the first point can be connected to the second one, third one and so on
#help-19
mental wharf
mental wharf
do you know about the choose function
autumn dove
No
mental wharf
its fine then
mental wharf
this seems like a problem to teach the choose function
autumn dove
Can you explain why this is the formula? Apparently its the answer
mental wharf
lets say one of the endpoints is a_1
how many options are there for the other endpoint
mental wharf
it should be in terms of n
mental wharf
the first point can be connected to the second one, third one and so on
remember this
mental wharf
there are n-1 options because it can be connected to any of the other points
mental wharf
now instead of a_1 lets say it was a_2 or a_3
how many options are there for the other endpoint
autumn dove
N-1
autumn dove
N-1
mental wharf
not quite
autumn dove
N-2?
mental wharf
no
autumn dove
Uh
mental wharf
it could be a_1, a_2, a_3...a_n
autumn dove
So n options
mental wharf
yes
so we have n(n-1)
now, dont forget that we are counting both a_1a_2 and a_2a_1 as different segments but are they?
autumn dove
No
mental wharf
np
autumn dove
.close
signal oar
\begin{problem} Let $V$ be a $K$-vector space with $n = \dim V < \infty$, and $\varphi: V \to V$ linear. Let $\varphi$ be nilpotent and $d \in \mathbb N$ minimal with $\varphi^d = \underline 0$. Show that[
\operatorname{ker}(\varphi) \neq {0_V} \text{ and } \operatorname{image}(\varphi) \subsetneqq V.] \end{problem}
signal oar
This seems similar to the one we did last time, @fresh ruin
So we just need to find something that makes phi zero, other than the 0 vector, right?
fresh ruin
yea something akin to the eigenvalues being 0 for some eigenvector, not sure how to do it with less tools though
echo ginkgo
So we just need to find something that makes phi zero, other than the 0 vector, ...
well d is the minimal power such that phi^d = 0, what can you say about phi^(d-1) ?
signal oar
well d is the minimal power such that phi^d = 0, what can you say about phi^(d-1...
It is nonzero
echo ginkgo
yea
echo ginkgo
so there's a v such that phi^(d-1)(v) != 0
signal oar
Yeah
echo ginkgo
what's $\phi(\phi^{d-1}(v))$ then ?
clever fjordBOT
aPlatypus
signal oar
Thanks
signal oar
if you're lazy you could just use rank-nullity
Btw, regarding
I think I found this on MSE: https://math.stackexchange.com/questions/3918658/minimal-polynomial-product
And apparently this is wrong?
According to the comment
Or am I missing something
signal oar
yea that question seems broken
Are you saying the problem is correct or the answerer on MSE is correct?
signal oar
<@332561465405865985>
I assume you are saying the problem is wrong?
echo ginkgo
yes
signal oar
what's $\phi(\phi^{d-1}(v))$ then ?
I assume we need something similar to this?
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celest aspen
can someone help me understand this question, dont get the square bracket formatting
celest aspen
desert marlin
They’re just parenthesis
ivory dock
The real question I guess is whether 3/n is part of the sum or not...
ivory dock
does it? I hate it when people don't use parenthesis with limits and cause confusion
same with sums and stuff
I guess it really depends on what notation op is used to by his teacher
celest aspen
ngl this is kind of confusing... 3/n is zero but k also approaches infinity, idk how to solve
this is a calc bc practice exam
but i never seen this format before
celest aspen
no clue, answer is 39
signal quest
i would assume that 3/n is part of the sum, otherwise they would have just put it in front or not even have included it
well
you can kind of treat it like a constant and pull it out though'
ivory dock
ye lol
signal quest
maybe try pulling 3/n out and expanding
celest aspen
3/n makes every term zero at infinity
signal quest
yeah but its a sum, not a sequence
celest aspen
idk how to solve for the sum tho
celest aspen
it kind of looks like a power series which are pretty difficult to find the sum of
im also confused at how the limit part plays into the equation, like what is the difference between just having n at infinity
also as n approaches infinity each term is divided by infinity no matter what K you are on
so shouldnt it all be zero
nvm i found the limits of sum definition
signal quest
honestly
celest aspen
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signal quest
this is reminding me of the integral definition
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dapper glacier
how would i go about solving this?
odd edgeBOT
how would i go about solving this?
crisp wadi
Start by expressing l in terms of k
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west merlin
i got it finally
line L can be seen as some line with form y=mx+b. where m is the slope and b is the y-intercept. L is tangent to y=e^x at (k, e^k). so their slopes must be the same at that point. thus m=y'(k).
and the y-intercept is given to you, 1/2
you should then have an equation for your line, with everything in place except for that value of k. you can find that by plugging in the point of intersection given (k, e^k) into the function of your line
you will need to use the lambert w function in order to solve the equation though
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eternal glade
when is this matrix diagonalizable? i got: either b,c=0 and every a or b,c!=0 and a is free to choose
eternal glade
is this correct?
