ur applying the wrong properties
#help-27
autumn geode
small urchin
<@&268886789983436800>
small urchin
Gpt users
sick valley
i made a mistake. that doesnt make me an idiot
Sorry
sick valley
Can i solve this pls
tiny hearth
yes please
sick valley
Anyway
small urchin
What !
sick valley
$\alpha^{\beta}=e^{\beta,\ln\left(\alpha\right)}$
small urchin
Why do I have to use it?
woven radishBOT
jandro
sick valley
Use this
sick valley
Let me explain 🤦♂️
small urchin
Why
sick valley
$\lim_{x\to{\infty}}{e^{\ln\left(\frac{1}{x}+1\right),x^{2}-x}}$
woven radishBOT
jandro
sick valley
So you can do this
small urchin
How you do it ?
sick valley
With the formula
small urchin
Which?
sick valley
However it seems I'm talking to myself
sick valley
**jandro**
.
modest dagger
<@&268886789983436800>
What is the issue? You think a user is giving you answers from chatgpt?
small urchin
But if you used it now
sick valley
?
small urchin
Yes
modest dagger
It doesn't come across to me that way.
small urchin
With the formula
.
sick valley
**jandro**
.
small urchin
And then you said: you definitely know how to do it?
I told them how to continue
Y
sick valley
????
small urchin
And you said that we continue with the formula again 🤦
sick valley
What are you talking about
modest dagger
**jandro**
This is a common strategy to apply. You can often rewrite limits in this form, apply continuity of e^x and work out the resulting limit in the exponent instead.
small urchin
I'll say later
sick valley
Correct .
small urchin
After this thing....
small urchin
And even before you tell me that you wrote the track wrong....very strange (twice)
small urchin
Can i continue?
Ok
small urchin
Ok
sick valley
😔
small urchin
How do we continue from that point
small urchin
$\lim_{x\to{\infty}}{e^{\ln\left(\frac{1}{x}+1\right)\,x^{2}-x}}$
Here
sick valley
We can use the power series expansion
small urchin
How
sick valley
$x=\infty$
woven radishBOT
jandro
modest dagger
Where did the -x come from?
small urchin
Ok
sick valley
$\ln\left(\frac{1}{x}+1\right)=\dfrac{1}{x}-\dfrac{1}{2,x^{2}}+o\left(\dfrac{1}{x^{3}}\right)$
woven radishBOT
jandro
sick valley
Its clear ?
sick valley
To have this
small urchin
Ah OK
sick valley
$\lim_{x\to{\infty}}{e^{\left(\frac{1}{x}-\frac{1}{2,x^{2}}\right),x^{2}-x}}$
woven radishBOT
jandro
sick valley
👍
small urchin
So what?
sick valley
$\lim_{x\to{\infty}}{\dfrac{1}{\sqrt{e}}}$
woven radishBOT
jandro
modest dagger
Let them finish
sick valley
Its Taylor
small urchin
OK Bye
sick valley
$\dfrac{\left(\dfrac{1}{x}+1\right)^{x^{2}}}{e^{x}}=\dfrac{1}{\sqrt{e}}+\dfrac{1}{3,\sqrt{e},x}-\dfrac{7}{36,\sqrt{e},x^{2}}+\dfrac{199}{1620,\sqrt{e},x^{3}}-\dfrac{3193}{38880,\sqrt{e},x^{4}}+\dfrac{46801}{816480,\sqrt{e},x^{5}}-\dfrac{6084467}{146966400,\sqrt{e},x^{6}}+o\left(\dfrac{1}{x^{7}}\right)$
woven radishBOT
jandro
sick valley
I got this from wolfram
devout snowBOT
sick valley
?
devout snowBOT
Available help channel!
modest dagger
I knew it
Just because you don't understand somebodies solution doesn't make it chatgpt. It doesn't help anybody for you to constantly insert questions in the middle of somebodies solution solely because you don't understand it before they finished their explanation to you.
devout snowBOT
Just because you don't understand somebodies solution doesn't make it chatgpt. I...
small urchin
Just because you don't understand somebodies solution doesn't make it chatgpt. I...
Go look at his old messages
modest dagger
The messages in this chat or others?
small urchin
The others too
modest dagger
I'm talking about this chat right now.
modest dagger
One sec
small urchin
You ask why and there is no answer
vapid nest
Go look at his old messages
Leave Jandro alone
tiny hearth
You ask why and there is no answer
you ask him so fast
small urchin
It is said because it is done this way
tiny hearth
do you know how long it takes to type latex?
you dont give him time to explain his reasoning
tiny hearth
and when he does you dont try to understand you just say i havent learned it or whatever
small urchin
When you see his messages you will understand
small urchin
$\dfrac{\left(\dfrac{1}{x}+1\right)^{x^{2}}}{e^{x}}=\dfrac{1}{\sqrt{e}}+\dfrac{1...
Long time to write in LaTeX? I do not think so
vapid nest
Long time to write in LaTeX? I do not think so
lmao it would take me a long time
small urchin
He wrote it in a very short time then I don't know
tiny hearth
He wrote it in a very short time then I don't know
that one is copy and paste from the looks of it
small urchin
Copied from where?
tiny hearth
wolfram alpha i guess idk
modest dagger
Nothing they posted seems obviously chatgpt from what I can tell.
small urchin
I don't think that's the case
autumn geode
it looked copied indeed i seen him send it instantly after his prev message
it would b impossible to type at the speed he did
esp in latex
autumn geode
it would b impossible to type at the speed he did
(if he was to type that all out manually)
tiny hearth
he copied a series expansion from a calculator? what's wrong with that?
his other attempts at explanations were authentic
modest dagger
I am not really interested in putting typing speeds under the microscope here.
heady plinth
autumn geode
I am not really interested in putting typing speeds under the microscope here.
i was js it was in less than like 3 seconds
modest dagger
i was js it was in less than like 3 seconds
Great. Lets take coak's advice? Lmao.
autumn geode
true this is a useless debate at the end of the day
modest dagger
$\dfrac{\left(\dfrac{1}{x}+1\right)^{x^{2}}}{e^{x}}=\dfrac{1}{\sqrt{e}}+\dfrac{1...
