@tall current Has your question been resolved?
#help-0
lone heartBOT
misty notch
Am I being stupid or is there a way to simplify this?
lone heartBOT
Am I being stupid or is there a way to simplify this?
misty notch
im trying to calculate the derivative of a function using the derivative limit rule, but i keep getting this in the denominator
alpine sable
Doesn't seem like there's any way to simplify it, but maybe you made a mistake in calculating the derivative?
alpine sable
I see
you might want to rationalize the fraction first
$\frac{1}{\sqrt{2x+3}}\cdot \frac{\sqrt{2x+3}}{\sqrt{2x+3}}$
misty notch
i kinda did that but not in the first step
wait let me take a pic of my work, but its abit untidy
ocean sealBOT
jswatj
alpine sable
i see
okay i think
do the h thing
then rationalize
i think you may have rationalized wrong
vernal thunder
Am I being stupid or is there a way to simplify this?
Can you do sum rule?
Actually that won’t help
misty notch
i think you may have rationalized wrong
i tried it with different examples, same outcome
so i have to rationalize first then do the limit whenever there is a root in the denominator
vernal thunder
Oh you’re doing limits
misty notch
yeh the teacher asked us to calculate them using the limit way not the fast way lol
misty notch
.close
karmic plume
Given 2 integers x,y satisfying : xy -23 ⋮ 24. Prove x^3+y^3⋮72
vernal thunder
Given 2 integers x,y satisfying : xy -23 ⋮ 24. Prove x^3+y^3⋮72
Are the 3 vertical dots equals
karmic plume
Are the 3 vertical dots equals
That means divisible
vernal thunder
Strange
karmic plume
Never saw that notation
maybe Vietnamese math uses this notation
karmic plume
oh yes of course
vernal thunder
So what’s the problem assuming the vertical dots are /
frigid hatch
divisible is not the same as divided by
vernal thunder
Now I’m getting confused, three dots mean divisible by or just divide
karmic plume
i'm confusing now bruh
uncut torrent
its saying that xy -23 divided by 24 gives an integer
karmic plume
Now I’m getting confused, three dots mean divisible by or just divide
three dots in vietnam means a number can divide another number
like 6/3 = 2
vernal thunder
Alright
grizzled mauve
so Americans write it the other way and use a line like
karmic plume
The result of this division is an integer
uncut torrent
Given 2 integers x,y satisfying : xy -23 ⋮ 24. Prove x^3+y^3⋮72
so this implies xy is a multiple of 25?
vernal thunder
so Americans write it the other way and use a line like
No need to stereotype people
karmic plume
or
24 | xy-23
(xy - 23)/24
grizzled mauve
I'm writing it that way so that Americans reading this chat know what i tmeans
vernal thunder
I'm writing it that way so that Americans reading this chat know what i tmeans
I KNOW EXACLY WHAT IT MEANS
DONT ASSUME AMERICANS ARE DUMB
uncut torrent
chill
uncut torrent
back to the question…
grizzled mauve
I wasn't sure what it means, I'm American, and sometimes I'm dumb even if generally I'm not, so relax
vernal thunder
I wasn't sure what it means, I'm American, and sometimes I'm dumb even if genera...
Wait you’re one of us
karmic plume
can anyone help me do that problem pls :))
frigid hatch
Wait you’re one of us
that makes it okay, lmao what
uncut torrent
so this implies xy is a multiple of 25?
@karmic plume
vernal thunder
@karmic plume problem please
karmic plume
so this implies xy is a multiple of 25?
no
slender gull
47
uncut torrent
ok non-zero multiple of 25
grizzled mauve
24 | xy - 23
prove:
72 | x^3 + y^3
vernal thunder
I assume those expressions must equate to each other
uncut torrent
oh im being silly
its been a long day lol
grizzled mauve
xy-23=24m ; (x+y)(x^2-xy+y^2)=72n
karmic plume
vernal thunder
Ok
karmic plume
xy-23=24m ; (x+y)(x^2-xy+y^2)=72n
right
karmic plume
i found that xy = 6m too
grizzled mauve
how'd you get that>
slender gull
using mod 24 seems more feasible
Exactly.
grizzled mauve
ah
karmic plume
=> xy = 2 (mod 3)
there are x = 1(mod3) and y = 2(mod3)
so x + y = 0 (mod3)
oh sorry
not xy
also
xy = 24k + 23 so x and y are odd
=> x + y = 0(mod2)
=> x+y = 0(mod6)
slender gull
Then, isn't your problem more or less solved?
slender gull
x^3 + y^3
karmic plume
x^3 + y^3 = (x+y)^3 - 3xy(x+y)
slender gull
= (x+y)((x+y)^2 - 3xy))
slender gull
Yes.
karmic plume
which it is, because x + y = 0 (mod 2)
e.x 4 can not divide 8
slender gull
which it is, because x + y = 0 (mod 2)
Nope.
