And go on from there
#help-33
tawdry rampart
<@755365572388323378>
Yes?
tawdry rampart
Np bro
hasty briar
And go on from there
how
marsh citrusBOT
@hasty briar Has your question been resolved?
marsh citrusBOT
@hasty briar Has your question been resolved?
hasty briar
uhh
limber trellis
how
if u take z = x + iy the remaining part is a constant ( a |z-1|) and 2i
so for it to be zero
y must be -2i
and x= -a|z-1|
from there u can solve for p and q
hasty briar
if u take z = x + iy the remaining part is a constant ( a |z-1|) and 2i
isnt the value of a |z-1| dependent of z? how is it a constant
limber trellis
isnt the value of a |z-1| dependent of z? how is it a constant
i meant real my bad
y must be -2 cuz the only other imaginary part 2
hasty briar
y must be -2 cuz the only other imaginary part 2
cant a |z-1| have a imaginary part?
limber trellis
cant a |z-1| have a imaginary part?
no they said a is real and mod of anything is a real number
wdym
|z| is always a real number its a value
it cant have an imaginary part
hasty briar
no they said a is real and mod of anything is a real number
a is real but if z (complex number) is multiplied wont it become imaginary?
limber trellis
it is πΏ
limber trellis
a is real but if z (complex number) is multiplied wont it become imaginary?
no mod of z = x+iy, |z| is defined as root x^2 + y^2
hasty briar
okay then yes y = -2
limber trellis
ye
hasty briar
lemme try it
limber trellis
sure
hasty briar
how do i calculate the max and min value of a
like differenciation method?
@limber trellis
hasty briar
yes
limber trellis
then u will get a limit on a
limber trellis
lmaoo
limber trellis
isok just try it
hasty briar
yes leme
limber trellis
let me know if u need any help
hasty briar
or u can check my ans
limber trellis
cuz that is the maximum value of a
thats what theyre asking
try taking p as root 5/4 and q as - root 5/4 and check
hasty briar
yes then we get the ans
limber trellis
oh nice
hasty briar
but how is a p
limber trellis
cuz they said p is max value a
and a is cannot be more than root 5 /4
so p is root 5/4
hasty briar
OH WAIT
sory
right
i read the ques wroong
i thought the roots were p and q
aaaa
limber trellis
your welcome
limber trellis
what grade r u in
limber trellis
thenksknss
no worries
hasty briar
mentally im in 2nd
hasty briar
as u mustve figured it out already
hasty briar
stop laughing at me π
limber trellis
u bought this upon ur self
hasty briar
uff
limber trellis
anyway i gtg now if u have any other doubts let me know
limber trellis
byee
hasty briar
.close
molten ferry
how to find torque created by F2 and F3
marsh citrusBOT
how to find torque created by F2 and F3
molten ferry
hasty briar
about which point
molten ferry
about which point
A
molten ferry
the distance is diagonal in this case tho
hasty briar
axis is perpendicular tothe plane right?
molten ferry
axis is perpendicular tothe plane right?
wdym
hasty briar
it should be perpendicular to the plane only
molten ferry
oh the plane as in rectangle
hasty briar
so for f3, torque would be f3 x root 10
hasty briar
oh the plane as in rectangle
yes
elfin berryBOT
Jash
molten ferry
for the net torque about A
hasty briar
no idts
molten ferry
no idts
what did i do wrong
like the first term is the torque by F1
the second term is by F2 and third by F3
hasty briar
like the first term is the torque by F1
the for first force, it is being applied in 2 directions
and so is f2
molten ferry
isnt it only the perpendicular force that matters
hasty briar
torque of f2 is in clockwise direction and anticlockwise both
molten ferry
they cancel?
hasty briar
yes
molten ferry
alr and is the torque by F1 equal to 2Fsin(45)
hasty briar
yess
hasty briar
yes cw
molten ferry
so the net torque is $F-2F\sin45$
elfin berryBOT
Jash
hasty briar
f root 10
molten ferry
why sqrt10
molten ferry
so r=sqrt10
molten ferry
root ( 3^2 + 1^2)
so $\tau_{net}=(\sqrt{10}-\sqrt{2})F$
elfin berryBOT
Jash
hasty briar
1/root 2
molten ferry
alr
marsh citrusBOT
@molten ferry Has your question been resolved?
hasty briar
@molten ferry wait
im so sorry π
i wasnt in my right mind
for 1, torque by f3 would be F only
as perpedicular dist is 1
NOT root 10
sorrryyyyy
so sorry
so for 1, it would be (1-root2)F
and for 2, it would be 0
obtuse plume
How can I find the normal of y = x + 1, with x being 2
marsh citrusBOT
How can I find the normal of y = x + 1, with x being 2
limber hearth
When you mean normal, you want to find perpendicular line ?
pulsar trout
How can I find the normal of y = x + 1, with x being 2
You can find the equation of the normal when you have a point and the slope
The slope of a normal is -1/m
obtuse plume
You can find the equation of the normal when you have a point and the slope
Well I have the equation of the tangent which is y = x + 1, the question now asks me to find the normal when x = 2
pulsar trout
Well I have the equation of the tangent which is y = x + 1, the question now ask...
This is the function itself
Can you find the point at x=2 first
obtuse plume
Well the question asks us "Find the equation for the normal of the line where the point is x = 2. a) y = x + 1
pulsar trout
Well the question asks us "Find the equation for the normal of the line where th...
