There are 6 ways with 6 and 0 with 7 though
#help-43
near crown
near crown
Yes
rich jay
hmmmmmm
maybe the student who wrote these is wrong
or the professor made a mistake
gpt o4 mini high says the same as us
6 for 6 and 0 for 7
near crown
yeah
rich jay
okay thanks bud, my whole class dosen't know the answer, bunch of potatos i guess xd
solved
near crown
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near crown
np
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untold wagon
I do not know where to begin:
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I do not know where to begin:
untold wagon
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untold wagon
<@&286206848099549185>
Anyone helping?
<@&286206848099549185>
<@&286206848099549185>
wide herald
untold wagon
i cannot make a large screenshot. just presss on each of them
untold wagon
<@&286206848099549185>
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long vigil
!status
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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
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untold wagon
yes i do not exactly understand how to comprehend the q
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plush mantle
I have to proof the circular motion of particle in this task. And this is the beginning part ,however, I do not understand how get Fx, Fy, Fz from calculating matrix I got j(dz/dt)Hx - k(dy/dt)Hx from this answer how we get thos projections??
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I have to proof the circular motion of particle in this task. And this is the be...
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lilac zinc
Я не очень понимаю обозначения но похоже что у тебя константный угловой момент, отсюда ты можешь вывести что траектории будут кониками
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pure cedar
A company produces computer at a cost of cx = 5000 + 3x dollar, where x is the number of computers produced, the selling price os each computer is sx = 15x + 200 sollar
find the revenue function rx in terms of x where rx reperesent the total revenue when x computers are sold
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A company produces computer at a cost of cx = 5000 + 3x dollar, where x is the n...
torn rose
I think revenue is like selling minus the cost
Revenue is supposed to be like profit I think
pure cedar
i checked dy
revenue is just the selling cost
cuz they say 100 dollar in sales is equal to 100 in revenue
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barren dawn
This looks like sx - cx = rx? Is this what you're looking for?
Revenue isn't only about selling, it's about making a profit after paying off the cost.
barren dawn
Yeah, revenue is the earnings in this context.
You factor in both the sales and the cost of manufacturing.
pure cedar
but that wont make sense cause at question b its looking for the profit
so it will be the same equation no?
profit will still be the sales - the cost
barren dawn
I think the first question asks you to stage the equation and the other question is for looking for the profit of x amount of computers?
pure cedar
find the prodit function px in terms of x where px reperesent the total profitwhen x computers are sold
barren dawn
This might take a minute.
pure cedar
its an easy question just i cant get around how they are wording this
barren dawn
I took a second look and it looks like rx = sx and px = sx - cx?
barren dawn
You can just flip it around.
pure cedar
i thought of this but i just dont know why its so easy
barren dawn
Maybe in larger operations, there are more factors from multiple functions? I believe it's for a little modular intuition here.
It is just that easy.
pure cedar
also when u wanna find the vertex of a quadtratic u use the form fx = a(x-p) power of 2 + q ya?
u just rewrite it
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fringe lichen
Hi, Im supposed to show that given a real vector space V and $v \in V{{0}$, span(v) is the smallest non trivial subspace, that is contained in span(v)
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Hi, Im supposed to show that given a real vector space V and $v \in V\{{0}$, spa...
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p1za
fringe lichen
Now my idea was to let U be some other subspace of V that is also contained in span(v)
and to show that $span(v) \subset U$
boreal girderBOT
p1za
fringe lichen
but since we assume $U \subset span(v)$ they both need to be equal no?
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p1za
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formal stirrup
in my fluids book it says that because the flow is incompressible and of uniform density in a constant cross section siphon, then the speed of the flow in the siphon must be constant due to the rate of volumetric flux being conserved
compact pewterBOT
in my fluids book it says that because the flow is incompressible and of uniform...
formal stirrup
however when i was doing another question, the fluid was draining out of a tank with constant cross section and it was slowing down as its height decreased (dependence on height)
how come it varies in this case but doesnt vary in the above case?
rigid perch
the speed of the flow must be constant across space (within a region of constant cross section), not necessarily across time
formal stirrup
but in this example they say the speed of the flow is the same at the top of the siphon and at the bottom
gilded urchin
as the amount of water in the tank decreased the pressure decreases and force is changing so density x acceleration x length changes
rigid perch
but in this example they say the speed of the flow is the same at the top of the...
at any given time, yes
formal stirrup
at any given time, yes
but
then how is there dependence on height
at any given time wouldnt the speed of the fow be faster at the top?
rigid perch
it's a dependence on the current height of the free surface relative to the bottom of the tank, not on the vertical coordinate of any other point under consideration
formal stirrup
ohhh
wait
so at the point of the free surface when it hits the top of the siphon and when it hits the bottom of the siphon the speed is the same
but
rigid perch
so the velocity at point P in this diagram depends on h, but not on z
formal stirrup
then how come u can use bernoulli's equation to find the pressure distribution throughout the fluid by asssuming the speeds at both points are the same
rigid perch
so the velocity at point P in this diagram depends on h, but not on z
because in this diagram the flow speed doesn't depend on z, it is the same at z = 0 as it is at z = h
formal stirrup
so the velocity at point P in this diagram depends on h, but not on z
like here
they assume the speed of the flow at B and C is equal to find the pressure distribution across the fluid in the siphon?
