,texconfig
#help-4
stark wedge
rocky lotusBOT
pliant palm
guys can we get back to my problem
pliant palm
no it's not commands š
lyric sundial
Oh sorry lol
pliant palm
yeah
lyric sundial
I replied to the wrong person
If you want to test commands and LaTeX, please go to #latex-testing
So that @pliant palm can post his questions
vale dockBOT
@pliant palm Has your question been resolved?
vale dockBOT
@pliant palm Has your question been resolved?
stark wedge
@pliant palm ive said all that i have to say rn: you need to relearn exponent laws, cause without those you'll just drown in anything logarithmic
formal yew
There is a coefficient on the sin term, I'm not sure how to deal with it, I haven't worked with the Euler's formula in a while
formal yew
I'm supposed to convert the number to polar form
stark wedge
i mean you can factor out the 10e^(-t/10)
formal yew
Maybe I should have started with that
stark wedge
so you get 10e^(-t/10) (cos(pi t + pi/4) + j10 sin(pi t + pi/4))
formal yew
i mean you can factor out the 10e^(-t/10)
Ye I did that but I don't know how to deal with the 10sin ... afterwards
stark wedge
let's just call the argument of both trig functions x
cos(x) + j10 sin(x)
cos(x) = (e^jx+e^-jx)/2 and sin(x) = (e^jx - e^-jx)/(j2)
this should do the trick?
like work through all that and i think you will end up with something workable
formal yew
Probably, I'm kind of remembering that, can you link a source for that so I can look it up deeper?
stark wedge
uhhh Wikipedia article for euler's identity i guess
or just look up trigonometry in terms of complex exponentials
formal yew
or just look up trigonometry in terms of complex exponentials
This is what I was remembering
I'll have to look it up
stark wedge
i gave you the necessary formulas
vale dockBOT
vale dockBOT
Available help channel!
rough talon
find all natural $n$ such that there exists a prime solution $p,q,r$ to $p^n+q^2=r^2$
rocky lotusBOT
skissue.in.a.teacup
rough talon
considering even odd either:
1.p,q odd r even
2.p,r odd q even
3.q,r odd p even
4.p,q even r even
for 1. since r is even then rhs is 4, but lhs is obviously greater than 4 so no
for 4. 2^n+2^2=2^2 doesent have natural solution n
for 3. then 2^n=r^2-q^2
by zsigmondy since 2|q-r then r^2-q^2 has a prime divisor thats not 2, so impossible
rough talon
for 3. then 2^n=r^2-q^2
by zsigmondy since 2|q-r then r^2-q^2 has a prime divis...
im not too used to using zsig so this could be completely false (please fact check this)
so whats left is p^n=r^2-4=(r-2)(r+2)
thats where im stuck
cloud coral
for 3. then 2^n=r^2-q^2
by zsigmondy since 2|q-r then r^2-q^2 has a prime divis...
Theres a solution here so something gone wrong
rough talon
oh wait n=2 is one of the exceptions to zsig
cloud coral
so whats left is p^n=r^2-4=(r-2)(r+2)
Over here notice that r-2 and r+2 are powers of p
rough talon
Over here notice that r-2 and r+2 are powers of p
oh wait yeaa i was thinking of that but i thought it didnt have to be as r-2 and r+2 arent powers of primes but i forgot p is prime :p
so r+2=p^m(r-2) => 2(p^m+1)=r(p^m-1)
r=2(p^m+1)/(p^m-1) needs to be an integer, if p^m=3, then r=4 which isnt prime
any other p^m>=5 except 3, (p^m+1)/(p^m-1)=1+2/(p^m-1), for any p^m>=5 then 3/2>=1+2/(p^m-1)>1, for twice this to be an integer would need to be in the form of a/2 for some integer a, and with the bounds the only possibility is a=3 => p^m=5 => p=5, m=1 => r=3 (prime)
thus (n,p,q,r)=(1,5,2,3) is a solution
so the only case left is 2^n=r^2-q^2
id reckon we can do something simmilar
cloud coral
Yeah powers of 2
rough talon
2^n=(r-q)(r+q)
r+q=2^m(r-q)
q(2^m+1)=r(2^m-1)
r/q=(2^m+1)/(2^m-1)
since gcd(2^m+1,2^m-1)=gcd(2,2^m-1)=gcd(2,-1)=gcd(2,1)=1, then (2^m+1)/(2^m-1) is unsimilifiable, since by checking we can see that r=/=q then that must imply that
2^m+1=r
2^m-1=q
uhhhhhhh
cloud coral
2^n=(r-q)(r+q)
r+q=2^m(r-q)
q(2^m+1)=r(2^m-1)
r/q=(2^m+1)/(2^m-1)
since gcd(2^m+...
Maybe start with r-q=2^a
r+q=2^b
solve for r, q in terms of a, b
rough talon
r=(2^a+2^b)/2=2^(a-1)+2^(b-1)
q=(2^b-2^a)/2=2^(b-1)-2^(a-1)
since a<b and r is odd then a=2+2^(b-1)
q=2^(b-1)-1
uhh am i srupid or does this go back
actually i feel like ive done something lime this but the base being 5 instead of 2, lemme try and find it
ok nvm i guess not
cloud coral
since a<b and r is odd then a=2+2^(b-1)
q=2^(b-1)-1
uhh am i srupid or does this...
Probably a slightly easier way to use
But now you see q is one less than a power of 2 and r is one more than a power of 2
Theres some factorisations you can use to find more information about b
rough talon
2^n=(r-q)(r+q)
r+q=2^m(r-q)
q(2^m+1)=r(2^m-1)
r/q=(2^m+1)/(2^m-1)
since gcd(2^m+...
if m is even, then qā”2^m-1ā”0 mod 3 => q=3k, since q is prime then k=1 so q=3, thus m=2 so r=5, which holds thus (4,2,5,3) is a solution
if m is odd then rā”2^m+1ā”0 mod 3 => r=3l, since r is prime then l=1 so r=3 and m=1 and q=1, but 1 isnt prime so no solution
so 1 and 4?
cloud coral
Yeah looks fine
rough talon
ok tyy
cloud coral
I just considered that 2^a+1 prime implies a=0 or is a power of 2
rough talon
I just considered that 2^a+1 prime implies a=0 or is a power of 2
wait what
cloud coral
Yeah because if a has an odd factor c then 2^(a/c)+1 divides 2^a+1
But yeah not needed, too complicated
Just doing the fermat/merscenne prime stuff
rough talon
ok tyy
vale dockBOT
Available help channel!
zinc fulcrum
\documentclass[12pt]{article}
\usepackage{amsmath, amssymb}
\usepackage{geometry}
\geometry{margin=1in}
\title{Task (d): Geometric Action of Linear Transformations}
\author{}
\date{}
\begin{document}
\maketitle
\textbf{Question:} Let ( n \in \mathbb{R}^{2 \times 2} ) be an invertible matrix with ( |\det(n)| = 1 ). Describe geometrically how such matrices act on vectors in ( \mathbb{R}^2 ), and explain why their inverses represent exact reciprocal transformations.