If you are using chatgpt please stop.
.close
devout snowBOT
devout snowBOT
Available help channel!
spring oak
devout snowBOT
spring oak
How to find left hand limit?
bright phoenix
At what point
spring oak
Any point
night shuttle
plug in calculator
bright phoenix
The left hand limit will not be the same at everypoint
bright phoenix
How you feel?
Elaborate your question please
spring oak
I meant how you felt that it will not be same at every point
devout snowBOT
@spring oak Has your question been resolved?
spring oak
.close
devout snowBOT
devout snowBOT
Available help channel!
sterile ivy
Is this equation invertible?
devout snowBOT
Is this equation invertible?
sterile ivy
$Y(T) = \frac{\mathrm{e}^{-3BT} \left(\mathrm{e}^{6BT} + 9\mathrm{e}^{4BT} - 9\mathrm{e}^{2BT} - 1\right)}{24B}$
woven radishBOT
! If you Dutch SEE my `about me
sterile ivy
B is a constant
Wolfram Alpha gave me this: but I don't know how to find these roots (where I replaced x with T and B with a)
does the first one just mean the first root of
$x^6 + 9 x^4 + 24 a^3 x - 9 x^2 - 1$
woven radishBOT
! If you Dutch SEE my `about me
polar chasm
It's quite probable that it has no nice roots
polynomials of degree 5 or greater can have solutions that aren't expressible in terms of standard functions
sterile ivy
$x^6 + 9 x^4 + 24 a^3 x - 9 x^2 - 1$
but is this the correct interpretation of the result? Do you understand why there is an x there? @polar chasm
?
polar chasm
but is this the correct interpretation of the result? Do you understand why ther...
Not sure where did the y(t) go
thats the only thing that im confused about
ill try to write my own interpretation to the solution
sterile ivy
ill try to write my own interpretation to the solution
alright curious to hear what you come up with! Here is the link of the wolfram alpha : https://www.wolframalpha.com/input?i=inverse+function+calculator&assumption={"F"%2C+"InverseFunction"%2C+"invfunction"}+->"(e^(-3+*+a+*+x)+*+(e^(6+*+a+*+x)+%2B+9+*+e^(4+*+a+*+x)+-+9+*+e^(2+*+a+*+x)+-+1))+%2F+(24+*+a)"
polar chasm
ohh you entered a instead of bt
sterile ivy
I think it just gives you the inverse equation
sterile ivy
Wolfram Alpha gave me this: but I don't know how to find these roots (where I re...
indeed: "where I replaced x with T and B with a"
polar chasm
which are logarithms of roots of the equation you gave above
polar chasm
why there is an x there
the roots of that equation dont contain x
the solutions are logarithms of roots of the equation you gave
sterile ivy
Wolfram Alpha gave me this: but I don't know how to find these roots (where I re...
there is an x term behind the 24 term, while there is no x term behind the other terms, something must have gone wrong
polar chasm
meaning logarithms of solutions to
x^6 + 9x^4 + 24ax^3 - 9x^2 - 1
huh
imma just solve it manually and see
sterile ivy
do you see what I mean ?
sterile ivy
imma just solve it manually and see
the inversion or the root?
polar chasm
**! If you Dutch SEE my \`about me**
Hmm, is it /(24B) or /(24BT)
polar chasm
the inversion or the root?
the inversion, the roots are unsolvable (analytically)
sterile ivy
/24B
(e^(-3 * B * T) * (e^(6 * B * T) + 9 * e^(4 * B * T) - 9 * e^(2 * B * T) - 1)) / (24 * B)
woven radishBOT
MethIsAlwaysRight
polar chasm
B is a constant, so we dont need to worry about it
and its basically a polynomial equation after substitution u := e^BT
$0=u^{6}+9u^{4}-24By\left(t\right)u^{3}-u^{2}-1$
woven radishBOT
MethIsAlwaysRight
polar chasm
now this equation has at most 6 solutions
solving for them, gives possible values of e^BT
sterile ivy
interesting
polar chasm
now taking log and dividing by B gives the value for T
polar chasm
interesting
note that the "B" or x shouldnt be an issue, because its just a constant
the polynomial ofc varies with different values of B
and so do the solutions
maybe we can do example
e.g. y(t) = 1, B = 2
that gives this polynomial:
,w 0 = u^6 + 9u^4 - 48u^3 - u^2 - 1
woven radishBOT
sterile ivy
hmm
polar chasm
the solution u = 2.83788 gives solution for u, which is e^BT
so e^BT = 2.83788
and hence, T = ln(2.83788)/B = ln(2.83788)/2
,w ln(2.83788)/2
woven radishBOT
polar chasm
or around 0.521529
sterile ivy
note that the "B" or x shouldnt be an issue, because its just a constant
well B is a constant, while x was replacing T, which is not a constant!
sterile ivy
so what would be the inverse equation? What is T(Y) ?
polar chasm
ill just quickly try if my solution worked
sterile ivy
curious to see what you come up with!
