we have that sin(-x) = -sin(x), so reflecting its graph horizontally is the same as reflecting it vertically, yes
#help-27
acoustic leaf
devout snowBOT
@halcyon yew Has your question been resolved?
jaunty bane
Can somebody please help me with this
devout snowBOT
Can somebody please help me with this
@jaunty bane Has your question been resolved?
jaunty bane
<@&286206848099549185>
brisk raptor
Can somebody please help me with this
graph |f(x) - L|
|f(x) - L| is the absolute difference between the function at x, and its limit.
essentially, its the distance between the two, so as x tends towards infinity, this will tend toward 0 because its getting close to its limit
jaunty bane
Okay
jaunty bane
|f(x) - L| is the absolute difference between the function at x, and its limit.
...
So what should I be doing on the graphing calculator
Sorry I'm just really confsued when it comes to epsilon stuff
brisk raptor
So what should I be doing on the graphing calculator
as x goes towards its limit (negative infinity), the distance between the output and the limit shrinks.
|f(x) - L| is our graph of the distance between the output of f(x) and the limit; so, "for some x, how close is the function to the limit"
epsilon is telling you "choose any distance you want, as long as its greater than 0, there is an x where f(x) is that far away from the limit"
so if you said epsilon is 1
you'd be looking for wherever f(x) is 1 away from its limit
if you said epsilon is 0.01, wherever f(x) is 0.01 away from its limit
and, as we've said twice, |f(x) - L| is the graph that tells you the distance for a given x
so if you want to know "where" f(x) is 0.01 away from its limit
brisk raptor
and, as we've said twice, |f(x) - L| is the graph that tells you the distance fo...
look at this graph and find where its 0.01
thats your upper bound, all x less than that will be closer
devout snowBOT
devout snowBOT
Available help channel!
sweet stone
im having trouble continuing with this question
devout snowBOT
im having trouble continuing with this question
sweet stone
could you explain how i would apply that to the problem
supple knot
could you explain how i would apply that to the problem
$\sum$ = sum. $\frac{d}{dx}$ = derivative
woven radishBOT
riemann
sweet stone
.close
devout snowBOT
devout snowBOT
Available help channel!
neon wagon
Alcohol in Blood
“Bin Zecher” has reached a blood alcohol level of 1.8‰ at 24:00 AM. According to a linear rule of thumb, the blood alcohol level decreases by 0.2‰ per hour. Another exponential model assumes that approximately 20% of the current blood alcohol level is reduced per hour.
• Formulate a function for the linear model describing the decrease in blood alcohol level.
how do i do this
neon wagon
is it f(x) = -0,2x+1,8
tall linden
Yes, assuming you're using permille as the unit
neon wagon
Yes, assuming you're using permille as the unit
• Show that the second exponential model can be represented by the function . b(t) = 1.8e^-0.2231t
how do i do this
the operator is „show“ so i dont have to do any calculations right
devout snowBOT
@neon wagon Has your question been resolved?
devout snowBOT
@neon wagon Has your question been resolved?
sleek pawn
having trouble following the logic here
devout snowBOT
having trouble following the logic here
sleek pawn
I get a = 1 and b = 5 but I don't know how we get the 6 in 6e^x
devout snowBOT
@sleek pawn Has your question been resolved?
sleek pawn
<@&286206848099549185>
devout snowBOT
@sleek pawn Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
lament schooner
how do i know precisely
devout snowBOT
how do i know precisely
lusty sapphire
how do i know precisely
Well there's only one force
devout snowBOT
@lament schooner Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
mighty copper
if it was clockwise instead of counter then how would my parametrisation change?
faint gorge
if it was clockwise instead of counter then how would my parametrisation change?