\bigskip
\textbf{Proof:} Since ( n ) is invertible and ( |\det(n)| = 1 ), the linear transformation ( T_n(\vec{v}) = n\vec{v} ) preserves area in ( \mathbb{R}^2 ). It may rotate, reflect, or shear vectors, but does not compress or expand space. Such transformations bend or redirect slopes smoothly without distortion.
The inverse ( n^{-1} ) satisfies ( T_{n^{-1}}(T_n(\vec{v})) = n^{-1}(n\vec{v}) = \vec{v} ). Thus, ( T_{n^{-1}} ) exactly undoes the action of ( T_n ). If ( T_n ) rotates by ( \theta ), ( T_{n^{-1}} ) rotates by ( -\theta ); if it reflects or shears, the inverse performs the reverse. Both preserve area due to the determinant condition.
\textbf{Conclusion:} Matrices with ( |\det(n)| = 1 ) bend space without distortion, and their inverses reverse this action precisely. Together, they form reciprocal transformations that preserve both area and structure in ( \mathbb{R}^2 ).
\end{document}
rocky lotusBOT
Asian Math Nerd
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lofty crown
Helllppo
sleek nebula
<@&286206848099549185>
!15m
vale dockBOT
<@&286206848099549185>
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.
sleek nebula
!occupied
vale dockBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
zinc fulcrum
maje a new help channel
ebon glade
who uses n as a name for a matrix
zinc fulcrum
who uses n as a name for a matrix
its in the question
ebon glade
well whoever wrote the question still made the decision to use n for a matrix
so my question still stands
midnight pier
well whoever wrote the question still made the decision to use n for a matrix
Free will
zinc fulcrum
as long as you know what n stands for
midnight pier
The person to write the question realized they has free will
zinc fulcrum
The person to write the question realized they has free will
exactly
is it good though
ebon glade
just because you have free will does not mean that you should use bad notation
zinc fulcrum
just because you have free will does not mean that you should use bad notation
calm down now
midnight pier
just because you have free will does not mean that you should use bad notation
Why not?
ebon glade
well I wouldnt call it a proof but its a description of whats going on, sure
midnight pier
just because you have free will does not mean that you should use bad notation
If I had free will
I would do anything I wanted
ebon glade
probably good enough for whatever you need it for
zinc fulcrum
\documentclass[12pt]{article}
\usepackage{amsmath, amssymb}
\usepackage{geometry}
\geometry{margin=1in}
\title{Advanced Task: Geometric Action and Eigenstructure of Invertible Area-Preserving Maps}
\author{}
\date{}
\begin{document}
\maketitle
\textbf{Question:} Let ( n \in \mathbb{R}^{2 \times 2} ) be invertible with ( |\det(n)| = 1 ). Analyze how such matrices affect orientation and structure in ( \mathbb{R}^2 ), and explain how their eigenvectors and inverses reflect this action.
\bigskip
\textbf{Proof:} The matrix ( n ) defines a linear map ( T_n(\vec{v}) = n\vec{v} ). Since ( |\det(n)| = 1 ), the transformation preserves area. If ( \det(n) = +1 ), orientation is preserved; if ( \det(n) = -1 ), orientation is reversed. The map may rotate, reflect, or shear vectors, but it does not alter global scale.
If ( n ) is diagonalizable, then it has real eigenvectors ( \vec{v}_1, \vec{v}_2 ) such that ( n\vec{v}_i = \lambda_i \vec{v}_i ). These vectors span invariant lines under the transformation. Since ( \det(n) = \lambda_1 \lambda_2 = \pm 1 ), the eigenvalues are constrained to lie reciprocally across the unit circle in ( \mathbb{R} ) or ( \mathbb{C} ).
The inverse ( n^{-1} ) satisfies ( n^{-1}n = I ), and geometrically undoes any rotation, reflection, or shear applied by ( n ). If ( \lambda ) is an eigenvalue of ( n ), then ( \lambda^{-1} ) is an eigenvalue of ( n^{-1} ) with the same eigenvector.
\textbf{Conclusion:} Matrices with ( |\det(n)| = 1 ) are structure- and area-preserving maps. Their eigenvectors mark stable geometric directions, and their inverses exactly reverse deformation, maintaining reciprocal behavior in slope, scale, and orientation.
\end{document}
rocky lotusBOT
Asian Math Nerd
Compile Error! Click the reaction for more information.
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zinc fulcrum
can you check this one as well
ebon glade
the eigenvalues do not have to be on the unit circle
leaden cargo
This again?
It was posted by another guy with a clear GPT formulated text
ebon glade
that explains it
leaden cargo
it is the 3rd time I see it
ebon glade
about the same kind of random more or less correct writing I would expect from gpt
leaden cargo
last time it talked about |det(n)| defining a norm on the field of matrices
they're doing better with prompts
zinc fulcrum
\textbf{Question:}
Let ( A, B \in \mathrm{GL}_2(\mathbb{R}) ) be invertible ( 2 \times 2 ) real matrices such that ( \det A = \det B = 1 ), i.e., both are area-preserving linear maps of ( \mathbb{R}^2 ). Suppose ( AB = BA ), meaning the two transformations commute. Prove that if ( A \neq \lambda I ) for any scalar ( \lambda \in \mathbb{R} ), then ( A ) and ( B ) share a common eigenbasis over ( \mathbb{R} ) or ( \mathbb{C} ). That is, there exists a basis of ( \mathbb{C}^2 ) (or ( \mathbb{R}^2 ), if possible) in which both matrices are simultaneously diagonal or triangular.
Geometrically, this means that if two area-preserving linear transformations commute and one of them is nontrivial (not a scalar multiple of the identity), then their actions are aligned along shared invariant directionsārotations about the same angle, shears along common axes, or dilations along reciprocal eigenspaces. This question probes the deep relationship between symmetry, structure, and the algebraic constraints imposed by commuting volume-preserving linear operators.
rocky lotusBOT
Asian Math Nerd
zinc fulcrum
\textbf{Proof:}
Let ( A \in \mathrm{GL}_2(\mathbb{R}) ) with ( \det A = 1 ) and ( A \neq \lambda I ). The characteristic polynomial is ( \chi_A(x) = x^2 - \operatorname{tr}(A)x + 1 ). Since ( A \in \mathrm{GL}_2(\mathbb{R}) ), it has two (possibly complex) eigenvalues ( \lambda_1, \lambda_2 ) satisfying ( \lambda_1 \lambda_2 = 1 ). Consider two cases.