polar chasm
,w (e^(-3 * 2 * 0.521529) * (e^(6 * 2 * 0.521529) + 9 * e^(4 * 2 * 0.521529) - 9 * e^(2 * 2 * 0.521529) - 1)) / (24 * 2)
woven radishBOT
polar chasm
hmm it looks close enough to be just a rounding error
sterile ivy
hmm it looks close enough to be just a rounding error
what it seems to me is that you are looking for solutions to the equation Y(T) = 0, is that a correct understanding?
or is this somehow important in finding T(Y)?
polar chasm
what it seems to me is that you are looking for solutions to the equation Y(T) =...
not really
ill show you how I got the inverse function
$y\left(x\right)=\frac{e^{-3Bx}\left(e^{6Bx}+9e^{4Bx}-9e^{2Bx}-1\right)}{24B}$
woven radishBOT
MethIsAlwaysRight
polar chasm
so basically we start with this
now we can note that there is a nice substitution u = e^Bx, which will simplify it a lot
$y\left(u\right)=\frac{u^{-3}\left(u^{6}+9u^{4}-9u^{2}-1\right)}{24B}$
woven radishBOT
MethIsAlwaysRight
polar chasm
that gives us this if im not mistaken
Small rearrangement and simplfiications give
$24By\left(u\right)=u^{3}+9u^{1}-9u^{-1}-1u^{-3}$
woven radishBOT
MethIsAlwaysRight
sterile ivy
looks good
woven radishBOT
MethIsAlwaysRight
polar chasm
ill replace y(u) with just y for now, as it will be the input to the inverse function
$0=u^{3}+9u^{1}-9u^{-1}-1u^{-3}-24By$
woven radishBOT
MethIsAlwaysRight
polar chasm
which gives this
now its almost a polynomial, except it has some negative powers there
so we multiply both sides by u^3
u^3
$0=u^{6}+9u^{4}-24Byu^{3}-9u^{2}-1$
like this
now it's a nice polynomial
heavy laurel
meth is right
woven radishBOT
MethIsAlwaysRight
polar chasm
**MethIsAlwaysRight**
now this can be solved for u, if we know the values of y (which is input to the inverse function) and also the value of B, which is a constant
then it becomes just completely normal polynomial
so to test it, we can choose e.g. B = 2 and y = 1
so we are solving for Y(T) = 1, when B = 2
sterile ivy
wait so there is no general solution?
polar chasm
wait so there is no general solution?
Not a closed form one
the 6 solutions are logarithms of the 6 roots of the equation above, all divided by B
sterile ivy
um so Y(T) = e^10^50 and B = 10^-35/3
polar chasm
those are quite large values
sterile ivy
does that make it harder?
polar chasm
potentially, because i dont think wolfram can handle this
sterile ivy
it's the 4-volume of an expanding universe under certain assumptions and the cosmological constant devided by 3 (as expressed in s^-2)
sterile ivy
it's the 4-volume of an expanding universe under certain assumptions and the cos...
Y is a 4-volume and B is the cosmological constant devided by 3
I am doing an physical calculation since I am curious about something
polar chasm
$0=u^{6}+9u^{4}-24\cdot10^{-\frac{35}{3}}\cdot e^{10^{50}}\cdot u^{3}-9u^{2}-1$
woven radishBOT
MethIsAlwaysRight
sterile ivy
but don't have sufficient math background for it...
polar chasm
this is the equation to solve
i dont think wolfram can handle that
but maybe some softwares designed for working with large numbers could do the job
sterile ivy
hmmm do you know any?
polar chasm
not really
sterile ivy
hmmm
polar chasm
ill try asking other helpers
sterile ivy
<@&286206848099549185> anyone here know how to solve this equation (or solve it approximately):
$0=u^{6}+9u^{4}-24\cdot10^{-\frac{35}{3}}\cdot e^{10^{50}}\cdot u^{3}-9u^{2}-1$
woven radishBOT
! If you Dutch SEE my `about me
sterile ivy
one solution is suffficient
sterile ivy
ill try asking other helpers
thanks! Let me know if you find someone
polar chasm
Got one idea
the u^2 term and -1 term appear insignificant
and if they got erased, it would be just depressed cubic
which is solvable
and it should give approximate solution
,w solve u^3 + 9u - 24*10^(-35/3)*e^10^50
woven radishBOT
polar chasm
what
thats obviously nonsense
it does have real solution
hmm actually
if i erased the 9u term
which is probably insignificant as well
it would be just cube root of 10^-(35/3) * e^10^50
which is around $e^{3\cdot10^{49}}$
woven radishBOT
MethIsAlwaysRight
polar chasm
that gives u
now u = e^BT
so e^(3*10^49) = BT
which means
T = 3*10^49 / 10^-35/3
,w 3*10^49 / 10^(-35/3)
woven radishBOT
devout snowBOT
@sterile ivy Has your question been resolved?
polar chasm
np
so basically the idea was removing the terms that dont have that much influence
that is: -9u^2, -1, 9u^4
polar chasm
alr
so the equation is 0 = u^6 + 9u^4 - 24*10^(-35/3) * e^10^50 * u^3 - 9u^2 - 1
now we can notice that if we remove the -1 from the end, the solution wouldnt change drastically
same with -9u^2
sterile ivy
yes we are looking for a very large u anyway
polar chasm
correct
polar chasm
because u^6 will be much much much larger than -9u^2
it will have much more influence
sterile ivy
hmmm
polar chasm
Yk what
lets assume we dont remove it for now
and lets just work with this
0 = u^6 + 9u^4 - 24 * 10^(-35/3) * e^10^50 * u^3 - 9u^2
divide everything by u^2
0 = u^4 + 9u^2 - 24 * 10^(-35/3) * e^10^50 * u - 9
and suddenly, the 9 becomes just a constant
sterile ivy
and suddenly, the 9 becomes just a constant
good argument
I am convinced
so
0 = u^4 + 9u^2 - 24 * 10^(-35/3) * e^10^50 * u - 9
how do we go from there?