10 = 0 mod 2
10 is not 0 mod 8 is it
grizzled mauve
yeah that's why I said "and" and then ran out of things to say after "and" because I thought we proved more than that
karmic plume
Nope.
10 = 0 mod 2
10 is not 0 mod 8 is it
yeah
grizzled mauve
got ahead of myself sorry
karmic plume
im feeling sleepy now bruh , bye
lone heartBOT
@karmic plume Has your question been resolved?
desert sage
Hi so I need to create a really hard (grade 10) trigonometry question and than solve it. Can someone help me with this. I need to learn the steps
old horizon
desert sage
Umm okay let me give you an example
I need something like this.
Brb
Okay im back
minor needle
I need something like this.
I can help you with the steps to this one if you want
desert sage
Okay
minor needle
desert sage
Btw Im looking for the height of the tree
desert sage
I think so, I'm just bad at it so i need some help
minor needle
hint: use tangent
minor needle
it is
minor needle
minor needle
this is what I was thinking about, you can see the solution above
vernal crag
u cant just solve with basic trig
u need to know trig function of added angles
like tan(a+b), tan(a-b)
desert sage
Yeah
desert sage
So how do I get the angle?
minor needle
So how do I get the angle?
so u have tan(alpha) = 1.75/16
desert sage
Right
minor needle
tan^(-1) also
desert sage
Tan-¹
minor needle
just notation
desert sage
RIGHT
minor needle
yes
minor needle
yes
minor needle
it will be useful but later
desert sage
Okay
desert sage
Got it
minor needle
then add height of the man and you're done
desert sage
Yeah
So wait
For opp is the answer 6.386?
No
I did it wrong
Thats impossible
Unless
minor needle
opp is 16 * tan(21.76)
desert sage
Yeah
lone heartBOT
@desert sage Has your question been resolved?
glossy burrow
i need to find an expression and i have no idea how
lone heartBOT
i need to find an expression and i have no idea how
@glossy burrow Has your question been resolved?
tidal lantern
An expression ? What is the question ?
lone heartBOT
glossy burrow
An expression ? What is the question ?
SORRY NVM ITS FINE
tidal lantern
No problem x)
lone heartBOT
Available help channel!
lime tartan
Collatz Conjecture 3x+1 problem
lone heartBOT
Collatz Conjecture 3x+1 problem
worn fox
?
alpine sable
Collatz conjecture is based on positive integers
lone heartBOT
@lime tartan Has your question been resolved?
keen pasture
Also there are discussions if 0 is even
abstract fractal
Also there are discussions if 0 is even
Elaborate
weary wyvern
That way we can solve Collatz Conjecture
Give this man a fields medal
tacit arch
can someone just close this and put me out of my misery
lone heartBOT
lone heartBOT
Available help channel!
rapid crest
How do you solve this? cos(x) + 2sec(x) = -3
I converted sec to tan^2x +1
but figured that wouldn't help
should I change to 1/cosx
and then add left side?
rapid crest
I tried doing it with that method and ended up getting no solution
abstract fractal
Sec isn't tan²x + 1
rapid crest
I think I did wrong
rapid crest
Sec isn't tan²x + 1
yeah
abstract fractal
sec²x is, but you don't have sec²x
abstract fractal
It's better to turn sec into 1/cos
abstract fractal
Why multiply by 2
rapid crest
but ended up getting cos^2x = -5
rapid crest
Why multiply by 2
the 2 infront of the secx
abstract fractal
Yeah, but that's not being divided
rapid crest
multiplied?
abstract fractal
2secx = 2/cosx
abstract fractal
I don't see how multiplying by 2 simplifies anything
rapid crest
what do you with the 2
abstract fractal
Nothing. Just leave it there. The more pressing matter is the cos in the denominator
rapid crest
I ended up getting cosx + 2/cosx = -3
then multiplied by lcm
both sides
which is cosx
and got cos^2x + 2 = -3cosx
actually idek anymore
I'll send the problem over
abstract fractal
and got cos^2x + 2 = -3cosx
So after getting this, what then?