Find the value of y when x=2
obtuse plume
3
pulsar trout
3
Are you studying calc 1 or precalc
cause the answer to finding the slope would be vary
obtuse plume
Are you studying calc 1 or precalc
cause the answer to finding the slope would b...
I'm pretty sure it's precalc, I'm not based in either UK or the US
Current chapter is about derivatives, asymptotes, limits and all that stuff
pulsar trout
So you haven't studied derivatives, right?
pulsar trout
Current chapter is about derivatives, asymptotes, limits and all that stuff
Oh great that makes explaining easier
obtuse plume
So you haven't studied derivatives, right?
I have a bit, from what I know is that f'(x) is the derivative of a function, where delta y / delta x is 'simplified'
pulsar trout
Delta y / delta x is the average rate of change
dy/dx is the instantaneous rate of change
obtuse plume
I learned today that instead of finding the limit we can also just use ax^n+bx = anx^n-1+bx^1-1....
yeah exactly so f(x+Ξx)-f(x)/Ξx
pulsar trout
How can I find the normal of y = x + 1, with x being 2
The slope of the function here is 1 since dy/dx is equal to one
So the slope of the normal will be -1/1 = -1
You have a point and the slope
Can you find the normal to the function
obtuse plume
Just to confirm, to find the equation for a tangent we can use the derivated function to find a in y = ax+b, and then find b by plugging in (x,y) from the normal function, correct?
obtuse plume
So the slope of the normal will be -1/1 = -1
I assume this is because of how we derivate the original expression of y = x + 1?
marsh citrusBOT
@obtuse plume Has your question been resolved?
frozen snow
I'm stuck, should I plug 4 and into the u formula and get new parameters? And is my process correct so far
marsh citrusBOT
I'm stuck, should I plug 4 and into the u formula and get new parameters? And is...
glass silo
You could either change the limits for the integral to be in terms of u (and probably really should!), or you could convert the result you found back to the original variables and use that instead...
Also where is that 1/60 coming from?
frozen snow
Also where is that 1/60 coming from?
I tried to eliminate the 100 and 0.6 in one go
frozen snow
You could either change the limits for the integral to be in terms of u (and pro...
And would that be 3+e^0.6(4) etc.
glass silo
I tried to eliminate the 100 and 0.6 in one go
I don't think you did that right 
frozen snow
I don't think you did that right <:sadcat:547124024585486359>
Should I change my u and du expressions is there another way to do it
glass silo
Well, you effectively have 100/0.6 that you're dealing with, which you want to simplify, right... 
frozen snow
why is the 0.6 in the denominator
glass silo
Because you have $\dd u = 0.6e^{0.6t} \dd t$ (you forgot the $\dd t$ in yours), which means that $\frac1{0.6e^{0.6t}} \dd u = \dd t$, so replacing the $\dd t$ in the integral you have gets you
[
\frac13 \int_1^4 \frac{100e^{0.6t} }{3 + e^{0.6t}} \dd t = \frac13 \int_{t = 1}^{t = 4} \frac{100 \cancel{e^{0.6t}} }{u} \frac1{0.6 \cancel{e^{0.6t}}} \dd u
]
elfin berryBOT
@glass silo
glass silo
(note that the limits in the second integral are actually the t values, rather than the u values, and so should be changed really!)
marsh citrusBOT
@frozen snow Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
round gorge
If you know the period and phase shift of a trigonometric function like sin cos, etc, how do you know what scale to put it in? I am struggling with knowing the best scale to use when plotting the function. For example, the image. The ps is -pi/6 and the period is 4pi. How do I know the scale of the graph
marsh citrusBOT
If you know the period and phase shift of a trigonometric function like sin cos,...
round gorge
my best answer is pi/12, but it seems too small
marsh citrusBOT
@round gorge Has your question been resolved?
round gorge
Any help?
solar heron
@round gorge what do you mean by "scale"? Do you mean the marks you want along the x-axis?
round gorge
<@579867729117315072> what do you mean by "scale"? Do you mean the marks you wan...
Yes, I want to make marks and label them. I want to ensure that my main points in my function are on labeled numbers as opposed to not being on the grid
solar heron
Let me think about that for a second
west vault
the first coefficent is a scale along y axis, coefficent inside sin is a scale along x axis
solar heron
I would think about the full period of your function. For example, this one is $4\pi$. Dividing this by 4 will give you how far you have to move along the x-axis (in this case) to hit the x-intercepts. And dividing by 8, gives placements for the maxes/mins. Not sure if that infor is helpful or not
elfin berryBOT
solar heron
So, start at $-\pi/6$, and move $48/8=6$ steps every time to find the important features
elfin berryBOT
round gorge
**twitch.tv/pencenter**
my question is how do i know what each step is.
Thats what im confused about, I know how to plot the points if I have the steps labeled
round gorge
So, start at $-\pi/6$, and move $48/8=6$ steps every time to find the important ...
and why 48?
marsh citrusBOT
@round gorge Has your question been resolved?
solar heron
and why 48?