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gray bronze
what is the difference between the two things you said? is every a different from a is free to choose?
echo ginkgo
b,c=0 / b,c!=0, you mean both are zero or both are non-zero right ?
@eternal glade
in that case, gg you're right
sharp flume
for finding antideriv
odd edgeBOT
for finding antideriv
marsh nacelle
I would divide each term by sqrt(t)
what do you mean bring sqrt(t) out of denominator
sharp flume
cant you turn it into a negative expnonet?
sharp flume
got it
marsh nacelle
Then you can integrate each part individually
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lavish frost
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lavish frost
how do you go about solving this
I know that when you get derivative of integral you basically replace t with x from the integral
and then apply chain rule if needed
zinc glacier
you can imagine the integral is some function F such that F' = 1/(2+t^4)
by ftc, the integral is F(x^3)-F(x^2)
then you take the derivative of that and use chain rule
odd edgeBOT
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lavish frost
I see
cedar geyser
how do i do a
odd edgeBOT
how do i do a
signal halo
how do i do a
Remember that the integral of f(x) is the area under the curve plus some constant
If it’s telling you the integral from -6 to 5 and you know the area under the curve there you can get the constant
And then you can use that constant to get the integral of the other section
cedar geyser
If it’s telling you the integral from -6 to 5 and you know the area under the cu...
so the area from -6 to 5 is 7
cedar geyser
And then you can use that constant to get the integral of the other section
how does that work tho
signal halo
so the area from -6 to 5 is 7
No
The integral from -6 to 5 is 7
This is different from the area under the curve
cedar geyser
oh yeah
cedar geyser
And then you can use that constant to get the integral of the other section
how do i use this to get the area of the other section?
signal halo
how do i use this to get the area of the other section?
Because the constant stays the same
Basically it’ll be like this
Given integral = calculated area + c
You use those to solve for c
And then you will have unknown integral = calculated area + c
You can solve that cuz you will already know c
cedar geyser
Given integral = calculated area + c
wdym calculated area?
signal halo
wdym calculated area?
Like the area you have to calculate by looking at the graph and using geometry
cedar geyser
Like the area you have to calculate by looking at the graph and using geometry
but how if im not given the -6 part of the graph
signal halo
but how if im not given the -6 part of the graph
It says 2 lines segments and a semicircle make up the graph
So the line from -2 to 0 (which is -x-1) goes all the way to -6
cedar geyser
So the line from -2 to 0 (which is -x-1) goes all the way to -6
on the answer tho they did something like this
signal halo
on the answer tho they did something like this
Oh yeah
Actually that’s the smarter way to do it
Then you only have to find the area under -2 to 5
cedar geyser
Actually that’s the smarter way to do it
How’s does that work tho
I don’t understand how that works
signal halo
How’s does that work tho
So by properties of integrals they are splitting it
Integral from -6 to 5 is equal to integral from -6 to -2 plus integral from -2 to 5
cedar geyser
Oh and because the upper and lower bound = each other this it is splittable
signal halo
Yeah
cedar geyser
Oh wait that actually makes sense
And then they moved the integral they solve for to the other side
signal halo
Yeah
cedar geyser
But how did they solve the area of the very right integral
signal halo
This only works in the case that the integrals share a start or endpoint tho
signal halo
But how did they solve the area of the very right integral
Just by looking at the graph and finding the areas of the triangles and the semicircle
cedar geyser
This only works in the case that the integrals share a start or endpoint tho
Wdym by that,
cedar geyser
Just by looking at the graph and finding the areas of the triangles and the semi...
But from 2 to 5 the shape isn’t really a semi circle
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surreal mountain
Can someone check if this is right? Its different from the answers i see online but i dont get how its wrong. The question is find the equation of the plane passing through P( 3, 5, -1) and contains L : x = 4 - t , y = 2t - 1 , z = -3t
surreal mountain
I got vector v and point Q from the given line equation
Found vector PQ and crossed it with v to find the normal vector
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@surreal mountain Has your question been resolved?