sterile ivy
should be the approximate order of T
this is promising
polar chasm
this is promising
sorry, had to leave for a while
anyway
0 = u^4 + 9u^2 - 24 * 10^(-35/3) * e^10^50 * u
this is when we erase -9
because its just constant, and it shouldnt be too significant
divide everything by u
and get
0 = u^3 + 9u - 24 * 10^(-35/3) * e^10^50
now this is already not so bad
it's a cubic equation
This is a solution of u^3 + pu + q = 0
I think
sterile ivy
sorry, had to leave for a while
no problem
alright
let me think if I can understand this
I will message you if not
polar chasm
This is a solution of u^3 + pu + q = 0
Okay anyway, one thing we can note is that in our case p is so large, that the q becomes basically insignificant
so we can further do one more and last reduction
0 = u^3 - 24 * 10^(-35/3) * e^10^50
and that's completely removing the term +9u, because its quite small in comparision to the other one
polar chasm
0 = u^3 - 24 * 10^(-35/3) * e^10^50
And this gives us u = cube root of 24 * 10^(-35/3) * e^10^50
I think that it shouldnt differ by more than 0.1% from the real solution
cube root of 24 * 10^(-35/3) * e^10^50 = (24)^(1/3) * 10^(-35/9) * e^((10^50)/3)
now that in turn equals 0.00037254738 * e^((10^50)/3)
e^((10^50)/3 - 7.89514633)
so u = e^((10^50)/3 - 7.89514633)
and u = e^BT
so e^BT = e^((10^50)/3 - 7.89514633)
or BT = (10^50)/3 - 7.89514633
so T = ((10^50)/3 - 7.89514633)/B = ((10^50)/3 - 7.89514633)/10^(-35/3)
= (10^50)/(3*10^(-35/3)) - 7.89514633) / 10^(-35/3)
the 2nd term is kinda insignificant, so ill just remove it ig
(10^50) / (3*2.1544347e-12)
1.5471963e+61
or approximately 1.5*10^61
damn my guess wasnt that bad when I look at it retrospectively
devout snowBOT
@sterile ivy Has your question been resolved?
undone bone
i'm tryna work out how set notations of quadratics inequalities work
acoustic helm
set intersection. The elements of the resulting set are the elements found in BOTH sets
undone bone
can u like kinda simplify that
acoustic helm
i'll give an example.
{2, 3, 4, 5} n {3, 4, 7, 9} = {3, 4}
acoustic helm
it reads as: "element k such that k is greater than -6root3"
should really be k in R
acoustic helm
but it means the set would be all real numbers greater than -6root3
so what would the other set be?
undone bone
k is less then 6 root3
acoustic helm
exactly, so what numbers are in both sets?
undone bone
anything between those 2
acoustic helm
yes, that's all the intersection is
restive river
um
inner viper
I have a question, Is it possible to discover equality between numbers with powers greater than 1? I need discover a equality in 3 and 5 with power than 1, I need to discover equality between them without doing my hand with.
A simple example, "2^4=4^2".
Anyone can help me pls?
Is there a formula for this?
inner viper
well thinked
inner viper
but can I convert both sides after finding an equality?
i need find an equality without change 3 and 5
I need this to prove my thinking on a question
I need to find an equality between 3 and 5 with a power greater than 1, in which the sum of the powers of the two numbers is equal to 59
until they answer me I will do my hand ;-;
grizzled creek
I need to find an equality between 3 and 5 with a power greater than 1, in which...
make your own help channel please
inner viper
ok
grizzled creek
is anyone familiar with a d r t table
what about it?
restive river
what about it?
r u familiar with it
ill assume u r
ok so i have this problem
.close
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
kindred yacht
What is the meaning of equal roots
safe jasper
two equal roots means the quadratic only has one solution
for example, x^2 + 2x + 1 = 0 has one solution (two equal roots), because it becomes (x+1)^2 = 0 --> x + 1 = 0 --> x = -1
kindred yacht
no
safe jasper
it's a super useful thing to do with quadratics
if you have a quadratic of the form ax^2 + bx + c = 0, then we say the discriminant of the quadratic is b^2 - 4ac
that number, b^2 - 4ac, is what decides the number of roots of your quadratic
when b^2 - 4ac > 0, you have two real solutions
when b^2 - 4ac = 0, you have one real solution (two equal roots)
when b^2 - 4ac < 0, you have two complex solutions
kindred yacht
What is the meaning of equal roots
ok but how do i solve this now
safe jasper
well you know that 4x^2 - 12x + c has two equal roots so its discriminant is 0
b^2 - 4ac = (-12)^2 - 4(4)(c)
= 0
solve for c
once you have c, it's a simple matter of solving the quadratic for part b
kindred yacht
is there no other way like without the discriminant
cauz they did not teach us that
so i am sure there might be another way
safe jasper
okay, geometrically a parabola has two real solutions if it intersects the x axis twice
so for an upward opening parabola
like this one (you know it opens upwards since coefficient of x^2 is positive)
if it intersects x axis twice then its vertex is below the x axis
if the parabola has no solutions, it doesn't intersect the x axis anywhere so vertex has to be above the x axis
if it only intersects the x axis once, that's only possible when the vertex is exactly on the x-axis
that vertex is exactly the one root
so you just need to find the x coordinate of the vertex of 4x^2 - 12x + c
devout snowBOT
dawn lintel
nvm its too complez
Just use b^2=4ac
devout snowBOT
Available help channel!
warm jay
devout snowBOT
warm jay
c) For m = 3 determine the solutions (xo, yo, Zo) of the system of equations, so that x_{0} + y_{0}*z_{0} = 4 and Xo, Yo, Zo are integers.