You can just switch the bounds e.g. instead from 0 to 2pi you go from 2pi to 0
mighty copper
You can just switch the bounds e.g. instead from 0 to 2pi you go from 2pi to 0
got it, thanks
.close
devout snowBOT
void knot
A is a m×n matrix. The rank of A is m<n, then can we say that Any m columns of A are linearly independent?
devout snowBOT
A is a m×n matrix. The rank of A is m<n, then can we say that Any m columns of A...
cold bough
no
just take the 1x2 matrix (1 0)
the rank=dim image=1<2
but the one column (0) is not l.i.
devout snowBOT
@void knot Has your question been resolved?
void knot
Then can we say that matrix A can be row-reduced to (I_m|O)?
stone stump
devout snowBOT
devout snowBOT
Available help channel!
devout snowBOT
@stiff token Has your question been resolved?
devout snowBOT
@stiff token Has your question been resolved?
devout snowBOT
@stiff token Has your question been resolved?
sacred dock
devout snowBOT
thin fern
devout snowBOT
@sacred dock Has your question been resolved?
wheat loom
The equation x²-ax+b=0 has two solutions x1 and x2. The couple (a,b)∈Q²
Lets take F a set
F={px1+q/(p,q)∈Q²}
Prove that x1∈F and (x1)²∈F and x2∈F
Who can solve this is literally smart
devout snowBOT
The equation x²-ax+b=0 has two solutions x1 and x2. The couple (a,b)∈Q²
Lets tak...
forest depot
The equation x²-ax+b=0 has two solutions x1 and x2. The couple (a,b)∈Q²
Lets tak...
What is F?
You look like you are dividing q by a pair of numbers
wheat loom
What is F?
A set
wheat loom
What is the definition for it
Bruhhh you don't know sets
forest depot
Oh wait you mean $F = {px_1 + q | (p,q)\in \mathbb{Q}^2}$?
woven radishBOT
Duhon
forest depot
You used a tilted bar and I got confused
wheat loom
forest depot
Well assuming p and q are literally any and all rationals, you can just say that when $p = \frac{1}{x_1}$ and $q = q_1 - 1$, you have that F is just the set of rational numbers, which of course contains the roots of that polynomial
woven radishBOT
Duhon
forest depot
But since that feels like cheating I'm suspicious that the question is being presented wrongly
wheat loom
But since that feels like cheating I'm suspicious that the question is being pre...
No the question is logic
forest depot
Actually nvm that would mean the set F does not necessarily contain the roots
wheat loom
Actually nvm that would mean the set F does not necessarily contain the roots
Sooo what
forest depot
I'm sorry brother but I literally don't get what u want me to say
wheat loom
I'm sorry brother but I literally don't get what u want me to say
The question is very clear
forest depot
The roots can be complex which means that F being just the real rationals, doesn't have them in there
Easy enough
But again
wheat loom
The roots can be complex which means that F being just the real rationals, doesn...
We didn't study complex numbers
forest depot
It feels like it's somehow missing the point so that's why I ask you to check if you asked it right
wheat loom
It feels like it's somehow missing the point so that's why I ask you to check if...
It's right 100%
wheat loom
The roots can be complex which means that F being just the real rationals, doesn...
The question has another solution without complex
forest depot
Then ok assuming the roots of that polynomial are always real, I suppose F does contain them since F is the same set as Q
wheat loom
Then ok assuming the roots of that polynomial are always real, I suppose F does ...
Why F is the same set as Q
forest depot
As I said, if $p_1, q_1 \in \mathbb{Q}$ and we take $p = 0$ and $q = q_1$, you have that F is just all of the rational numbers
woven radishBOT
Duhon
wheat loom
As I said, if $p_1, q_1 \in \mathbb{Q}$ and we take $p = 0$ and $q = q_1$, you h...
Replacing terms is illogic
forest depot
How
forest depot
I'm saying that, given p and q are both any and all rational numbers, you could make the argument that the subset where p = 0 and q is just itself is contained in F
And so Q is contained in F
And since F is, quite plainly, contained in Q, F = Q
wheat loom
I'm saying that, given p and q are both *any and all rational numbers*, you coul...
Why you don't try to write x1 like px1+q
If you do that you will solve it
dry geyser
I'm saying that, given p and q are both *any and all rational numbers*, you coul...
I think p and q could be irrational too
forest depot
I think p and q could be irrational too
He states that $(p,q)\in \mathbb{Q}^2$
woven radishBOT
Duhon
dry geyser
Ah yeah my bad, I meant x1 and x2
dry geyser
You can use midnight formula to denote x1 and x2, right? I think you could express one in terms of the other
wheat loom
You can use midnight formula to denote x1 and x2, right? I think you could expre...