rigid perch
it must be equal at B and C, since the velocity at B is Q/A and the velocity at C is Q/A
gilded urchin
the speed in a pipe is equal because its area of cross section is equal at any given point
formal stirrup
but isnt the the pressure throughout the fluid aka not at the surface
u said that the speed at B and C is equal when the surface of the fluid reaches those points
gilded urchin
think of it like this: when some amount of water leaves point C then theres a pressure difference which is taken away by equal amount of water at B by being displaced towards C and we know v = Q/A, A=const , Q= const, therefore V=const
rigid perch
wdym by "the surface of the fluid"? the siphon is full of fluid, there is no surface unless you count the walls of the siphon
formal stirrup
it's a dependence on the current height of the free surface relative to the bott...
oh what did u mean by this then
maybe i didnt get it
rigid perch
that's for the case of draining a tank
formal stirrup
i think i cget what u mean now tho, like the fluid speed does change but at that given point in time throughout the siphon its constant?
so at the height h_0 let's say the speed of the fluid is constant throughout the siphon (due to incompressible flow of uniform density in a constant cross section siphon), but the speed will change as it moves through the siphon
rigid perch
the speed is the same throughout the siphon, but that speed will change over time, yes
formal stirrup
ye i got it now
gilded urchin
the speed is the same throughout the siphon, but that speed will change over tim...
the speed of all water molecules at any given time are constant? even if the molecule is just outside the tank but somewhat in the stream?
rigid perch
well the speed of the fluid is, which is in general a sort of "local average" speed of the individual molecules
and given the assumption that the fluid is inviscid and incompressible, and the flow is 1D
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cedar solar
Hey guys, I need to find x>0 to this series to be convergent. I found 0<x<1. But the answer sheet says it is 0 < x equal or less to 2. Any chances of it being wrong?
compact pewterBOT
Hey guys, I need to find x>0 to this series to be convergent. I found 0<x<1. But...
short ferry
Hey guys, I need to find x>0 to this series to be convergent. I found 0<x<1. But...
I think you're right
it converges for -1 <= x < 1
cedar solar
yeah, but the question limits it to x>0, so I came up with 0<x<1
perhaps the answer sheet is indeep wrong so
short ferry
either that, or perhaps you misread the question
but its possible that the answer sheet is wrong, it happens
cedar solar
Determine x>0x>0 so that the given series is convergent
letter b
I think what I did is right, i'll keep up with that
ty
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frank zodiac
Am i setting this up incorrectly?
jacobian is -1
x = 5u + 4v
y = -u-v
compact pewterBOT
Am i setting this up incorrectly?
jacobian is -1
x = 5u + 4v
y = -u-v
kind crane
show how you got your limits
frank zodiac
it's just determinant of partial x/partial u, partial x/partial v, partial y/partial u, partial y/partial v right?
long delta
U just derivate for jacobian
kind crane
show
frank zodiac
OK
u = x + 4y (eq 1)
v = -x-5y (eq 2)
Solve eq 1 for x
x = u - 4y (eq 3)
Substitute into eq 2
v = -(u-4y)-5y
Solve for y
y = -u-v
Substitute into eq 3
x = u - 4(-u-v)
x = 5u + 4v
@kind crane
kind crane
looks right
did you make a rounding mistake
or are you supposed to leave in exact form
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frank zodiac
or are you supposed to leave in exact form
okay thank you so much, maybe there is issue in the system i will send to my professor even tho he take like 2 day to reply
next latch
how to do this? i don’t know how i would find angles or find vector a plus vector b from this point onward
compact pewterBOT
how to do this? i don’t know how i would find angles or find vector a plus vecto...
next latch
yeah so i first drew those two lines
then i changed the location of vector a
so that it would be tip to tail to vector b
kind crane
that doesn't look like 40 degrees
next latch
and then i added them together, forming the resultant vector
kind crane
you're not asked to find the direction of a+b, but a-b
next latch
oh
next latch
let me try that
thank u
what is it asking me to find when it asks for the direction?
like the angle…?
i’m confused
@kind crane
that’s what i did
that’s what i did for question b) as well but idk if it’s right
<@&286206848099549185>
kind crane
like the angle…?
unclear to me, but yea angle is one interpretation
use $\vec{u} \cdot (\vec{v}-\vec{w}) = \vec{u}\cdot \vec{v} - \vec{u}\cdot \vec{w}$
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riemann
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acoustic yarrow
which ever gives u a positive answer
junior vault
well you know the two curves intersect at x = -1 and 3 so in that region one must be greater
can plug in a value in the region to determine which one
(x = 0 would be most optimal here)
junior vault
well the way you find the area between curves is you subtract the greater curve's area by the smaller one
junior vault
yes
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granite mortar
Im trying to solve question e, since its absolute value do I just find the integral of both -x and x and then add them together?
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Im trying to solve question e, since its absolute value do I just find the integ...
subtle zealot
|f(x)| in this case makes any negative f(x) positive
so that means if your function dips below the x axis, reflect it so it becomes above the x axis then take the area of that
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restive monolith
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restive monolith
what did i do wrong
the correct answer is 3pir
fuck
nvm i see
i wrote y incorrect at the start
<@&286206848099549185>
I got the wrong answer again
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dawn quiver
when you multiplique (1-cos theta) (1-cos theta) = 1 - 2 cos theta + cos theta * cos theta
you wrote - cos theta * cos theta
restive monolith
you wrote - cos theta * cos theta
oh i see it
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gilded atlas
Can someone help explain where this guy got the 3000/250 from? Why did he suddenly double it
compact pewterBOT
Can someone help explain where this guy got the 3000/250 from? Why did he sudden...
stark marsh
Can someone help explain where this guy got the 3000/250 from? Why did he sudden...