\emph{Case 1: ( A ) is diagonalizable over ( \mathbb{R} ).} Then ( A = PDP^{-1} ) for some diagonal ( D ), and the commutation ( AB = BA ) implies ( D(P^{-1}BP) = (P^{-1}BP)D ). Since diagonal matrices commute only with other diagonal or block-triangular matrices, ( P^{-1}BP ) must preserve the eigenspaces of ( D ), i.e., it is diagonal or triangular. So ( A ) and ( B ) are simultaneously triangularizable and share a common eigenbasis.
\emph{Case 2: ( A ) has complex eigenvalues.} Then ( A \sim R(\theta) ), a rotation matrix. The set of matrices commuting with ( R(\theta) ) is the centralizer of ( R(\theta) ), which consists of all matrices representing linear combinations of rotation and scaling in the same direction. So ( B ) must also preserve the complex eigenspaces of ( A ). Hence, ( A ) and ( B ) are simultaneously diagonalizable over ( \mathbb{C} ).
Thus, ( A ) and ( B ) always share a common eigenbasis in ( \mathbb{R}^2 ) or ( \mathbb{C}^2 ).
rocky lotusBOT
Asian Math Nerd
zinc fulcrum
.close
north scarab
hey guys
rocky lotusBOT
north scarab
did I do something wrong
abstract island
Why did you conclude the limit to be undefined?
open abyss
h/h?
north scarab
Why did you conclude the limit to be undefined?
because the x are getting canceled out and I canāt get rid of h
Q8) a
sleek nebula
because the x are getting canceled out and I canāt get rid of h
you have h/h, what does that evaluate to?
abstract island
- You can get rid of the h
- Even if you couldnāt, that doesnāt make the limit undefined (e.g., is the limit of h as h -> 0 undefined?)
north scarab
you have h/h, what does that evaluate to?
0
north scarab
yeah it cant be possible because the denominator must not equal to 0
lyric sundial
What's 3/3? And 5/5?
sleek nebula
yeah it cant be possible because the denominator must not equal to 0
but they defined it as a limit, so the denominator and the numerator are equal in this sense
north scarab
What's 3/3? And 5/5?
1
lyric sundial
Then what's h/h?
stable island
bro those fractions are 1 whole
storm perch
yeah it cant be possible because the denominator must not equal to 0
But this is a limit, we simplify all of the algebra before we apply the actual limit
north scarab
it is 1 whole but if i sub h in?
storm perch
it is 1 whole but if i sub h in?
We are taking a limit, remember
north scarab
is my working out correct tho?
lyric sundial
No, because that limit is not undefined
storm perch
is my working out correct tho?
Up until the undefined part, yes
flat ice
storm perch
so the limit is equal to 0
So close
storm perch
ok if i remove undefined, so the answer is h/h?
What is x/x?
storm perch
or if x is 0
Well, the limit will approach 1 regardless
What is $\frac{0.000001}{0.000001}$, for example?
rocky lotusBOT
;(
storm perch
So your limit is approaching one, but the function is not necessarily defined at zero
That is where your confusion is
,w plot x/x
rocky lotusBOT
open abyss
Looking qualitatively, the fraction h/h will approach 1 from the left and the right but it will not be defined at h = 0
I meant 1 my bad
analog raft
How do I make these two equations equal? (more explanation pending just claiming this channel before someone else does)
analog raft
I was trying to use this equation to replace the top part
replacing 1 with a, and x with... oh that should be b
steady charm
the bottom integral diverges
analog raft
new one, still has issues though
analog raft
the bottom integral diverges
how do I undiverge this integral? I havent learned this stuff in maths yet so I'm kinda oblivious
steady charm
well the integral measures the area under the curve. and in this case there is infinite area so the whole integral doesn't have a value except maybe infinity
there is a way to assign values to divergent integrals called the cauchy principal value although desmos will not have a function for that
drifting hornet
How do I make these two equations equal? (more explanation pending just claiming...
Why? What are you even doing it for?
analog raft
Why? What are you even doing it for?
just overcomplicating the a/b/beca equation
drifting hornet
make it integral of a/sqrtb instead
analog raft
idk what that means
rocky lotusBOT
MathIsAlwaysRight
drifting hornet
is this good enough?
vale dockBOT
vale dockBOT
Available help channel!
cobalt crow
vale dockBOT
cobalt crow
@warped heart isomorphism = epimorphism and monomorphism
warped heart
Please don't ping me unsollicited; otherwise, yes
cobalt crow
srry I saw you typing, my bad
warped heart
Isomorphism <=> det(f) nonzero
(Because it's a square matrix)
So it's (again) the same method as all the exercises you did so far!
Except this time in the condition defining S you also have the same value a that appears in the matrix for f
cobalt crow
(Because it's a square matrix)
this follows from rank nully?
warped heart
This follows from the fact that if dim(V)=dim(W) and f:V->W is linear, then f iso <=> f mono <=> f epi
cobalt crow
Isomorphism <=> det(f) nonzero
but we want NOT an isomorphism
warped heart
But in fact, it should be a result in your notes that f iso <=> det(f) nonzero
warped heart
but we want NOT an isomorphism
Yes, so what do you need then?
cobalt crow
which means either the det is zero or Im(f) = codomain(f)
cobalt crow
Yes, so what do you need then?
is possible that if f is not an isomorphism, then f is epimorphism or f is monomorphism or f is neither
warped heart
This follows from the fact that if dim(V)=dim(W) and f:V->W is linear, then f is...