Niceee
X1+x2=a
X1×x2=b
dry geyser
I think the first one will be what you need here. For (x1)^2 you just gotta square the formula and write it in the form px1+q again
Neither of the 3 should be too difficult with that approach
wheat loom
I think the first one will be what you need here. For (x1)^2 you just gotta squa...
Hmmmm ok
devout snowBOT
@wheat loom Has your question been resolved?
devout snowBOT
timber pebble
what have you tried
granite anchor
timber pebble
no i mean to solve the problem
maybe you can try expressing the volume of the prism in terms of the side length of the boxes?
how many boxes long, deep, and high is it?
is what 54
so we want to find the width, and depth, and height of the prism in terms of boxes
you should use the picture they give you to count
okay
no
,calc 12 * 6 * 6
woven radishBOT
Result:
432
cool, we counted right
but its 432 little boxes
whats the volume of a little box
eager nova
That information is given
timber pebble
That information is given
its not important
how much space is in a little box
its 1/2 inch on a side right
so whats the length width and height
1/2 inch high
1/2 inch long
1/2 inch wide
volume of a box is L * W * H
calculate the volume of a little box
yea
so we have 432 boxes
and each box is 1/8 cubic inch
,calc 432 * 1/8
woven radishBOT
Result:
54
@restive river Has your question been resolved?
verbal beacon
Calculate the volume
devout snowBOT
devout snowBOT
Available help channel!
weak sphinx
I need help with this question on rational expressions. Especially with the "5x^3 + 17x^2 +6x"
devout snowBOT
I need help with this question on rational expressions. Especially with the "5x^...
royal radish
I need help with this question on rational expressions. Especially with the "5x^...
multiply the left side
by x-3 over 5x^2 +2x
and multiply the right side by
5x^3 +17x^2 +6x over 9-x^2
wait
nvm
devout snowBOT
@weak sphinx Has your question been resolved?
devout snowBOT
@weak sphinx Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
silent sandal
Ok so this is my the problem I'm currently working on. I'm trying to use the comparison test and p test to determine if it's convergent or divergent but I can't figure out what im doing wrong.
So suppose we know that f(x) < g(x)
We know that if f(x) is divergent, then g(x) must also be divergent.
We also know that if g(x) is convergent, then f(x) must be convergent.
So now we have the function $\int_2^\infty \frac{1 + \sin x}{x^3} , dx$
Now, lets create a simpler integral that we can use the P test on:
$\int_2^\infty \frac{1}{x^3} , dx$
Now we know that:
$\int_2^\infty \frac{1 + \sin x}{x^3} dx > \int_2^\infty \frac{1}{x^3} dx$
Now that we have an integral in the form of \int_2^\infty \frac{1}{x^P}, we can use the P test.
Since $3 > 1$, we know that \int_2^\infty \frac{1}{x^3} converges.
Unfortunatly though, that doesn't really help me figure out whether $\int_2^\infty \frac{1 + \sin x}{x^3} converges or not. What can I do?
devout snowBOT
Ok so this is my the problem I'm currently working on. I'm trying to use the com...
royal radish
what are u comparing what to
silent sandal
im trying to compare $\int_2^\infty \frac{1 + \sin x}{x^3} dx > \int_2^\infty \frac{1}{x^3} dx$
woven radishBOT
dingypine
silent sandal
but that doesnt really help
fair juniper
what if the numerator was 2?
silent sandal
because the smaller one converges
silent sandal
what if the numerator was 2?
For which?
fair juniper
the one you can change
timid nest
**dingypine**
sin x could be negative?
silent sandal
Well if the numerator was 2, then it would be >= at certain points
fair juniper
what are bounds for sinx
silent sandal
-1 < x < 1
fair juniper
what are bound for 1+sinx
silent sandal
0 < x < 2
silent sandal
I'm honestly not sure, are you referring to $\int_2^\infty \frac{1}{x^3}$ as the one with the p test? Or $\int_2^\infty \frac{2}{x^3}$
woven radishBOT
dingypine
fair juniper
you goal is to do what
silent sandal
Find a function that is bigger than than the original one so i can use the p test
timid nest
well, u can only compare when u are sure that a even greater integral converge
fair juniper
ok, so why did i tell you to try 2?