A period of 4pi with step size 6, gives 48 steps altogether
round gorge
A period of 4pi with step size 6, gives 48 steps altogether
so just always make the step size the phase shift? What if the step was a strange number like pi/13. It wouldn't fit in the period nicely
solar heron
so just always make the step size the phase shift? What if the step was a strang...
in this case 4 times 13 = 52, so the approach is the same. just more annoying π
ah i see the problem, 52/8 = 13/2
but every even multiple will "take care" of the weird denominator we would get
round gorge
but every even multiple will "take care" of the weird denominator we would get
Sorry can you clarify what you mean by that?
round gorge
solar heron
round gorge
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
novel bear
marsh citrusBOT
novel bear
I'm missing something and I can't quite figure it out
valid cape
the function approaches the same sign as x approaches 2
so (x-2) should have an even power
similarly, the function approaches the opposite sign as x approaches 6, thus (x-2) should have an odd power
valid cape
uh, you might want to zoom in a bit btw
valid cape
when I put in a power for (x-6) the graph gets wonky
because the function is decreasing from -infty to 2
try putting in a minus sign before the function
valid cape
and there you go
marsh citrusBOT
marsh citrusBOT
Available help channel!
rocky nova
If I have a group like Z^*_p where p is a prime number is any int 1 to n-1 a generator for the set?
marsh citrusBOT
If I have a group like Z^*_p where p is a prime number is any int 1 to n-1 a gen...
rocky nova
\
brave marsh
No. In general it's not 'easy' to find generators to Z*p.
1 clearly isn't
And for instance in $\Z_{11}^*$, $3$ isn't a generator.
elfin berryBOT
Azyrashacorki
brave marsh
It's just a common example.
marsh citrusBOT
marsh citrusBOT
Available help channel!
heavy blade
im confused by both questions...
for part a, from my understanding of a unique solution is that the determinant when u inverse the matrix is 0 but when i found the determinant in this case it was 0... so im not even sure....?
for part b, I converted the matrix to 3 planes and choose 2 planes to find a line by eliminating a variable and i did that twice and both the lines i found where the same so it proves it is consistent but how do i show for the second part of b?
marsh citrusBOT
im confused by both questions...
for part a, from my understanding of a unique s...
marsh peak
What do you mean by "when you inverse the matrix is 0"? Can you name a matrix whose inverse happens to be the zero matrix?
heavy blade
What do you mean by "when you inverse the matrix is 0"? Can you name a matrix wh...
the determinant was 0 when i inversed this matrix
marsh peak
You can't invert a matrix with determinant 0
heavy blade
oh? so what would i do here?
marsh peak
A linear system of n equations and n variables does not have a unique solution iff the determinant of the matrix is 0, so you have already shown part a
heavy blade
A linear system of n equations and n variables does not have a unique solution i...
oh lol so if there was a unique solution then the determinant would be anything other than a 0?
marsh peak
Yeah
heavy blade
Yeah
ahhh ok i get it, but for part b where it says to show that the general solution can be written as that, if the determinant is 0 how would i show that the general solution is that?
marsh peak
Just solve the system, augment the matrix and row reduce or whatever you prefer
heavy blade
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
golden cosmos
is there a difference between line integral of scalar funtions and line integral of a vector field
marsh citrusBOT
is there a difference between line integral of scalar funtions and line integral...
marsh citrusBOT
@golden cosmos Has your question been resolved?
limber oasis
marsh citrusBOT
limber oasis
stared for an hour
limber oasis
||Then OQR is 40||, ||and x is 90+40||
what explain
whered u get 90
i understand the 40
limber oasis
OH
faint narwhal
late geode
inscribed angle theorem is simpler
consider that inscribed angle <SQR
and central angle <SOR
are subtended by the same arc
marsh citrusBOT
@limber oasis Has your question been resolved?
lethal lodge
prove by induction that: $10^{n-4} < n!\ \forall n\ge 9$
marsh citrusBOT
prove by induction that: $10^{n-4} < n!\ \forall n\ge 9$
elfin berryBOT
maxy
faint narwhal
I mean the left side is always only multiplying 10, and n! After n=9, it is always multiplying 10 and higher, just solve that 10^5 smaller than 9!
marsh citrusBOT
marsh citrusBOT
Available help channel!
keen gulch
I am stuck there: how do I solve that limit without Hopital Theorem?
late geode
,rotate
elfin berryBOT
faint narwhal
Wt is nim
keen gulch
nim?
faint narwhal
Nvm
keen gulch
I use t cause x tends to pi/4, which is not helpfull for using notable limits
keen gulch
that writing is poor,
is that supposed to be **s**in
Yeah, what else could it be?
i know i have a bad writing but not that bad xD
late geode
just making sure, it doesn't look anything close to an s
all the other letters looked fine
anyway, after doing that sub, use the compound/difference identities
keen gulch
The what?
quaint elm
,tex .sum diff trig
keen gulch
Like multiplying for (cosX + sinX)?
elfin berryBOT
hayley is stateside!!
quaint elm
those?
late geode
what are you expecting
keen gulch
late geode
i mean what method are you expecting
keen gulch
Notable limits i think
keen gulch
Like multiplying for (cosX + sinX)?
yeah, i mean that i should be able to solve this with ONLY notable limits or tricks, like this one
keen gulch
keen gulch
That is the way you suggested me to do, and is an approach that i can use but i'd like to know if i can find an other approach
keen gulch
did you try starting with conjugates
That is what i tried to do but wasn't able to get the result
late geode
show what you managed to do
keen gulch
It's bad written, let me re-write for better understanding
(cosx + sinx) is not a problem of the limit cause it's a costant, it's not 0
And i think that i have complicated the limit by doing so and not simplified it...
late geode
use the sub from earlier
or you could use conjugates after doing the sub,
order doesn't really matter
keen gulch
where should i use the sub on the limit?