I dont know what should i do
plush grail
warm jay
?
devout snowBOT
@warm jay Has your question been resolved?
warm jay
i done some resarch i i should do something like
det of deltaX / det of A(3)
but if i do det of delta X it give me 0
0/5
and i dont know if its rigt
right
<@&286206848099549185>
clear needle
The det of A is wrong
warm jay
Id give 7.5
i will work on my back after I am done working on this problem
one muscle a time
warm jay
The det of A is wrong
let my check
merry grotto
i will work on my back after I am done working on this problem
Look
do not overwork
its good
dont put tension on it
that much
or else
muscle fibres
will tear
negative growth.
Its good.
Enough for now.
merry grotto
do you know how to resolv the problem
lemme check real quick
merry grotto
it is kinda wrong
merry grotto
The det of A is wrong
ye exactly
warm jay
i recalculetd
its 0 now
and i dont know how to calculat the ecuation sistem if the matrix is ireversable
glacial helm
<@&286206848099549185> is when is arctanx>1
warm jay
?
devout snowBOT
@warm jay Has your question been resolved?
devout snowBOT
@warm jay Has your question been resolved?
warm jay
.close
devout snowBOT
devout snowBOT
Available help channel!
restive river
Hello, a friend of mine had this question
devout snowBOT
Hello, a friend of mine had this question
restive river
lusty sapphire
Hello, a friend of mine had this question
!status
devout snowBOT
Hello, a friend of mine had this question
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
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devout snowBOT
I have the solution but I am stumped
Show your work, and if possible, explain where you are stuck.
restive river
Solution to a similar problem
No clue why
Any clue?
Just help me to solve this from scratch, please
<@&286206848099549185>
sage burrow
if A = {3,5,8,9} and A\B = {3,8 } what do you know about B then?
sage burrow
yes.
restive river
But it should contain 5 and 9
sage burrow
yes
restive river
I need help from here
sage burrow
you now that B contains 5 and 9 and does not contain 3 and 8, what about 1,2,4,6,7?
restive river
!help
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restive river
The distance betweeen bases on a base ball diamond is 90. ft. How far is it between third and first base?
lusty sapphire
The distance betweeen bases on a base ball diamond is 90. ft. How far is it betw...
Draw a diagram, and use your geometry knowledge
restive river
I want to know if it's equal to 180
lusty sapphire
I want to know if it's equal to 180
No
restive river
I can't take photos but i'll explain so I think the sides of the triangle are 90. (Both sides) and using the pythagorean theorom to find the hypotenuse(distance between third and first base) it equals 127.27
lusty sapphire
I can't take photos but i'll explain so I think the sides of the triangle are 90...
Sounds right
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visual drum
I have no idea how to do this should I
find a single a or b?
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I have no idea how to do this should I
find a single a or b?
visual drum
Q34
glad patio
You might be able to find a^2 in terms of a (and hence b from a+b = -3) if you substitute a into the quadratic 
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native heart
True/false: every vector space over R contains a subspace isomorphic to R^n for some n>=0
i found this math stackexchange result, but i was wondering about how to see this for the zero vector space over R?
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True/false: every vector space over R contains a subspace isomorphic to R^n for ...
sand dove
True/false: every vector space over R contains a subspace isomorphic to R^n for ...
{0} is by convention R^0
torn vessel
any linear transformation maps 0 to 0
so you'd just have the identity map from {0} to {0}
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limpid sable
how would you find x?
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how would you find x?
dense jay
limpid sable
righttt
omg u sub !
but not u sub just using a lwetter fr
ok thanks chat
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solar goblet
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jaunty abyss
Hello
Is it okay if I change the 4x-45 in
90-x=4x-45
to 45-4x or would that have a different meaning?
jaunty abyss
Aw ok
Asking for this question.
I wrote down 45-4x because that’s the order in which they said it
Next time how can I know to change the order?
Soooo
? Lol
timber swan
can you help??
acoustic leaf
the issue is that "less than" is ambiguous phrasing
jaunty abyss
Oh okay
spiral hollow
the issue is that "less than" is ambiguous phrasing
not really
in this case its straightforward
4x - 45
spiral hollow
x less than y is equivalent to x subtracted from y
if they said "minus" instead of "less than", your original answer would be correct. it would be 45 - 4x
jaunty abyss
Oh ok
native heart
could someone help me with this true/false? i tried to think of concrete examples (R^2 sending everything to origin, R^3 sending everything to x-axis) and it seems true but idk about general cases
devout snowBOT
could someone help me with this true/false? i tried to think of concrete example...
upper schooner
Do you know any formulas that link the dimension of the kernel and the dimension of the linear map's domain?
upper schooner
It's all good, don't worry about it (also the hint I had wouldn't have been helpful, so there's that 
)
native heart
It's all good, don't worry about it (also the hint I had wouldn't have been help...
i think it wouldve been helpful though right? rank nullity theorem?
upper schooner
i think it wouldve been helpful though right? rank nullity theorem?
