But what value should we give it
#help-10
rocky goblet
it's also relevant because it means you're not dealing with real numbers, so you can't necessarily expect "ln" to mean anything
wide star
well exponents exist I don't see why ln would not
rocky goblet
there could be multiple definitions of ln that are equivalent about real numbers but only because of properties that real numbers have like division existing, or lack of zero divisors
violet kindle
Exponents exist for what?
south oracle
well exponents exist I don't see why ln would not
ln((-3)²) =/= 2ln(-3)
wide star
my system where 1/0 is defined
rocky goblet
i honestly have no idea what you're planning on using this "system" for
south oracle
ln((-3)²) =/= 2ln(-3)
Just because exponents exist on some numbers doesn't mean the exponent rule works
violet kindle
my system where 1/0 is defined
I'm enthralled and fascinated now
I've looked through your server history
I am highly invested in z = 1/0
wide star
aren't logs just one of two inverses of exponents
if exponents exist why would logs not?
grizzled shore
Can you show the full question that you have from wherever
violet kindle
ln(1/0)
grizzled shore
So you stop xy’ing us
violet kindle
if exponents exist why would logs not?
Multiple questions here: what do you mean two inverses, also exponents and logs do exist
so idk what u mean
wide star
Multiple questions here: what do you mean two inverses, also exponents and logs ...
in my system
grizzled shore
What is your system
wide star
exponents exist in my sytem
south oracle
Okay
rocky goblet
if exponents exist why would logs not?
well for the natural numbers, exponents exist but logs don't (for instance log base 2 of 3 is not a natural number)
grizzled shore
If it is not the same system everyone else uses
violet kindle
Nobody knows your system
rocky goblet
exponents exist in my sytem
how are they defined?
grizzled shore
Then you need to define your system explicitly
wide star
how are they defined?
where z=1/0
violet kindle
Wow
This is groundbreaking stuff
You are trying to define stuff using z with axioms that dont allow for z
That is where all of this fails
wide star
why would they not allow for z
as far as I can tell they only don't allow for an answer to 0x=1
violet kindle
Correct me anyone else if im wrong, but the real numbers are a field, and one of the definitions of a field is that the additive inverse does not have a multiplicative inverse
1/0 is the multiplicative inverse of 0, the additive inverse
Thus it does not exist
If you want to construct a number system where it does, you may have to build it axiomatically
wide star
then I guess its not a field
rocky goblet
1/0 is the multiplicative inverse of 0, the additive inverse
they're not using "/" to mean multiplicative inverse
rocky goblet
the actual defining rule of the system is that z^2 = z, and then you get a completely reasonable commutative ring
i don't remember what the definition of / is
wide star
What is it then?
its division except x/0 = x*z and z*0=0
violet kindle
Is 1/0 just a symbol for z and youre considering R adjoin z with these arbitrarily defined definitions?
Or something
I'm too tired for this
rocky goblet
anything divided by a+bz for nonzero b is zero
if b is zero and a isn't then you just divide each coefficient (as real numbers)
anything divided by zero is that thing multiplied by z
wide star
and this is why I didn't want to say what my number was
violet kindle
Well you would have had to because you are working in an entirely different number system than the reals
And asking a question about ln of a number implies reals i would assume
violet kindle
anything divided by a+bz for nonzero b is zero
if b is zero and a isn't then you...
I'm invested in this now
wide star
And asking a question about ln of a number implies reals i would assume
why would you not assume complex numbers
tardy epoch
and this is why I didn't want to say what my number was
If you can't answer basic questions about "your number" then maybe it's a problem with your number and not logarithm
wide star
I just want a formula for ln(x) so I can use it to find find ln(z) and whatever else I might need to test
violet kindle
The formula for ln(x) is ln(x)
wide star
If you can't answer basic questions about "your number" then maybe it's a proble...
it's not that I can't answer them, it's that i'm tired of answering them just for people to say its not possible
tardy epoch
it's not that I can't answer them, it's that i'm tired of answering them just fo...
Then you aren't answering them, are you?
You're just ignoring the flaws
wide star
Then you aren't answering them, are you?
what????
I answer the questions and then they still say "its dumb" or "it's not possible"
so I just stoped saying things that would lead to questions about 1/0
tardy epoch
You're just ignoring the flaws
That's an example of this
The"it's not possible" part
wide star
no one has pointed out a real flaw in over 6 months
tardy epoch
If by "real flaw" you mean you ignoring flaws or moving goalposts, then I agree
hot hazel
look
the standard definition of logarithm does not allow for taking the log of 1/0
you could try to define that in a semi-sensible way
but this server aint gonna be able to figure out what "sensible" means to the context youre using 1/0 in
unless you give that context
wide star
bruh guys all I asked if if there were any other formulas to solve ln(x) using only + - * / ^ √
violet kindle
People gave the answer
hot hazel
but you rejected that because it doesnt work for 1/0
wide star
is that the only one?
hot hazel
i mean you could come up with arbitrarily many "formulas" for logarithm
but none of them will be finitary closed-forms
if thats what you mean
all of them will either require an infinite process, or involve some function "outside" of what you listed
otherwise we wouldn't bother giving ln(x) a special name
we'd just use that function
wide star
all of them will either require an infinite process, or involve some function "o...