Re-read this part
In fact, if f is mono, then it is also epi
So if f is not mono, it is not epi
Next, the condition that f(10,1,13) be in S means that f(10,1,13) is a vector that satisfies the condition x1-ax2=0, which gives you a second equation in a
cobalt crow
So if f is *not* mono, it is *not* epi
right
warped heart
I suspect both will be quadratic equations in a, and only one solution in common so perhaps only one value for a in the end
You'll have to do the computations to know for sure 
So your first job is to compute det(f) and solve the equation det(f)=0
Then, to inspect the second condition, you have to express (10,1,13) in the basis B
To compute its image under f
cobalt crow
So if f is *not* mono, it is *not* epi
if f is not epi, then its not mono aswell
cobalt crow
So if f is *not* mono, it is *not* epi
but since f is NOT a isomorphism, is possible that f is NOT mono and f is NOT epi
cobalt crow
ok so only possibility for f for it to be not an isomorphism is when its not mono and not epi, otherwise we get a contradiction
warped heart
Yeah
cobalt crow
ok and if its not mono its not epi, because rank nullity, let me find det(f)=0, the not mono condition
warped heart
Yeah, the determinant is easy to compute here
cobalt crow
first row cofactors expansion
rocky lotusBOT
warped heart
So that gives you the only two options for f to not be an isomorphism: either a=-3 or a=2
There is one last condition to check though
cobalt crow
cobalt crow
Then you need to compute the product of the matrix with (9,1,-3)
but f(x) ā S
how do I write that in the equation
cobalt crow
ok
cobalt crow
And then *check* if it is in S
vale dockBOT
@cobalt crow Has your question been resolved?
cobalt crow
do you see the mistake @warped heart srry for the ping
I will double check If i found the coordinates of (1,1,13) in basis B correctly
but something feels off
,w det {{1,0,0},{1,a,3},{-1,2,a+1}} = 0
rocky lotusBOT
cobalt crow
,w {{1,0,0},{1,2,3},{-1,2,3}}*{{9},{1},{-3}}
rocky lotusBOT
vale dockBOT
vale dockBOT
Available help channel!
pseudo python
can someone explain how to do this cos inverse (x^2 -11)
pseudo python
if anyone can explain using the number lines that would be easier too
noble anvil
can someone explain how to do this cos inverse (x^2 -11)
You've done it correctly till the number line part
The union part for the first case is correct too
For the second case you need to see where the negative sign is
@pseudo python
pseudo python
For the second case you need to see where the negative sign is
second case?
noble anvil
pseudo python
ohh okay also i think in the first one won't it be like ] instead of ) next to the 10 values
noble anvil
Oh yeah lol
noble anvil
Yeah now do this
pseudo python
Yeah now do this
for second case ?
pseudo python
ohh wait
pseudo python
Check what the inequality is
?
noble anvil
Intersection or union?
pseudo python
intersection
noble anvil
Correct
pseudo python
ok wait i try and then ask u
noble anvil
Indeed
noble anvil
Yes
opal pendant
vale dockBOT
opal pendant
can someone explain this step
tepid wind
,w simplify (x + sqrt(10)) * (sqrt(7 + 2x) + sqrt(5) + sqrt(2))
rocky lotusBOT
trail patrol
can someone explain this step
Just substitute x = sqrt(10) and then simplify
rocky lotusBOT
Civil Service Pigeon
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Available help channel!
abstract iron
I have found the parametrization for X, x(t,s) = (st,st^2,st^3) but I don't know how to find an equation for the closure and show it's exactly X
vale dockBOT
I have found the parametrization for X, x(t,s) = (st,st^2,st^3) but I don't know...
@abstract iron Has your question been resolved?
abstract iron
<@&286206848099549185>
ashen prawn
1. You can get rid of the h
2. Even if you couldnāt, that doesnāt make the limit...
we can definetly cut h
the derivative is defined in such a manner tbh
patent cargo
I have found the parametrization for X, x(t,s) = (st,st^2,st^3) but I don't know...
This should be correct, lemme check b) and c)
vale dockBOT
@abstract iron Has your question been resolved?
patent cargo
Not used to writing in Englisch, I hope itās fine
getting some food now, solving c and d later
abstract iron
getting some food now, solving c and d later
alright thanks!
leaden cargo
getting some food now, solving c and d later
!nosolution
I forgot the command, you're supposed to guide through, not just solve
vale dockBOT
getting some food now, solving c and d later
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
patent cargo
!nosolution
Sorry my first answer ever
Umm ok so do u understand b?
And what do you have on c so far?
patent cargo
@abstract iron what do you have on c so far and do you have any questions about b?
abstract iron
<@344082376248524800> what do you have on c so far and do you have any questions...
So the closure is the border right, like when 2x = y squared
patent cargo
Yup
Havenāt you talked about a way to calculate closures in school yet in general? (If this is homework)
abstract iron
We have but I kinda forgot about it
patent cargo
Prolly read through you notes once again?
āYou canāt draw a tree without knowing what a tree is ā
vale dockBOT
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Available help channel!
halcyon lintel
f1x = ccw
f1y = cw
f2x = ccw
f2y = cw
f3x = ccw
f3y = cw
f4x = ccw
f4y = ???
halcyon lintel
can somebody confirm the x/y rotations from Point A for each force shown
vale dockBOT
@halcyon lintel Has your question been resolved?
trail patrol
Well
CCW means counterclockwise rotation and CW clockwise rotation, right?
The force that passes through the point does not cause rotation because it acts on the zero arm, you did not take that into account
I mean the forces components
@halcyon lintel
halcyon lintel
The force that passes through the point does not cause rotation because it acts ...
hey sup
yea
cw =clockwise
ccw = counterclockwise
trail patrol
Great
trail patrol
The force that passes through the point does not cause rotation because it acts ...
Do you understand this line?
halcyon lintel
no
are you tlaking about force 1?
the one on the very left?
or which force you we talking about here?
trail patrol
Besides, what exactly is the question - to determine the rotations of these forces (their components) with respect to point A, right?
noble anvil
!xy
vale dockBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
trail patrol
the one on the very left?
Yes, for example
halcyon lintel
i just want to know the direction of fx and fy components in respect to point A, cause if I can figure this out, I know how to solve the rest
but i keep getting screwed with the directions
noble anvil
direction in respect to a??
halcyon lintel
ye
noble anvil
or direction in which they rotate about a??
trail patrol
f is the resultant force?
noble anvil
or direction in which they rotate about a??
These are two different things.
halcyon lintel
does it matter which force it is cause it doesnt say
it just shows F as shown in the visual
trail patrol
i just want to know the direction of fx and fy components in respect to point A,...
What are fx and fy?
noble anvil
What even is your axes convention
halcyon lintel
what do you mean what is fx and fy? you want actual numbers?
noble anvil
We want your axes convention.
trail patrol
or direction in which they rotate about a??
I think he means this since he used CCW/CW to describe the rotation
noble anvil
I think he means this since he used CCW/CW to describe the rotation
Prolly
halcyon lintel
all i want to know is the rotation of the fx and fy components in resepect to point A
that's it
noble anvil
...
halcyon lintel
whether its clockwise or counter clockwise
noble anvil
We want your axes convention.