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sweet blade
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blissful sonnet
hi
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dry ice
Where do we get that (x+9) from? I can do the long division I just do not know how to do that part on the right and also what it means
viral forum
!help
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nimble blaze
dry ice
thank you
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restive sparrow
Is the solution for dy/dx=y/x y=cx or y=c|x|
odd edgeBOT
Is the solution for dy/dx=y/x y=cx or y=c|x|
molten vector
As far as i'm aware the mod x is only so that lnx is possible, I think as soon as you raise e to both sides you can remove it
restive sparrow
As far as i'm aware the mod x is only so that lnx is possible, I think as soon a...
Ah
Photomath confused me
molten vector
Looked it up, you don't technically need it because whether x is positive or negative, this sign will be absorbed into the constant C
So theoretically yes you could add it there, but whether you do or don't, your constant will be positive or negative once you solve for it and will be correct either way
restive sparrow
So theoretically yes you could add it there, but whether you do or don't, your c...
I see i see
Ty
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nova falcon
hello, it here i can ask for help ?
odd edgeBOT
hello, it here i can ask for help ?
nova falcon
ok ok so
odd thunder
yea
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nova falcon
<@&286206848099549185>
fleet nest
Al Kashi @nova falcon
nova falcon
Al Kashi <@787996859649359906>
but how i deduce that the formule is a^2= b^2 + c^2 -2bc cos (Â) ?
with my last results
fleet nest
vect(BC)**2 = ||BC||**2 = a**2
nova falcon
ok ok and
fleet nest
show me what you found for 2 and 3
nova falcon
alors c'est en français donc
fleet nest
alors c'est en français donc
?
nova falcon
i write my results in french so
nova falcon
ça me pose pas de problème
roh
en gros pour la 2) j'ai utilisé la relation de Chasles
nova falcon
tu fais aucun effort mdrr
non mais arrh
nova falcon
en gros pour la 2) j'ai utilisé la relation de Chasles
pour prouver BC^2=BA^2 +AC^2 + 2(BA.AC), j'ai mis d'abord BC=BA+AC
fleet nest
pour prouver BC^2=BA^2 +AC^2 + 2(BA.AC), j'ai mis d'abord BC=BA+AC
ok ok
c'est ça
BA.AC = BAxACxcos(BA,AC)
nova falcon
puis j'ai mis le tout au carré car (u.v)^2= u^2.v^2 + 2(u.v)
nova falcon
t'es en quelle classe pour savoir ?
Première
fleet nest
ok ok ça va
si tu m'avais dit plus j'aurais eu peur
cos(BA, AC) = cos(AB, AC + pi)
= -cos(AB,AC)
nova falcon
puis la 3) j'ai utilisé la relation v=-u et la relation de chasles pour trouver -BA . AC/II ABII . II ACII
fleet nest
=-cos(A)
nova falcon
ok ok
fleet nest
bah c'est fini là
fleet nest
j'ai capté
oui non ? ;-;
nova falcon
AAAAH ok ok c'est bon
fleet nest
B
subtle heron
Hi, can somebody help me understand how does a tomographic reconsturction works? So from what Ive understood, lets say that we have a scanner, that rotates 360 times to make one slice, for each slice we calculate a Radon transform which yields the intesity at such projection line and after the whole rotation cycle (360) we end up with a sinogram for that specific slice. My question is, why cant we just do the inverse radon transform to obtain a tomographic image?
subtle heron
So if i understand it correctly, the process is: rotation -> radon transform which gives intensity going through specific projection line of tissue -> some process which is not inverse radon transform to construct a 2d image of all the instenities through the issue and then do this for whole object to have 3d model
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@subtle heron Has your question been resolved?
burnt dragon
Can someone please explain why this is true
odd edgeBOT
Can someone please explain why this is true
zinc venture
the water is increasing, but the rate at which the level of water (h) is slowing down, so the graph is concave down
zinc venture
the questiuon asks abt teh rate of h tho
zinc venture
the height is increasing, but it increases slower as the radius of the cone increases
yeaa
burnt dragon
so for every idk cm of h, it needs more time to fill up because surface is larger
zinc venture
think of the volumeof a cone and area of a circle
burnt dragon
okay i think ill just try to explain it in more peasant terms to myself otherwise my brain will blow up lol
but thanks for the help! i think i get it...maybe...probably 
fringe rune
okay i think ill just try to explain it in more peasant terms to myself otherwis...