an infinite process isn't a problem
hot hazel
then take any of the standard series expansions, e.g. this one
rocky goblet
(that's not going to work because division isn't defined for these numbers)
hot hazel
i am not sure why the logarithm would be coming up in a context where division doesnt make sense.
tardy epoch
(that's not going to work because division isn't defined for these numbers)
Which is why their "number system" is nonsense and this is all a waste of time
rocky goblet
i am not sure why the logarithm would be coming up in a context where division d...
i don't know either
...i mean they have defined a symbol that they named "/", it's just not division
wide star
(that's not going to work because division isn't defined for these numbers)
well division with denominator of 1/0 is a slight problem in some contexts
violet kindle
Just make new axioms for everything 
hot hazel
$\ln(z) = -\sum_{n=1}^{\infty}\frac{(-1)^{n}z^{n}}{n}$ for $\Re(z) \in (-1, 1]$
now i doubt your object follows any sensible ordering
but if you wanted to try to define the logarithm without definining division by 1/0
this might be the closest thing
oops
warm shaleBOT
namington
hot hazel
better
violet kindle
How did you try it exactly
hot hazel
i mean theres a bunch of similar series you could try
the taylor series centred at 1 is $\ln(z) = \sum_{n=1}^{\infty}\frac{(z-1)^n}{n}$
warm shaleBOT
namington
hot hazel
radius of convergence is 1
it is impossible to pick a particular interpretation of logarithm that makes sense for whatever context youre working in without knowing what your goal is
wide star
How did you try it exactly
hot hazel
its possible, for example, that trying to find a formula is the wrong approach and instead you should just go with the lie-theoretic generalization of the logarithm
i.e. the exponential is the map to a lie group from its associated lie algebra and the logarithm is its inverse
unfortunately i am not sure of a way to define division by 0 in a lie algebra.
rocky goblet
where z=1/0
...also for any definition of ln that's consistent with what you said exponentiation is, ln(z) doesn't exist
hot hazel
it might also be useful, for example, to try to view your structure - whatever it is - as some sort of matrix group
in which case defining exponentials and pseudologarithms is immediate (just use the matrix exponential)
again, i do not know a way in which you'd do that in your particular case, and i would bet money on it being impossible to do so in a good way
but you could try
if theres no approach along these lines, i doubt this server would be able to help you
(and in a formal sense, the lie group and matrix group approaches i outlined are basically equivalent)
(or rather, the latter is a special case of the former)
the point is that, without knowing what your goal is in defining a logarithm for your object, we wont really know what perspective makes sense
wide star
in which case defining exponentials and pseudologarithms is immediate (just use ...
do matrix exponentials do the same thing as normal exponents?
hot hazel
in a certain sense, yes
but i wouldnt necessarily expect it to commute with the standard exponent on your structure, if the map into the matrix group is particularly esoteric
(that is to say, the matrix exponent of the matrix representation might not agree with the standard exponent of the complex-number representation)
so idk whether thats useful to you or not
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
misty gate
hi
obtuse pebbleBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
misty gate
Please only use the <@&286206848099549185> ping **once** if your question has no...
appologies
bot
spring trail
so u can change that expression into (4ab-70(a+b)+35^2)^3
check it
if u know abt roots of polynomials its very simple else u can just find the roots of the quadratic ig
spring trail
yessir
misty gate
helo
spring trail
hi
full granite
Im curious why do we get the same number of values for the x as its exponents?
spring trail
so u can change that expression into (4ab-70(a+b)+35^2)^3
@misty gate check this out
misty gate
Im curious why do we get the same number of values for the x as its exponents?
tricky trik mcq
spring trail
Im curious why do we get the same number of values for the x as its exponents?
not always true btw
polar fossil
Im curious why do we get the same number of values for the x as its exponents?
that's called the fundamental theorem of algebra
full granite
not always true btw
Yea ik..
misty gate
so u can change that expression into (4ab-70(a+b)+35^2)^3
umm why
spring trail
do u know how to deduce a+b and ab from from equations?
misty gate
yeah
full granite
that's called the fundamental theorem of algebra
Hmm.. ill look into it
spring trail
the c/a and -b/a thing
misty gate
yes
spring trail
well so i turned it into a uselful form
now just look for those two and sub in the values
misty gate
oh -35/a = sum
spring trail
Hmm.. ill look into it
u can just think about how the number of turning points would depend on the exponent; im not to sum abt it formally either
polar fossil
oh -35/a = sum
+35/a = sum
misty gate
2/a= product
spring trail
-(-35)
spring trail
umm im not sure if both those a represent the same things...
ruby path
so u can change that expression into (4ab-70(a+b)+35^2)^3
I doubt this is the way to do this
misty gate
umm im not sure if both those a represent the same things...
me too
misty gate
I doubt this is the way to do this
full granite
u can just think about how the number of turning points would depend on the expo...
number of turning points 😨
ruby path
Instead, using this quadratic make a new one with roots (2a - 35)^3 and (2b - 35)^3 and find the product of roots of that quadratic
misty gate
Instead, using this quadratic make a new one with roots (2a - 35)^3 and (2b - 35...