Ricky read my message
trail patrol
Oh, it dawned on me
halcyon lintel
what do you mean by that?
noble anvil
What is x and what is y for you
trail patrol
By fx and fy he means the components of each force
noble anvil
x is the horizontal?
halcyon lintel
the standard x (horizotal) y vertical axis
noble anvil
By fx and fy he means the components of each force
im aware
noble anvil
yeah ok then your x is the horizontal
halcyon lintel
why would x be the vertical?
noble anvil
now can you explain why you think f1x rotates about A at all?
halcyon lintel
that's what im askiing...it looks as if f1x is completely on the x-axis of point A
noble anvil
why would x be the vertical?
it can be anything, it's up to you to define it. If we had worked with a different axes convention than yours we would have had to redo the whole thing.
noble anvil
that's what im askiing...it looks as if f1x is completely on the x-axis of point...
Indeed
trail patrol
that's what im askiing...it looks as if f1x is completely on the x-axis of point...
Yeah, and what does that mean?
halcyon lintel
0
noble anvil
Wdym 0
noble anvil
So the moment of force is 0?
Correct
Now can u apply the same for fy
Keep the formula in mind btw
halcyon lintel
yea but the force isn't pointing 180deg. you can see it's pointing upwards to the left
so there must be some fx rotation
noble anvil
$MOF = Force * r_{perpendicular}$
rocky lotusBOT
Executor (ask on server b4 DM)
noble anvil
so there must be some fx rotation
We just determined that it passes through the perpendicular line
Which means $r_{perpendicular}=0$
rocky lotusBOT
Executor (ask on server b4 DM)
halcyon lintel
so if there's no rotation, is the fx value positive or negative?
im guessing positive then right?
noble anvil
Fx is the force, MOFx is the moment of force by Fx
Which one do you want, make it clear
halcyon lintel
you're kinda confusing me even more
trail patrol
so if there's no rotation, is the fx value positive or negative?
it depends on the adopted system, but in general it is negative (assuming a regular Cartesian system)
noble anvil
If you're finding MOF1x then there's no reason for us to care about F1X here
since $r_{perpendicular}=0$
rocky lotusBOT
Executor (ask on server b4 DM)
halcyon lintel
it depends on the adopted system, but in general it is negative (assuming a regu...
yea it's just the standard cartresian system otherwise i wouldve stated which system i was using
trail patrol
yea it's just the standard cartresian system otherwise i wouldve stated which sy...
Then it's negative since it acts to the left
halcyon lintel
thta's what i was thinking
trail patrol
But according to your question it doesn't matter
halcyon lintel
so f1x = its negative so doesnt that also mean it would rotate cw?
trail patrol
As already said
halcyon lintel
since cw = negative?
trail patrol
so f1x = its negative so doesnt that also mean it would rotate cw?
Nope
Re-read the previous messages
halcyon lintel
i dont know even know which message you're referring to
its ok...i
hopefully others will chime in
trail patrol
You wrote yourself that there is no moment from this component
Since the arm in respect to point A is zero
halcyon lintel
yea but didnt you also say the value was negative since the fx is pointing left?
trail patrol
Just because a force component has a value, it does not mean that it causes a moment
The moment is defined with respect to a point or axis (here with respect to a point), if we took another point it could exert a moment
If the arm weren't zero
halcyon lintel
can i show you a different example?
trail patrol
Yeah, sure
halcyon lintel
k one sec
trail patrol
Look here, it passes through A => the moment from this component in respect to point A is zero
trail patrol
Want to find out for yourself, it's simple, imagine towing a car, does the towed car rotate while driving?
trail patrol
,rccw
rocky lotusBOT
trail patrol
for f1x = no rotation?
Exactly
halcyon lintel
f2x = no rotation?
trail patrol
For f2x there is a rotation (according to the drawing)
halcyon lintel
if you took fx from the bottom though
wouldnt the force be going directly to the left on the x-axis of point a?
trail patrol
This doesn't matter, according to the axiom of mechanics a force can be moved along its line of action without changing the external effect it has on a rigid body
This means that the total moment about point A won't change anyway
halcyon lintel
ok so back to this example
becaues for forceX is pointing AWAY from point A...fx would cause no rotation
becaues regardless which FX you choose, top or bottom, it makes no difference
is that correct?
for Force2X, there would be CW rotation becaues it'spulling to the right about point A?
Force2Y = no rotation becaues it's pulling AWAY from point A?
trail patrol
This is true, but the question is why complicate things, besides you would have to determine the position of the force attachment point (and there are no grids in the upper position as you can see)
trail patrol
for Force2X, there would be CW rotation becaues it'spulling to the right about p...
I agree
trail patrol
Force2Y = no rotation becaues it's pulling AWAY from point A?
I agree x2
halcyon lintel
but dont you calculate the distance from the tail part of the force?
so for force 1
trail patrol
but dont you calculate the distance from the tail part of the force?
You calculate the arm of the force from the point of application of the force
trail patrol
f1y moment = 15*2
One grid is 2?
halcyon lintel
it should actually be 30
for f1y
cause the force is 30 (hypotenuse)
so if we scale up the height and width, y would be 30
trail patrol
It should be 34 * sin(15/17)
halcyon lintel
is that correct?
to get the moment of f1y?
if pictured the force as a triangle......h=15, w=8......we use py.theorem to find hypotenuse
so that would be 17
but the force is 34
trail patrol
I didn't get it, why do we have to scale that? First of all, these 15 and 8 are the dimensions of this force, right?
Yea
halcyon lintel
I didn't get it, why do we have to scale that? First of all, these 15 and 8 are ...
um
halcyon lintel
we scaled up the y and x so we can calculate the moment forces
or else the 15 and 8 dimensions wouldn't be scaled correctly with the 34N force
like a triangle that has
width=8
height=15
should have a hypotenuse of 34N
trail patrol
if 15 and 8 are the dimensions on which the force acts (i.e. in units of length), then you are wrong
halcyon lintel
so we use py.theorm with height and width which equals to 17 which gives us the hypotenuse
so now the triangle has
w=8
h=15
h=17
halcyon lintel
if 15 and 8 are the dimensions on which the force acts (i.e. in units of length)...
which?
halcyon lintel
its just the ratio or angle
like if you wanted to make a triangle out of the 34N force
34N would be the hypotenuse
so you just do arctangent
arctangent(15/8)
which is 61.9
but i dont need to figure out the angle right now cause i already know the FX and FY
remote current
if 15 and 8 are the dimensions on which the force acts (i.e. in units of length)...