The one I was thinking of, yea (but that would only really allow you to deduce something about the image of T, the image would have dimension 5, which I guess helps a bit with intuition, but doesn't tell you a lot about the dimension of V beyond considering the image is a subspace of V )
native heart
The one I was thinking of, yea (but that would only really allow you to deduce s...
i was thinking dim F^5 = dim Ker T + dim Im T
5 = 0 + dim Im T <= dim V
dim V >= 5, which makes the statement false
upper schooner
i was thinking dim F^5 = dim Ker T + dim Im T
5 = 0 + dim Im T <= dim V
dim V >=...
Well, you'd have to give an example where it's false, but that's the thinking behind it (it could be the case that dim(V) = 5, in which case you don't have a contradiction at that point!) any space which has dimension strictly greater than 5 would do (e.g. set V to be F^6 and let T set the last coordinate to zero, and "include" the first five ones)
native heart
Well, you'd have to give an example where it's false, but that's the thinking be...
right, but since they didnt specify V i would just think that putting true would imply its true for any arbitrary V
upper schooner
right, but since they didnt specify V i would just think that putting true would...
correct, which is why you should bring a specific counterexample of V to show the statement false 
native heart
correct, which is why you should bring a specific counterexample of V to show th...
right, thanks :D
native heart
back to this though, would this be true?
upper schooner
And it may be worth thinking about the "send the last few coordinates to zero" idea here too 
Actually, I'm fried 
upper schooner
back to this though, would this be true?
Let's assume we have one solution, x0, to that, so that T(x0) = b - can you cook a new, different, solution from x0?
native heart
Let's assume we have one solution, x0, to that, so that T(x0) = b - can you cook...
hmmm what do you mean by that
upper schooner
As in, let me give you one solution, x0, can you name me another one (in an abstract sense, if needed?)
native heart
As in, let me give you *one* solution, x0, can you name me another one (in an ab...
i cant think of anything :(
upper schooner
i cant think of anything :(
Awww, fair enough 
new question, can you define the kernel of a linear map for me? And what it means to be linear?
native heart
yeah
Ker(T) = {v in V | T(v) = 0}
Linearity: for x,y in V, c in F,
T(x + cy) = T(x) + cT(y)
upper schooner
Ker(T) = {v in V | T(v) = 0}
Linearity: for x,y in V, c in F,
T(x + cy) = T(x)...
Uh-huh, nice 
soooo, from those, say I had a general x in the space V, and v from the kernel of T, can you rewrite T(x + v) for me?
native heart
T(x + v) = T(x) + T(v) = T(x)
upper schooner
i cant think of anything :(
Yep, now, back to the question
upper schooner
Yep, and as the dimension of the kernel is nonzero, there are infinitely many nonzero choices for v
Soooooo 
native heart
so theres infinitely many solutions if a given solution exists
but a given solution might not exist?
since dim domain > dim codomain by rank nullity... there is some v in V that is not mapped to
right
wait
dim V > dim im
upper schooner
Yep, you needn't have a solution existing (e.g. take V to be F^3, and T(x, y, z) = (x, 0, 0), then T(x, y, z) = (0, 1, 1) has no solution)
upper schooner
so theres infinitely many solutions if a given solution exists
...but the moment you have just one solution, you immediately get infinitely many, so it's impossible to have only a unique solution
upper schooner
(of course, for the purpose of the question, showing one solution forces infinitely many is sufficient to conclude it's a true statement, cause if the "no solutions" part isn't true, the "infinitely many" part is, so it's inconsequential to us whether "no solutions" is possible or not)
native heart
(of course, for the purpose of the question, showing one solution forces infinit...
wait im kind of confused
what do you mean by that
upper schooner
To show a general statement "A or B" is true, you only need at least one of those to be true
So if you can show that whenever "A" isn't true, "B" is, you're happy, because you'd have "B" true if "A" weren't
upper schooner
Awwww it's more of a side comment than anything, but always useful to know these things, makes life a bit easier 
native heart
yep :D
like the R^2 case where T sends everything to the origin right
in that case if we choose b = origin, "A"/no solutions would be fales and "B"/infinitely many solutions would be true and vice versa for b not 0
upper schooner
Yep, even better example than the one I thought of too!
native heart
i feel my brain expanding 🤯
wait this might be a little out of scope but the thought just suddenly came
what if instead
V was a vector space over lets say Z/nZ
which has finite # of elements
native heart
Uh-huh, nice <:SCgoodjob2:750436894915166321> soooo, from those, say I had a gen...
would the same logic still apply? like for this
like the idea was that you can get infinitely many elements from the kernel right
lets just say V = (Z/2Z)^3 over F = Z/2Z, then we might not necessarily be able to get infinitely many elements in the kernel right...
even though dim(Ker(T)) = 2 can still hold
with your example, like T(x,y,z) = (x,0,0)
upper schooner
Good question tbh 
I would want to say it doesn't, the idea of before being that "hey, there's infinitely many choices for the coefficients of the basis vectors", which holds over any field with infinitely many elements (e.g. the rationals and above), whereas for finite fields there isn't
Mind you, I might be cooked, so don't hold me to that one 
native heart
Mind you, I might be cooked, so don't hold me to that one <:NervousSweat:1076076...
LOL felt that fr 🫠
native heart
Good question tbh <:catThink:519997422194393108> I would want to say it doesn't,...
but yeah thats what i was thinking too
thanks for all ur help i appreciate it sm 😭 🙏
upper schooner
thanks for all ur help i appreciate it sm 😭 🙏
Awww, a pleasure, have a good one!
native heart
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cosmic igloo
Hello! I wanted to ask about boundary curves and their orientation. for this problem, with the unit normal pointing outwards, why is C1 CCW and C2 CW?