oh yeah that waht the teacher tot
symmetric root
ruby path
Do you know how to do it
misty gate
trans of eqns
ruby path
yes
ruby path
let y = (2a - 35)^3
misty gate
ok
ruby path
Can you now find a in terms of y
spring trail
that seems weirdly cyclic...
misty gate
in place of a?
ruby path
Then find the product of roots of the resulting quadratic
misty gate
or x?
ruby path
x
misty gate
ok
ruby path
It should be a quadratic
Or maybe you can be smart about it and you don't have to fully cube and ruin your life
misty gate
but the coefficient of x^2 is a
ruby path
so?
misty gate
the it ll be a cubic
ruby path
how does that make it a cubic
ruby path
The roots of your new equation will be $\sqrt[3]{y_1}$ and $\sqrt[3]{y_2}$
warm shaleBOT
neonperseus
misty gate
how
ruby path
Well because it's a quadratic in y^(1/3)
misty gate
Well because it's a quadratic in y^(1/3)
yes ok
bruh can you also simplify please
pls pls
ruby path
what
ruby path
no
ruby path
**neonperseus**
Can you find y_1*y_2
misty gate
Can you find y_1*y_2
nope it getscomplex
ruby path
Can you find $\sqrt[3]{y_1y_2}$
warm shaleBOT
neonperseus
ruby path
**neonperseus**
If you know this
misty gate
for that i need to form quad in that which i cant
spring trail
still wondering why my method was rejected; i thought u'd somehow eliminate a but dont see that happening either
ruby path
$a\left ( \frac{u + 35}{2} \right )^2 - 35\left ( \frac{u + 35}{2} \right ) + 2 = 0$
warm shaleBOT
neonperseus
ruby path
You don't even need to do much
You need to find the coefficient of x^2 and the constant term
you don't need to open it up and make it a quadratic
ruby path
yes
misty gate
you don't need to open it up and make it a quadratic
hmmm ok
whole dock
still wondering why my method was rejected; i thought u'd somehow eliminate a bu...
I agree
I dont see how it's wrong
spring trail
u'd need to cube the c/a here as well to arrive at the answer, right?
ruby path
I didn't reject it
spring trail
nvm that
misty gate
that why it get complex for me
whole dock
,w 8 - 70 × 35 + 35^2
warm shaleBOT
ruby path
$ax^2 -35x + 2 \equiv a(x - a)(x - b)$
warm shaleBOT
neonperseus
misty gate
the ans is 64
ruby path
$ax^2 -a(a + b)x +a^2 b$
warm shaleBOT
neonperseus
ruby path
Doesn't matter does it
whole dock
,w -1217^3
spring trail
it should matter
warm shaleBOT
ruby path
Not sure what you mean
misty gate
Not sure what you mean
.
misty gate
it should matter
.
misty gate
,w -1217^3
.
sage geode
The roots of p must be complex conjugates of one another, meaning it's some k(x - ai)(x + ai) where k and a are some real values (and k is nonzero)
So p(x) = k(x^2 + a^2)
And p(p(x)) = k(k^2(x^2 + a^2)^2 + a^2)
So p(p(x)) has roots x such that (x^2 + a^2)^2 = -a^2/k^2
misty gate
hm
sage geode
Yeah cuz it's said that p(x) = 0 implies x is purely imaginary, meaning that p(p(x)) = 0 implies p(x) is imaginary which is impossible if x is purely real or purely imaginary
misty gate
hmmm
lethal sand
well no it's not really impossible, it just means that the solution to p(p(x))=0 is complex
ruby path
misty gate
anyway, are you doing some kind of tests?
naw bruh its a pyq
misty gate
you seem eager to get the answer
lol
misty gate
you seem eager to get the answer
i am very eager in every task
lethal sand
then perhaps you should calm down and wait for help, and might as well have a bit of effort in solving the problem
misty gate
then perhaps you should calm down and wait for help, and might as well have a bi...
noted
👍🏻
.close thanks all
dapper bloom
This might be stuff the people who check these help channels don't know.
I don't know much complexity theory at least.
I'm not sure what exact channel would work for complexity theory. I'd probably try #discrete-math if nobody comes along who can help in the help channels.
It would also be good to ask if there is a more appropriate channel if you post to the discrete channel too just in case.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stoic token
I need help with this question , I want to know if the 2 answers I got from 2 methods are equal or not ?
obtuse pebbleBOT
I need help with this question , I want to know if the 2 answers I got from 2 me...
errant gulch
I need help with this question , I want to know if the 2 answers I got from 2 me...
use this as a reference and proceed further.....
stoic token
I already used this method it gave me this answer
But the log method gave me another answer , i just want to know if they are equal or not
🤔
errant gulch
trigonometry !!!!!
thick chasm
But the log method gave me another answer , i just want to know if they are equa...