Let me type a solution
Ill show you how you can prove it
burnt dragon
oo okay thatd be great
zinc venture
so for every idk cm of h, it needs more time to fill up because surface is large...
yah, u kindaaa got it here
fringe rune
$$\frac{dV}{dh} = \frac{2}{3} \cdot \pi * r$$
$$\frac{dh}{dt} = \frac{dh}{dV} * \frac{dV}{dt}$$
fringe rune
dV/dt is the change in volume of water?
Wait sorry i typed it wrong
fringe rune
$$V = \frac{1}{3}\cdot\pir^2h$$
$$\frac{dV}{dh} = \frac{1}{3} \cdot\pir^2$$
$$\frac{dh}{dt} = \frac{dh}{dV} * \frac{dV}{dt}$$
$$\frac{dh}{dt} = \frac{3}{\pir^2} * \frac{dV}{dt} = \frac{3}{\pi*r^2} * k$$
clever fjordBOT
Melkor
burnt dragon
fringe rune
therefore $$\int{dh} = \int \frac{3}{\pi*r^2}*k dt$$
clever fjordBOT
Melkor
fringe rune
$h = \frac{3}{\pi*r^2}kt$
clever fjordBOT
Melkor
burnt dragon
no its fine no worries
i dont think im actually supposed to know this so the explanation i got is okay
fringe rune
my brain has stopped working
burnt dragon
no fr same
burnt dragon
oh
zinc venture
concave down
zinc venture
its derivative is a downwards slope
the derivative is the rate at which water is being added
its going down because there is a larger radius
i think this is right lol but im not rlly sure
zinc venture
👍 have good day
odd edgeBOT
fringe rune
thanks a lot of both of u!
hmm although im getting h proportional to t^1/3 or cube root of t
fringe rune
i dont get how you got this tho
fringe rune
hmm although im getting h proportional to t^1/3 or cube root of t
which is a concave down function since f'(t)>0 and f''(t)<0 for all t>0
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flint shore
I did (1 + a/n)^n = e^a
with n+k and n+2k
then I got e^k/e^2k = e^-1 (e^-1 is the result of the equation ln(e³x) = 2
e^-k = e^-1 so I'd say the result is 1
but the paper says the result is -1
the paper could be wrong tho it wouldn't be the first time
fringe rune
I did (1 + a/n)^n = e^a
with n+k and n+2k
then I got e^k/e^2k = e^-1 (e^-1 is th...
I got the same answer as you did
fringe rune
so the paper ans is probably wrong
Yeah
fringe rune
I'll show to my teacher tm thx
Nice nw
flint shore
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cobalt forge
how is the first picture not a redex
odd edgeBOT
how is the first picture not a redex
cobalt forge
the second picture is the whole term and the second picture is a part of it
when i look at the answer sheet they didnt count the term in the first picture as a redex, why can we not apply the outer x inside
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digital nest
A 20N painting hangs on a nail in such a way that the supporting rope is at an angle of 60°. What is the stress in each segment of the rope?
pastel orbit
A 20N painting hangs on a nail in such a way that the supporting rope is at an a...
have you tried drawing a picture?
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copper raptor
how would i go about solving this problem? i know i’m supposed to use derivatives to solve this problem but i don’t know how i should apply derivatives to solve it
summer cradle
comic sans
dense mirage
use the equation of a line y-y_1 = m(x-x_1), m is the derivative at A, and A=(x_0,y_0)
or whatever way you find the equation of a line with a point and the gradient
signal quest
comic sans
Peak math typesetting wym
copper raptor
.reopen
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copper raptor
use the equation of a line y-y_1 = m(x-x_1), m is the derivative at A, and A=(x_...
so for m im finding the derivative of the equation at A? how would i do that 😭
i don’t get how to find the derivative at a point 😭😭😭
thick harness
you just need to find the derivative then plug in the x value the find the value of the derivative at the point
if that makes sense
naive python
is this correct?
odd edgeBOT
is this correct?
half fulcrum
you just multiply the outside exponent with the inside exponents
naive python
so is it correct
hushed gate
is this correct?
