in your venn diagram!
gusty valley
also what would "c" be in this case?
do you think it's possible to make a venn diagram on which premise 4 is also satisfied? That would consistute a counterexample to the intuitive idea that the premises entail the conclusion
gusty valley
also what would "c" be in this case?
Do you understand why there can be no c is this case? c is defined such that P(r | p) = P(r)
gusty valley
The question: *Generally* if p is evidence for q, and q for r, then p is evidenc...
<@&286206848099549185> any good with probability theory and logic around? We are stuck...
Would be very curious to hear your thoughts :) <3
thorn bay
You need to mak emore precise what you mean by the existence or non-existence of "c"
"c is defined such that P(r|p)=P(r)" doesn't make sense because c doesn't appear in those expressions
furthermore adding a premise of the non-existence of something can break your probability measure, once you define c (you haven't yet, as I said), you're much better off with something like P(c) = 0 than saying "c does not exist", unless you're really careful about the probability axioms
trim joltBOT
@gusty valley Has your question been resolved?
gusty valley
"c is defined such that P(r|p)=P(r)" doesn't make sense because c doesn't appear...
the question is to get precise on c
If I knew how exactly to define c
then my question would be solved
I give a bunch of conditions that the definition of c has to satisfy
gusty valley
furthermore adding a premise of the non-existence of something can break your pr...
what I mean is that there is no event satisfying all the conditions required for an event to qualify as being a c
thorn bay
I give a bunch of conditions that the definition of c has to satisfy
Ah, I hear. Unfortunately I'm ill-equipped to answer your question.
I suspect it may not be a probability question at all, it might be a question about model theory
or modal logic
which are not my specialties
are you familiar with those
gusty valley
The question: *Generally* if p is evidence for q, and q for r, then p is evidenc...
Does this informal reasoning (ignore everything except for the first paragraph) make sense to you? I think it's very intuive.
thorn bay
let me read it again
Yeah it make sense, emotionally. Don't ask me to prove it
Do you know about formal systems?
summer tapir
do you think it's possible to make a venn diagram on which premise 4 is also sat...
ok
gusty valley
Yeah it make sense, emotionally. Don't ask me to prove it
haha. That's exactly the question though hahah
summer tapir
green makes blue more probable
and blue makes red more probable
gusty valley
but, indeed it's hard
summer tapir
haha. That's exactly the question though hahah
so how would you make c in this situation?
summer tapir
well, c needs to be made more probable by p and make r less probable
well, that you can do almost always, just take c = p-r
unless r contains p
gusty valley
well, that you can do almost always, just take c = p-r
ye
gusty valley
Do you understand why there can be no c is this case? c is defined such that P(r...
@summer tapir have we resolved this?
summer tapir
ye
so your premise 3 would need to be incredibly strong if you said there is no such c
gusty valley
so your premise 3 would need to be incredibly strong if you said there is no suc...
yes
in a sense
summer tapir
wdym in a sense?
gusty valley
Do you understand why there can be no c is this case? c is defined such that P(r...
well, there is no c if it's false that P(r | p) = P(r). And ¬(P(r | p) = P(r)) is not a very strong condition.
that's what I mean by in a sense
gusty valley
so premise 1 and premise 2 are entirely useless?
well, the point is to find a formalization of the informal thought expressed by premise 3 such that premise 1 and premise 2 are not entirely useless
we want to make the transititivity inference from premise 1 and 2 to the conclusion valid
by adding some additional premises
if our additional premises make it such that premise 1 and 2 are superfluous
then we have achieved our aim
gusty valley
The question: *Generally* if p is evidence for q, and q for r, then p is evidenc...
do you understand the informal reasoning that I outline here? Does it make sense to you, intuitively? @summer tapir
summer tapir
well, it kind of makes sense, but not something i would trust (intuitively)
thorn bay
As I said, I dont think it's probability you want, I think you're looking for a formal system of some kind
@gusty valley I can tell you the basics of what that means, but I'm far from an expert in them
and I cant promise you a better job of explaining than chatgpt or wikipedia
gusty valley
ye no I know a bit about formal systems and modal logic. I don't think it will help
thanks for offering @thorn bay
trim joltBOT
@gusty valley Has your question been resolved?
trim joltBOT
@gusty valley Has your question been resolved?
plain iron
how do you do 8
trim joltBOT
how do you do 8
hidden dew
how do you do 8
I would expand it then take the derivative
waxen rover
I would expand it then take the derivative
The easier way is to write x^-2 as 1/x^2
hidden dew
The easier way is to write x^-2 as 1/x^2
well expanding it will just make it a power rule problem
plain iron
i used the product rule and got (x^-2)(3ex^2)+(ex^3 + 3)(-2x)
waxen rover
well expanding it will just make it a power rule problem
Mb, I was trying to say the same thing as you.