They should give the same answers. Check your working if it doesn't matches
stoic token
Wdym by working?
stoic token
Yeah they are correct
But isn't there a way through which we can convert them into same thing
errant gulch
then both answers would be equal
in the end the what's the position of sec^2 x
after the bracket before the bracket ?
stoic token
Before
errant gulch
multiplied to x cot x ?
stoic token
It's multiplied to cotx
errant gulch
aight
errant gulch
the portion after the + in both the solutions is same
obtuse pebbleBOT
@stoic token Has your question been resolved?
stoic token
Thanks man for helping out yeah the second part is same in both answers and the part before + is also a little bit , same I think they have to be same , because of it , Once again thank you for assistance 👍
obtuse pebbleBOT
Available help channel!
knotty pendant
is the inverse of log_2 (2x-2) = 2^2x-2
obtuse pebbleBOT
is the inverse of log_2 (2x-2) = 2^2x-2
warm shaleBOT
alonelybean
knotty pendant
whats f and g
sage geode
Some functions, you can consider $f(x) = \log_2{x}$ and $g(x) = 2x - 2$ for this problem
warm shaleBOT
alonelybean
knotty pendant
(2y-2)(log_2 y )
sage geode
Are you sure? Simplify $g^{-1}(f^{-1}(x))$ step by step
warm shaleBOT
alonelybean
sage geode
(Oh and it doesn't mean the product of g^-1 and f^-1)
sage geode
[ f(x) = \log_2{x} \implies f^{-1}(x) = 2^x]
[ g(x) = 2x - 2 \implies g^{-1}(x) = \frac{x}2 + 1]
[ g^{-1}(f^{-1}(x)) = g^{-1}(2^x) = \dots]
Can you continue this?
Oops wait
knotty pendant
can u just do 2^y = 2x-2 then inverse is 2^x = 2y-2
warm shaleBOT
alonelybean
knotty pendant
2^x/2 +1
warm shaleBOT
alonelybean
knotty pendant
oh ye therea another question thats hard x^rootx = (root x)^x
idk how they get 1 as an answer
x^x^1/2 = (x^1/2)^x
x^x^1/2 = x^x/2
x^1/2 = 1/2x
2x^1/2 = x
4x = x^2
x^2-4x = 0
x = 0 or x = 4
sage geode
root as in square root?
sage geode
,w solve x^(sqrt(x)) = (sqrt(x))^x
warm shaleBOT
sage geode
Let's see
Oh, I see
You can take log_x only when x is a positive number besides 1
So before that step you need to consider two cases
x = 1 or x =/= 1
sage geode
x^1/2 = 1/2x
You used a logarithm to get to this equation without realising it
polar fossil
when faced with some stupid stacked exponent equation, taking a log of both sides is often the best way to simplify it
knotty pendant
isnt when base the same the expoents equal
sage geode
Again, the base has to be a positive number other than 1
If any base worked, then we would have the following implications:
0^1 = 0^2 -> 1 = 2
1^1 = 1^3 -> 1 = 3
(-1)^2 = (-1)^4 -> 2 = 4
knotty pendant
so first step to log both sides
sage geode
Yes, but don't forget to consider x =/= 1 to do that
(The case x <= 0 is immediately out of our consideration since sqrt(x) has to be defined and 0^0 is undefined)
knotty pendant
wat does x = / = 1 mean
sage geode
x is not equal to 1
sage geode
If you want to take the logarithm*
knotty pendant
but ur final answer for x can be 1
sage geode
Yes, because you have to consider the cases x = 1 and x =/= 1 separately
In the first case you check whether x = 1 is indeed a solution or not to the original equation (it so happens that x = 1 is actually a solution, so we still count it)
And in the other case you take log_x of both sides and continue (the step is valid since x is suitable as a base)
knotty pendant
what if x=1 not a solution
sage geode
what if x=1 not a solution
Then x = 1 is not a solution, just don't mention it in the final answer
sage geode
log base what?
sage geode
Eh, actually any base works
knotty pendant
ye but i would have to write log_10 every time
polar fossil
nah just write log and refuse to clarify
sage geode
It may looks like you avoided considering the x = 1 case by taking log_10, but it will come back after one or two steps
polar fossil
90% of the time it doesn't matter
knotty pendant
so in the first step of these quesions i should frirst sub in x=1
sage geode
rootx logx = x log rootx
Because then you have rootx logx = x/2 logx
Then you may or may not cancel out logx on both sides depending on whether logx is zero or nonzero
That is, x = 1 or x =/= 1
knotty pendant
so i should use ln just in case
sage geode
so in the first step of these quesions i should frirst sub in x=1
No, not always
knotty pendant
sub in x=1 for first case
sage geode
so i should use ln just in case
Generally just pick a base which will make things cancel out
E.g. it would make more sense to take log_2 in 2^x = 10^x than ln
sage geode
sub in x=1 for first case
If necessary, yes
knotty pendant
this question only have x instead of numbers so ig ln more suitable
sage geode
Taking log_x will be way faster, but, yeah, any log works in this case
sage geode
Right
knotty pendant
x(1-1/4x)=0
sage geode
Correct, now, can x be 0? (look at the original equation)
sage geode
Yes
sage geode
x(1-1/4x)=0
So this turns into 1 - x/4 = 0
knotty pendant
1-1/4x = 0 x = 4
sage geode
Yup
knotty pendant
wow
thanks
ur rlly smart lol
and good at explaining this stuff
alright im gonna go write this down in a book have a good rest of ur day
cya
.close
obtuse pebbleBOT
sage geode
Cya
obtuse pebbleBOT
Available help channel!
pearl mason
Hi can someone help me
obtuse pebbleBOT
Hi can someone help me
pearl mason
. We have divided three equal triangles with three different medians Can you make a triangle? Hint: the median is a line segment that connects from one vertex to the middle of the opposite side.