*2/2
easier to simplify
short ferry
Can someone help explain where this guy got the 3000/250 from? Why did he sudden...
its basically the same thing as dividing both the numerator and denominator by 5
and a particularly simple way to divide stuff by 5 is multiply it by 2 and then divide by 10
since multiplying by 2 is quite easy, and dividing by 10 is even easier (just cancelling 0)
gilded atlas
Can I apply this method of multiplying by 2 and then dividing it by 10 to any question if I ever encounter something similiar where I could divide both the numerator and denominator by 5?
short ferry
Can I apply this method of multiplying by 2 and then dividing it by 10 to any qu...
Yeah, definitely
you can also just use it in your head, thats probably simpler
i use it whenever i need to divide sth by 5
carmine garden
I'm trying to integrate the given function over the given curve, the function whose gradient is F is is y^2 arctan(x)
\
We thus have 2t\cdot \arctan(t^2), which when integrate gives 2π/4
compact pewterBOT
I'm trying to integrate the given function over the given curve, the function wh...
carmine garden
is that right
carmine garden
Just trying to figure out what causes this discrepancy
wait, did I make a mistake
yup
timid lodge
oh lol
timid lodge
oh guess I messed up too lmao
this is what i get for doing things in my head, I feel you
carmine garden
one last one
I'll do part (b) first
Trying to figure out what F is the gradiennt of
nothing, I suppose?
I'll have to brute force this, won't I
timid lodge
might have to if it isn't immediately obvious yeah
you know the denominator of grad f has to be x^2+y^2, so itll be some quotient rule junk
carmine garden
,w derive \sqrt{1+{y^2}/{x^2}} wrt x and y
boreal girderBOT
carmine garden
nope, this ain't it
ln(x^+y^2) and \sqrt{x^2+y^2} won't work either
ooh
arctan(y/x)
,w derive arctan(y/x) wrt x and y
boreal girderBOT
carmine garden
that works
it isn't defined at the origin, thus it isn't path independent on R^2
does that work
timid lodge
issue is that just because the mixed partials are equal, it does not imply path independence
if they're asking you to show b is true, it means you can't find a grad f for this field
fair raft
F is closed but not exact idk if it helps
try to integrate F on the unit circle, it will give u a non zero value and then use green theorem to show that for any closed loop not enclosing the origin, the integral should be 0
it should work
pearl sierra
Doesn’t showing that in part a) they’re not equal to each other show that it’s not path independent
carmine garden
issue is that just because the mixed partials are equal, it does not imply path ...
yea
pearl sierra
By greens
carmine garden
Doesn’t showing that in part a) they’re not equal to each other show that it’s n...
right
fair raft
Doesn’t showing that in part a) they’re not equal to each other show that it’s n...
no
domain needs to be simply connected
F is undefined at (0,0)
fair raft
try to integrate F on the unit circle, it will give u a non zero value and then ...
do this
pearl sierra
Oh ok yes that is true
carmine garden
try to integrate F on the unit circle, it will give u a non zero value and then ...
got it
thanks
I'll close this for now, if that's fine
fair raft
np u welcome
carmine garden
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dark ermine
The series doesn’t converge for x>=1 for sure
slim garnet
The series doesn’t converge for x>=1 for sure
so then x has to be less than 1 as per geometric?
dark ermine
so then x has to be less than 1 as per geometric?
It just shows the radius must be less than or equal to 1. This is not just a geometric series because of the (n+1). You need to use the ratio test to find the correct radius of convergence
slim garnet
yess I simplified using the radius test to limit n to infinity |x^n|
dark ermine
Yeah then 1 should be correct
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ionic niche
Did I do this right?
compact pewterBOT
Did I do this right?
twilit quail
yeah but make ur steps clearer. I was confused by this, but i get what u mean
and then plug x into the original equation to get a point
wanton inlet
A good way to quick check is calculate y with the x value you found, then go graph the original function , either by hand or desmos, and see the point you computed, if it was a critical point or nah, (lowkey this is tedious now that im typing it out)
Ofc you’re welcome here anytime either way
ionic niche
yeah but make ur steps clearer. I was confused by this, but i get what u mean
Oh yeah I skipped a few steps but Ty
ionic niche
A good way to quick check is calculate y with the x value you found, then go gra...
Ig yeah I did do that, but If I didn’t include 0 as on one of my critical points would I be marked wrong
woeful basalt
Ig yeah I did do that, but If I didn’t include 0 as on one of my critical points...
Do we have to show the biceps?
ionic niche
Do we have to show the biceps?
Lmao my bio is. Joke with my friends don’t take that too literal
wanton inlet
Ig yeah I did do that, but If I didn’t include 0 as on one of my critical points...
Nope, it just isn’t one
woeful basalt
Lmao my bio is. Joke with my friends don’t take that too literal
I’ll send if you actually want
😭
wanton inlet
Aight the cat is going wild im out
ionic niche
Nope, it just isn’t one<:catwhy:608492030489919508>
At what point would I have gotten 0?
ionic niche
I’ll send if you actually want
I mean I doubt I’ll be impressed but sure LMAO
woeful basalt
I mean I doubt I’ll be impressed but sure LMAO
mean but alr
wait so
what answer did yall get
@wanton inlet
the critical point I mean
Because erm … x = 1 is the actual critical point..
wanton inlet
At what point would I have gotten 0?
At 0 and i think another number since it’s a quadratic, maybe it’s a complex value, either way why would 0 be a critical point in this instance?
wanton inlet
Because erm … x = 1 is the actual critical point..