You mean, replace the x with t (so that t tends to 0) and then use the sub equation again?
late geode
use the
t = x - pi/4
idea
keen gulch
Yeah, but i still have to use the sub equation to solve this exercise.
I was just wondering if there is an other approach other than this and Hoptial
late geode
none that i can be bothered thinking about
some trig identities/properties will be involved
keen gulch
So, we always talk about goniometric proprieties, right?
I mean, i was wondering if this exercise could be solved without goniometric proprieties (like a polynomial limit) but i think that it's not possible
i have to use goniometric proprieties for sure
Alr, thank you for your help and your time : )
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
zinc heart
What makes a function continous and differentiable on a close interval and also what makes it not?
marsh citrusBOT
What makes a function continous and differentiable on a close interval and also ...
devout mauve
it needs to satisfy the relevant definitions
tho I feel that will be unsatisfying
what kind of answer do you want to hear?
zinc heart
I guess just cases where the function wouldn't be continous or differentiable
devout mauve
do you mean like visually from the graph?
devout mauve
its not continuous if there is for example a jump
and not differentiable if there is for example a corner (like in |x|)
devout mauve
yes
zinc heart
what about like sharp points if that makes any sense
zinc heart
How come
devout mauve
the slope jumps
zinc heart
but like mathematically why
and sorry if this is tedious im just trying to get a better understanding of math in general
devout mauve
the relevant limit doesnt exist
marsh citrusBOT
@zinc heart Has your question been resolved?
marsh citrusBOT
@cyan pasture Has your question been resolved?
kind ridge
looks correct to me
tawdry rampart
DOPPELGANGER TYPE SHIT
marsh citrusBOT
@cyan pasture Has your question been resolved?
kind ridge
hehe
marsh citrusBOT
@cyan pasture Has your question been resolved?
marsh citrusBOT
@cyan pasture Has your question been resolved?
sacred leaf
I need help in Calculus 3, I dont understand what other points can be min or max:
marsh citrusBOT
I need help in Calculus 3, I dont understand what other points can be min or max...
sacred leaf
So if found the max and min for the boundary (max = 5 at (1,0) and min= -7 at (-1,1))
<@&286206848099549185>
floral abyss
you should get the derivative in the different variable
marsh citrusBOT
@sacred leaf Has your question been resolved?
sacred leaf
you should get the derivative in the different variable
Can you be more precise?
which derivative fx or fy?
floral abyss
let me see
floral abyss
ok
get both partial derivatives
respecto to x, and respect to y
then make each of them = 0
floral abyss
you have a system of 2 equations with 2 unknown values, x and y
if you divide the 2nd eq by 3 and add it to the first eq
you'll get an eq to resolve with the (-b+-sqrt(b^2-4ac)/2a)
there you have two potential values for your minimum/maximums in x
same with y
sacred leaf
They will be the critical points?
floral abyss
I've gotten x1=0, x2=-8/90
yep
let me see with y
0and -4/135
I think
now replace those values in the main function
and you'll get your values
sacred leaf
it gives -0.019 which is not a minimum no? since I got a min of -7 with the boundary
floral abyss
the second value of y doesn't apply
is negative
there's your function
Finding the critical points: Calculate the partial derivatives of the function and set each derivative equal to zero to find the critical points (a, b).
Use the second derivative test: Define the determinant D = βΒ²f/βxΒ² βΒ²f/βyΒ² - (βΒ²f/βxβy)Β². Evaluate D and the partial derivatives at the critical points:
If D > 0 and βΒ²f/βxΒ² > 0, then there is a local minimum at (a, b).
If D > 0 and βΒ²f/βxΒ² < 0, then there is a local maximum at (a, b).
If D < 0, there is a saddle point at (a, b).
sacred leaf
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
sweet quarry
Is this right?
marsh citrusBOT
Is this right?
ornate girder
I believe you need to convert to radians first
sweet quarry
Yea thatβs what I did
ornate girder
oh, sorry, hard to tell with the picture
sweet quarry
60 degrees is pi/3
ornate girder
right yeah
sweet quarry
Yea itβs kinda messy srry
marsh citrusBOT
marsh citrusBOT
Available help channel!
red tartan
hi guys, In the concavity should I take into account -1 and 2 or should I not? because in the domain doesn't take it into account
marsh citrusBOT
hi guys, In the concavity should I take into account -1 and 2 or should I not? b...
@red tartan Has your question been resolved?
red tartan
<@&286206848099549185>
marsh citrusBOT
@red tartan Has your question been resolved?
deft hawk
My highschool teacher told me to solve this problem by parts, but does anyone know how i could solve it, bec i tried many times
marsh citrusBOT
My highschool teacher told me to solve this problem by parts, but does anyone kn...
brave marsh
I think a substitution first could make it a bit simpler before IBP
amber birch
indeed sub in $u = x^2$ first
elfin berryBOT
south, just south
amber birch
THEN do IBP
marsh citrusBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
vast shoal
Oh mb network
marsh citrusBOT
@deft hawk Has your question been resolved?