<@&286206848099549185>
jagged falcon
Can you make a triangle from what?
pearl mason
From this 6 parts
jagged falcon
What do you mean by making a triangle from these 6 parts?
pearl mason
We have 3 equal triangle
We divide these 3 triangles to 6 parts
Now we are gonna make a big triangle by this 6 part's
timid silo
I think the eqn. is wrong. It's given that the roots of the eqn. are a and b but the eqn. is 'ax^2+35x+c=0". There should be a constant term before x^2.
full granite
I think the eqn. is wrong. It's given that the roots of the eqn. are a and b but...
Isn’t a the constant term?
timid silo
If the constant term before x^2 is 2 then option C is the correct answer.
pearl mason
. We have divided three equal triangles with three different medians Can you mak...
????
glossy basalt
. We have divided three equal triangles with three different medians Can you mak...
i think yes
timid silo
Isn’t a the constant term?
No, 'a' is a variable but acc. to question, a and b are both roots of the eqn. and that's the problem.
glossy basalt
glossy basalt
can you use anydesk?
nope
full granite
No, 'a' is a variable but acc. to question, a and b are both roots of the eqn. a...
Heh.. i thought the a/b/c’s were considered coefficients which are constants by nature
How did you solve this sir
glossy basalt
pearl mason
look we should made a triangel with all 6 parts!
glossy basalt
look we should made a triangel with all 6 parts!
yep!
glossy basalt
like now. i'm trying
how's it going?
pearl mason
how's it going?
so bad
pearl mason
i can't make a triangle
glossy basalt
hmm
try using the same color for the same side of the triangle
like red, green, blue maybe
pearl mason
pearl mason
pearl mason
glossy basalt
glossy basalt
pearl mason
Dudeee!
glossy basalt
lone dirge
Nice
pearl mason
<:hype:484391278704853022>
pearl mason
But they are overlapping right?
yeah. real sizes
glossy basalt
<:sotrue:826971355542192148>
if you're done with the question you can close it by typing .close 😆
lone dirge
So how do you prove it's always possible?
pearl mason
So how do you prove it's always possible?
they don't ask that.
lone dirge
Just interested...
pearl mason
Just interested...
yeah me too^^
lone dirge
Can you name the different triangle parts and show where they are in the original splits and then in the final triangle
Maybe a1, a2, b1,b2, c1,c2
I wanna see it
lone dirge
or maybe do it with this coloring
lone dirge
Cool thanks
true spire
i have a weird question
obtuse pebbleBOT
i have a weird question
true spire
obtuse pebbleBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
...i don't think this question really means anything without further elaboration
true spire
...i don't think this question really means anything without further elaboration
what do you mean
rocky goblet
"3x + 4y + 5z" isn't a statement
hollow river
It's an expression
rocky goblet
there's no x,y,z for which 3x + 4y + 5z would be "false" or anything, since it's a number
so just saying "3x + 4y + 5z" doesn't give any information about x
rocky goblet
ok that makes a lot more sense
true spire
i hope so...
true spire
ok that makes a lot more sense
i dont get how should i even start
i tried giving a bunch of values
rocky goblet
well i think the most obvious first observation here is that x can't be 12 (or anything greater than 12)
true spire
yeah ok i see
rocky goblet
since then 3x would be 36 (or bigger), and then we add positive integers to it, and there's no way you get 35 by doing that
true spire
since then 3x would be 36 (or bigger), and then we add positive integers to it, ...
yep
rocky goblet
but x also can't be 11
33 + 4y + 5z = 35 doesn't have any solutions for y,z being positive integers, you would need 4y + 5z = 2
rocky goblet
...yeah given the small numbers here you could just try every value of x in descending order until you get a solution
true spire
...yeah given the small numbers here you could just try every value of x in desc...
so now i tried x=8, y=2, z= 1 which gives:
21+8+5= 34
so i'm 1 short
what do i do now?
rocky goblet
3*7 is 21
true spire
because 4 should be multiplied by 2 since its value is less then 5's
im pretty sure of the rest
now i could lower x and/or get y and z higher i suppose
rocky goblet
because 4 should be multiplied by 2 since its value is less then 5's
...are you sure?
that would minimize the value of 3x + 4y + 5z, but we're trying to make it exactly 35
since we're 1 short that seems to imply we should tweak y and z to make the number a bit bigger
true spire
since we're 1 short that seems to imply we should tweak y and z to make the numb...