It is
wanton inlet
Actually yeah
woeful basalt
x = 1
wanton inlet
Yeah
wanton inlet
Now this convo made me sure i need sleep
ionic niche
At 0 and i think another number since it’s a quadratic, maybe it’s a complex val...
i wish I can do math in my head
Oops I didn’t mean to do that
woeful basalt
i wish I can do math in my head
ionic niche
wait I just searched the answer and it said one of the critical points is (0,0) ;-;
What would that possibly mean
twilit quail
wait I just searched the answer and it said one of the critical points is (0,0) ...
x can't be 0 because you can't divide by 0
ionic niche
x can't be 0 because you can't divide by 0
Yeah ik
wanton inlet
Mathway
You can peacefully ignore it
Not because it’s mathway
But because the derivative didn’t show it
If there was another value
ionic niche
yeah I figured, Ty queen
wanton inlet
It wouldve been x to the power of two
wanton inlet
yeah I figured, Ty queen
Anytime
ionic niche
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wicked lake
what i have so far
a = 4
u = e^10x
du = 10e^10x dx
and i think the formula is for arcsin
arcsin(u/a) + c
bronze narwhal
what i have so far
a = 4
u = e^10x
du = 10e^10x dx
and i think the formula i...
$$\sqrt {a^2 - u^2}$$ is what u wanna achieve
boreal girderBOT
JustToPro
bronze narwhal
so thtas why u converted 16 into 4^2 and got a as 4
why not do the same with the "u" term (e^10x) D:
bronze narwhal
yeah i think thats good
wicked lake
how about the other problem
bronze narwhal
,w integrate e^(5x) / sqrt(16-e^(10x))
boreal girderBOT
bronze narwhal
ok , whats the other problem
wicked lake
here
boreal girderBOT
bronze narwhal
i mean yeah
but usually we pick u , such that the function is simplified way more
bronze narwhal
like here u = e^5x simplifies the function so much and the top is gone
imagine if u did u = e^10x , like u said (woulldnt be so ez)
!done
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cinder owl
btw the matrix A is just the matrix to the left of the line
thick rose
What exactly are you struggling with?
cinder owl
i dont even know what it is asking about
like what is x
and how does a matrix multiplied by it become e1
kind viper
like what is x
the vector of unknowns in a linear system
have you ever seen a system of equations written in matrix form?
cinder owl
have you ever seen a system of equations written in matrix form?
yep
so we multiply the vector x by A and see if that can equal e1
?
kind viper
you could say that...
cinder owl
ok for the first q i get x-zm=1
y+z(m+3) = 0
z(m(m+3))
=0
is this the right steps
compact pewterBOT
@cinder owl Has your question been resolved?
cinder owl
@kind viper
kind viper
m(m+2)z not m(m+3)z
otherwise thats correct for writing out the system Ax = e_1 in equation form
can you find a value of m for which this system has no solutions?
kind viper
no
look at the last equation, which only involves z and no other variables
z * m(m+2) = 0
is it possible for m to be such that there's no value of z which makes this work?
this is going to be a "think about this" question not a "plug shit into a formula" question
cinder owl
z could be 0 no matter what m is right
and if z=0 then y=0
and x = 1
for e2,
z * m(m+2) = 1
m could be 0 but then u would get 0 = 1
same for -2
@kind viper
kind viper
z could be 0 no matter what m is right
yes exactly
so in fact this system is always consistent
cinder owl
Ok
cinder owl
so in fact this system is _always_ consistent
but then for ii its not consistent when m=0,-2?
kind viper
indeed
compact pewterBOT
@cinder owl Has your question been resolved?
kind viper
it says its wrong
can you show part (a) for reference
i think we may have missed something
which is also kind of making me confused about it all lol
cinder owl
can you show part (a) for reference
kind viper
ok right
so then in fact the system Ax = e_3 corresponds to taking this submatrix
and the last equation is not m(m+2)z = 1 but m(m+2)z = m+2
which is consistent for m=-2 (but for m=0 it still isn't)
and actually our reasoning was wrong for Ax = e_1 but we got lucky
Ax = e_1 would have required this
cinder owl
is this because the matrix M is actually not the matrix A, but instead its the matrix you get after she does the row echelon stuff
so for the first question it wouldve been m+3=0?
kind viper
is this because the matrix M is actually not the matrix A, but instead its the m...
yes
kind viper
so for the first question it wouldve been m+3=0?
no
for (b)(i) the crucial equation would still be m(m+2)z = 0
and that's still always consistent
cinder owl
oh right yeah
why do u take the first column for e1 and the third for e3
why isnt it rows
kind viper
rows mean individual equations within a system...
it would make no sense to try and pluck a row out of the right half of this aug matrix
cinder owl
that means that the columns are all potential solutions for the left matrix
but still
at the start, when u had the original matrix A they said they appended the identity matrix on the right
what is the connection between that and solving for e1
like if they had appended a different matrix
would that mean you would then be solving for that new one
wait nvm
i think i get it
solving for e1 for matrix A is the same as solving for [0,1,0] for matrixM
kind viper
i dont have enough energy to say anything more nuanced than "yes" right now
cinder owl
ok makes sense ty
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keen glacier
If you have a surface {z = 4-x^2-y^2, z > 0}, and you plug in x^2+y^2 = 5, would the result be undefined? or what would it be?
compact pewterBOT
If you have a surface {z = 4-x^2-y^2, z > 0}, and you plug in x^2+y^2 = 5, would...
hushed magnet
it just means that there is no intersection between those surfaces
keen glacier
don't we need to find the domain first?
which is x^2+y^2<=4 I believe
so anything outside the domain u can't plug in
compact pewterBOT
@keen glacier Has your question been resolved?
faint dawn
hey, ive got to calculate this determinant, and from what ive seen, some people got to a triangular matrice but i dont really understand how to. can anyone explain please? ive tried but instead the closest things ive got to is something like:
1 2 ... n-1 n
1 -1 .. -1 -1
. . . .