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Hello! I wanted to ask about boundary curves and their orientation. for this pro...
acoustic leaf
we must have C1 counterclockwise to ensure the right orientation of the normal vector, then C2 is just there to "cancel out" the rest of the surface
cosmic igloo
hmm ok
i get that C1 has to be CCW for the right orientation but i don't exactly understand what is meant by C2 "cancelling out" the rest of the surface
i mean i kind of get it
but idk i can't exactly think of a concrete reason
acoustic leaf
in stokes' theorem there must be only 1 curve bounding the surface. so we can imagine the surface from C1 extending all the way upward, then C2 has part of the surface with opposite orientation, so that integrating both will cancel out the shared part
finite cradle
Can someone please help answer this $\int (1-x)^4$ Is my answer correct? First, I used u-substitution. $u=1-x$ then $\int u^4$ using power rule $\frac{u^5}{5}$ substituting the original value $\frac{(1-x)^5}{5}+ C$
devout snowBOT
Can someone please help answer this $\int (1-x)^4$ Is my answer correct? First, ...
woven radishBOT
chobu nomu
safe jasper
i believe you're missing a factor of a negative sign
sonic smelt
You seem to have forgotten about the differentials
safe jasper
you should always keep track of the dx and du and stuff
not only is it good notation, it prevents errors like this from happening
you had $\int (1-x)^4 dx$
then if $u = 1-x$, $du = -dx$ so $dx = -du$
woven radishBOT
neil
safe jasper
then your integral would become $\int - u^4 du$
woven radishBOT
neil
finite cradle
oh i see
finite cradle
you had $\int (1-x)^4 dx$
then if $u = 1-x$, $du = -dx$ so $dx = -du$
can you please explain how you came up with $du=-dx$?
woven radishBOT
chobu nomu
stray flame
-ve sign b4 x
safe jasper
if $u = 1 - x$, then $\frac{du}{dx} = -1$
woven radishBOT
neil
safe jasper
you usually can't interpret derivatives as fractions like du divided by dx but with integration sometimes you can
so i just multiplied the dx over
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past scaffold
Why isn't 0+0+0+0+0+0+0+0+0.... not equal to 0
devout snowBOT
Why isn't 0+0+0+0+0+0+0+0+0.... not equal to 0
safe jasper
why would this not equal 0?
is there even a way to write this infinite sum in a way that gives you something other than 0?
sturdy mirage
Why isn't 0+0+0+0+0+0+0+0+0.... not equal to 0
Who's bullying you into thinking this isn't 0? We need names.
stray flame
Fr
sturdy mirage
Wait.
graceful cosmos
What's the original question?
sturdy mirage
"isnt" "not". Are you asking why all those do sum to 0?
past scaffold
But if ur asking for limit of that
So we can say 0×infinite = 0 ?
No limit
Just exact 0 and uhh "exact" infinite
stray flame
Yes I think
sturdy mirage
Anything times 0 is 0.
past scaffold
Ok ty
stray flame
Actually
sturdy mirage
If you really wanted to prove it, you could use induction.
stray flame
No
graceful cosmos
Infinity isn't a thing you can multiply by
sturdy mirage
it's a theory, but his theoretical infinity still has a value, since it's not a real infinity.
If he's looking for an "exact" infinity, it's not an actual infinity.
opal scroll
This is not how infinity works
sturdy mirage
hence, a fake infinity.
opal scroll
What
opal scroll
it's a theory, but his theoretical infinity still has a value, since it's not a ...
This is gibberish
sturdy mirage
It doesn't have to work if it's not infinity.
It makes sense if you think about it.
opal scroll
No I can assure you it doesn't
sturdy mirage
Not being open to the discussion just means you're being mean without listening.
opal scroll
There is no discussion since you haven't said anything of substance
safe jasper
It makes sense if you think about it.
i just bought a telepathic candle. it makes scents if you think about it.
sturdy mirage
And you have? All you've said is that I'm speaking nonsense.
sturdy mirage
i just bought a telepathic candle. it makes scents if you think about it.
It smells pretty good from over here.
opal scroll
"0 x infinite" is not a well-defined notion
sturdy mirage
i didn't say it was.
opal scroll
But in the right contexts you can absolutely speak rigorously about infinite objects
sturdy mirage
I said a number times 0 is 0. Infinity is not a number.
opal scroll
Define number
sturdy mirage
Depends on our universe of discourse.
opal scroll
This whole "infinity is not a number it's just a concept" thing is silly
safe jasper
out of curiosity i know in axiomatic set theory we use nestings of the empty set to define numbers, is there a similar axiomatic buildup of infinity?
opal scroll
This is getting off topic for a help channel. And I'm not sure exactly what you mean by "axiomatic buildup of infinity"
sturdy mirage
Considering the guy hasn't responded in a long time, I'm assuming he's done with the conversation.
opal scroll
An infinite set is a set with infinitely many elements
sturdy mirage
But an infinite set can be countably infinite.