OHhh
yeah ok i got it
tawdry pier
true spire
i was about to go into the wrong direction
tawdry pier
true spire
thank you @rocky goblet
tawdry pier
can somebody help me with o levels math
true spire
let me close this so its yours @tawdry pier
rich plume
can somebody help me with o levels math
!help
obtuse pebbleBOT
can somebody help me with o levels math
Please read #❓how-to-get-help
true spire
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obtuse pebbleBOT
obtuse pebbleBOT
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gentle pumice
Hi I need help doing this I'm stuck her and I don't know how to continue
royal flint
figure out all he points through which the function passes through and then substitute them in the function to find a and b
gentle pumice
figure out all he points through which the function passes through and then subs...
I tried doing this
Is this correct?
royal flint
this seems to be correct 👍
obtuse pebbleBOT
obtuse pebbleBOT
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supple mulch
Hi, I just got started doing my math homework project for summer and encountered this question: Factories 6a^2 +12ab so I did it and I got 6a(a+2b) but when I open it I don't get 6a^2+12ab I get 6a^" + 12b where am I wrong thanks in advance!
obtuse pebbleBOT
Hi, I just got started doing my math homework project for summer and encountered...
high lily
wdym by
$$6a^{"} + 12b$$
warm shaleBOT
ℝamonov
high lily
what were your steps in expanding
6a(a+2b)
supple mulch
what were your steps in expanding
6a(a+2b)
I did
6a times a
and 6a times 2b
wait
I'm dumb
nvm
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obtuse pebbleBOT
obtuse pebbleBOT
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broken coral
can someone help i was thinking to change into polar coordinates but the i dont have the intervalles for R so.....Determine the volume integral of F(x,y,z) = z * (x2 + y2) 0≤ z ≤1; -1 ≤ y ≤ 1; −sqrt(1−y²)≤ x ≤ sqrt(1−y²)
obtuse pebbleBOT
can someone help i was thinking to change into polar coordinates but the i dont ...
@broken coral Has your question been resolved?
obtuse pebbleBOT
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shadow lava
obtuse pebbleBOT
shadow lava
Where did the S go
It was there in the second and third expression but then it vanished
Also, can we call this integral symbol “S”? Or is there a more commonly used term to use
shadow lava
shouldnt even have been in the second expression
Weird…
shadow lava
shouldnt even have been in the second expression
it is added by Professor Leonard here and I copied it down
trim portal
Even Professor Leonard can make mistakes
kind hawk
prof leonard did not write what you wrote
shadow lava
Oh my bad
royal basin
prof leonard is using → where = would have been appropriate
kind hawk
I'm annoyed by his use of arrows. is that a thing he does?
shadow lava
Lol ya I’m not sure why he’s using arrows
Alright thanks that makes sense now
I’m trying to remember the rule for differential of 5x
d/dx is just 5, I believe
But d/dx of 5x^2 is 10x
So if I reverse engineer this..
royal basin
go back to derivatives
royal basin
i mean ok on the one hand you're trying to remember the power rule which you've forgotten
but on the other hand "reverse engineering" is def not the way to go about doing that imo
shadow lava
but on the other hand "reverse engineering" is def not the way to go about doing...
ah OK.. when I am finding the inverse of the derivative, I kinda look at that as "going backwards in time", from the derivative
to find the integral
kind hawk
that helps for simple functions. harder ones? not so much
shadow lava
oh OK
I will have to just use the formulas, and stop thinking forward <-> backward
to save myself headache
and less error prone
"differential" vs "derivative" .. ummm
I'm still a bit rusty with Calc 1
gotta refresh
can someone explain the difference between these two words?
not finding via Google, maybe ChatGPT can answer it tho
royal basin
"differential" is basically never used as a noun in calc 1
no chatgpt cannot answer it get it the fuck out of your head that chatgpt could do even remotely useful shit with math
shadow lava
no chatgpt cannot answer it get it the fuck out of your head that chatgpt could ...
with terminology it's good
with math it's not quite there yet
royal basin
you do not want to even utter the word "differential" in a calc 1 class basically
shadow lava
polar fossil
I'd call dx an infinitesimal rather than a differential
south oracle
It's called differential in serway&jewett's books though
kind hawk
I would just call dx notation cause understanding what it actually is, is much harder
tardy epoch
kind hawk
calling this infinitesimal is not good
shadow lava
lol
tardy epoch
It's called differential in serway&jewett's books though
Or an actual book if you can get it
tardy epoch
calling this infinitesimal is not good
But also don't use differential if you don't know what you're doing @shadow lava
tardy epoch
you do not want to even utter the word "differential" in a calc 1 class basicall...
Like Ann said
shadow lava
but I'm taking calc 2 now
so maybe it will come up?
I can post my outline again if that helps
the course is not called "Calc 2" in Canada
oh, it's in the course title actually lol
"Differential & Integral Calculus II"
odd that I don't see the word Differential elsewhere, only in the title
Thomas' Calculus: Early Transcendentals, Single Variable, (ed. 14) Books a la Carte edition plus MyLab Math, (Pearson).
tardy epoch
"Differential calculus" is just the description of the type of calculus, not an actual mathematical object like chatgpt said
tardy epoch
no chatgpt cannot answer it get it the fuck out of your head that chatgpt could ...
