yes that makes sense but how did he only lose 5 from his bank account instead of 10, and tom gets the full 10 back
#help-38
olive fractal
nimble shuttle
so 20 in total from his own money
trim lichen
yes that makes sense but how did he only lose 5 from his bank account instead of...
he didn't lose $5 from his bank account
olive fractal
he pulled 20 out of the atm, paid 15 for the vape
5 from tom + 5 left over is 10
so he only paid back 5
nimble shuttle
he pulled 20 out of the atm, paid 15 for the vape
yeah pulled 20 has from tom 10
so has 30 in total
15 vape 5 lost 10 back to tom
trim lichen
i think you are deliberately trying to confuse us or yourself
olive fractal
YES
okay
it makes sense
if i pretend i never used toms money
then it makes sense
nimble shuttle
Exactly you never did
trim lichen
he pulled 20 out of the atm, paid 15 for the vape
money going IN:
- $10 from Tom
- $20 from ATM
money going OUT: - $15 to the vape shop
- $10 back to Tom
- $5 on the street
everything checks out. total in = total out
where is the issue
trim lichen
with these convoluted financial scenarios you need to sit down and calculate every participant's money in and out carefully
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hard musk
Hello
hard musk
for this question i am resolving in the direction of the ramp, and i am not supposed to use thehighlighted force
This is the full question
I would like to ask
i understande that r2 is perpendicular so there should be no value there, so it my diagram incorrect?
thankytou in advance
hidden vortex
!15m
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shy wind
hard musk
sorry i forgot
dusky mortar
what do you mean by 'no value there'
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hard musk
what do you mean by 'no value there'
as its perpendicular to the ramp, the should be nothinng int the ramp direction using trig
becaue i resolveed in the driection of the ramp
so do you think the diragram i drew is wring
beacasue online most people draw the triangle in i and j direction for this paritualr c, but i drew perp to ramp
hard musk
what do you mean by 'no value there'
am i ado you think its the issue with thew diagarm?
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void dew
!occupied
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unreal sail
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unreal sail
No clue what I’m doing
summer haven
No clue what I’m doing
First it's not possible to have a negative number of bass so you can eliminate all points left of the x axis
Negative amount of time*
unreal sail
Gotcha
summer haven
So, can you identify which graph corresponds to which inequality?
summer haven
Also would you like just a pic of the graph
Nah I can see enough
unreal sail
Ok
summer haven
Unfortunately no
Okay so you first would replace the inequalities with equal signs
So
- y = 500(1.2)^x
- y = 2000 - 10x
now can you try and identify each of these 2 on tje graph?
unreal sail
Yes
summer haven
I’m thinking it’s the ones in the green and orange?
Those are regions, not equations
unreal sail
Then no I can’t
summer haven
okay i unfortunately gotta sleep
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vocal epoch
was tryna graph a rational function using derivatives and the graphs supposed to look like this
vocal epoch
problem is when i was testing my values n stuff i was getting funky ass intervals of increase n decrease
this what i got for f'x
this was the test thing i was doin
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fathom jungle
was tryna graph a rational function using derivatives and the graphs supposed to...
im not completely familiar with graphing tools but it looks to me like your graph is of f(x) not its second derivative
@vocal epoch
second derivative^^^
first derivative:
vocal epoch
yea i have that
vocal epoch
im p sure the first derivative here is done right
idk why when i test it im getting wrong intervals of increase and decrease
oh my god i just realized why it was wrong
i was putting it in my calculator with the denominator bracket squared instead of cubed 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀 🥀
fathom jungle
rip
fathom jungle
yeah i ran thru this 3 times and found no issues
vocal epoch
my bad bro 💔
boreal geode
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boreal geode
Hello is this right
trim lichen
#7 is not written in standard form so it's not right even though the value is (presumably) correct
boreal geode
Oh is my answerr not in standard form
clear cloud
Second seems ok
boreal geode
Oh
boreal geode
it's not. do you know what standard form means?
I think so
boreal geode
a x 10^b
trim lichen
a * 10^b and what should a and b be?
boreal geode
But 0<a<10
boreal geode
b can be any nunber
boreal geode
**1 ≤** a < 10,
Oh
trim lichen
b can be any number at all?
boreal geode
b can be any number at all?
I believe so
trim lichen
is $2 \times 10^{0.5}$ standard form?
solid kilnBOT
Ann
boreal geode
I think so
trim lichen
no it's not
trim lichen
the exponent on 10 should be an integer.
boreal geode
I didn’t know
trim lichen
now you do
boreal geode
my ignorance
trim lichen
in fact the way to do this would be to write 6.4 * 10^143 as 64 * 10^142
breaking off a ten so that the exponent on the 10 is even and you can root it cleanly
and you also get 64, which also has a clean square root
trim lichen
you were uninformed or you forgot something
but i refuse to make any judgment on your intelligence from just this
boreal geode
lmao even if I can told I probably won’t know to do that 😞
Thank you for ur help
Have an great day or night
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flat steppe
can someone help me understand how to graph log and ln functions, i did "learn" it in class, but i just really don't understand
bright quarry
sal khan
flat steppe
?