Such as the set of natural numbers.
opal scroll
Yes? That's not relevant to what I said
sturdy mirage
But every natural number times 0 is 0.
safe jasper
i guess i meant that in the same way one could define 0 = empty set, 1 = {empty set}, 2 = {empty set, 1}, ...
opal scroll
You sure are saying facts
safe jasper
is there a rigorous set theoretic buildup of infinity
other than saying "it's the cardinality of an infinite set"
opal scroll
I mean you could say there exists an injection from omega into it
But that requires already having a notion of ordinals
safe jasper
ah it seems like ZFC took infinity to be an axiom
opal scroll
We should leave this help channel though. This is very off topic
sturdy mirage
Every message sent in here means the channel takes longer to self close
opal scroll
ah it seems like ZFC took infinity to be an axiom
The axiom of Infinity is a thing yes. If you're asking how exactly that's formulated. But this is my last message here
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signal lava
!help
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signal lava
what did i do wrong
ugh
i already se my mistake
i didnt distribute the negative sign to the positive 2
only the 7
why do i keep making these silly mistakes??
how to prevent them?
its like im blind sometimes
but my whole process is right
yes
but i keep making these mistakes
how do i prevent them
its like i misread it forget about it
im so close
to getting good
help
did i do this right
i need help someone
signal lava
stray flame
Ye they r right I think
final torrent
dawg
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kindred yacht
how do i solve this
devout snowBOT
how do i solve this
kindred yacht
simplify
radiant anvil
simplify
radiant anvil
what have u tried
kindred yacht
i tried multiplying both the terms in the nubmerator and factor it
did the same with the denomintor
radiant anvil
try to factor it first
kindred yacht
but there was nothing in common to coninue
kindred yacht
try to factor it first
i did it
radiant anvil
no factor it before multiplying
kindred yacht
no factor it before multiplying
but how am i supposed to know when to do it before and when to do it after like some problems require me to multiply then factorise some are before multoplying
radiant anvil
the stuff that u have to expand before factoring are in the form of stuff+stuff. in this case we have it in the form of (stuff)(stuff). so u can just try to factorise it directly
radiant anvil
tysm i got the answer
good job
kindred yacht
the stuff that u have to expand before factoring are in the form of stuff+stuff....
oh ok ty
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restive river
Suzzie’s mom is making homemade wafer cones that will be used for her princess castle birthday cake. Each cone will be 6 cm diameter wide and 10 cm tall. How big must she make each cone.
HINTS: Use surface area, but you will not have a base. You will also need to find the slant height first!
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Suzzie’s mom is making homemade wafer cones that will be used for her princess c...
restive river
.help
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woven radishBOT
Result:
10.440306508911
Ok
Around
It
No inside
Total
Ok
So later al
2 pi radius squared + 2 pi r height
So just the height then
Idk it's not including the radius
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fallen trench
What it means: 10 modulo (10n − 1)
And how means x ≡ y mod(k)
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What it means: 10 modulo (10n − 1)
And how means x ≡ y mod(k)
lunar harbor
What it means: 10 modulo (10n − 1)
And how means x ≡ y mod(k)
What it means: 10 modulo (10n − 1)
the remainder when 10 is divided by (10n-1)
And how means x ≡ y mod(k)
x and y have the same remainder when divided by k
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dark peak
How do you prove a number is prime?
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How do you prove a number is prime?
humble gyro
How do you prove a number is prime?
Do you know the definition of a prime number?
dark peak
yes..?
sonic smelt
See if it holds (i.e., whether there are any positive divisors of the integer besides 1 or itself)
Or use wilson's theorem
dark peak
Can you do it algebraically? i do alevel maths
dark peak
Well, what is it?
a number only divisible by 1 and itself?
humble gyro
a number only divisible by 1 and itself?
Yes, an integer greater than 1 that's only divisible by 1 and itself
For example, is 29 prime?
dense lynx
How do you prove a number is prime?
depends a lot on the number
for sufficiently large numbers proving they’re prime is extremely difficult
sonic smelt
A fast general way to check whether an integer n > 1 is prime would be to see if n is divisible by prime numbers <= sqrt(n)
dark peak
For example, is 29 prime?
Yes
dark peak
A fast general way to check whether an integer n > 1 is prime would be to see if...
ah okay
humble gyro
Yes, that's one way to prove that a number is prime. You could just check all the numbers below 29 and see if 29 is divisible by them. But if you take a look at the divisors of any number:
168
2 * 84
3 * 56
4 * 42
6 * 28
7 * 24
8 * 21
12 * 14
14 * 12
21 * 8
...
you can see that the pairs start repeating after you pass sqrt(168). It cannot have two divisors that are both larger than sqrt(168), since the resulting number would be more than 168
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frail osprey
Hey. So I've normally been solving these questions using slope intercept form. (y = mx + c). This involves me finding the gradient and solving for c. This is wayyyyyyyyyy quicker than that. Are there any caveats to using the point slope formula?
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mystic sluice
No
modest hawk
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modest hawk
Help how do I solve this
polar chasm
17B4AF ig? Or have you tried it already?
modest hawk
Idk let me check
mystic sluice
lol
pale bolt
17B4AF ig? Or have you tried it already?
free automated captcha solver
modest hawk
17B4AF ig? Or have you tried it already?
Wow thank you so much I've been struggling this for hours
polar chasm
Wow thank you so much I've been struggling this for hours
....
it says that you have 300 seconds to do that
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twilit wraith
steel gazelle
Hi, this is more of a wording problem lol. But are those two problems solved any different or are they asking for the same thing basically?
devout snowBOT
Hi, this is more of a wording problem lol. But are those two problems solved any...
steel gazelle
I'm not sure if there's a difference when it says, passing thru a point and contain a point
cloud linden
same thing
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dusty mesa
Hi does this makes any sense ? I don't know how to continue. The question SIMPLIFY
devout snowBOT
Hi does this makes any sense ? I don't know how to continue. The question ***SIM...
dusty mesa
...well probably?
Then what is correct
Uh cos4x=cos(2x+2x)?
cos(a+b)= cosacosb-sinasinb
And then i guess i continue
Just second
untold bough
Hi does this makes any sense ? I don't know how to continue. The question ***SIM...
this is fun im trying it out