Wrong formula for good answer
naive python
i dont have to play with the denominators?
half fulcrum
it sould be 2^(2/3) * x^(6/12)
half fulcrum
yes
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clever violet
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clever violet
how do i determine the coordinates/
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clever violet
<@&286206848099549185>
clever violet
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formal crest
i need help understanidn on how to write the ned behaviour for NPV/x int
formal crest
i dont understand how we got what we got for 1/f(x) for the bottom part
i understand where we got the numbers but idk the rest
its unit recipricols btw
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white flax
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dusk lark
swap x and y
dusk lark
so you get x = y^3+2y+3
white flax
so you get x = y^3+2y+3
yes
dusk lark
what do you have to do?
white flax
find the inverse
dusk lark
thats the inverse ig?
white flax
derivative of the inverse
empty cedar
white flax
i just dk how to find the inverse
empty cedar
differentiate on both sides
dusk lark
do i need to use this formula or something? <@1206794487464992818>
yes
its smth like that
empty cedar
where did you get this?
its a property?
white flax
differentiate both sides of this?
white flax
its a property?
i haven't been taught it hmm
empty cedar
oh
white flax
differentiate both sides of this?
@empty cedar
empty cedar
yea
white flax
so find f'(x)?
empty cedar
no no
white flax
but then what lol
empty cedar
wait lemme send the image
white flax
ok
white flax
is the answer 1/5
yes
feral solar
differentiate both sides of this?
no
use the sum rule
end with 3x^2+2 as the derivative of f(x)
white flax
oh i'm dumb
white flax
@empty cedar he legit just uses the definition of derviatives
white flax
then get the inverse
no
white flax
get the inverse of f(x)
you can't
white flax
that's the problem
white flax
do you know how to get the inverse?
try it
white flax
just say x=y^3+2y+3 and solve for x
solve for it then
empty cedar
that wont work
white flax
you can't lol
empty cedar
you can do it by the property of inverse and differentiate
feral solar
wdym
empty cedar
feral solar
you plug in the inverse
empty cedar
that's helpful though
its just saying f(x) = f(x)
empty cedar
thats what
white flax
you can do it by the property of inverse and differentiate
what is g(x) here?
empty cedar
what is g(x) here?
look at the first line
white flax
yeah because when you plug y into the inverse you get back x right?
okay that makes sense
empty cedar
yeah because when you plug y into the inverse you get back x right?
yep
white flax
hm
white flax
here wait here is the sample solution he wrote
he just guesses i think which is super strange
empty cedar
what 😭
empty cedar
amazing 😭
empty cedar
yea
white flax
and gets -1
so (-1, 0) is on f(x)
then he just flips it for the inverse
so (0, -1) is on f'(x)
so f'(0)=-1
that's so stupid LMAO
ngl
empty cedar
that genius 😭
white flax
that genius 😭
it like works
just like tons of stuff to remember
😭
okay thanks man for the help
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whole haven
hi, is this correct?
odd edgeBOT
hi, is this correct?
whole haven
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 34 ft, express the area A of the window as a function of the width x of the window.
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whole haven
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boreal yacht
I can help
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boreal yacht
To express the area ( A ) of a Norman window as a function of the width ( x ), we need to consider both the rectangular and semicircular parts of the window.
Let’s denote:
( x ) as the width of the window (and also the diameter of the semicircle).
( y ) as the height of the rectangular part of the window.
( r = \frac{x}{2} ) as the radius of the semicircle.
The perimeter ( P ) of the window, which is the sum of the width of the rectangle, the height of the rectangle (twice since there are two sides), and the circumference of the semicircle, is given as 34 ft. Therefore, we have: [ P = x + 2y + \pi r ] [ 34 = x + 2y + \pi \frac{x}{2} ]
Now, we need to express ( y ) in terms of ( x ) using the perimeter equation: [ 2y = 34 - x - \pi \frac{x}{2} ] [ y = 17 - \frac{x}{2} - \frac{\pi x}{4} ]
The area ( A ) of the window is the sum of the area of the rectangle and the area of the semicircle: [ A = xy + \frac{1}{2} \pi r^2 ] [ A = x\left(17 - \frac{x}{2} - \frac{\pi x}{4}\right) + \frac{1}{2} \pi \left(\frac{x}{2}\right)^2 ]
Simplifying the expression, we get: [ A(x) = 17x - \frac{x^2}{2} - \frac{\pi x^2}{4} + \frac{\pi x^2}{8} ] [ A(x) = 17x - \frac{x^2}{2} - \frac{\pi x^2}{8} ]
So, the area ( A ) of the Norman window as a function of the width ( x ) is: [ A(x) = 17x - \frac{x^2}{2} - \frac{\pi x^2}{8} ]
This function will give you the area of the window for any given width ( x ), as long as the perimeter remains 34 ft. Remember, this is a simplified model and assumes the thickness of the window frame is negligible. If you need to account for the frame, additional adjustments would be necessary
odd edgeBOT
To express the area ( A ) of a Norman window as a function of the width ( x ), w...