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torn shale
so, factorizing this, i used the method where we multiply 2t^2 and 3 by (the coef of t^2 which is 2.)
so it became 4t^2 + 7t + 6, which we can factorize like this --> (2t+1)(2t+6) which also simplifes to 2(2t+1)(t+3)
anything wrong with what i did? (i didnt get to my main concern yet)
lusty fractal
so, factorizing this, i used the method where we multiply 2t^2 and 3 by (the coe...
U factorized it incorrectly
(2t + 1)(2t + 6) = 4t^2 + 14t + 6
hidden dew
so, factorizing this, i used the method where we multiply 2t^2 and 3 by (the coe...
well looking at dividing by 2 would yeild your given polynomial factored
torn shale
it was me applying the method incorrectly
i realized what ive done wrong
ty tho
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lusty fractal
2t^2 + 6t + t + 3 ---> 2t(t + 3) + (t+3) -> (2t+1)(t+3)
Grouping might've been an easy way
Look into the divide and slide method as well its quite good
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quartz mauve
How to solve this problem??
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How to solve this problem??
left oriole
try plugging in (0,2) and see what you get
onyx snow
ye
tidal dune
you want to plug in both points and divide the equations
onyx snow
you plug in the other point and get another equation
divide the equations to eliminate a and solve for b
quartz mauve
Maybe refresh your systems of equations
I'm lookng at previous chapters and I don't see anything on systems of equations
tidal dune
It's usually taught in algebra 1 but easy to forget since it's not used a ton
there's some stuff on khan academy for sure
it's not the most complex but worth taking a look at
quartz mauve
okay like what I am plugging for a(b)^x?
quartz mauve
I guess that was wrong
seems like this has two right
seems like this explanation is using logs not equations
quartz mauve
divide the equations to eliminate a and solve for b
this explanation was close but left out b^4
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shell rose
Guys how can i solve this one:
[x - y - z = 1
[2x + y +3z = 6
[mx + y + 5z = 13
dapper swift
Guys how can i solve this one:
[x - y - z = 1
[2x + y +3z = 6
[mx + y + 5z = 13
infinitely many solutions, exactly one solution, or no solution?
there's a variable m
shell rose
Exercise says to find a number for M that makes the equation possible and impossible
dapper swift
okay
dapper swift
Guys how can i solve this one:
[x - y - z = 1
[2x + y +3z = 6
[mx + y + 5z = 13
do you know what Gaussian elimination or row reduction is?
shell rose
The row reduction one is the one that focus on 2 equations at the same time?
Like to remove y
You do by canceling out 2 equations
dapper swift
yes, if you try to eliminate one variable, that's how
shell rose
Yea
dapper swift
in row reduction you don't write down x, y, z though
you just write down the numbers
so x - y - z = 1 becomes 1, -1, -1, 1
dapper swift
i tried that but result came as x(m-5) = 0
okay that doesn't seem right
,w rref {{1,-1,-1,1},{2,1,3,6},{m,1,5,13}}
solid kilnBOT
dapper swift
ah whatever it doesn't matter if you didn't row reduce, you should still get the same answer
I thought you did it by row reduction and I was confused
shell rose
Idk what was row reduction, sorry 😅
In brazil here its called "escalonamento"
idk if its the same thing
prime crystal
dapper swift
In brazil here its called "escalonamento"
not the same thing, so I'm talking about eliminação de Gauss
oh wait that's a different name for the same thing apparently
dapper swift
from x (m - 5) = 0 you have two possibilities
either x = 0, or m = 5 (or both at the same time)
so you need to go back and sub m = 5 in
shell rose
Oh
shell rose
this would just cancel everything
dapper swift
if you know about systems of linear equations, 6x + 4z = 14 and 3x + 2z = 7 are linearly dependent
you can multiply the 2nd equation by 2 and get the 1st equation
so when m = 5, how many solutions are there for x, y, z?
shell rose
x and z would be 0, dont? but what about y?
dapper swift
x and z would be 0, dont? but what about y?
not when m = 5
dapper swift
This 2 can cancel eachother
yeah, so you get 2 equations but 3 variables x, y, z
2 unique equations
odd sky
What's m here
shell rose
5
dapper swift
What's m here
wdym by here
shell rose
But i still couldnt fallow, im sorry
dapper swift
yeah, so you get 2 equations but 3 variables x, y, z
this tells you that there are infinitely many solutions
odd sky
Is it equation m = 5?
odd sky
this tells you that there are infinitely many solutions
Yeah
dapper swift
x - y - z = 1 and 2x + y + 3z = 6 are two unique equations: the 3rd equation depends on the other two
if you sub in x = 1, you get solutions for y, z
odd sky
BC those lines r same means they interact every point
shell rose
So for m = 5 there are infinite solutions, and m != 5 there are no solutions?