still parrot
i dont understand why this is wrong
marsh citrusBOT
i dont understand why this is wrong
still parrot
i plugged in pi over 6 to all the x values
and got pi/6 (sqrt3 / 2) - (1/2) over (pi/6)^2
so i cancelled one of the pi/6
to get (sqrt3 / 2) - (1/2) over (pi/6)
then multiplied top and bottom by two
to get (sqrt 3) - (1) over (pi/3)
and then the final answer
what did i do wrong
brave marsh
From what you're describing you're going from $\frac{\frac{\pi}{6}\cdot \frac{\sqrt{3}}{2} - \frac{1}{2}}{\frac{\pi^2}{6^2}}$ to $\frac{\frac{\sqrt{3}}{2} - \frac{1}{2}}{\frac{\pi}{6}}$ which you can't do
elfin berryBOT
Azyrashacorki
main idol
There's no factor of x on the second term
still parrot
**Azyrashacorki**
oh
brave marsh
I'm actually surprised this compiled in one go
still parrot
wait then what am i supposed to do
brave marsh
You can still simplify both terms a bit, it depends how much the platform you're working on wants things to be simplified to the fullest
still parrot
From what you're describing you're going from $\frac{\frac{\pi}{6}\cdot \frac{\s...
wait can i know why you cant do that?
cause its just pi/6 over (pi/6)^2 isnt it
brave marsh
Because pi/6 is only a factor of the first term in the numerator, not the second
brave marsh
Nw
marsh citrusBOT
Available help channel!
gusty patio
I don't know how to even start this
marsh citrusBOT
I don't know how to even start this
red nimbus
sin(x) β x linear approximation around x = 0
meager acorn
Mhm
gusty patio
$(e^{sinx})'=e^{cosx}*e^{sinx}$?
elfin berryBOT
Falco
meager acorn
Nop
red nimbus
If you use the linear approximation you have the form 0/xΒ² = 0 remember x approaches 0 but never is
gusty patio
cosx*e^(sinx)?
meager acorn
Yes
gusty patio
Can you explain why? Bc I don't get it
red nimbus
chain rule
meager acorn
Ok so
Chain rule yes
Consider t=sinx
So then
e^sinx = e^t
Differentiate wrt to x
Ull get
dy/dx = e^t*dt/dx
dt/dx is cosx
gusty patio
Ok, now I get it thanks
$\lim_{x\to 0}\frac{e^x-e^{sinx}}{x^2} = \lim_{x\to 0}\frac{e^x-e^{sinx}cosx}{2x} = \lim_{x\to 0}\frac{e^x-e^{sinx}(cosx)^2+e^{sinx}*sinx}{2}$
elfin berryBOT
Falco
elfin berryBOT
Falco
marsh citrusBOT
@gusty patio Has your question been resolved?
limpid beacon
How do I find the distance between C' and D'?
I tried using the pythagorean theorem but it gave me sqrt(45)
marsh citrusBOT
How do I find the distance between C' and D'?
I tried using the pythagorean theo...
limpid beacon
I get sqrt(45) if I scale it to 3. If I don't, I get sqrt(5) instead. Which is useless?
Khan Academy says the distance is 6 for the scaled version. And I get sqrt(45) which is approximately 6,708203932
night blade
Can you like
Label which point is which better
Cuz rn, the way I see it is line C'D' just a vertical line
marsh citrusBOT
night blade
And if that is the case, their distance is just 2 and line CD would be 6
marsh citrusBOT
Available help channel!
still temple
marsh citrusBOT
marsh citrusBOT
@still temple Has your question been resolved?
wheat pond
still temple
I am quite confused on what to do with the honey comb
What?
Is that for all letters??
Which one is letter a b and c?
SO C IS THE ONLY INCORRECT THING I DID
DG ITTT
Wait...
We might be both wrong
<@&286206848099549185>
My answer was only 15/2
I didn't make it to a decimal
I mean for letter a π
What did you do in letter c?
YEAH
I used arithmetic sequence, arithmetic series and geometric series
Eh sure
marsh citrusBOT
@still temple Has your question been resolved?
limpid olive
marsh citrusBOT
tight kite
what is that
limpid olive
That is a code :))
tight kite
what do you need help with
sharp elk
may i have some help
marsh citrusBOT
@limpid olive Has your question been resolved?
full flume
idk wth that is lmao but transcribed for posterity
910 80,x2:0, 3'8x1-0, (=) Β±20, 72() 262(=)
1(=) Β±1 (=) 72 910 80,x2;0,
dull slate
Trying to apply function of $\sqrt{\sum_{i=1}^{dimensions} ((Start_i+t(End_i-Start_i)-Other_i)^2)}$ to a line. So far as I have seen, form is like $\int_C f(...) ds$ to $\int_0^1 f(...) \sqrt{x'(t)+y'(t)... to dimensions}$. I keep getting like just one distance, what am I doing wrong? X E.
marsh citrusBOT
Trying to apply function of $\sqrt{\sum_{i=1}^{dimensions} ((Start_i+t(End_i-Sta...
dull slate
How do I translate that to ds instead of dt?
This is for a straight line in 3+D. X E.
I should be getting like a sum of distances right?
elfin berryBOT
maybeJosiah
dull slate
<@&286206848099549185> No answer yet, is this not simple enough? In case it helps, I am trying to average a function over a line. X E.
spark siren
maybe your question isnt clear enough.
dull slate
How could I be more clear?
spark siren
!original
marsh citrusBOT
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.
dull slate
I am getting average of all distances from another point to a line segment and I do not know how to set up an integral for it. X E.
There is no original problem except as I stated. X E.
spark siren
you are starting your question with "trying to ..." so you describe what you do. maybe you should describe the goal you want to achieve.
dull slate
I am getting average of all distances from another point to a line segment and I...
This is goal. X E.
Beyond that, I am trying to compare average distances of shapes but that is not important much. X E.
Like we have point P, try to get average of all distances from a line segment AB defined by points A and B. X E.
dull slate
you are starting your question with "trying to ..." so you describe what you do....