@boreal yacht Has your question been resolved?
raw trail
Why is the topologist sine curve connected but not path connected?
desert marlin
what's the dfn of path connected
raw trail
For two arbitrary points in S there is a continuous path connecting the two points that lie in S
desert marlin
keyword continuous
try proving there is not a continous path between these two points
desert marlin
idk just somewhere over there
raw trail
Yes I think
desert marlin
(0,0) I didn't read the axis
raw trail
Cuz it’s the y axis from -1 to 1
summer cradle
idk just somewhere over there
well every point over there is connected to the other green point 
desert marlin
well every point over there is connected to the other green point <:hmmge:115302...
(0,0)
ma;am
summer cradle
raw trail
Yeah intuitively it’s not path connected
But I’m not getting the connected part
Like why is it connected
desert marlin
<:bleakkekw:913344117981999125>
who in their right mind would make their axis not centered at (0,0). Insane only pedestrian mathematicians would do this
desert marlin
Like why is it connected
what's the defn of connected
summer cradle
this isn’t super intuitive but the key is (0,0) is a limit point
desert marlin
It cannot be broken into two open sets that is disjoint
okay, try proving that this cannot be broken into two open sets that are disjoint
and actually their closures are disjoint
raw trail
Yeah I’m not getting this part
I tried thinking about it
Like in the proof
I read other proofs
But I’m stuck
desert marlin
Show a proof you're not getting, and explain what's confusing you about a particular step
then we can help
raw trail
Well intuitively speaking it doesn’t make sense though
Cuz we r getting arbitrarily close to the y axis
Not touching it
But somehow it is commected
Connected
desert marlin
the reason is because any open set containing the points that are arbitrarily close as you say above
will contain within its closure, the origin
raw trail
Wait would you mind elaborating a bit
desert marlin
So suppose you can seperate this into two disjoint open sets A and B
such that Aclosure intersect B is empty, and Bclosure intersect A is empty
raw trail
Ok
desert marlin
very bad drawing of the scenario
but imagine anything like this
where the open sets are meeting at some points on the nice part of the curve
clearly this will fail
see the yellow and green lines
say yellow is A and contains everything to the left of that point
and the green is B and contains everything to the right of that point
Either
- we're missing a point in between yellow and green, as the sets are open
or
- yellow and green are the same point
in which case their intersections are not empty
so it fails if we try doing something like that
raw trail
Can you explain 1 plz
desert marlin
since the sets are open, they do not contain their boundary points
raw trail
Ohhh
desert marlin
so
this was the "easy" example to see anyways
because
clearly something is going on near the origin
right
raw trail
Yes
desert marlin
say we split it into A and B differently
such that A contains the origin, and say B contains everything else
raw trail
Ok
desert marlin
The closure of B
will include the origin
because as you said earlier
the curve oscillates arbitrarily close to the origin
which contradicts that B closure intersect A is empty
raw trail
Right and the origin is the limit point
desert marlin
yes
This was just like a very heuristic explanation and would not be a good proof
but that's why it is connected
raw trail
Ooooo
That’s cool
Would u mind if I add u as a friend
U r so smart
Like legit
Everyone I met today was super smart lol
desert marlin
Sure
odd edgeBOT
summer cradle
Everyone I met today was super smart lol
phew good thing you didn’t meet me
raw trail
phew good thing you didn’t meet me
U r smart lol
Super smart
Yup stop shaking ur head
It’s true
odd edgeBOT
Available help channel!
raw trail
Maybe consider it’s complement
brittle notch
help
in probability 'and' means u multiply probabilities
'or' means u add
now what is probability of getting 3?
@wide crescent
brittle notch
then what is the prob of getting odd number 2nd time?
brittle notch
in probability 'and' means u multiply probabilities
'or' means u add
..
is it and or or?
brittle notch
2/12 * 1/2
odd edgeBOT
desert marlin
that's not allowed
azure turtle
It's fine
New here
Or maybe we can just ping to warn them?