hidden dew
Mb, I was trying to say the same thing as you.
happens
hidden dew
i used the product rule and got (x^-2)(3ex^2)+(ex^3 + 3)(-2x)
what's the derivative of x^-2 ?
hidden dew
is it -2x^-1
still no
hidden dew
so it should be (3ex^2)/x^2 + ((ex^3+3)(-2))/x^3 ?
could be simplified cuz this looks ugly ngl
it's not wrong tho
plain iron
i ended up getting 3e + (-2ex^3 - 6)/x^3
i dont know what to do from here tho im ps its wrong
hidden dew
i ended up getting 3e + (-2ex^3 - 6)/x^3
I would accept this but idk about the one teaching you
trim joltBOT
@plain iron Has your question been resolved?
waxen rover
Are you familiar with rules of differentiation?
waxen rover
Yes
plain iron
yea i know product and quotient
waxen rover
Then, just differentiate both sides using the rules you know and plug in x=2 at the end
trim joltBOT
@plain iron Has your question been resolved?
wraith hinge
yea i know product and quotient
fun
wraith hinge
If f(x) = 2g(x) + h(x) then f’(x) = 2 g’(x) + h’(x) then you subby in :>
waxen rover
subby I like that
wraith hinge
- Constant multiple rule
2.simple differentiation of g and f
wraith hinge
For q18, make sure you check your work properly
Only read below when you have tried it
|| If you have a constant, C, then D/Dx of C = 0. The indefinite integral would be the opposite resulting in an arbitrary constant, C||
nova pumice
trim joltBOT
nova pumice
Can someone explain to me how a (1/n)^3 appears
on the bottom
i dont know how the sin(1/n) >0
correlates to that
empty orchid
Can someone explain to me how a (1/n)^3 appears
Because $\sin^3\qty(\frac1n)=\qty(\sin(\frac1n))^3$
solid kilnBOT
;(
solid kilnBOT
;(
empty orchid
!redir
trim joltBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
empty orchid
And please delete those 2 messages
Cluttering the thread
Please stop trolling/posting random stuff in here
dull temple
hi
trim joltBOT
dull temple
i think they left the server as soon as i spoke
dull temple
yes
trim joltBOT
Available help channel!
wraith hinge
Im supposed to find 2 of these that work and find out the 2 that don’t work. I also need help understanding why 2 of those wouldn’t work.
Cos( )=sq root of 3/2=tan( )
Tan( )=0=sin( )
Cos( )=-1=tan( )
Tan( )=undefined=sin( )
I tried plugging in cos(30) for the first one but I don’t think it would work for tan. And the other ones just confuse me, I’m not the best at trig
polar ocean
Hmm the ranges of sine cosine and tangent will probably come in handy here
Or maybe just for that last one
wraith hinge
Im allowed to use radians or degrees for them but I prefer degrees unless it has to be radians
Im j really confused
I feel like all 4 don’t work
polar ocean
Because sine and cosine only have ranges between 1 and -1
Are we just trying to find values that fit in the blank spaces?
wraith hinge
Yeah sorry
polar ocean
Alright
Well the second one is pretty easy to realize that it works
You’re just looking for the values of sine and tangent that just equal zero
wraith hinge
What do I put for that in degrees? 180 and 0? Or are they both 0
polar ocean
Yeah I think they’re both 0
Unless we need to find all values that work
Or just one
polar ocean
Yeah if you look at a right triangle and take one angle of it, the tangent of that angle is the opposite side over the adjacent side
I can grab a picture if that helps
wraith hinge
Well in terms of this stuff
How would I know how to do tan
Like for example the first one
How would I do tan for the square root of 3 over 2
If it doesn’t exist
Well it exists on the unit circle but like
Idk idk how I’d write tan if it’s not x (cos) or y (sin)
polar ocean
Hmm well
For the first one like I said ranges will help
Think about the range of cosine
It only outputs values between 1 and -1
So is there any way cosine can output square root of 3/2?
polar ocean
I’m talking about all the possible values you can get from cosine
It has a maximum and a minimum output
wraith hinge
Wouldn’t. That just be every x on the unit circle
wraith hinge
Oh
polar ocean
So cosine can’t go higher than 1 or lower than -1
wraith hinge
Well I used 30 degrees
For that
But I just don’t get how tan would work
So I feel like that’s one out of the 2 that don’t work
polar ocean
No 30 works
Yeah sorry
Uh for tangent I don’t see why there shouldn’t be a value for that
wraith hinge
Well what would it be cuz I’ve tried searching it up
And it gave me decimal
And it’s only supposed to be in degrees
Or radians
polar ocean
Yeah I’m not sure you’re gonna get a nice answer for that