abstract fractal
I'd rather know what you did than what your teacher did
abstract fractal
Be more specific
rapid crest
I looked at the answer rn
I multiplied by cos(x) on both sides
from this cos(x) + 2/cos(x) = -3
to cancel out the denominator
rapid crest
nvm I get it now. Sorry for wasting your time
Do you mind me asking more questions in case I get stuck?
abstract fractal
That's the point of the help channels, after all
rapid crest
sometimes I get confused interpreting my teachers work
For a problem like this would you use double angle formulas and try to simplify everything into one value
like for example in terms of sin or cosine
abstract fractal
You could use double angle formulas, yeah. You would also want to get everything in terms of sines and cosines, generally, because it makes simplification easier
rapid crest
I used it and got (cos^2x - sin^2x + cosx +1)/ (2sinx)(cosx) + sinx
but don't know what to do afterwards
abstract fractal
Notice that cotx = cosx/sinx
rapid crest
I could factor sinx on bottom
abstract fractal
I could factor sinx on bottom
After doing this, you can multiplying by something to simplify a bit
abstract fractal
Yep
rapid crest
There is no need for double angle?
abstract fractal
And then almost everything is in terms of cos. Only exception is the sin²x, but you can easily make that cos
rapid crest
And then almost everything is in terms of cos. Only exception is the sin²x, but ...
oh I see
you use pythagorean identities right
abstract fractal
There is no need for double angle?
Wdym? You used the double angle formulas to get it to that large fraction
rapid crest
so cos^2x - 1
abstract fractal
so cos^2x - 1
Not cos²x - 1
rapid crest
and then thought of factoring out
rapid crest
Not cos²x - 1
yes my bad
abstract fractal
Since everything is in terms of cos, all that's left is to solve for cosx
rapid crest
alright ima try the problem out and see if I can solve
alright I got this
(sinx)(cos^2(x) + sin(x)cos(x) + 1 / (sinx) = cosx
abstract fractal
Why do you still have a bunch of sines
rapid crest
and then if I simplify do I get cos^2(x) + cos(x) + 1 = cos(x)
rapid crest
Why do you still have a bunch of sines
just realized lol
abstract fractal
I don't know what it simplifies to. I don't have any paper nearby and I'm too tired to grab some
rapid crest
hmm
oh wait that was prove the identity problem
should have specified
:/
just realized rn
abstract fractal
Right
abstract fractal
I'm too tired to work this one out. I'm afraid I can't help too much on this one
rapid crest
No problem, thanks for the help!
I'll ask on another channel and close this one
.close
wind bloom
idk how to do 38
lone heartBOT
idk how to do 38
tacit arch
add 360 until you get a positive number
wind bloom
but how would i sketch it
tacit arch
add 360 until you get a positive number
by sketching the result from this
wind bloom
so 205?
tacit arch
,calc -515 + 720
ocean sealBOT
Result:
205
ya
lone heartBOT
lone heartBOT
Available help channel!
tight gulch
what does exp stand for in this context?
lone heartBOT
what does exp stand for in this context?
tight gulch
fluid basin
the exponential function
tight gulch
7^(3x)?
fluid basin
$exp(x) = e^x$
ocean sealBOT
romeofoxtrot
fluid basin
where e is euler's number, 2.7818.....
lone heartBOT
fluid basin
no problem
lone heartBOT
Available help channel!
sharp moth
How does he know it's increasing or decreasing?
lone heartBOT
How does he know it's increasing or decreasing?
sharp moth
carmine harbor
@golden bronze open your own channel
golden bronze
how
tight gulch
@golden bronze #❓how-to-get-help
carmine harbor
It can be positive and negative based on x
That’s what helps us find an infection point
We set it equal to 0
And solve for x
sharp moth
Critical point
carmine harbor
Oh yes sorry it’s critical point
Inflection point is 2nd derivative and curvature
We then look the behaviour
To the “left” of x when x sets the function to 0 and the “right”
And that tells us if it’s a max or a min
carmine harbor
How does he know it's increasing or decreasing?
Do you understand that a derivative is the slope of the tangent line
If the slope of the tangent line is always positive
The function is always increasing
sharp moth
If you were to graph it, it would be a tangent line
carmine harbor
Yes the derivative of a point
Is the slope of the tangent line at that point
If the derivative is 0
What does that mean about the function ?