<@&268886789983436800> idk if I should ping or not
viscid flint
.close
odd edgeBOT
odd edgeBOT
Available help channel!
cinder perch
what topic is this?
odd edgeBOT
what topic is this?
cold swift
alright
cold swift
it’s centered at 0
clever fjordBOT
y0shi
cold swift
notice how it’s alternating signs
cinder perch
let me think
cinder perch
Yeah
Wait my laptop screen just died
Gimme a minute
I didn’t even see the - sign
ok its back
-1^(n)
right
cold swift
well yes it’s alternating
cinder perch
oh
cold swift
to get it to alternate
cinder perch
-ln6?
oh right
damn tahts cool
so for taylor series i just convert the stuff
i watched this video from this guy
but it juts clicked
ty
cold swift
yeah
you just need to remember series representation for like sine cosine ln and e^x
and maybe the geometric series one too
cinder perch
ln?
i watched organic chem tutors
to start
so i tihnk i rember taht
0+1(x-c)^1/1!
if i remember
cold swift
it doesn’t have the factorial
true garnet
odd edgeBOT
@cinder perch Has your question been resolved?
finite palm
just started two variables functions can anyone explain why the level curves of f(x,y) = xy look the way they do. We learnt that you can find what a level curve looks like by setting f(x,y) to 0 but that doesnt seem to work
fervent hawk
I'm not very familiar with the topic, but I hope I can help.
since when we plot the graph for f, we will usually set z=f(x,y)
so, setting f(x,y) to a constant 'a' is just saying that drawing a line on the plane z=a
where the line will be f(x,y)=a
fervent hawk
just started two variables functions can anyone explain why the level curves of ...
which in such case, xy=a we have x=a/y
and for special 'a' such as 0
the line will be non very typical
while it still works
fervent hawk
i couldnt wrap my head around it
it's alright, we've all been there
odd edgeBOT
odd edgeBOT
✅
finite palm
Just started two variables graphs and having trouble sketching level curves and sketching the 3d graphs
u cant just post a messsage over mine
primal token
odd edgeBOT
odd edgeBOT
@primal token Has your question been resolved?
fickle blaze
I need help with math
odd edgeBOT
I need help with math
fickle blaze
I believe I need to work on the arrange
but I cant find all the one with my calculation
hello?
@icy vault are you still there?
okay
thanks for cooperation
.close
odd edgeBOT
odd edgeBOT
Available help channel!
elfin warren
"Determine some values of α and β for which the line integral
I =....
becomes independent of the choice of integration path γ. Determine for these α and β:
(a) a potential Φ(x, y) to the field F(x, y), such that F(x, y) = ∇Φ(x, y);
(b) the value of I along some curve γ that runs from (0,0) to (1, 1) through I = Φ(1, 1) − Φ(0, 0) ;
(c) the value of I along the distance from (0,0) to (1, 1) by direct calculation"
elfin warren
i dont really understand what i am supposed to do here
true garnet
same
elfin warren
haha
true garnet
sorry that was useless lol but i dont know the math or the language lol
elfin warren
its okay
odd edgeBOT
@elfin warren Has your question been resolved?
odd edgeBOT
@elfin warren Has your question been resolved?
odd edgeBOT
@elfin warren Has your question been resolved?
elfin warren
.close
odd edgeBOT
odd edgeBOT
Available help channel!
zenith mountain
Hello, I saw this question on a practice paper and couldn't figure it out, so here's my working out so far. I've labled the area of shape A and n, the area of shape B as n + 70, and i know if I can figure out the area of shape a, i can just square root it and add 4 since root n = Length of line on shape B - 4. I think the question might have smth to do with simultaneous questions but I cant figure it out. Its a calculator paper so i'll be able to use a calculator for the question.
ivory dock
Hint : Write out all equations you can, for both surfaces of A and B, and then observe them as a system of equations
zenith mountain
Alright, thanks, give me a min or 2
oh, i think i got it
alr, so we know that n + 70 = L ^2 (where L is the length of one side on shape B)
and we also know that n = (b-4)^2, where n is the area of shape A and we get the (b-4) bit from on side on shape A being 4 less the one side on shape B
now we can rearrange both for n
ivory dock
Not quite right
ivory dock
maybe try to make your lettering a bit more clear
so we have shape A having sides a
and shape B having sides b
zenith mountain
oh, alr, ill edit it
ivory dock
as you said a^2 + 70 = b^2
so far so good
but what about the second equation?