So once again, listen to Ann
polar fossil
we sometimes talk about "the differential operator" which is just d/dx (or whatever other variable is relevant) but it's rare to talk about a "differential" as a noun
shadow lava
call me crazy, but I still think ChatGPT has potential to help students a lot more with math
maybe it's not there yet, but not impossible to imagine one day
tardy epoch
All you're doing Avid with being lazy and using chatgpt is making it harder for us to actually to teach you actual math rather than the pop math chatgpt is trained on
south oracle
And that one day seems very far from the current stage right now for me
tardy epoch
maybe it's not there yet, but not impossible to imagine one day
Nobody is saying anything about its future use
shadow lava
All you're doing Avid with being lazy and using chatgpt is making it harder for ...
but that's like saying to the first students using a calculator, "all you are doing is being lazy and making it harder for us to actually teach you actual math rather than pop math into the calculator"
tardy epoch
You don't understand chatgpt do you
Calculators are vetted devices created by actual engineers, based on actual math
Chatgpt just scrapes anything on the web
shadow lava
AI is in the very early stages.. it's going to revolutionize the world, and a lot of industries, including education
kind hawk
maybe going to. but right now, no. at least not math
you cant trust it. that makes it extremely bad to learn from
tardy epoch
Nobody is saying anything about its future use
.
shadow lava
you cant trust it. that makes it extremely bad to learn from
regulation is going to need to step in, to "vet" approved AI
for example, imagine watching a YouTube video, or a court video testimony, without realizing it's a complete fabrication, but appears 100% believable
it's going to be a tough problem to solve for sure
with regulation there will be certain sites you can trust, perhaps OpenAI will be one of them in the future
AI to generate and approved regulated AI to fact check on top of that
something along those lines
anyways, understood about differentials
thank you
.close
mystic raft
hi i need help with calculating this
obtuse pebbleBOT
hi i need help with calculating this
mystic raft
what is the area of a cube that was put in a ball witch r=3cm
tardy epoch
Surface area or volume?
tardy epoch
Do you know if the diagonal of the cube is the diameter of the sphere
polar fossil
so what's the constraint on the cube?
polar fossil
3cm radius on the ball, I could chuck a tiny dice cube in there and that would be valid?
thick oracle
lol
polar fossil
can you describe this with words?
mystic raft
so if i had the edges of that cube sitting on the inside surface of that ball
i dont know how to explain it to you
polar fossil
is it the edges that are sitting on the surface?
or is it the corners?
or the faces?
tardy epoch
i dont know how to explain it to you
Just show the original problem
Screenshot it picture is best
polar fossil
what is this distance, in blue?
tardy epoch
Show it anyway
mystic raft
aight
tardy epoch
it would mean nothing to yall
You don't know that
tardy epoch
,rotate
warm shaleBOT
tardy epoch
what is this distance, in blue?
Yea it's what Hayley is saying
mystic raft
polar fossil
that looks to me like a ball was put into a cube
mystic raft
the inside of a cube is a ball that has a cube in it
wtf
<@&286206848099549185>
someone help
timid silo
what’s the question what
mystic raft
look
daring glacier
what to find?
timid silo
which cube
mystic raft
and that cube is inside of a ball witch radius is 3cm
tardy epoch
Yea it's what Hayley is saying
@mystic raft can you answer Hayley's question
mystic raft
what is this distance, in blue?
r=3cm
timid silo
no
mystic raft
R=6
timid silo
oh
mystic raft
d is 2xr
timid silo
i was confused
timid silo
wait yes it is nvm
timid silo
the cubes surface area is 216cm
mystic raft
tell me
timid silo
you say the spheres radius is 3cm
mystic raft
ye
timid silo
then i multiply by 2
to get the diameter
so that’s 6
then that’s equal to the height of the cube
since it’s a cube the width and height are =
so 6x6
36cm is the area of one face
times that by 6
you get 216
mystic raft
you got it right
timid silo
nice
mystic raft
look at this image have you done it like this
timid silo
side length would be diagonal / sqrt3
so the diagonal of the cube would be 6cm
the side length would be 6cm / sqrt3 which is ≈ 3.46cm
then you do the same steps to get the surface area of each face which is to just square that
you get 12 cm for each face
times that by 6 you get 72cm for the surface area of the smaller cube
mystic raft
timid silo
i think i typed that
so the side lengt right
so you told me the diameter of the sphere is 6cm
which means the diagonal of the cube would also be 6cm
now i have to divide it by sqrt3
to get a side length of the cube
mystic raft
diameter ofsphere=diagonal of cube
timid silo
inside or outside
mystic raft
i look up to you
polar fossil
mystic raft
mate took me 5 days to find this answer ey and i didnt even find it you found it for me
timid silo
it’s alright did i explain it well
mystic raft
@hayley we found the answer and yes thats the right translation
mystic raft
it’s alright did i explain it well
yes somewhat but i need to translate it to my language so i can understand it better
i get lost in translation
timid silo
yes somewhat but i need to translate it to my language so i can understand it b...
sure one sec
what language
Dužina stranice bi bila dijagonala / sqrt3.
Dakle, dijagonala kocke bi bila 6cm.
Dužina stranice bi bila 6cm / sqrt3 što je približno 3.46cm.
Zatim iste korake primenjujete da biste dobili površinu svake stranice, što je samo kvadriranje tog broja.