dapper swift
if you sub in x = 2, you also get solutions for y, z
you could sub in anything for x and still get solutions for y, z
dapper swift
So for m = 5 there are infinite solutions, and m != 5 there are no solutions?
no, you didn't check the case when m != 5
dapper swift
from x (m - 5) = 0 you have two possibilities
that case is when x = 0
so you can now sub in x = 0 and find y and z
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sage geyser
super quick question
trim joltBOT
super quick question
sage geyser
in double/triple integrals, symmetry of tri fnsg can often make the integral equal 0
is volume signed?
if it's signed, i can lleave it as 0. if it's unsigned, i'd need to go back and use symmetry to find the "absolute" volume, no?
for example $$\int_0^{\2pi} \int_0^{\pi / 2} \int_0^1 \left( \rho \sin(\phi) \sin(\theta) \right) \rho^2 \sin(\phi) , d\rho d\phi d\theta$$
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Vague Disbeliever
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sage geyser
equals 0 because it resolves to pi/16 ∫_0^2pi sin(theta) dtheta
but hypervolume could be signed or unsigned
so depending on that i'd need to know whether to do pi/16 * 2 * ∫_0^pi ...
or just leave as 0
ionic pendant
volume is not usually signed but the integral always returns signed volume/hypervolume etc
sage geyser
hmm let me think
triple integral questions dont really ask for hypervolume
it's more common for like temperature or mass of a surface
FUCK
those are positive quanitites
so i would need to resolve symmetry?
ionic pendant
they do give hypervolume but that's not the usual interpretation
certainly they can give negative quantities sometimes, e.g. integrating charge density to get charge
sage geyser
well yeah the triple integral also accumulates over everypoint on the surface
sage geyser
certainly they can give negative quantities sometimes, e.g. integrating charge d...
hmm you are correct
ok let's say this is a question that asks for mass of the region
ionic pendant
equals 0 because it resolves to pi/16 ∫_0^2pi sin(theta) dtheta
where did the 2pi in the upper bound come from here?
sage geyser
i would nee dto resolve symmetry?
sage geyser
where did the 2pi in the upper bound come from here?
$\iiint_V y , dV$ given $V$ is a region bound by $z = \sqrt{1 - x^2 - y^2}$ and the $xy$-plane.
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Vague Disbeliever
sage geyser
so z >= 0 and x^2 + y^2 + z^2 = 1
you get $\rho \in [0, 1]$, $\phi \in [0, \frac{\pi}{2}]$, $\theta \in [0, 2\pi]$
solid kilnBOT
Vague Disbeliever
sage geyser
since the xy plane cuts the sphere into a hemisphere
ionic pendant
**Vague Disbeliever**
well certainly you would expect this integral to be 0 since the region is y-symmetric
if the question was asking for mass, then that would require y to be the mass density. but mass density can't be negative, so the question would be poorly formulated
in general the physical quantities which are always positive are like that because the things you are integrating to get them are always positive
sage geyser
**Vague Disbeliever**
this was the question specifically
no application
just evaluate integral
would 0 be the correct answer
ionic pendant
yes, if you're not given a specific application i wouldn't assume any
sage geyser
how would i resolve symmetry without access to the graph of the thing
asuming its something positive
ionic pendant
if you want to reduce an integral to a multiple of some smaller integral due to symmetry then it will help to make a rough sketch of the region of integration
it doesn't have to be super precise, just qualitatively correct
for homework problems you can also use a 3D graphing calculator to check that your sketch is correct
sage geyser
👍
wait uh sorry i have to go to sleep xd umm i guess you could give your answer and maybe force itt o auto close
or something
but i need to go
thank you
ionic pendant
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shell rose
Guys, i need another help.
But now with simplex method for linear programing
minimization
Z = x - 7y
restrictions:
1x + 1y =< 12
-1x + 2y =< 4
fierce lake
What are you stuck on
vagrant kraken
minimize x-7y if x+y=<12 and -x+2y=<4?
fierce lake
minimize x-7y if x+y=<12 and -x+2y=<4?
Yeah
shell rose
yea
shell rose
What are you stuck on
I mean i got some results but they are not matching with chat gpt
maybe i did something wrong
fierce lake
Guys, i need another help.
But now with simplex method for linear programing
mi...
Draw the regions onn the graph
vagrant kraken
is there a special way you need to do it?
fierce lake
X + y <=12 and -x+2y <=4
shell rose
is there a special way you need to do it?
Using the simplex method
fierce lake
Hold on there shoukd be more restrictions
vagrant kraken
nvm then, I am out
shell rose
the x and x2 must be positve
fierce lake
Is there. Conditions like. X>=0 y>=0
fierce lake
the x and x2 must be positve
x2?
fierce lake
Ok
Plot this region on the graph
You'll get a quadrilateral
Now idk what theorem this is, but I've heard that the value given to you to minimise will be achieved at the vertices of this quadrilateral
So put those values in Z, see which one is least
That's your answer
shell rose
But wouldnt just be guessing the answers?