Just multiply the forces by 1/2 and it makes sense, just dont forget to scale it back up when youre done with math. I assume one unit length in this case is 2N which is confusing
halcyon lintel
it just needs to be scaled up so that the width and height is equal to 34N (aka the hypotenuse
halcyon lintel
Just multiply the forces by 1/2 and it makes sense, just dont forget to scale it...
im the one that actually needs help lol
trail patrol
I understand your concept, and it's perfectly understandable, but yeah with such assumptions it makes sense
halcyon lintel
there's not really any assumptions
but anyway, this is beyond my original question....
trail patrol
Okay, let's proceed
halcyon lintel
not sure if even still understand the whole direction thing since we got so off topic
trail patrol
With the moments
remote current
Just confirming whether f4x is cw or ccw right?
halcyon lintel
i need to undestand the direction for fx and fy for all four forces
i keep getting them mixed up which messes up my final answer
trail patrol
So for f2 I agree completely
trail patrol
f2x - there is a moment CW
f2y - no moment
halcyon lintel
wait
trail patrol
Let's continue
halcyon lintel
dont give me answers for f3 f4
trail patrol
Ok
halcyon lintel
f3x = negative rotation....
because
like you mentioned earlier, if you take the top fx, it would rotate around point A ccw
correct?
wait
wait
its below point A
so its CW
or negative value
f3x = negative
f3y = no rotation
trail patrol
f3x = negative
You mean CW?
remote current
Depends which side of the point its on iirc
halcyon lintel
why? can cw mean positive in other contexts?
nevermind. lets just forget it.
ok f4
trail patrol
you can take any form you want for equations, the important thing is to stick to one convention
you will simply get opposite signs (as if you multiplied the equations by minus 1)
halcyon lintel
f4x = neg/cw
f4y = neg/cw
halcyon lintel
the first force messed me up
so because the force is pointing AWAY from the pivot A
FX will have 0 rotation
but if F1x was pointing the exact way but downwards, then Fx would be cw/neg right?
cause then the top f1x would be rotating cw around point A
trail patrol
I recommend you to draw the components of the force, it will be easier for you then
trail patrol
remote current
I have no idea how to approach f3, is it external force? Its not in the grid
trail patrol
And you were right before, f1x is 16 and f1y is 30, I got a brain lag š„²
I plugged sin(15/17) instead of just 15/17...
But nvm
halcyon lintel
noble anvil
I have no idea how to approach f3, is it external force? Its not in the grid
I think to visualise it better we can consider F3 as a free vector here, and displace it forward (to the left side)
this is just for understanding purposes btw
it is perfectly fine to solve f3 as it is
remote current
I think to visualise it better we can consider F3 as a free vector here, and dis...
Yeah fair, im just used to the scalar moment equation
noble anvil
it is perfectly fine to solve f3 as it is
Just need to use F* r_perp
trail patrol
in terms of direction understanding
Yes, they seem correct
halcyon lintel
this was another question i was given.....i think i was able to solve it as long as my directions are correct
fx = cw
fy = ccw
are my directions correct?
noble anvil
About which point
halcyon lintel
D
trail patrol
I have no idea how to approach f3, is it external force? Its not in the grid
The thing is in mechanics there is an axiom which says that without disturbing the equilibrium of a rigid body, we can move the point of application of a force anywhere along its line of action
noble anvil
Yes they are correct
noble anvil
The thing is in mechanics there is an axiom which says that without disturbing t...
? Is that a thing??
Hm
halcyon lintel
Yes they are correct
was that to my question?
noble anvil
yes
halcyon lintel
cool...thanks
noble anvil
? Is that a thing??
Ok now that i think about it it does seem like a thing
noble anvil
I think to visualise it better we can consider F3 as a free vector here, and dis...
Which is why this would work 
trail patrol
Let a force P act on a rigid body, applied at point B. At point A, a zero pair is added ā consisting of two equal and opposite forces: P1 and -P1. As a result, the system now consists of three forces: P, P1, and -P1. Next, a second zero pair is subtracted from the system ā consisting of the original force P (at point B) and the force -P1 (at point A).
In the end, only the force P1 remains.
This is why basically
halcyon lintel
thanks everyone for your help...i'll leave this chat open so you guys can continue your discussion
noble anvil
Alrighty, i gotta go now if you guys dont have anything else to say @trail patrol @remote current should i close
.close
sly cargo
how do i graph 23:36 on https://www.youtube.com/watch?v=x32Zq-XvID4
hot tide
how do i graph 23:36 on https://www.youtube.com/watch?v=x32Zq-XvID4
wdym by "how do i graph"
like how to make a graph like that?
sly cargo
wdym by "how do i graph"
yeah
how do i make a circle graph that moves like that
on desmos
glad minnow
why doesnt this work?
vale dockBOT
why doesnt this work?
plush crater
as x tends to 0, where does 1/3x tend to?
glad minnow
as x tends to 0, where does 1/3x tend to?
dne?
plush crater
so do u understand why we cant write 0
vale dockBOT
vale dockBOT
Available help channel!
crude swan
So i have a question, if x > -1 and x < 1, isnt there a decimals that fit both inequialities?
crude swan
lost marlin
final adder
well in the question it stated that x<-1 and x>-1, not the other way around
stark wedge
both inequalities involve -1 not 1
final adder
wait sorry typo
stark wedge
So i have a question, if x > -1 and x < 1, isnt there a decimals that fit both i...
you mean x > -1 and x < -1
the number in both is -1
and there is no such thing as a number that's both above and below -1 at the same time!
crude swan
i dont get it
stark wedge
do you think there's some number that fits both
x > -1
AND
x < -1
at the same time?
yes or no
crude swan
When x is > -1 i have drawen the line there, and when x < -1 i have draven the second line there, if we connect them we get some space between
stark wedge
what does this mean?
noble anvil
What is that
stark wedge
and you didn't answer my yes/no question
crude swan
and you didn't answer my yes/no question
i dont know, so i didnt answer because of that
crude swan
When x is > -1 i have drawen the line there, and when x < -1 i have draven the s...