Dobijate 12cm za svaku stranicu.
Pomnožite to sa 6 i dobijate 72cm za površinu manje kocke. @mystic raft
mystic raft
so what i was doing i was calculateing the surface for the ball
idk
i even tried to put this question to AutoCAD
timid silo
so what i was doing i was calculateing the surface for the ball
ohhh
native cradle
what is mode
obtuse pebbleBOT
what is mode
forest sinew
,w statistical mode
warm shaleBOT
forest sinew
fantastic as usual
forest sinew
what is mode
its the most common
forest sinew
happy to help but maybe google would be helpful? i mean learning mean, median, and mode is a quick read
native cradle
ty
obtuse pebbleBOT
@native cradle Has your question been resolved?
copper token
what does log do
obtuse pebbleBOT
what does log do
forest sinew
undoes exponent
copper token
what does that mean
forest sinew
think about how division undoes multiplication
azure anchor
it is the opposite operation to exponentiation
copper token
it is the opposite operation to exponentiation
what is exponentiation
forest sinew
like repeated multiplication
empty cypress
what is exponentiation
$a^x$
warm shaleBOT
polar fossil
what does log do
counts the number of digits in a number
obtuse pebbleBOT
Available help channel!
pearl prairie
Whats the formula for the curvature K?
I wrote down magnitue of T'(t)/ magniture of v(t)
but I searched it up and saw smth else
obtuse pebbleBOT
Whats the formula for the curvature K?
I wrote down magnitue of T'(t)/ magniture...
@pearl prairie Has your question been resolved?
fierce vale
Hello
warm shaleBOT
adamchebil33
sacred root
Use Am-Gm....
fierce vale
what is that?
fierce vale
no
warm shaleBOT
_basudev
fierce vale
never seen that before
solar trellis
Maybe write lhs - rhs as a sum of squares or use calculus on it
vestal hull
Let f: A→B a function such that P, Q ⊂ A. Prove that f_(P) - f_(Q) ⊂ f_(P-Q)
obtuse pebbleBOT
Let f: A→B a function such that P, Q ⊂ A. Prove that `f_(P) - f_(Q)` ⊂ `f_(P-Q)...
vestal hull
f(x)∈f_(P)-f_(Q)
f(x)∈f_(P) ∧ f(x)∉f_(Q)
x∈P ∧ x∉Q
x∈(P-Q)
f(x)∈f_(P-Q)
Is that correct?
obtuse pebbleBOT
@vestal hull Has your question been resolved?
vestal hull
```
f(x)∈f_(P)-f_(Q)
f(x)∈f_(P) ∧ f(x)∉f_(Q)
x∈P ∧ x∉Q
x∈(P-Q)
f(x)∈f_(P-Q)
```
...
I'm not convinced at all
obtuse pebbleBOT
@vestal hull Has your question been resolved?
brisk matrix
```
f(x)∈f_(P)-f_(Q)
f(x)∈f_(P) ∧ f(x)∉f_(Q)
x∈P ∧ x∉Q
x∈(P-Q)
f(x)∈f_(P-Q)
```
...
the third line is wrong, assuming f_(P) = f(P)
obtuse pebbleBOT
@vestal hull Has your question been resolved?
trim portal
Is it false? It seems to be true
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
solar gorge
please help with this integral
obtuse pebbleBOT
please help with this integral
brisk matrix
have you heard of trigonometric substitutions
solar gorge
have you heard of trigonometric substitutions
i stumbled accross that today, do i need to learn that?
frosty brook
thats a weird ass integral
brisk matrix
it would be helpful for this integral
rich tapir
please help with this integral
the integrand can be rewritten as
$\frac{1}{(\sqrt{x^2+\frac{1}{4}})^3}$
nice
warm shaleBOT
alihsaas
rich tapir
yah from here you can see the trig sub you shoulf use
frosty brook
wait tf
obtuse pebbleBOT
@solar gorge Has your question been resolved?
proven zephyr
i don't think turning the /2 in the power is really necessary
you can just leave it as it is.
doesn't really matter tho
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
gloomy tusk
I got 3.1699 but the correct answer is 80
obtuse pebbleBOT
I got 3.1699 but the correct answer is 80
gloomy tusk
can anyone help me?
unkempt bramble
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
unkempt bramble
4^4^n = 4^3^4
That's the mistake
unkempt bramble
Yup
gloomy tusk
or i cant just simply change it?
gloomy tusk
i cant seem to use the right one😭
rich plume
$a^{b^{c}}\ne\left(a^{b}\right)^{c}$
warm shaleBOT
beard420
gloomy tusk
okay ill try
rich plume
$a^{b^{c}}=a^{\left(b^{c}\right)}$
warm shaleBOT
beard420
rich plume
Note: go from top to bottom
unkempt bramble
Note: go from top to bottom
Yea
polar fossil
counterargument: just take the log of both sides until you think it's in a useful state
gloomy tusk
counterargument: just take the log of both sides until you think it's in a usefu...
this one really helps thanks a lot
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obtuse pebbleBOT
obtuse pebbleBOT
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fathom flicker
|| ||
fathom flicker
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