silent sandal
Because it's bigger than the original
fair juniper
bigger or equal, but thats good enough
silent sandal
So $\int_2^\infty \frac{2}{x^3} >= \int_2^\infty \frac{1 + \sin x}{x^3} , dx$
fair juniper
>
woven radishBOT
dingypine
fair juniper
if you want to avoid that, you can also use 3
silent sandal
Ok so that means since the bigger one converges, the smaller one should also converge
So basically, you found a function that has greater than or equal to bounds than 1 + sin(x), and we were able to use the p test
I just wanna know though, how did you know to search for a bigger function than a smaller function? @fair juniper
fossil locust
I just wanna know though, how did you know to search for a bigger function than ...
intuitively, sin x grows slower than x, but x/x^3 = 1/x^2 whose integral converges by the p-test
so yeah first make a guess as to whether it converges or diverges by a comparison
and then the specific proof technique you need is the comparison test, so a smaller integral than a convergent integral will also converge
odd lake
I just wanna know though, how did you know to search for a bigger function than ...
the logic behind it is the "domination", if you want to prove that a function converges, you have to find a function that dominates it (its bigger or equal), if the bigger one converges so does the smaller one, if the smaller one converges, you know nothing about the bigger one
devout snowBOT
devout snowBOT
Available help channel!
ionic stump
real quick, when taking second partials fxx and fyy should have the same sign right
devout snowBOT
real quick, when taking second partials fxx and fyy should have the same sign ri...
ionic stump
.close
devout snowBOT
fossil locust
real quick, when taking second partials fxx and fyy should have the same sign ri...
the answer is no btw
if they have a different sign you have a saddle point
devout snowBOT
Available help channel!
hard trout
devout snowBOT
torn bane
can someone help me with D
what is the divergence of F
hard trout
is it 0+0+0 = 0?
torn bane
i thought we paramterize it first
parameterizing comes later, first what does the divergence theorem tell you
devout snowBOT
@hard trout Has your question been resolved?
quartz seal
is always 0.01 off
devout snowBOT
is always 0.01 off
quartz seal
am i wrong or my cauculator is kinda broken
cause pie is already in 9 digit
plz help
acoustic leaf
what did you try?
acoustic leaf
and what did you get as a result?
quartz seal
104.7197551
acoustic leaf
yes, and if you round to two decimal places?
acoustic leaf
if they ask for "2 decimal places" the assumption is that you should round rather than truncate
devout snowBOT
devout snowBOT
Available help channel!
sand quarry
Why exactly does the Fourier transform happen to be a one-to-one mapping while the Laplace transform is not?
devout snowBOT
Why exactly does the Fourier transform happen to be a one-to-one mapping while t...
@sand quarry Has your question been resolved?
balmy pawn
i dont understand what the question wants from me
devout snowBOT
i dont understand what the question wants from me
devout snowBOT
@balmy pawn Has your question been resolved?
balmy pawn
<@&286206848099549185>
balmy pawn
i dont understand what the question wants from me
uhhh this thing
answer is 14 somehow
balmy pawn
<@&286206848099549185>
red sluice
Ye
topaz axle
it's an arithmetic progression yes
balmy pawn
how does it work
devout snowBOT
@balmy pawn Has your question been resolved?
balmy pawn
.close
devout snowBOT
devout snowBOT
Available help channel!
smoky gale
I think she didn’t name the sides correctly ?
a should be always the bottom hypotenuse.
restive river
Yes?
dense jay
i dont get what you mean, calling things a or b or c doesnt really matter
dense jay
could call the sides x, p and w if you wanted 🙄
smoky gale
could call the sides x, p and w if you wanted 🙄
@dense jay
restive river
'a' need not be at the bottom, who told you that?
smoky gale
smoky gale
'a' need not be at the bottom, who told you that?
If you find area of triangle, you use the formula P = a*h / 2
restive river
Ok, and?
smoky gale
And?
dense jay
they are just variables, dont be so rigid, damn
restive river
(ah)/2 = (ha)/2
smoky gale
(ah)/2 = (ha)/2
feral agate
b is not necessarily the longer side
smoky gale
feral agate
If you're thinking a is the shorter side and h is the hypotenuse here then you're wrong
smoky gale
.close
devout snowBOT
modest dagger
<@477755746499428362>
<a:text_upstupid:874058775378661426>
This is a really rude way to react to a volunteer trying to answer your question.