It is neither increasing or decreasing at that point
This is a critical point because it often means that the function is switching from increasing to decreasing or vice versa
sharp moth
Positive derivative
Okay so how does that explain whether he knows it's decreasing and increasing or vice versa?
carmine harbor
Okay so he finds the critical point first
sharp moth
This part has me confused
carmine harbor
Than he looks to the left of the critical point
X=2
So he finds an x that is less than 2
Let’s say 1
Plug 1 into the function
sharp moth
and just graphs it
carmine harbor
And the the answer is negative
sharp moth
and from that he determines if it is increasing or decreasing.
carmine harbor
So we know it’s decreasing
carmine harbor
and from that he determines if it is increasing or decreasing.
You don’t need to graph it
You look at local behaviour of critical point
sharp moth
And the the answer is negative
What determines if the answer is negative?
carmine harbor
We put in a value lower than x=2
So say our critical point is 2
Which it is in this case
We would see what happens to x=1 and x=3
So we first try x=1
sharp moth
So we first try x=1
Okay because you read the graph from the left?
carmine harbor
Yeah it looks easier that way we are just conditioned left to right
sharp moth
Yeah it looks easier that way we are just conditioned left to right
and because it's one less then two, the answer is negative?
carmine harbor
So our equation for the first derivative is 2x-4
Plug in x=1
2-4=-2
So the function is decreasing
Plug in x=3
6-4=2
Function is increasing
Does that make sense?
You really need to understand what a derivative is
sharp moth
slope of a tangent line at a particular point
so when you plug in x what are you doing to that original derivative equation?
carmine harbor
You are evaluating the derivative at a particular point
Of x
You are finding the slope of the tangent line at a point x
When our derivative is positive our function is increasing
When it’s negative it’s decreasing
Does this make sense to you
When our function is decreasing the derivative is negative when it’s increasing the derivative is positive
sharp moth
Yes, I do understand
sharp moth
Is this question asking me to find 8 critical points?
lone heartBOT
Is this question asking me to find 8 critical points?
abstract fractal
I don't think there's necessarily 8, but yeah, find all the critical points
slim fern
lone heartBOT
slim fern
I've gotten so far as to find that there are 13! ways to arrange all the chairs around the tables.
I also know that there are 14*13 ways to find a pair of chairs (including opposites)
But I'm not sure where to go from there
copper stone
i would say 14C2 - 7
placid zinc
There's 14 ways to choose the first chair, and 12 ways to choose the second. Since order doesn't matter, I am double counting. So, I divide by 2 to fix
14×12/2
real gazelle
I have a sequence $$s_1 = \sqrt2$$ and $$s_{n+1} = \sqrt{2 + \sqrt{s_n}}.$$
Does anyone have any bloody idea how to prove that $$s_{n+1} > s_n?$$
Only hints necessary, you don't have to give the answer.
real gazelle
I've noticed just by graphing it that $$\sqrt{2 + \sqrt{s}} > s$$ is true for all positive $s$ less than the fixed point
copper stone
I have a sequence $$s_1 = \sqrt2$$ and $$s_{n+1} = \sqrt{2 + \sqrt{s_n}}.$$
Does...
did u try proof by induction?
ocean sealBOT
Eric Tao (he/him)
real gazelle
fixed the typo
copper stone
induction makes it trivial
try it, you will see that the result comes directly @real gazelle
if not i will help
real gazelle
do you mean you want me to show that s2 > s1 and that if s_n+1 > s_n then s_n+2 > s_n+1
copper stone
yep
real gazelle
aight
ocean sealBOT
Eric Tao (he/him)
lone heartBOT
real gazelle
that's really neat
lone heartBOT
Available help channel!
lapis juniper
i must be dumb or smth but I can't prove this
lone heartBOT
i must be dumb or smth but I can't prove this
lapis juniper
sorry it's in french but it says "Prove that, if n ∈ N, there exists an odd integer λ_n such that :"
I tried an induction (idk if it's the right word ?) but I cant pass the heredity part
$$5^{2^{0}} = 5$$ and $$1+\lambda_0 2^{0+2} =5$$ with $$\lambda_0=1$$ so P(0) is true
ocean sealBOT
Elayos
ocean sealBOT
Elayos
lapis juniper
$$\iff 25\times5^{2^{n}} = 25 + \frac{25}{2}\lambda_n2^{n+3}$$
ocean sealBOT
Elayos
lapis juniper
$$\iff 5^{2^{n+1}} = 1 + 24 + \frac{25}{2}\lambda_n2^{n+3}$$
ocean sealBOT
Elayos
lapis juniper
but i cant go further
<@&286206848099549185>
well I guess nobody likes my exercise 🥲 its ok
lone heartBOT
@lapis juniper Has your question been resolved?