. . . .
0 0 (2) 0 0
0 0 2 0
compact pewterBOT
hey, ive got to calculate this determinant, and from what ive seen, some people ...
@faint dawn Has your question been resolved?
compact pewterBOT
@faint dawn Has your question been resolved?
faint dawn
.close
quartz yoke
small confusion with the definition of function
consider R: A->B
then does every element of A need to have an image of it
compact pewterBOT
small confusion with the definition of function
consider R: A->B
then does every...
sturdy forge
no if B is the codomain, yes if B is the image
quartz yoke
no if B is the codomain, yes if B is the image
mhm
sturdy forge
I think usually B is written to be the image
quartz yoke
yea
sturdy forge
wait sorry I misread your question
the answer is yes
because A being the domain of R means that R(a) is defined for all $a\in A$
boreal girderBOT
00100000
quartz yoke
👍 thanks
sturdy forge
I originally thought you were asking if A is necessarily surjective 😅 my bad
quartz yoke
.solved
flat inlet
Can anyone check my proof for exercise 20:
-Closure under addition
{a_n+b_n} is in V because it is a sequence with real entries (from closure of fields such as the realms under addition). It is unique because the sum of each entry a_n+b_n is unique by field axioms
-Closure under scalar multiplication
Similarly seen from closure of multiplication in fields
-Addition is commutative and associative
Follows from commutativity and associativity of fields
-Existence of zero vector
Define {0_n} such that 0_n=0 for every natural number n. Then we verify that {a_n}+{0_n}={a_n+0_n}={a_n} from additive identity of a field.
-Additive inverses of vectors
For arbitrary sequence {a_n} in V define {(-a)_n} such that (-a)_n=-(a_n) for each n. Then it is easy to verify indeed that {a_n}+{(-a)_n}={0_n} from additive inverses of fields.
-1x=x for each vector x
Follows from multiplicative identity for fields such as the realms
-(ab)x=a(bx)
(ab){a_n}={(ab)a_n}={a(ba_n}}=a({ba_n})=a(b{a_n}) from associativity of multiplication for fields
-a(x+y)=ax+ay
a({a_n}+{b_n})=a({a_n+b_n})={aa_n+ab_n}={aa_n}+{ab_n}=a{a_n}+a{b_n} from distributivity of multiplication over addition for fields
-(a+b)x=ax+bx
Similar to the previous one but makes use of distributivity with commutativity of addition
compact pewterBOT
Can anyone check my proof for exercise 20:
-Closure under addition
{a_n+b_n} is...
flat inlet
Oh
flat inlet
Np
lime juniper
Can anyone check my proof for exercise 20:
-Closure under addition
{a_n+b_n} is...
looks good, but I would say you have to explain why you know that {a_n+b_n} converges if a_n and b_n do. It could be a short explanation, but you should say it anyway
compact pewterBOT
@flat inlet Has your question been resolved?
tight aurora
compact pewterBOT
tight aurora
Am I missing something or are dy/dt and dx/dt mixed up?
kind viper
yeah looks like they are
tight aurora
Don’t go to Rutgers guys
civic quartz
who
tight aurora
I’ve found so many mistakes in this guys notes
eternal pulsar
On a scale of 1 to 10, how fucked are you for your finals?
civic quartz
oh
tight aurora
On a scale of 1 to 10, how fucked are you for your finals?
For Calc 2 I think I’m chillin and that’s my hardest class this sem
Got 72 80 and 86 on my midterms which are all a B lol
improvin tho
warped oar
Out of?
eternal pulsar
Lock in 😭
warped oar
bruh
tight aurora
What
warped oar
Which class are you?
tight aurora
Class of 28
eternal pulsar
Yeah
tight aurora
I got all A’s rest of my classes
eternal pulsar
Good luck with that GPA man 
tight aurora
Good luck with that GPA man <:bleak:877093280905592842>
I’m a cs major so it might get a lil worse ngl
I got it tho
Imma be the best McDonalds worker ever
tight aurora
Me fr
tight aurora
What
eternal pulsar
Imma be the best McDonalds worker ever
No you’re gonna be fine bro
compact pewterBOT
compact pewterBOT
Available help channel!
median dust
Once again, i need help figuring out the fractions for this. Specifically the bottom roq
And if ive asked you to DNI, simply DNI!
compact pewterBOT
Once again, i need help figuring out the fractions for this. Specifically the bo...
compact pewterBOT
turbid surge
Hey, did you learn these terms in your material?
median dust
Hey, did you learn these terms in your material?
those are the ones i use
But
I didnt memorize
Its incrdibly hard for me to memorize
compact pewterBOT
Available help channel!
sudden carbon
how do i do this
compact pewterBOT
how do i do this
kind crane
<@&286206848099549185>
!15m
compact pewterBOT
<@&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.
@sudden carbon Has your question been resolved?
sudden carbon
<@&286206848099549185>
compact pewterBOT
@sudden carbon Has your question been resolved?
lusty ferry
compact pewterBOT
lusty ferry
need to solve this diff eq
from what i've seen
it's not homogeneous
it's non linear
and it's not a bernoulli diff eq
i could do this
oh okay
so just solve from there
not too bad
u sub?
wheat pasture
I wouldn't suggest a sub personally 
not sure of the ways you've learned, but I'd suggest splitting the 1/(y^2 - 169) up 
lusty ferry
ahh
yeah that could work
okay it's a diff of squares
so PFD maybe
alright cool
thanks!