Or should i do with the values i got?
Like i got this in the final
but chat gpt said to do (x-1) in minimizing
fierce lake
But wouldnt just be guessing the answers?
No its a theorem
It's proven to be true
For any optimisation
jagged wharf
$T_4$: $X$ is a $T_1$ space, and for any disjoint closed sets $A,B$ in $X$ there are disjoint open sets $U,V$ with $A\subset U$ and $B\subset V$.\
$T_3$: $X$ is a $T_1$ space, and for any closed set $A\subset X$ and any $x\in A^c$, there are disjoint open sets $U,V$ with $x\in U$ and $A\subset V$.\
I'm struggling showing $T_4$ space is a $T_3$ space given the fact that $X$ is $T_1$ iff ${x}$ is closed for every $x\in X$. I choose $A={x}$ and $B$ to be any closed set that does not contain $x$ in the definition of $T_4$. Then these are disjoint closed sets in $X$, and so there are disjoint open sets $U,V$ such that $A\subset U$ and $B\subset V$. Now how does this show it is a $T_3$ space?
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psie
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boreal geode
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boreal geode
I am not sure how to do it
delicate bobcat
Let's start from the 1st poistion
What do you think we can put in the 1st place given that the integers are greater than 40.000?
And they're odd
trim lichen
!occupied and also don't ask for ppl to do things for you.
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@boreal geode Has your question been resolved?
boreal geode
What do you think we can put in the 1st place given that the integers are greate...
Ohh I get it now thank you
teal vale
Hi, i need help.
i can't figure where to start.
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Hi, i need help.
i can't figure where to start.
solid kilnBOT
Koren
trim lichen
are you sure you wrote this correctly
c is mentioned only once and doesn't appear in the equation
solid kilnBOT
Koren
spiral ocean
just an idea...
it looks kind of like average value theorem
which states that
[ f(c) = \frac{\int_a^b f(x) dx}{b-a}]
solid kilnBOT
k
spiral ocean
in our definition ${b-a = n}$
solid kilnBOT
k
spiral ocean
using inequality
teal vale
The arithmetic average is greater than the geometric average which is greater than the harmonic average is what i know
idk anything related to integrals (in this course ofcourse)
spiral ocean
For ${m = \min{f(x)}}$ and ${M = \max{f(x)}}$ over that interval
[ mn \leq \int_a^b f(x) dx \leq Mn ]
solid kilnBOT
k
spiral ocean
oh
teal vale
sorry for your time :(
spiral ocean
nah its ok
teal vale
anything else you can think of?
maybe how you prove this theorm?
teal vale
The arithmetic average is greater than the geometric average which is greater th...
should be something related to this
and The Intermediate Value Theorem
teal vale
this is the solution in my language.
i gave AI it to translate and latex.
see:
Given $n$ numbers $f(x_1), \ldots, f(x_n)$, there exists a largest number and a smallest number (since this is a finite set of numbers), and we denote:
[
\max{f(x_1), \ldots, f(x_n)} = f(x_i), \quad \min{f(x_1), \ldots, f(x_n)} = f(x_j)
]
where $1 \leq i, j \leq n$ (not necessarily unique). Therefore, their arithmetic mean will be bounded as follows:
[
f(x_j) \leq \frac{f(x_1) + \ldots + f(x_n)}{n} \leq f(x_i).
]
According to the value of the function averaged over the interval between $x_i$ and $x_j$, we get that for some $\alpha$ between $x_j$ and $x_i$, the following holds:
[
f(x) = \frac{f(x_1) + \ldots + f(x_n)}{n}.
]
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Koren
spiral ocean
Define ${M = \max{f(x)}}$ and ${m = \min{f(x)}}$,
[ \frac{mn}{n} = m \leq \frac{f(x_1) + \dots + f(x_2)}{n} \leq \frac{Mn}{n} = M]
solid kilnBOT
k
teal vale
i just found this solution but i can't understand it
teal vale
i still don't understand what theyre saying :(
teal vale
yeah
spiral ocean
For some ${i,j \in [a,b]}$. Since ${f(x_i) = m \leq f(c) \leq f(x_j) = M}$, there exists a ${c \in (x_i, x_j)}$
solid kilnBOT
k
spiral ocean
So
(x_i, x_j) is a subset of [a,b]
So in general
There is a solution is [a,b]
Ya?
spiral ocean
Ye
teal vale
tysm
forest falcon
2nd one
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red loom
<@&268886789983436800>
sage python
Can someone help me prove that this is Big Theta of lg(n)?
sage python
My understanding is that we effectively want to prove that the two summations that are being multiplied by 1/n, both sum to Big Theta (nlgn), which means we can divide that by the 1/n, leaving us with Big Theta (lgn). I am having trouble proving that those two sums equal Big Theta (nlgn), however.