novel night
In the inductive case, are you saying $5^{2^{n+1}} = 25\times 5^{2^n}$? Because it should be $\left(5^{2^n}\right)^2$.
ocean sealBOT
daveamayombo
novel night
I think I'd also rephrase the problem as showing $5^{2^n} - 1$ is divisible by $2^{n+2}$.
ocean sealBOT
daveamayombo
lapis juniper
oooooh yeah I forgot about the brackets my bad
thanks for pointing out the hole
okay I succeeded thanks !
novel night
👍
lapis juniper
.close
copper heron
what is x if
lone heartBOT
what is x if
frosty venture
lone heartBOT
frosty venture
does this graph work given those limits and points?
ignore the lines in the top left
lone heartBOT
@frosty venture Has your question been resolved?
tribal oxide
does this graph work given those limits and points?
f(x) is a function?
Then this graph fails the vertical line test
So not a function
frosty venture
f(x) is a function?
hmm how do i fix it to pass vertical line test
because with the infinities doesnt it not pass it automatically?
tribal oxide
because with the infinities doesnt it not pass it automatically?
No there should be ways to do it
Look at the graph of y=1/x to check how they work
frosty venture
Look at the graph of y=1/x to check how they work
right but dont we have it going possitive and negative on both sides in this?
like this
tribal oxide
right but dont we have it going possitive and negative on both sides in this?
Ur question just says -inf for tend to 5 from the left side and inf, for tend to 5 from the right side
frosty venture
gotcha one sec
frosty venture
im confused on how to do it with 4,-3 with it going to positive infinity from the right side
tribal oxide
im confused on how to do it with 4,-3 with it going to positive infinity from th...
Wdym?
tribal oxide
No it doesnt seem correct 🤔
frosty venture
oh rip
tribal oxide
I dont write out every number bte just the important ones💀
frosty venture
lol ight
tribal oxide
isnt that just 1,-4?
U mean the point (1,-4)?
frosty venture
ya
tribal oxide
No its the opposite
tribal oxide
Also im not sure what the point discontinuity at (4,-3) is doing, but its not a problem as it wont make the question wrong
frosty venture
Also im not sure what the point discontinuity at (4,-3) is doing, but its not a ...
ahhh i didnt see the negative in front of the 4
ty
one sec ima try graphing this thing again
this is what i got before graphing the lines
woudl the infinities be switched around?
tribal oxide
Why do you think they wud be switched around tho
frosty venture
the negative means theyre coming in from the left or going to the left?
tribal oxide
Which negative
frosty venture
x-->5^-
tribal oxide
5- means we are approaching 5 from the left side
frosty venture
so that looks good then?
tribal oxide
Yes
frosty venture
everything here before i connect them looks good?#help-0 message
tribal oxide
Yes
tribal oxide
For continuity at a point a,we need lim x-->a f(x) =f(x). Here lim doesnt exist
tribal oxide
final product look good?
Yes
frosty venture
Yes
whats the best way to "prove" the solution is correct?
is there even a way b/c for the upcoming quiz we get a similar problem and we have to prove it
is there a way to plug it into desmos?
@tribal oxide
frosty venture
.close
neat sierra
lone heartBOT
neat sierra
does does gker phi = hker phi => h{-1}g in ker phi?
its probably sth really basic, i just dont remember
merry depot
multiply by the left inverse of h
neat sierra
$h^{-1}g \ker \phi = \ker \phi$
merry depot
then h^(-1)gker(phi) is a coset of ker(phi) that is equal to ker(phi)
ocean sealBOT
KN
merry depot
so h^(-1)g must be in ker(phi)
neat sierra
since ker phi is a group?
obtuse quarry
how do i do 1.c) ?
lone heartBOT
how do i do 1.c) ?
median oar
im just gonna assume we're talking projectile motion in highschool
so it's a parabola
we can pin a unique parabola with 3 distinct points
we wanna construct a function here that's h(t)
height as a function of time
obtuse quarry
height as a function of time
this is what i needed tysm!