.close
naive oar
compact pewterBOT
mortal bay
no, the last one is incorrect
you have to view the rats as
distinct entities
for thr first one... each rat can be given any one of the 4 drugs so
we have 4 ways of doing it
and theres 11 rats so it should be 4¹¹... hmmm
@naive oar
compact pewterBOT
@naive oar Has your question been resolved?
shy valley
why is the result of simplifying the red expression the blue result and not the green result?
compact pewterBOT
why is the result of simplifying the red expression the blue result and not the ...
dusty harbor
why is the result of simplifying the red expression the blue result and not the ...
because both terms are not to the power of 3/10
only z is
(15z)^3/10 would be the green answer
dusty harbor
no problem
compact pewterBOT
compact pewterBOT
Available help channel!
austere hornet
how come its only x=-4 and not the other endpoint, 4?
compact pewterBOT
how come its only x=-4 and not the other endpoint, 4?
compact pewterBOT
compact pewterBOT
Available help channel!
carmine garden
compact pewterBOT
carmine garden
This paramatrization works well enough
so we have $\sigma_{u} = ( 2u, \sin(v), \cos(v))$ and $\sigma_{v} = (0, u\cos(v), -u \sin(v))$
boreal girderBOT
What a wonderful world !
carmine garden
The cross product is $(-u \cos^2(v), u \sin^2(v), 2u^2 \cos(v))$
boreal girderBOT
What a wonderful world !
carmine garden
the norm is then $\sqrt{4u^4+u^2}$
boreal girderBOT
What a wonderful world !
carmine garden
We then have $\int_{0}^{1} \int_{0}^{π/2} (u^2 \sin(v) \cos(v)) \cdot \sqrt{4u^4+u^2} du dv$
boreal girderBOT
What a wonderful world !
forest token
compact pewterBOT
forest token
im thinking that min speed occurs when the ball is at maximum height when it grazes the wall
and range = R/2
but im not able to use this
compact pewterBOT
@forest token Has your question been resolved?
forest token
<@&286206848099549185>
tired bear
umm
where exactly did you get this from
because i am not getting a very nice answer
forest token
where exactly did you get this from
teacher sent worksheet
boreal girderBOT
forest token
oh what did u get as the velocity
tired bear
thats the hard part
now i need to substitute it in the first v = f(theta) relation i got and use some very painful trig identities
forest token
the answer is 3 btw
tired bear
this is a bit too cruel even for jee
forest token
this is a bit too cruel even for jee
lol you should see some of the other questions
so pissing off
@tired bear what would we get if we differentiate trajectory equation and equate to 0?
tired bear
<@702550180154834984> what would we get if we differentiate trajectory equation ...
in terms of theta?
tired bear
yeah ig
forest token
then would we get the minimum value of theta
but not sure how we use this to get velocity
@tired bear any update or should i just ask it as a doubt?
tired bear
<@702550180154834984> any update or should i just ask it as a doubt?
ok so got till here
but getting some answer in the form shown in question with some flipped signs
forest token
oh
forest token
ok so got till here
wait so after u got theta u substituted it in f(theta) to get velocity?
and u took x = R/2 and h = Hmax?
forest token
i never assumed x and h
oh its not an assumption.. isnt it supposed to be that
tired bear
because im not sure
sometimes it may just look like common sense
but idk if it will actually work
forest token
sometimes it may just look like common sense
yeah logically speaking,
if the ball grazes the wall at its maximum height speed will be minimum right? or is it just an assumption
oh wait no your right lol
cause they want answer in terms of x and h
what was i doing
@tired bear thanks a lot for helping man i think ill just ask my teacher
.close
compact pewterBOT
compact pewterBOT
Available help channel!
broken lantern
help, why
kind viper
$2 \tan^{-1}(z) = \tan^{-1}\paren{\frac{2z}{1-z^2}}$ as long as $z \in (-1,1)$
boreal girderBOT
Ann
broken lantern
I have never seen this fabulous, wonderful thing in my life, what am I doing
short silo
Perhaps let y=2arctan(cosx)
And then manipulate to look like rhs
Whcjh should show its true
broken lantern
not an LHs RHS questioin, I need to find x
broken lantern
okay wait I have a problem
short silo
What's the question
broken lantern
**Ann**
so I do recognise this formula because I have written it (took me a min since I haven't used it) but my dumdum school has banned us from using inverse trig formulas
short silo
Yh ive never seen that formula before
But whats the question?
Ill attempt it myself
short silo
Bet
broken lantern
the only other option I see is through trial and error
short silo
Yh i feel like a identity would be nice to use
short silo
Whats the bottom bit
broken lantern
Whats the bottom bit
that's from the solution
like, after they apply the identity
short silo
That's stupid lmao
But its likely that you will need to just prove the method and act like u didnf ude it 😂
If ur skl doesn't want u to just quote it
broken lantern
my school wants me to jump off a roof
compact pewterBOT
Available help channel!
carmine garden
Okay, so now I want to figure out the boundary of a truncated paraboloid
compact pewterBOT
Okay, so now I want to figure out the boundary of a truncated paraboloid
carmine garden
So if I were to consider this as a subset of R^3, the entire thing would be the boundary, right
Like why is it the biggest circle?
.close
tepid schooner
Very Basic probability theory. I'm wondering how the intersection of two independent events A and B are obtained by multiplying. I can derive the formula from that of conditional probability which I intuitively understand.
My problem is, the formula for "A intersection B" when both A and B are independent looks like finding the size of the cartesian product of A and B divided by the size of the cartesian product of the sample space S into itsel (SxS). That doesn't sound like "intersection" to me.