For more context, this summation is averaging the time it takes to find a specified element in a sorted list via a binary search algorithm, given that each element in the list has equal probability of being equal to that specified element.
zinc ginkgo
Can someone help me prove that this is Big Theta of lg(n)?
doesn't look right. show the original problem.
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jagged wharf
Is every collection of sets that is closed under finite intersections, contains the whole set X and the empty set, a base for a topology of X?
jagged wharf
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chilly blaze
for this question why does the sign change the second last step
clear cloud
sqrt(x²) = |x|
And |x| = -x if x < 0
So since x -> -inf
The -sqrt(x²) = -|x| = -(-x) = x
clear cloud
Yw
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sage python
doesn't look right. show the original problem.
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void dew
how the hell do i do this
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how the hell do i do this
void dew
<@&286206848099549185>
i know that there are 3 differnet types of them
like verital horinztal and oblique?
how to finde them
plus domain and range for these set of problems
huh
delicate bobcat
how to finde them
Well, the 3rd type we won't need it in this question
I mean the oblique asymptote
void dew
oh okay
delicate bobcat
They're homographic functions in the canonical form already
void dew
the heck\
delicate bobcat
Do you know what I'm talking about?
void dew
no
delicate bobcat
Lemme find a proper photo
delicate bobcat
It's a special case of this function
delicate bobcat
Where A, l and h are constants to be found
void dew
yea
delicate bobcat
This is excatly what we call the canocial form of the homographic function (the fancy words doesn't matter in fact)
delicate bobcat
The asymptotes in such a case are:
VA -> x = l
HA -> y = h
delicate bobcat
so the form of somthing/x-somthing+or-something
Yes, basically
delicate bobcat
So, you just need to specify l and h to get them, but if you want I can give you a more detailed explanation
void dew
So, you just need to specify l and h to get them, but if you want I can give you...
no deatiled please
i get confused then
delicate bobcat
And explain why is that (I mean, why the asymptotes are like that)
But to solve this, it isn't necessary
delicate bobcat
So, let's get started with an example
void dew
for the x axis and the y axis
delicate bobcat
Let's take a)
delicate bobcat
l = 3, ye
void dew
so a=1 l=3 y=2
yea
so then for the first one
it be
a=1
l=3
and h=2
and i do the same for the rest of them
delicate bobcat
Exactly, from here we specify the asymptotes
delicate bobcat
Tell me what the asymptotes are for a) firstly
void dew
Tell me what the asymptotes are for a) firstly
the vertial or v=3
and the horiznatl or h=2
delicate bobcat
l=3 doesn't represent an equation in the Cartesian Plane
We need to have x = ... or y = ...
void dew
ah tnak you
but what about domain and range
is it just the point of the vertial asstymome
delicate bobcat
I think you can proceed with the rest, but now we also are supposed to find the range and the domain
void dew
is the domain the same thing as the point of the verital asimtoype
so like x not equal to 2
delicate bobcat
is the domain the same thing as the point of the verital asimtoype
Wdym? I guess you're thinking about excluding that value from the domain?
delicate bobcat
Naah
You said x isn't 2 (it should be 3, but I guess you understand it)
So why did you change it like that?
delicate bobcat
If we plugged x = 3 into our function we wouldn't get any result (it'd be undefined), so we have to exclude this number from the set of possible values (i.e. form the domain), this is how it works in general
delicate bobcat
Why like that?
void dew
Why like that?
becuase i think my teacher wnats it like that
i dont know what from she wnats it in
form
delicate bobcat
Can't be like that, since it's wrong. The domain is all values of x you can plug into the function and get a result
delicate bobcat
You can also read it from the graph, but here you don't have it, so it's better to recall the definition
delicate bobcat
x not equal to 3
Not equal to 3, because x = 2 is valid
delicate bobcat
So, basically in all of the examples you're supposed to check when the denominator is zero and exclude that value from your set
delicate bobcat
If you meant your teacher want you to set domain using the interval notation, you obviously can do it as well
solid kilnBOT
Modus
void dew
$$x \neq 3 \equiv y \in (-\infty, 2) \cup (2, \infty)$$
solid kilnBOT
ppq#7826
delicate bobcat
Or:
solid kilnBOT
Modus
void dew
i will use the firsy one
delicate bobcat
They're all equivalent forms
void dew
x is not equal to 3
can you do the smae with y
like y is not equal to 2
as that is the other asymentopye
delicate bobcat
Yes, it works for y as well
delicate bobcat
Yes, it works for y as well
It's because the fraction 1/(x-3) for very large (or very small) x is close to zero, so we leave with that 2 (but y never achieves it)
delicate bobcat
Yes
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lost ruin
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lost ruin
Q11
stoic garden
Asymptote of the function as x -> -inf
stoic garden
You must essentially find the most dominant part of each term
For example, within $\sqrt{x^2 + 2\cdot \sqrt{x^2 + 1}}$, \
$x^2$ dominates $2\cdot\sqrt{x^2 + 1}$
solid kilnBOT
@stoic garden
stoic garden
@lost ruin so what does $\sqrt{x^2 + 2\cdot\sqrt{x^2 + 1}}$ simplify to as $x \to -\infty$?
solid kilnBOT
@stoic garden
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sage python
.reopen
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sage python
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https://www.math.umd.edu/~immortal/CMSC351/notes/binarysearch.pdf
https://disco...