When x is > -1 i have drawen the line there, and when x < -1 i have draven the second line there, if we connect them we get some space between
stark wedge
When x is > -1 i have drawen the line there, and when x < -1 i have draven the s...
those are two different points though
let me repeat myself:
it is impossible for x to be both left of -1 and right of -1 simultaneously!
crude swan
ok, i dont get it but ig its enough to know that this is the case then.
stark wedge
what's there not to get
like...
it is impossible for x to be both left of -1 and right of -1 simultaneously!
which part of this is unclear?
crude swan
well my example i draw, its making me confused
slate folio
you're confusing yourself
stark wedge
you're confusing yourself with it for sure
noble anvil
well my example i draw, its making me confused
What is that curve supposed to mean
stark wedge
can you simply read my statement WITHOUT looking at your own confusing drawing?
crude swan
What is that curve supposed to mean
When x is > -1 i have drawen the line there, and when x < -1 i have draven the second line there, if we connect them we get some space between
noble anvil
Ok, and that space ur talking about does not meet the conditions we need
Any point in that space
Will either be greater than, equal to, or less than -1
It cannot be any two of these three things at once
stark wedge
It cannot be any two of these three things at once
i said this exact same thing twice before but somehow it was not clear
noble anvil
Kek i didnt read sorry
crude swan
i said this exact same thing twice before but somehow it was not clear
You didnt talk about the space between the points.
but anyway
thanks
.close
bitter mural
How do I find AI and BI if <ABE = <CBD, and AB=6cm
vale dockBOT
How do I find AI and BI if <ABE = <CBD, and AB=6cm
bitter mural
Without using cos(60)*AB=AI
slate folio
just turn it into an equilateral triangle
bitter mural
just turn it into an equilateral triangle
I don't know if its an equilateral triangle
slate folio
reflect triangle ABI along the line AI
stiff lily
this setup looks sus
slate folio
ye idk what is this trying to do
bitter mural
reflect triangle ABI along the line AI
What would I do next?
bitter mural
can you see an equilateral triangle?
it looks like an isosceles triangle
slate folio
but there are two angles equal to 60
bitter mural
Oh yeah equilateral
stiff lily
<BAE = <CAD
under these conditions E and O would be the same point
bitter mural
> <BAE = <CAD
under these conditions E and O would be the same point
Oh I made a typo there
wait nvm
slate folio
> <BAE = <CAD
under these conditions E and O would be the same point
what the hell is E tho
oh you made a typo
stiff lily
in the original statment, E would have had to been the centre, from congruence/perp bisector theorem
question is fixed now
stiff lily
can you show the original question
why are you trying to do this without trig
bitter mural
I just realized that I misread the problem
I figured it out now
thanks for the help
.close
sinful belfry
hiiiii i need help i have a maths test tommorrow and im really scared
open niche
hiiiii i need help i have a maths test tommorrow and im really scared
Should then go ahead and study
If your goal is to do good
And come back here with any questions on what you dont understand
sinful belfry
Should then go ahead and study
I just have to pass
im really horrible at maths i have adhd and i just cannot do maths in general
i have a lot of formulas what do i do and how to approach them?
open niche
i have a lot of formulas what do i do and how to approach them?
Study the book
Fully
Dont just look at the highlighted stuff or whatever
You got a full day do 1 full reading
Of all the theory
sinful belfry
thing is all i struggle with is the exam questions neverrrrr are the way book exercises are presented
open niche
Then come here every time you get stuck understanding and ask
sinful belfry
You got a full day do 1 full reading
I don't have a full day only 1 night š¤£
open niche
thing is all i struggle with is the exam questions neverrrrr are the way book ex...
Dont go on exercises
First read 1 time the theory
In order
slate folio
Then come here every time you get stuck understanding and ask
do not ask during the exam tho
sinful belfry
theories wont help because the tests are from exercises :c
open niche
If you dont understand something come ask
sinful belfry
*do not ask during the exam tho*
what if I do š
sinful belfry
ok but genuinely if i could I'd just use chatgpt
open niche
You ask before a test question to better understand theory so you can apply it
slate folio
what if I do š
šØ
noble anvil
what if I do š
sinful belfry
I am a psychology student I DO NOT NEED MATHS
open niche
If you dont understand theory you cant use it most of the time
sinful belfry
<:Ban:676361542714785803>
rlly???!
open niche
If you dont understand theory you cant use it most of the time
And questions probably boosts progress by a crazy amount
sinful belfry
damn bro š
stark wedge
yeah test cheating is a bannable offense on here no exceptions
sinful belfry
thought u guys r chill lol
alr alr
but genuinely if they were gonna cheat
and had their phones with them
just use gpt man
open niche
I mean up to you what you do
sinful belfry
nah i have to study phones arent allowed.. š
noble anvil
thought u guys r chill lol
Nah we're extremely unchill
noble anvil
Nah we're extremely unchill
Giant sticks up our butts fr
sinful belfry
smoking za while i do maths šÆ
frozen ledge
sinful belfry
LMAOOOOOOOO
open niche
How is there no auto ban
sinful belfry
LMAOOAO stop as a kanye fan thats FUNNY
noble anvil
How is there no auto ban
It did prolly
rigid whale
hiiiii i need help i have a maths test tommorrow and im really scared
Just practice the problems a lot
slate folio
there's a movie on japanese exam cheating technology tho...
rigid whale
Math is not something you can learn over night
open niche
It did prolly
Damn delay crazy
rigid whale
To learn math, you must practice
sinful belfry
there's a movie on japanese exam cheating technology tho...
thank god im serbian š¤£
sinful belfry
Math is not something you can learn over night
BRO I HAVE TOOOOOOOO PASSSSSS
rigid whale
thank god im serbian š¤£
iz cega imas kontrolni majke ti
sinful belfry
JUST PASS..
sinful belfry
iz cega imas kontrolni majke ti
OMGGGGGGGGGGG
sinful belfry
iz cega imas kontrolni majke ti
ur serb??? š
rigid whale
yeah
sick yacht
Need some assistance with these 2 polynomial function graphs
This is my progress, any thoughts?
frozen ledge
Need some assistance with these 2 polynomial function graphs
when is the test due?
how much time is left to finish your test
sick yacht
Itās not a test just self practice
frozen ledge
sick yacht
Iām serious
frozen ledge
sick yacht
Parents want me to study to take calculus next year so I am practicing to take a credit by exam
So this is self taught and I have been using YouTube videos for most things until I got confused with this
frozen ledge
so why does it tell you to print it out and submit it for grading
(16 points)
in ninth grade they made me do the same shit
sick yacht
It is a pdf of a quiz?
frozen ledge
good luck bro
sick yacht
But itās not for a grade because I am doing it for practice
frozen ledge
šš»
stark wedge
Need some assistance with these 2 polynomial function graphs
!occupied
vale dockBOT
Need some assistance with these 2 polynomial function graphs
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #āhow-to-get-help for instructions).
stark wedge
this is @sinful belfry's help channel even though the name doesn't show up
vale dockBOT
sinful belfry
But itās not for a grade because I am doing it for practice
use gpt lol people here won't help
wow he got banned?
vale dockBOT
Available help channel!
restive crest
so, i gotta find all z in C (C for set of complex numbers) such that.