obtuse quarry
im just gonna assume we're talking projectile motion in highschool
yes
median oar
the 3 points we know are,
on start t=0, h = 25
when t =2, h = 45
and t=5, h=0
with this information we can make our parabola
neat sierra
why is xnx^{-1} in H?
lone heartBOT
why is xnx^{-1} in H?
neat sierra
x is an element in G right, not neccecerily in H. So how do we know xnx^{-1} is in H for sure
ok nvm
.close
chrome olive
Looking into compound interest and I'm a bit stumped:
Trying to figure out how to increase Deposits/Withdrawals by a %/(or flat numerical increase) every year & tie that into figuring out what will the total be after x years
lone heartBOT
Looking into compound interest and I'm a bit stumped:
Trying to figure out how ...
@chrome olive Has your question been resolved?
covert juniper
I’m looking at the proof of this theorem, I understand everything expect why we can conclude that the n element a^0,…,a^{n-1} are unique? Thanks
novel night
a has order m, so a^m is the first power of a that equals 1. And n is less than or equal to m.
lone heartBOT
Available help channel!
covert juniper
a has order m, so a^m is the first power of a that equals 1. And n is less than...
Ah ok, thanks. Not that’s it’s relevant to the proof, but a^0,…,a^{m-1} are also distinct right?
novel night
Correct. That's true for any a, in any group, where m is the order of a.
covert juniper
Correct. That's true for any a, in any group, where m is the order of a.
Great, thank you. One last thing, because the a^0,…,a^{n-1} are unique, how can we conclude that <a>=G?
novel night
Because the group is generated by x, which has order n... so there are n elements total in the group. If you list n distinct elements like a^0, ... a^(n-1), you must have listed every element in the group.
lone heartBOT
vale wigeon
a substitution almost suggests itself
vale wigeon
u := sin(x) is what i would've gone with.
tropic oasis
it's sin^2(x)
oh wait
that's equivalent to
(sin(x))^2?
so i can use chain rule on that?
tropic oasis
are you familiar with substitutions in general
sort of yes
i did two problems previous
i just
dont really like
understand them when they get complex
vale wigeon
ok so substitute u := sin(x) as i suggested
du = cos(x) dx
so you will have $\int_{\sin(\pi/4)}^{\sin(\pi/2)} \frac{1}{u^2} \dd{u}$
ocean sealBOT
Ann
tropic oasis
how did we move the sin into the limits?
i'm at
du/cosx = dx
oh wait
i’m here
vale wigeon
do not forget to recalculate your bounds
vale wigeon
in a definite integral when you substitute u := g(x) the bounds go from [a, b] to [g(a), g(b)]
tropic oasis
oohhh
okay
so whatever i set for u
is the function that i apply onto the limits?
tropic oasis
ohh okayy
tropic oasis
look up "substitution in definite integrals"
ill watch a video after
and i guess now i solve the limits
and subtract one from the other?
vale wigeon
bad wording
vale wigeon
...
still bad wording
there exists a charitable interpretation that makes what you said correct but it is kind of a stretch
you have your integral
$\int_{1/\sqrt{2}}^{1} \frac{\dd{u}}{u^2}$, now calculate it
ocean sealBOT
Ann
tropic oasis
isnt sin(pi/4) = sqrt(2)/2
tacit arch
,calc sqrt(2/2)
ocean sealBOT
Result:
1
@tropic oasis Has your question been resolved?
fervent marsh
can somebody help me please
lone heartBOT
can somebody help me please
fervent marsh
.close
lone heartBOT
lone heartBOT
Available help channel!
sterile stone
lone heartBOT
sterile stone
is there a difference between radians and degree
when answering this
actually im not sure how to answer this
sin would be 10sqrt3/20 right
woeful pulsar
sin of R? opposite over hypotenuse
gray isle
10sqrt(3) isn't opposite of R
gray isle
where did your confusion of the opposite side come from
sterile stone
where did your confusion of the opposite side come from
we dont talk about it
but I get it now
thanks
.close
sterile stone
lone heartBOT
sterile stone
alright
lethal tendon
looks good to me
native blaze
Why is 0.9 repeting equal to 1?
lone heartBOT
Why is 0.9 repeting equal to 1?
vale wigeon
are you familiar with geometric series?
and with infinite series in general, which is the means by which infinite decimals (repeating or otherwise) are given meaning?