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lime sphinx
!nopdf
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dawn pivot
<@&268886789983436800>
turbid gazelle
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turbid gazelle
why if d divides c then there are solutions?
trim lichen
why if d divides c then there are solutions?
did you read the last paragraph in your image
turbid gazelle
just read it
d divides a and m so u can divide them by d
and since d|c u can divide c by d
how does doing all of that actually give you the unique solutions though?
it just seems to me like a lot of random operations
trim lichen
which one of these best describes your doubt?
(A) "Why does any of this give me any solutions at all?"
(B) "I get why this gets me some solutions, but why do I get all the solutions this way?"
(C) "Secret third option."
trim lichen
A
ok right in this case
do you understand that any solution of (a/d)x = c/d (mod m/d) also solves ax = c (mod m)
or actually maybe it would help to do an example problem
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mighty pilot
Is this not correct? 0.4 * 0.3 is 0.12, so I rounded down, but it seems like it shouldn’t be rounded. Idk what I did wrong
mighty pilot
Better photo
jagged phoenix
Is this not correct? 0.4 * 0.3 is 0.12, so I rounded down, but it seems like it ...
What are you assuming to multiply in the first place
mighty pilot
Isn’t A n B equal to a*b?
Or is that only for dependent events
Because it doesn’t state which one it is
mighty pilot
I’m confused
Is it different based on if its dependent or independent? How am I supposed to know which is correct
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dusty sleet
!occupied
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dusty sleet
And also, it sounds scam
tired badger
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tired badger
Q461
Shouldnt the answer be 5*6?
cuz every team has to play with 5 teams and there are 6 teams overall
hallow cliff
That would be the number of times they play each other exactly twice
fossil folio
cuz every team has to play with 5 teams and there are 6 teams overall
team 1 playing team 2 would hence be different from team 2 playing team 1
hallow cliff
cuz every team has to play with 5 teams and there are 6 teams overall
If team A played with team B, team B doesnt need to play A again
tired badger
That would be the number of times they play each other exactly twice
ohhhhh
obtuse stratus
Depending on the real parameter α, solve the equation:
αx − 3α = 1 + x
fossil folio
Once you get all the terms with x on one side, you can factor out x
obtuse stratus
so, x(α-1)=3α+1 ???
fossil folio
so, x(α-1)=3α+1 ???
Yeah
obtuse stratus
then, x should be 3α+1 / α-1
round imp
so, x(α-1)=3α+1 ???
That is correct.
fossil folio
Easy
round imp
then, x should be 3α+1 / α-1
seems right
obtuse stratus
that's it???
fossil folio
that's it???
Yep
round imp
that's it???
Yes
obtuse stratus
thank you!!!
round imp
Were essentially making x the subject here
round imp
thank you!!!
np
obtuse stratus
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narrow oxide
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narrow oxide
.
narrow oxide
Because they subtracted it
But we have changed the initial beginning sigm do all change?
narrow oxide
Is positive 90
Oh
narrow oxide
It’s just subtracting equations
Oh than you
narrow oxide
I’ll give you an example
Sure
untold pier
3x -2y= 0
4x -5y = 3
delicate bobcat
You have to apply that minus sign to all the terms of 2nd equation, not only to the 1st one
untold pier
We don’t need to solve this
it becomes:
3x -2y=0
-(4x-5y)=3
So you subtract 4x and add 5y
And subtract
narrow oxide
Hm
narrow oxide
Minus minus 90
I understood by this thanks
untold pier
Because subtracting a negative is positive
untold pier
I understood by this thanks
Welcome
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fair forge
if for nroms $|| .||_a, || .||_b$ there are constants c,C>0 such that the inequality here is satisifed, does it mean $||x_n||_b->x_0$ imply $||x_n||_a->x_0$?
solid kilnBOT
Accelerator
fair forge
(in R^n)
fair forge
well it works
solid kilnBOT
Ann
trim lichen
like exactly this
fair forge
are you sure you meant $\nrm{x_n}_b \to x_0$
yes
trim lichen
and what's x_0
fair forge
x_0 just being a vector in R^n the sequence converges to
trim lichen
ok but $\nrm{x_n}_b$ is a sequence of real numbers
solid kilnBOT
Ann
trim lichen
i think you may have meant something else
fair forge
ok but $\nrm{x_n}_b$ is a sequence of real numbers
oh i see
trim lichen
and maybe you are asking whether the following is true: if a sequence x_n converges in norm b, does it also converge in norm a to the same point
fair forge
so swap x_0 with L \in Reals
fair forge
and maybe you are asking whether the following is true: if a sequence x_n conver...