Example: Probability of rolling a die that is an even number (P(A) = 3/6), followed by a die that is less than 5 (P(B) = 2/6) is P(A).P(B) = 6/36
I don't intuitively get how this makes sense with the formal definition of event set A and B having an intersection.
compact pewterBOT
Very Basic probability theory. I'm wondering how the intersection of two indepen...
slate sand
What’s the definition of independent events?
tepid schooner
Informally, one event happening doesn't effect the odds of the other
Formally I only know the formula sadly.
P(A intersection B) = P(A).P(B)
If A and B are independent events
tepid schooner
Intersection would show the parts set A and B have in common, I can't get that from that formula
In my mind, intuitively basically
small mason
rather than a typical venn diagram with ellipses, its more helpful to consider a 2x2 table. The rows are "A" and "not A"
The columns are "B" and "not B"
kind viper
for intuition you can think about a deck of cards without jokers
when drawing a single card, the events "draw a spade" and "draw a face card" are independent of each other for example
slate sand
Intersection would show the parts set A and B have in common, I can't get that f...
The problem here is that we aren’t saying A ∩ B = AB
We are asking about the probability of such an event
tepid schooner
The problem here is that we aren’t saying A ∩ B = AB
Yes this what is confusing me because it very much looks like that to me
slate sand
Venn diagrams aren’t so helpful because Venn diagrams visually depict adding and subtracting areas
Whereas here we want to talk about the product of the areas as a %
It visually doesn’t make sense to multiply to parts of a Venn diagram together
tepid schooner
My mental model for this, is I'm viewing say two dice rolls with a sample space of 36 outcomes, and the events A and B I described as 6 specific outcomes within those
But this doesn't translate into an intersection in my head, it's just cartesian products.
slate sand
There’s no Cartesian products going on here
tepid schooner
It shows all the ways A and B can be combined
slate sand
Yes but not quite
tepid schooner
And SxS
slate sand
Suppose your sample space was all the 36 outcomes
Then A is an event
Here the sample space = {1, 2, 3, 4, 5, 6} x {1, 2, 3, 4, 5, 6} in the Cartesian product sense
And A is the event {(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}
B is the event {(1,1), …, (1,4), (2,1), …, (2,4), …, (6,1), …, (6,4)}
Now they have some intersection
tepid schooner
Yes that makes more sense
tepid schooner
So sorry for that but honestly that cleared it all up. Thanks for the help
Almost I'd say, you can add more if you have more to say
slate sand
so here P(A) = P({(2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}) = 18/36 = 1/2
P(B) = P({(1,1), …, (1,4), (2,1), …, (2,4), …, (6,1), …, (6,4)}) = 24/36 = 2/3
so P(A)P(B) = 1/3
on the other hand A ∩ B = {(2,1), (2,2), (2,3), (2,4), (4,1), (4,2), (4,3), (4,4), (6,1), (6,2), (6,3), (6,4)}
and P(A ∩ B) = P({(2,1), (2,2), (2,3), (2,4), (4,1), (4,2), (4,3), (4,4), (6,1), (6,2), (6,3), (6,4)}) = 12/36 = 1/3
since P(A ∩ B) = P(A)P(B) we say A and B are independent events
tepid schooner
Yes this absolutely clarified all I had in my head 👍
Wish I could save this thread, thanks a lot for your response
slate sand
you can save this link
tepid schooner
.closed.
slate sand
.close
safe silo
how to solve it
compact pewterBOT
how to solve it
kind viper
how can you tell the nature of roots of a quadratic without finding the roots themselves?
safe silo
how can you tell the nature of roots of a quadratic without finding the roots th...
but don't know how to write in a structured way
kind viper
i do not understand either of your questions
the letter a was present in the original equation. why would it be a mystery that it is still present in D?
and also i invited you to take this and write it down and simplify it. i am not going to do it for you, you have to simplify it yourself.
safe silo
why is there an 'a' variable in the the equation
safe silo
and also i invited you to take this and write it down and simplify it. i am not ...
ok wait then
kind viper
why is there an 'a' variable in the the equation
because the question is set up this way?
you're examining a quadratic equation with a real parameter called a.
safe silo
you're examining a quadratic equation with a real parameter called _a_.
what now?
kind viper
fix these mistakes
safe silo
fix these mistakes
ok..now??
kind viper
show me what you have.
safe silo
kind viper
ok
now solve the inequality -36a^2 + 120a - 100 < 0.
solving for D
it has to be less than 0
your own words
safe silo
ok..i got the answer but still don't understand the concept and why a is equal to 5/3??
@kind viper
or why a less than 5/3
kind viper
would you like my honest but unpleasant feedback
kind viper
i think you didn't really "get the answer" but instead went through the motions with no understanding of what you were actually doing
it would be more helpful if you had a habit of putting not just a soup of symbols in your work but a few words every now and then
such as:
"To solve this inequality let's first find where D = 0"
then you get a double root and can conclude: "so this quadratic is zero at a = (the root), and is always positive/always negative everywhere else"
safe silo
then you get a _double root_ and can conclude: "so this quadratic is zero at a =...
okay
i will remember this
but can you tell me how to prove that roots of this eq. will be non real complex
floral fjord
ok so what did you not understand?
safe silo
i found out that 5/3 is the root which will make this eq. 0...
but how do i prove that all other roots are going to be non real complex
floral fjord
ok let me see
bleak dock
now solve the inequality -36a^2 + 120a - 100 < 0.