native blaze
are you familiar with geometric series?
yes
as in an arithmetic series with a common ratio?
vale wigeon
i don't know what you mean by "arithmetic series with a common ratio"
but anyway
0.9999... is the sum of the geometric series 0.9 + 0.09 + 0.009 + 0.0009 + ...
the first term is 0.9 and the common ratio is 0.1
native blaze
Yes but that series does not end
So to say there is a sum is moot
It has a limit
Proof: Assign each term of the series to the smallest known particle in the universe. Then; there exists no size particle such that the number of terms in the series is exhausted. Thus, the existence of infinite series is disproven.
keen socket
vale wigeon
Proof: Assign each term of the series to the smallest known particle in the univ...
well if you're gonna be the kind of person to deny the existence of infinite series and go full crank mode to shout "infinite series dont real!!!" then we have little if anything else to talk about
native blaze
well if you're gonna be the kind of person to deny the existence of infinite ser...
So you are saying limits are mathematically invalid?
That is "crank" to me
weary wyvern
man's trying to sound like einstein from that nat geo show
native blaze
Let me describe more concretely what I mean
vale wigeon
the sum of an infinite series is defined to be the limit of its partial sums, if said limit exists.
it is not "moot" to say that an infinite series has a sum.
native blaze
But there exists no number, not even grahams number, amount of terms that can satisfy the limit sum
vale wigeon
so what
native blaze
If I ask you what pi plus e is, can you give me an answer?
native blaze
exactly
vale wigeon
if you want it to however many decimal places, tell me how many
vale wigeon
?
sorry, let me restate what i said.
if you want it to some number of decimal places, tell me how many decimal places you want.
that's got to be a natural number, for obvious reasons, but if you're going to give me something other than that i'll round to the nearest integer anyway.
native blaze
I want the number of decimal places it takes such that if it were on the left side of the equation, it would equal pi plus e on the right
This is not "crank", here this mathematician explains it
proofs have constructive content, and what you get out of these constructions isn't much more than you put in.
mortal trellis
native blaze
A(0)∧(∀x.A(x/2)⇒A(x))⇒∀x.A(x)
Then any proof of a forall-exists statement has to be realized by a polynomial time computable function.
Explain this then
native blaze
https://i.imgur.com/fgfQXrP.png
your google search results vary depending on your search history
If this is too complex a question I apologize, I am a grad student
sleek gyro
its not too complex a question
but your objection, as wildberger's, is not mathematical
this is purely a philosophical objection
wildberger rejects certain axioms and constructions purely on philosophical opinion
which he is, as you are, allowed to do
however if you ask a question on this server, everyone will assume that you do the "standard" mathematics, that everyone else (save wildberger and a few other people) are doing
native blaze
So? Math is made foundational off of set theory which is based off of the peano axioms
Its not too far a stretch to ask foundational mathematical questions, no?
sleek gyro
so what is your question?
native blaze
a reasonable objection to ultrafinitism
I am not aware of any and would like an explanation
sleek gyro
this is not a mathematical question
the answer is "I dont want to do this kind of mathematics, i like what i am doing currently"
native blaze
Ok then, in the future I will note to not ask foundational questions and limit the remit of my queries
.close
main ether
lone heartBOT
main ether
i understand that im supposed to find all the numbers that dont have a 5 or 7
and then subtract that from the total outcomes
main ether
i understand that im supposed to find all the numbers that dont have a 5 or 7
but i have no clue how to find this
frigid rune
i understand that im supposed to find all the numbers that dont have a 5 or 7
since you are looking at only 4 digit numbers, think about what each digit can be and then use that to find the number of integers with no 5s or 7s
like normally each digit could be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ( except the first digit which cant be 0 )
which gives you 9 * 10 * 10 * 10 = 9000 total 4 digit numbers
main ether
ahhhh yes that makes sense, i will try it now
give me a moment
ok so i tried this
first digit: cannot be 0, 5 or 7 therefore 7 choices
second: cant have 5 or 7 therefore 8 choices
third: cant have 5 or 7 therefore 8 choices
fourth: cant have 5 or 7 therefore 8 choices
so 7 * 8 * 8 * 8 = 3584
frigid rune
yep
main ether
9000-3584=5416
frigid rune
correct
main ether
my dude thank you so much
frigid rune
np
main ether
this is the first time ive asked for help in the server lol
i really appreciate it, you made it really clear to understand
.close
native cloud
Why isn't this online platform accepting my answer?