Trying and failing to integrate a function over a straight line. All lines are straight in this case. What form should I use? X E.
spark siren
sorry, i still dont get it. can you show a sketch for a simple case?
dull slate
Does this help?
normal moss
Do you have one point and many line segments or one line segment and many points?
dull slate
One line segment and one point. X E.
normal moss
Where is the average then?
spark siren
one line and one point gives one distance.
normal moss
Even if you had finitely many things there would be no need for integrating so I'm assuming one of these two collections must be infinite?
dull slate
one line and one point gives one distance.
Uh, comparing distances of all lines from each point on line segment to other point. X E.
normal moss
"All lines from each point" what is our collection of points and what is our collection of lines here?
dull slate
Even if you had finitely many things there would be no need for integrating so I...
A line can be considered any number of points depending how many intermediates you define. X E.
normal moss
Great, but we need to know BOTH what our collection of lines are and what our collection of points are to even begin talking about distances between objects in these sets.
dull slate
"All lines from each point" what is our collection of points and what is our col...
Collection of points is on original line segment, collection of lines is from collection of points to other point to compare with. X E.
normal moss
Okay so we start with a single fixed line segment and some fixed separate collection of points?
dull slate
Okay so we start with a single fixed line segment and some fixed separate collec...
A single line segment that contains a set of points and another point. X E.
normal moss
Okay, if we start with a fixed line segment we're already talking about a set of points. Line segments are sets of points.
If we have only one extra point outside the segment, typically people call the distance from the point to the line the length of the segment connecting the point and line perpendicularly
Since that's the smallest distance between the two.
There's only one such distance...
So then you mean
dull slate
But I am looking for average, not minimum. X E.
normal moss
We have a point and a line segment and you want the average of the distance between the point and every point on the line segment?
dull slate
Correct. X E.
normal moss
Okay, this is just the average value of a function I think?
This mf
The idea generalizes to n dimensions
dull slate
Yeah but I can't get applying to a line correct, it keeps having just like one distance, not a sum over what number of set is. X E.
normal moss
Here your function is just the distance function between your fixed point and points on your line.
dull slate
Tried, I think that is a fail. X E.
It is a single integral, that is about all I know. X E.
normal moss
I'm fairly certain this works and is exactly the quantity you want. Whether or not you can evaluate it or set it up is a different issue to do with your own skill (and also tbh how hard the problem is).
In n dim this should be an iterated integral rather than a single one I think.
spark siren
Tried, I think that is a fail. X E.
it will work.
dull slate
Form then?
normal moss
Like if you have a function f(x,y,z) you would have a triple integral iirc?
dull slate
iirc?
dull slate
Okay, yeah. X E.
normal moss
If nothing else you should have the basic idea of your problem a little more clear here. You have a fixed point and line segment you wanna know the average distance between the fixed point and all points on your segment.
Actually wtf is the volume of the region of integration here?
spark siren
express every point C on AB as A+t(B-A), where 0<=t<=1 calculate the distance PC as a function of t.
dull slate
Why not a single integral instead? sqrt is hard to do multiple times. X E.
normal moss
express every point C on AB as A+t(B-A), where 0<=t<=1 calculate the distance PC...
Are you trying to reduce this to a single integral this way?
dull slate
express every point C on AB as A+t(B-A), where 0<=t<=1 calculate the distance PC...
Tried, what is integral form?
normal moss
It might be reducible to one?
dull slate
Are you trying to reduce this to a single integral this way?
Yes. X E.
normal moss
Not you
dull slate
Okay. X E.
spark siren
Tried, what is integral form?
i again dont get your question. i showed you haw to make a distance function, dootdooter showed you how to calc the mean of a function.
do it.
normal moss
Tried, what is integral form?
You would integrate from 0 to 1 the distance from your fixed point to A+t(B-A) basically
dull slate
So $\int_0^1 f(t) dt$ as with original? Tried, fails. X E.
elfin berryBOT
maybeJosiah
normal moss
I don't think this fails theoretically josiah
You should be careful to understand WHY things fail.
dull slate
True. X E.
normal moss
It's kinda misleading to say it fails without telling ppl why because then ppl can't address that part of the issue
spark siren
its more or less senseless if you repeat permanently "tried, fails". it works. if you fail, you made a mistake.
normal moss
Iirc the integral calculation was too hard and approximation wasn't so great either
For them
dull slate
For any line it is not a sum though as it seems it should be. It is like one distance. That one that was too hard was polygons. X E.
normal moss
its more or less senseless if you repeat permanently "tried, fails". it works. i...
Part of the context here is them trying to do graphics stuff where things can be generally correct but not so viable for their application.
normal moss
For any line it is not a sum though as it seems it should be. It is like one dis...
Which thing do you think should be a sum?
The integral we're discussing shouldn't just be a sum
Riemann sum approximations will be literal sums.
dull slate
Which thing do you think should be a sum?
Integral of f(t) dt. X E.
normal moss
Yeah that shouldn't be a sum?
Should be some integral of a square root of a sum I guess.
Not the same as just a sum
dull slate
True it is not just a sum but it should somehow be like divide by length of line to get average over line. That does not work. X E.
That triple integral would be volume seemingly, not trying for that. X E.
normal moss
True it is not just a sum but it should somehow be like divide by length of line...
In this case the division by length ends up being trivial
If you parameterize in a way that your integral has bounds 0 to 1 that length is just 1.