restive crest
What i tried is, let z = a + bi -> z = |z|(cos x + sin x) = |z|e^(xi)
then z^5 = ((|z|)^5)e^(5xi) then 3(z^5) + 2(|z|)^5 + 32 = 0 -> 3(((|z|)^5)e^(5xi)) + 2(|z|)^5 + 32 = 0 but since 2(|z|)^5 is a real and has no imaginary part, then 2(|z|)^5 + 32 is also real and has no imaginary part, but this is only possible if 3(((|z|)^5)e^(5xi)) also has no imaginary part which implies e^(5xi) = 1 which is only possible if 5x = pi + 2kpi for some integer k, then e^(5xi) = 1 and 3(((|z|)^5)e^(5xi)) + 2(|z|)^5 + 32 = 0 -> 3(|z|)^5) + 2(|z|)^5 + 32 = 0 -> 5(|z|)^5) + 32 = 0 -> (|z|)^5) = -32/5
is the way i'm solving this right?
merry crystal
e^(5xi) = 1
what are you doing here
restive crest
can it be any other value? i need 3(((|z|)^5)e^(5xi)) to be -2(|z|)^5 - 32 which is real and has no imaginary part
that implies 5x = pi + 2(pi)k for some integer k, right?
merry crystal
or just Ļk
restive crest
oh, wait, can also be e^(5xi) = -1
restive crest
hmm, thanks for the correction, let me keep attacking the problem
vale dockBOT
@restive crest Has your question been resolved?
restive crest
now consider k even and odd
i don't understand well why i have to consider both k even and odd for 5x = pi + 2(pi)k, can't i just say x = (pi + 2(pi)k)/5 for any 0 <= k < 5?
k being an integer/natural of course
merry crystal
for k even, we have
5r^5 = -32
we want solutions with r>0
since we took it to be the modulus
restive crest
hmm, let me re-read the material, i don't understand 100% this
wraith barn
HI UYS
merry crystal
,w 1+1
rocky lotusBOT
merry crystal
something like that
merry crystal
no problem
spring jackal
$1 + 1 \equiv 0 \pmod 2$ actually
rocky lotusBOT
haseeb
spring jackal
winter crater
Could someone help me figure out what I'm doing wrong? The assignment specifically asks for induction, and a,h are positive reals
wild linden
,rccw
rocky lotusBOT
wild linden
@winter crater you messed up the inequality
winter crater
Where?
winter crater
In the case of k+1?
winter crater
I see, thank you. I'll take another crack myself in the morning š¤¦
wild linden
Well, technically also the second one doesn't need one. Because it's a^1 but that's probably what messed you up
winter crater
Yeah, I think I was looking at that a instead of the one in the statement
magic sentinel
How Do I do part ii)
vale dockBOT
How Do I do part ii)
wraith heart
Yea
magic sentinel
how do I do it without coz the test aint give me one
also, do I use x = 9 or x = 8.5
magic sentinel
but how can I find all those given that n is not found
They go on to form a quadratic from this
i understand mu and sigma, but how did they -0.4. Also for normal approx, shouldnt we use continuity correction
@wraith heart do you calculoate z score from calculator stat function or smthn
magic sentinel
How Do I do part ii)
<@&286206848099549185>
vale dockBOT
@magic sentinel Has your question been resolved?
magic sentinel
ik how to read one
but i wouldnt have access to one during an exam
How did they calculate the z score
to be -4
without on
stone aspen
<@261933205387477002> do you calculoate z score from calculator stat function or...
which calculator
magic sentinel
How Do I do part ii)
I'll start from the beignning
Can someone explain how they got -0.4 as the z score
mystic harness
You will be given a chart or calc on your exam
magic sentinel
if they didnt have table
mystic harness
Or, they'll give you a few values you need
magic sentinel
You will be given a chart or calc on your exam
In this exam there wasnt a chart
unless they got on the day itself
mystic harness
<@&268886789983436800>
magic sentinel
My second question is
Why did they not use continuity correction
If its normal approximation
Should it be 8.5 instead of 9
stone aspen
not using continuity correction can be excused due to the specification
of a LARGE sample space
magic sentinel
can i simplify root 0.09 n to 0.3 root n
stone aspen
LARGE pool of people, the Ā±0.5 can be excused (hoeever i do agree it sjouldve been used)
gilded barn
ahhh sure excused
stone aspen
makes the algebra cleaner
stone aspen
can i simplify root 0.09 n to 0.3 root n
i dont see why not
as for the z score i once again ask you what calculator you have
but tbh inferring from the fact that it's given to 4dp it's highly highly likely a table was given
magic sentinel
it was not given in the paper
i assume that that the teachers handed it out not part of the paper
hence not shown
gilded barn
without table , you have to calculate this yourself
$P(Z \le z)=\int_{-\infty}^{z} \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}dx$
rocky lotusBOT
ćøćć»ć¼
stone aspen
it was not given in the paper
tables are usually given out in extra material
like formula sheets
the question sheet will usually just contain.... questions
magic sentinel
in our syllabus, usually given out as part of question
like a small relevant portion of the table
stone aspen
hmm well is the above integral in your syllabus
magic sentinel
im assuming the students did use it but not like within the test paper of formula sheet
magic sentinel
hmm well is the above integral in your syllabus
i dont think so
our teachers say its a long and complex formula
so i assume its not taught
anyway most likeley they used formula sheet
I got n = 97 with continuity correction
thanks guys
.close
vale dockBOT
vale dockBOT
Available help channel!
stuck night
can someone teachme how to solve this ?
vale dockBOT
can someone teachme how to solve this ?
tidal swift
so the boats have rectangular cross-sections
unreal warren
this is always something I like to do, just break down the question
tidal swift
sketch them on your diagram. what do they look like?
unreal warren
yumi wake up...
unreal warren
stuck night
thanks in advance
unreal warren
so breaking down the question:
tidal swift
have you tried sketching the boat on the diagram?
stuck night
not yet
tidal swift
give it a shot
tidal swift
what does it remind you of?
what is the line that the bottom of the boat makes called (as a part of the circle)?
unreal warren
main question: if waterway is filled with 4.5 ft of water underground, what is the max width the boats can be?
oh nvm
seia is probably smarter than me š
stuck night
what is the line that the bottom of the boat makes called (as a part of the circ...
semi circle?
stuck night
okay im bad this ;-;
stuck night
uhh
tidal swift
(the corners of that line touch the semicircle. sorry for poor drawing)
stuck night
i knoiw that but i forgot tyhe name.. QnQ
cloud coral
secant?
tidal swift
it's not a secant
it doesn't extend past the semicircle
calling that a secant implies the boat can puncture the waterway
tidal swift
i knoiw that but i forgot tyhe name.. QnQ
aye alright, i'll give you the name
this line is called a chord
stuck night
š„ŗ it went over my head
tidal swift
aye anyway
stuck night
kinda liek this
tidal swift
yep, correct. but now we don't have the angle. but we do have the radius
stuck night
yes