yes exactly that
trim lichen
yes exactly that
ok alright
fair forge
as in, x_n -> x_0, when n->+inf, and it's by norm b
trim lichen
note that $x_n \xrightarrow{\nrm{\cdot}b} x_0$ means $\lim{n \to \infty} \nrm{x_n - x_0}_b = 0$
solid kilnBOT
Ann
fair forge
note that $x_n \xrightarrow{\nrm{\cdot}_b} x_0$ means $\lim_{n \to \infty} \nrm{...
ty so much mate
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wraith hinge
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ionic pendant
i don't really see why that should be the tangent line
if anything the function has a vertical tangent there
because a vertical tangent exists where the slope approaches +/- infinity (as it does in this case)
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wraith hinge
if anything the function has a vertical tangent there
non differetiable functions have vertical tangent lines only ?
ionic pendant
well they can also have no tangent lines
wraith hinge
how would that be
ionic pendant
particularly if the slope approaches a different value from each side, as in |x|
or oscillate wildly, as in sin(1/x)
wraith hinge
also could you check the rest of my doubts in stack exchange ive been stuck on all of this since the last 12 hrs my brain is fried lmao
wraith hinge
because a vertical tangent exists where the slope approaches +/- infinity (as it...
either one value right
like LHD=RHD equal to either -/+ infty
ionic pendant
either one value right
like LHD=RHD equal to either -/+ infty
no it should be both sorry misread
ionic pendant
depending on how you define the tangent line, either it doesn't have one or it has a vertical tangent
wraith hinge
does the function y=x^2/3 have a tangent
its LHD and RHD are different
right
+infty and -infty
wraith hinge
depending on how you define the tangent line, either it doesn't have one or it h...
mhm
wraith hinge
its LHD and RHD are different
could you recheck 😓
so it doesnt have a tangent at x=0
ionic pendant
they are different but both of those are a vertical line
ionic pendant
well following that definition yes. but also if you have a slope of +infinity that's a vertical line and a slope of -infinity that's also a vertical line. so in some sense they still agree with each other
wraith hinge
for some reason , the textbook im refering to says it has a vertical tangent and the class im refering to ( he doesnt refer to the textbook) says otherwise , ie it doesnt exist
textbook
tangent to a curve at point P can be drawn even though dy/dx does not exist at point P
therefore x=0 is a tangent to y=x^2/3 at 0,0
ionic pendant
well in the very specific case where dy/dx approaches infinity it can, because there is a single type of line (vertical) with undefined/infinite slope
ionic pendant
for some reason , the textbook im refering to says it has a vertical tangent and...
well it gets into how exactly you define a tangent line, using different definitions you can get different conclusions
wraith hinge
mhm alr
hey another doubt
what is a tangent graphically @ionic pendant :O
it isnt just a line that cuts through one point
right
there are infinite such lines
nimble niche
It's a line that cuts through a point on a curve while not intersecting any other point on the curve
ionic pendant
it's a line where if you zoom in enough at the point of tangency, the line and the function almost perfectly overlap
wraith hinge
It's a line that cuts through a point on a curve while not intersecting any othe...
so does the book im refering to
wraith hinge
it's a line where if you zoom in enough at the point of tangency, the line and t...
i see
nimble niche
https://math.stackexchange.com/questions/4241302/can-a-tangent-touch-a-curve-at-...
O i'm wrong lol
wraith hinge
from my understanding by now
- if the function is differetiable at the point , then a tangent exists with slope equal to the derivative to the function at that point
2)if the function is non-differentiable at that point , then IF LHL=RHL=+/- infty , then only a tangent exists , which is a vertical tangent , if LHL not equal to RHL then no tangent exists for that point
am i right
nimble niche
Hm to define it better, a tangent is a line that cuts through a point on a curve, having the same slope as that of the curve at that point
nimble niche
Hm to define it better, a tangent is a line that cuts through a point on a curve...
Not necessary that it cannot touch any other point
wraith hinge
Hm to define it better, a tangent is a line that cuts through a point on a curve...
mhm
gentle crag
Hm to define it better, a tangent is a line that cuts through a point on a curve...
you would have to say what the “slope of a curve is” without making this definition circular
wraith hinge
you would have to say what the “slope of a curve is” without making this definit...
i was about to say that :O
nimble niche
Slope of the curve would be the derivative of the curve at that point
gentle crag
Slope of the curve would be the derivative of the curve at that point
then you are just saying that the tangent line is the line whose slope is the derivative
wraith hinge
Just to given a visual example on what cloud said
thank you , im understanding it better now :D
nimble niche
then you are just saying that the tangent line is the line whose slope is the de...