Which is what Thm suggested.
normal moss
You can think of their approach as transforming the problem so that the segment lies on an axis
We don'f care about where the pt and segment actually lie
Just their relative distances
dull slate
On a polygon I have to divide by area, I am still unsure considering I use 1 to 0 on that too. X E.
I also tried using from start x to end x values, still same non-sum. X E.
normal moss
The 1 to 0 thing works here because we have control over how we parameterize the line. If we had our line written as the vector equation y=mt+b (here y,m,b are vectors and t is a scalar) with t ranging from 2,4 for ex we could just scale t by the distance 4-2 and change our bounds to get an equation that traces the same segment with parameter ranging between 0 and 1
I could be off by a factor or so on the scaling point
But that general trick allows us to choose our bounds for tracing the segment.
There are multiple ways to parameterize a curve usually.
dull slate
What would be sum on line form then?
Maybe 0 to length of line?
I tried form of integral over dx with others relative to x in case that helps. Still no sum over line. X E.
dull slate
Like what would give sum of all distances of points on line segment?
normal moss
I think what ThM suggested does basically that.
normal moss
It's gonna be their suggestion up to like a scalar multiple.
dull slate
Which is formulated how?
normal moss
**maybeJosiah**
This was basically their idea
dull slate
And it is not sum form, it is single distance form. X E.
normal moss
Take your fixed point as C and r(t) as the equation of your line segment parameterized from 0 to 1 like they suggested. f(t)=dist(C,r(t)) integrate for t from 0 to 1.
normal moss
And it is not sum form, it is single distance form. X E.
The integral replaces the sum here.
We can use a sum if we have only finitely many points. But we don't have that now.
Hence the integral.
If you mean the sum in the distance formula, that's just part of f(t).
dull slate
By sum form I mean like you divide by segment length to get average. X E.
dull slate
Take your fixed point as C and r(t) as the equation of your line segment paramet...
And the integration is?
So that was $\int_{Line} f(t) dr$?
elfin berryBOT
maybeJosiah
dull slate
Code stuff. X E.
normal moss
The bounds would just be 0 to 1 with this approach
dull slate
From Wolfram Alpha, results of integration. X E.
dull slate
The bounds would just be 0 to 1 with this approach
True but it is not sum form as I was saying. X E.
That is JS. X E.
Could it be Wolfram is just bugging or there is a different solution for from 1 to 0 instead of indefinite integral usage?
normal moss
All you're talking about afaict is the difference between the average or the integral here. You can figure out this from the average value integral in the one var case I mentioned.
dull slate
All you're talking about afaict is the difference between the average or the int...
Where?
spark siren
True but it is not sum form as I was saying. X E.
integral is the sum form for the infinitesimal case.
dull slate
It should be but it is not coming out to that. X E.
spark siren
you stlll claiming things without any argument. my solution gives you an integral.
spark siren
why shold i run this in a browser?
dull slate
It gives you a sense of how wrong current solution you are suggesting is. X E.
JS can only be run in browsers. X E.
Feel free not to. X E.
You could also run in some online tool. X E.
spark siren
only in the case if we believe that this code gives an idea for a correct result. this is to prove.
so its up to you to explain why this code should give the right result.
i wont do it this way.
dull slate
Shall I give you a screenshot then?
spark siren
well, i think we should agree to disagree. you do not accept my solution, so why should we continue the discussion?
dull slate
Here are results. First line is like should be supposedly. X E.
155/588 is not even close to range of possible values. X E.
This is for a line 100 or more out in each direction. X E.
First line is result, ignore next 2, then next line, first is length of line, others are lengths on line from point to consider against. Last is center to point, others are ends to point. X E.
It is on bottom right. X E.
spark siren
you are showing that your code doesnt give you the result you expect. well, ok. and whats my part to this code?
dull slate
It is an implementation exactly as you suggested for math and it does not work. X E.
A better one with what values, first and second are line points, other is to compare with. X E.
spark siren
in which line i can see the integral i suggested?
dull slate
in which line i can see the integral i suggested?
Where last result-= or last return in first function. X E.
That was result from a sumation like sqrt(A+Bt+Ft^2) where each coordinate is part of those letters. X E.
That sqrt being f. X E.
spark siren
its still your implemetation. not my suggestion. anyway. from myside everthing is said.
spark siren
well, i think we should agree to disagree. you do not accept my solution, so wh...
this.
dull slate
Full code, sorry. X E.
spark siren
if you wanna have a mathematical discussion write f(t) in a mathematical notation, solve the integral in a mathematical notation, and then we can look if there is a mistake. maybe.
dull slate
Integrate[Sqrt[A+B t+F t^2],{t,0,1}], Well, Wolfram always exceeds computation time for this so I guess I am stuck. X E.
Alright, let us calculate using this then?
And also, it is like before, $(x+t(x1-x)-P)^2$ so $(x-P)(x-P)+2t(x-P)(x1-x)+(t(x1-x))^2$ per dimension. X E.
elfin berryBOT
maybeJosiah
elfin berryBOT
maybeJosiah
dull slate
Actually, we can consider it to be sum per dimension, not just that one thing per variable. X E.
I could continue but why? I already implemented this in JS as up there. X E.
I can't solve with definite integral but indefinite integral definitely should work. X E.
Well, I guess I am going with this is accurate though it might not be. If I can't make it work then I guess I come back. X E.