It doesn't deal with surfaces, it deal with lengths, so there should be no squares involved in it
zenith mountain
i was thinking that since i have n = b^2 - 70, and the other equation, n = (b -4)^2, i could just expand out the second equation. This gives me n = b^2 - 8b + 16, and now since both are equal to n, i could make a new equation where b^2 - 70 = b^2 - 8b = 16
wait, that last = is suppose to be a +
ivory dock
the second equation is wrong
zenith mountain
srry, let me rewrite it
zenith mountain
alr, so then rn we have a^2 = b^2 - 70, and a^2 = (b-4)^2
ivory dock
ok, that second equation is wrong
now tell me, why does it have squares in it?
squares denote surface, that second equation stems from lengths
it should have no squares
zenith mountain
i was thinking that since a = b-4, i could rewrite it as a^2 = (b-4)^2, i wanna try to make the equations equal so i could just take away the b^2 from both and just rearrange for the value of b
yes
ivory dock
No need to square that
just plug in a in the first equation now
a = b-4
this, you have it
zenith mountain
alright, then for the first equation, we have a^2= b^2 - 70
if we plug in our value of a
we get (b-4)^2 = b^2 - 70
alr, now we expand out
ye
alr, so now we have b^2 - 8b +16 = b^2 - 70
we take away b^2 from both sides, leaving us with -8b +17 = -70?
oh yeah, srry, misclick
now we can just - 16 from both sides, giving us -8b = - 54
now we divide by -8
giving us b = 6.75
I think thats right, thats what i got when i did the working out, ima double check
oh, i added 16, i didnt take it away
that gives us-86
10.75
115.5625, but since it said 3sf, its 116 cm^2
alr, thanks to both of u, i appreciate it
.close
odd edgeBOT
odd edgeBOT
Available help channel!
hearty kelp
odd edgeBOT
signal quest
that seems reasonable
hearty kelp
thank you sm
signal quest
the domain from $(-{\infty}, 0)$ isn't defined
clever fjordBOT
Cyphercrit
signal quest
@hearty kelp
wait
that says range lol
but your answer is still fine because the range never goes to infinity
hearty kelp
but your answer is still fine because the range never goes to infinity
oh wait yeah ur right i was just going to say this
hearty kelp
odd edgeBOT
ivory dock
ye
ivory dock
ye
hearty kelp
it wouldnt be A right
slender plume
C?
hearty kelp
yeah
slender plume
What are those things caleld
ivory dock
Matrices
hearty kelp
it wouldnt be A right
@ivory dock just to make sure
ivory dock
How long are you taking this quiz lol, ye you good
hearty kelp
How long are you taking this quiz lol, ye you good
man its a 15 question semester exam so im scared lool
ive been posting here all day
.cose
.close
odd edgeBOT
odd edgeBOT
Available help channel!
tawny terrace
Why is y=0, when x approaches -∞?
odd edgeBOT
Why is y=0, when x approaches -∞?
torpid owl
because of the negative exponent
ember oak
Why is y=0, when x approaches -∞?
As $x$ approaches $-\infty$, what does $-x^4$ approach?
clever fjordBOT
SWR
tawny terrace
infinity no? you get basically (-1x)^4 which is (-1(-∞))^4
ember oak
infinity no? you get basically (-1x)^4 which is (-1(-∞))^4
Okay, think about this: As $x\to\infty$, what does $x^4$ approach?
clever fjordBOT
SWR
tawny terrace
infinity
ember oak
So if $x^4$ approaches $\infty$, what does $-x^4$ approach?
clever fjordBOT
SWR
tawny terrace
negative infinity
ember oak
there you go
tawny terrace
yes but now I'm struggling to understand how -x^4 when it approaches -infinity, it's still -infinity
ember oak
Because you're basically doing $-(-\infty)^4$
clever fjordBOT
SWR
odd edgeBOT
odd edgeBOT
Available help channel!
sour basin
$\sqrt[6]{-8}$ how can i find the solutions with moivres theorem. I am not sure how to find r or the angle
clever fjordBOT
Benschko
sullen ferry
try writing the number as the root of a polynomial
mortal trench
$\sqrt[6]{-8}$ how can i find the solutions with moivres theorem. I am not sure ...
Hint: exponentiation distributes over multiplication
sour basin
so like this:
$\z^6+8=0$?
clever fjordBOT
Benschko
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