lone heartBOT
Why isn't this online platform accepting my answer?
frigid rune
Why isn't this online platform accepting my answer?
try without the i
viscid moat
hello how can i find the image of this matrix
lone heartBOT
hello how can i find the image of this matrix
vale wigeon
Im(T) is the span of [1;0;1;0], [1;1;1;1] and [2;1;2;1]
viscid moat
wait thats it ?
woeful pulsar
$\Lambda$ and $\Phi$ are bases
ocean sealBOT
Element118
viscid moat
the base thing is whats confusing me
okay lets say i found Im(T)
and i wanna find Ker(T)
woeful pulsar
it's all vectors in the domain that go to 0
viscid moat
so in order to find it i gotta put the matrix i have equal to a zero's matrix
and i gotta find its rank or something ?
lone heartBOT
@viscid moat Has your question been resolved?
native blaze
if i quantify x over a set, what is the term of the set in relation to x?
native blaze
would the set be the domain of x?
native cloud
Elucidate please
native blaze
ok
if x is quantified over the real numbers, can I say x is in the domain of R
or that the domain of x is R
@native cloud
weary wyvern
if i quantify x over a set
what does that even mean
native cloud
I don't understand either
native blaze
As in if I want to prove a property of x, I need to quantify it first
like saying for all x is an element of the reals, x + 1 > x
Have you never encountered the words "For All" or "There exists" in math?
That is quantifying a variable
alpine sable
would the set be the domain of x?
yeah probably
weary wyvern
That is quantifying a variable
ah that's what you mean
to quantify something, you need a statement involving x like P(x)
native blaze
yeah probably
Ok, thank you. I find it funny how @native cloud and @weary wyvern , two helpers with the tag "advanced", have never come across set quantification which I am learning as a freshman
weary wyvern
i haven't heard the term "quantification" much
but ofc i know what for all and there exist means
native blaze
to quantify something, you need a statement involving x like P(x)
it can be as simple as let x be an element of R, right? I don't need an assertion
weary wyvern
i assumed by "quantifying" x you meant saying "for all x in a set" or "there exists an x in a set" such that ...
native blaze
yea
weary wyvern
? so you need a P(x)
native blaze
or just stating x is an element of a set
that is quantifying too
but doesn't specify a P(x)
mortal latch
gigaclaim
mortal latch
for formal languages/grammar/regular expressions
for this regular language:
what does the + change? is it the same as just L(((01111)*(00)*)*)
like for this previous question:
i can tell it has to start with 0, then can have none or infinite '11's afterwards, then none or infinite of both of those together
but with the first thing i posted i feel like im missing something
omg nevermind the + means OR
verbal elbow
Hi whats the fourth root of the cube root of the square root of 2^24?
verbal elbow
I put 2 on the test (the test is over im not cheating)
also looking how to solve it not just an answer which i could get from google
alpine sable
$\sqrt[4]{\sqrt[3]{2^{24}}}={\sqrt[3]{2^{24}}}^{\frac{1}{4}}={{{2^{24}}^{\frac{1}{3}}}^{\frac{1}{4}}={{2^{24}}}^{\frac{1}{12}}=2^2$
ocean sealBOT
Toby
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
verbal elbow
thank you
alpine sable
forgot the squareroot
verbal elbow
yeah
alpine sable
(2 is correct)
alpine sable
yw :)
verbal elbow
.close
lone heartBOT
vale wigeon
**Toby**
Compile Error! Click the <:errors:504266556054962196> reaction for more...
missing parentheses here
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
Right, so I've tried the obvious thing of considering every combination of 3 points being on the grid of 4x4, which is 16C3
...And from there I suppose I must eliminate triangles which can't be formed. But I'm not sure how to go about doing that
well you need to make sure the vertices are not colinear
Okay, so that will eliminate 3 points lying on the same row/column, right?
Oh wait, so I do 4C3 to figure out how many ways that can happen for each row
yeah, and diagonal
the harder ones to count are the diagonals
Yep, and and multiply by...
10, 4 for the row, 4 for the column, 2 for the 4 pointed diagonals
And then the uhhhh 3 pointed diagonals
Which are in 4 rotations
Oh that makes so much sense
Thank you
so 16C3 - 10(4C3) - 4
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pliant oxide
lone heartBOT
pliant oxide
how do u solve for x and y for this?