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
sterile rivet
hello
sterile rivet
can anyone explain this to me?
this is linear algebra null space / column space
im confused about why we needed to find the solution of null space here and what information it gives.
im also wondering how they knew to choose that kind of matrix like what the line of thought behind it was
pls help!
main idol
this xbar is in the null space of A
still palm
How this happens when we increase one quantity by 2 and other decreases by 2
main idol
How this happens when we increase one quantity by 2 and other decreases by 2
!occupied
marsh citrusBOT
How this happens when we increase one quantity by 2 and other decreases by 2
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #βhow-to-get-help for instructions).
sterile rivet
oh right
wait
so it says there is more than one solution to xbar
that means x is not trivial
but im stuck there
how do i go from there?
main idol
i don't know what you're stuck on
sterile rivet
i just dont know how to solve the problem
sterile rivet
ohhh
no i have no idea
one dimensional i think means that the basis has one vector?
but i dont know how to connect that to a matrix
main idol
sterile rivet
thank you ill watch this video
i think i understand now
so for an easy example, i could choose a matrix with dimension 1, rank 1, and 2 columns
then, i can find the column space of the matrix i make
for A, the column space is (1,0).
im really lost
what does this line mean?
full flume
the zero vector won't ever contribute to the span. it's just adding linear combinations of zeros
sterile rivet
why did they add the linear combinations of zeros?
wait the span S is talking about the column space of A right?
how did they get the null space to be (0,1)
π
why is it right to say the null space is not in the span so every vector in Rm cannot belong to S? how did they connect those two ideas?
pls elp!
marsh citrusBOT
@sterile rivet Has your question been resolved?
marsh citrusBOT
@sterile rivet Has your question been resolved?
marsh citrusBOT
@sterile rivet Has your question been resolved?
vestal drum
I wasn't entirely sure how to deal with the negative in part b, and I'm wondering where the faults in my progression were. Is it the derivative of x? Was I supposed to implement the -1 some other way? I'm curious.
marsh citrusBOT
I wasn't entirely sure how to deal with the negative in part b, and I'm wonderin...
stoic slate
cunning fiber
I wasn't entirely sure how to deal with the negative in part b, and I'm wonderin...
????
,w differentiate -1/(x+8)^2
elfin berryBOT
vestal drum
hang on
lol, i see
So I've got a separate integral, I'm wondering how the -1/2 will be implemented
wait, got it
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
velvet cairn
Can every even number except 2 be expressed as the sum of two prime numbers ?
gilded sage
probably idk
stoic slate
That question should not be posted here
velvet cairn
Ahh it's dumb
I just searched and realised there's already a conjecture like this to be proven
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
lime shuttle
for c, if the correct graph is C in (b), would it be A?
marsh citrusBOT
for c, if the correct graph is C in (b), would it be A?
lime shuttle
this problem took me forever
glacial chasm
Is it to your right or to the graph's right?
I think if it is the latter it should be B, if it is the former then it is C
wary kite
did you get part b right
wary kite
whatβs the order of the 5 number summary btw
lime shuttle
so the blue lil line on the left is the min, the start of the blue box is q1, the median is the black line in the mid of blue box, the end of the blue box is q2, and the end of blue line on right is max
they r in order
kindred vigil
ya im 99% sure
The middle line in the box corresponds to your middle datapoint, which is quite far to the left of your biggest data point but quite close to your smallest data point
positive skew would be correct i'm pretty sure; the terminology is confusing
glacial chasm
i think its A
so shouldn't it be B? Can you explain your reasoning?
wary kite
yea so if you did the 5 number summary right then part b is correct and you should be able to tell its skewed right
kindred vigil
so shouldn't it be B? Can you explain your reasoning?
"right skew" means there's some outliers to the far right of your middle
lime shuttle
ya but i think the symmetry within the box
means its A
if the box had more fat on the right side of the median
wary kite
no, consider the tail end
lime shuttle
it'd be skewed right
wary kite
it'd be skewed right
yes
it is skewed right
itβs clumped towards the left which means the tail is on the right
wary kite
^
lime shuttle
"When the median is in the middle of the box and the whiskers are roughly equal on each side, the distribution is symmetrical (or βnoβ skew)."
i think im right
with A
WAIUDGHAUDGAWYD
but then
ur explanation also makes sense
like mf huh
kindred vigil
If I was a teacher I'd accept either answer
lime shuttle
frrr LOL
wary kite
"When the median is in the middle of the box and the whiskers are roughly equal ...
itβs clear, look at the whisker
the right whisker is much longer
lime shuttle
Ya ima just go with ur answer
skewed right
if its wrong ill have to question my prof
so confusing
this site even states its up to the whiskers
wary kite
i mean they literally exaggerated how short the left whisker was for this reason
you canβt even see the left whisker
kindred vigil
Your friend is wrong
marsh citrusBOT
wary kite
marsh citrusBOT
Available help channel!
lunar walrus
How to solve linear equations?
marsh citrusBOT
How to solve linear equations?
lunar walrus
I donβt get it
glacial chasm
give me an example
glacial chasm
Ok try to transfer (1/2)(x) to the left hand side
glacial chasm
Manipulate the equation so that one side have all the x, and the other side have all the variable, so you can simplify it
lone heart
Like how do you figure out thatβs what u need to do?
You want all the terms with a variable on one side of the equals sign and everything else on the other side
marsh citrusBOT
@lunar walrus Has your question been resolved?
marsh citrusBOT
@lunar walrus Has your question been resolved?
still temple
how u do this
marsh citrusBOT
how u do this
sinful thistle