Yeah, if the function is differentiable.
ionic pendant
it's a line where if you zoom in enough at the point of tangency, the line and t...
we can express this mathematically using the tangent line equation
[ f(x) = \underbrace{f(a) + (x-a) f'(a)}{\text{tangent line}} + R(x) ]
where $R(x)$ is an error term which goes to 0 at a (and also has to go to 0 sufficiently quickly):
[ \lim{x \to a} R(x) = 0, \qquad \lim_{x \to a} \frac{R(x)}{x - a} = 0 ]
note that this definition does necessarily exclude non-differentiable functions
solid kilnBOT
cloud
ionic pendant
the conditions on the error term is what makes the graphs look identical if you zoom in enough
ionic pendant
it's the difference between the function and its tangent line approximation
wraith hinge
OHH
alr alr
thank you so much
AHHHH
tysm tysm
im feeling relieved after 12 hrs
eh
ill check if i have a few more doubts left
lost ruin
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ancient trout
translate
forest needle
What have you tried?
lost ruin
What have you tried?
Everything
forest needle
Try putting x=1/m and lim m tends to 0
jagged perch
did u try expansions? i deduced that doing it would be lengthy and unsignificant
too hectic tbh
lunar stirrup
did u try expansions? i deduced that doing it would be lengthy and unsignificant
i think u have to reduce is first before expansion
a^2-b^2 = (a-b)(a+b)
and since its log u can convert both into 1 term
and make it into 1+y kind of format
jagged perch
yes definetly we can
lost ruin
then u should have gotten the answer
I didnt try developement limité
Cest la seul chose que jai pas appliqué
J’ai oublié les formules
lunar stirrup
J’ai oublié les formules
u shouldnt forget
lunar stirrup
Cest la seul chose que jai pas appliqué
then try it out
(i understand only simple french)
lost ruin
(i understand only simple french)
Yeah ive noticed that ure on learning french server
lunar stirrup
oh lmao
lost ruin
u shouldnt forget
forest needle
Try putting x=1/m and lim m tends to 0
forest needle
yeh that's what I got as well
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compact badge
Hey the answer is positive infinite
ln(x)/x would be 0 if you look at their graphs together
x has a large increase than ln(x)
As it approaches infinity, the value of ln(x)/x would approach 0
Another useful thing for prev qn
forest needle
I tried again and I got 1 mb made a calc error last time
compact badge
I tried again and I got 1 mb made a calc error last time
got 1 ?
forest needle
yeh wait I'll send
forest needle
empty orchid
Hey the answer is positive infinite
!nosols
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Hey the answer is positive infinite
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
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violet depot
Guys, what the formula for RAM
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Guys, what the formula for RAM
violet depot
You know, computer memory
soft lintel
Would you mind elaborating? What do you mean by "the formula for RAM"? What does RAM stand for to you?
clear cloud
Formula for random access memory ?
violet depot
Formula for random access memory ?
Yeah that
OK, just hear me out, OK?
Let's say t is a variable
The first time t=27
The second time t=73
what is a formula that can tell Me what t equals the first time
soft lintel
clear cloud
formula = boolean operation ?
violet depot
formula = boolean operation ?
?
What is so confusing about this
I just would like to know a formula that can replicate memory
clear cloud
I don't get the use of "formula"
violet depot
I don't know what else to use
clear cloud
Ah
violet depot
Mathematical equation
soft lintel
Neither the "replicate memory" part, it's quite unclear
violet depot
Neither the "replicate memory" part, it's quite unclear
OK, I'm just gonna show it with you
clear cloud
I just would like to know a formula that can replicate memory
Register ?
violet depot
Neither the "replicate memory" part, it's quite unclear
t=3
now t=29
what was t the first time I told you
clear cloud
27
clear cloud
The first time t=27
I mean
But what do you want to get with this t ?
You want a program to keep it in mind ?
And give another value to t ?
violet depot
But what do you want to get with this t ?
t is just a random variable
violet depot
You want a program to keep it in mind ?
yes, the previous values
clear cloud
And you want to this with nor gates?
violet depot
And you want to this with nor gates?
If {set = 1 and r=0}=1
i'm finna crash the fuck out
.close
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rapid vortex
I’m having trouble researching how to solve this problem. I can’t figure out what keywords or such I should be using.
rapid vortex
The dotted line can rotate around 0,0, is fixed in length, is connected to the upper line at its mid point, and the upper line cannot change y position. It should be able to move +-1.5 on x
I am trying to calculate how long the dotted line should be in order to meet these constraints, and how the connection point deviates from its initial position along the dotted line.
Sorry if this is poorly explained, let me know if I can clarify something
delicate bobcat
If the length of the dashed line is constant and the line at the top cannot change its y coordinate, then what you wrote is contradictory, because rotating it by any angle will make (provided it is still connected to the center of the line at the top) this line longer
i.e. these lines aren't equal length