can you write -36a^2 + 120a - 100 as a perfect square? @safe silo
floral fjord
ah
bleak dock
well, a constant multiplied by a perfect square trinomial
safe silo
can you write -36a^2 + 120a - 100 as a perfect square? <@1059796693140377682>
maybe no
floral fjord
think about it
bleak dock
basically, complete the square of this
floral fjord
hint take - common
safe silo
4?
floral fjord
as a perfect square
floral fjord
ok
bleak dock
😞sorry i don't understand
any perfect square is going to be zero or greater than zero
floral fjord
9a^2-30a+25<0
bleak dock
*any* perfect square is going to be zero or greater than zero
just think about the graph of y = x^2 for example
safe silo
9a^2-30a+25<0
ok..then
bleak dock
yes, $(3x - 5)^2 \ge 0$ for all real $x$
boreal girderBOT
south
bleak dock
if we want $(3x - 5)^2 > 0$, well then $x = 5/3$ is the only value where $(3x - 5)^2 = 0$
boreal girderBOT
south
floral fjord
less than 0?
bleak dock
can you write -36a^2 + 120a - 100 as a perfect square? <@1059796693140377682>
well this becomes -4(3a - 5)^2 < 0 then
so we do indeed get (3a - 5)^2 > 0
safe silo
why (3a - 5)^2🥲
i am not good at graphs too
@bleak dock
@floral fjord i have to solve this question by this night..please help me with this
bleak dock
*any* perfect square is going to be zero or greater than zero
this is really important
safe silo
this is really important
i get that
bleak dock
why (3a - 5)^2🥲
https://www.youtube.com/watch?v=WOb25i8FBBw
do you need this?
safe silo
i can solve the eq. by any method right?
floral fjord
what
bleak dock
i can solve the eq. by any method right?
well if you know the roots, you can backtrack your way, e.g a = 5/3 is a root of 3a - 5, and it's also a root of 6a - 10 and so on
but it can't be 6a - 10 based on the coefficients
I think you'd confuse yourself
bleak dock
oh
have you seen this though?
it's the wavy curve method actually
but it's explained really simply, well cause the focus of that video is just on quadratics
find the roots and sketch the shape
concave up for a > 0
concave down for a < 0
compact pewterBOT
@safe silo Has your question been resolved?
gaunt wave
Is my answer the correct one, because it contradicts the stuff that's written on the internet. I take an area of 1/4th of the circle 22/7×7^2 ×1/4 = 154/4 and subtract half an area of one 4th of the square 7×7/2=49/2, 154/4 - 49/2=56/4. Thus, i get a half an area of one of those shapes and then i after i multiply it by 2 i get an area of one such shape 56/2. Considering the fact that there are 4 shapes like that i multiply the area of on such shape 56/2 by 4. 56×2=112
compact pewterBOT
Is my answer the correct one, because it contradicts the stuff that's written on...
vivid raven
Is my answer the correct one, because it contradicts the stuff that's written on...
i dont see a fucking shaded part
gaunt wave
it talkes about those circle-like figures
vivid raven
it talkes about those circle-like figures
the butterfly wings?
gaunt wave
yeah
i'm sorry for my camera being awkward
I've seen answers on the web that are fundamentally different, but they don't make any sense to me
that's why i wanted to check if i am right or not
vivid raven
uh
eternal pulsar
Is my answer the correct one, because it contradicts the stuff that's written on...
That seems like the correct method.
vivid raven
area of shaded part = area of square - 4 x area of segment
gaunt wave
this is what i have found on the web
the mathgpt was giving me the same answer
but it doesen't make much sense to me
vivid raven
this is what i have found on the web
are there only 2 shaded parts?
gaunt wave
there are 4 of them
eternal pulsar
this is what i have found on the web
That’s for the outside parts.
Which is indeed in two parts.
I’m referencing the white area of AOD and BOC.
vivid raven
the angle is so akward i dont see any shit shade
vivid raven
this should be better
i think thats the area of the square - area of petal x 4
eternal pulsar
this should be better
Hmm. Then it should be multiplied by two, so technically your answer and the other answer is wrong.
You got the area of the petals though.
signal mist
@gaunt wave What level math is this for?
gaunt wave
<@1288600686375866398> What level math is this for?
basic planimetry
just school planimetry
signal mist
basic planimetry
Is that College or Grade school
vivid raven
Is that College or Grade school
tbh this suits for grade 5.
eternal pulsar
Off topic.
gaunt wave
You got the area of the petals though.
so the area of 4 petals is indeed 112?
gaunt wave
22/7 as the value of π 😭
you just reduce fractions
eternal pulsar
so the area of 4 petals is indeed 112?
Your method is correct, yes. I don’t know about the values. You might want to check them again, because that’s the only thing I see off here.
vivid raven
22/7 as the value of π 😭
22/7 is approx 3.14
next fiber
22/7 being approximated as pi is one of the sins of math but that's besides the point
ive never actually seen a problem ask you to intentionally do that
next fiber
22/7 is approx 3.14
im aware but doesn't change how wrong it is to say that
gaunt wave
it's a preparation sample test to prepare for college exams
long vigil
22/7 being approximated as pi is one of the sins of math but that's besides the ...
thr only good approximation is pi=3=e
eternal pulsar
!redir
next fiber
thr only good approximation is pi=3=e
the engineer approach
compact pewterBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
next fiber
also why did you do 7^2/2 for the area of a smaller square?
gaunt wave
also why did you do 7^2/2 for the area of a smaller square?
it's an area of a half of a smaller square
long vigil
the engineer approach
🗿
eternal pulsar
Anyways.
gaunt wave
basically the triangle
next fiber
each side is 14 so a smaller square would just be 7^2 unless im missing something?