Don't do this kind of thing here.
devout snowBOT
Available help channel!
granite anchor
devout snowBOT
granite anchor
so i got -pi/3 for this but when i put it into some AI it says pi/2
im not sure what i did wrong because i used disk method and they used shells
i just integrated that function from 0 to 1 and then multiplied pi
what did I do wrong
i dont really know when to use what method
.close
restive river
I need demonstration of partial fraction decomposition for a friend, thanks in advance
devout snowBOT
I need demonstration of partial fraction decomposition for a friend, thanks in a...
winter torrent
mans was READY
winter torrent
restive river
thanx a lot
granite anchor
thanx a lot
ofc
smoky gale
Give me table for:
Hektoliter, dm, etc milliliter centiliter mililiter
polar chasm
restive river
Just search on google; it's available.
polar chasm
this?
restive river
There ain't hectolitre.
faint zinc
There ain't hectolitre.
Yes there is
smoky gale
Give me for measurement
faint zinc
what do you mean "for measurement?"
Are you trying to convert between cubic meters and liters?
restive river
1m^3 = 1000L
0.1m^3 = 1 hectolitre
faint zinc
If so, the table in the wikipedia article I linked provides that
smoky gale
So it’s milli, centi, deci, and above liter, deca, hecto, kilo.
thin basin
restive river
smoky gale
.close
devout snowBOT
devout snowBOT
Available help channel!
buoyant escarp
I need help with this problem;
devout snowBOT
I need help with this problem;
buoyant escarp
im not sure if im doing this correctly?
would that -x^2 work?
<@&286206848099549185>
sonic parrot
Can you do the next step plz
buoyant escarp
Can you do the next step plz
so.
adding that - to the x^2 was on the right path...
sonic parrot
<@&286206848099549185>
You should do it for everything
sonic parrot
adding that - to the x^2 was on the right path...
Yeah but I'm confused if you mean it only for x^2 or everything cause you should do it for everything
buoyant escarp
You should do it for everything
that helps solved the next issue of what to do with the 37 and 5
sonic parrot
that helps solved the next issue of what to do with the 37 and 5
37-5=32
buoyant escarp
ye
buoyant escarp
-3y-5y=-8y
oh mb, made a mistake there, i did -3y+5y=2y lol
sonic parrot
oh mb, made a mistake there, i did -3y+5y=2y lol
That's why you should be careful lol
buoyant escarp
Tell me when you complete
uhhh erm heh.
pretty susure i did something wrong...
waitnoh.
huh. The x^2
sonic parrot
uhhh erm heh.
The left side equation you forgot the minus sign on 20
buoyant escarp
ohh
buoyant escarp
Fix that and show
buoyant escarp
got it. Thank yoyou so much for yoyour help!
sonic parrot
got it. Thank yoyou so much for yoyour help!
No problem
buoyant escarp
No problem
say... do i have to sqrt the 25?
sonic parrot
say... do i have to sqrt the 25?
Yeah x can be 5 or-5
sonic parrot
i see. then it probably wants that as the answer instead of (25,-4) lol
Probably lol
buoyant escarp
Yeah x can be 5 or-5
-5?
buoyant escarp
thought it just be +5 only since... both 25s are +
hm. Thank you again, for your help.
.close
devout snowBOT
devout snowBOT
Available help channel!
little helm
My approach so far is that I assume a half-open interval [0,1) bijective on the example set I_x and if I can show that this is bijective, then the set I, which has I_x as a subset, must also be uncountable. But I can't get any further after that
devout snowBOT
My approach so far is that I assume a half-open interval [0,1) bijective on the ...
sonic parrot
My approach so far is that I assume a half-open interval [0,1) bijective on the ...
What's the question
little helm
Show that the set I of all inductive subsets of
R is uncountable.
Note: First consider that for all x ∈ ]0, 1[ the sets Ix := N∪{x+n | n ∈ N}
are inductive.
devout snowBOT
@little helm Has your question been resolved?
little helm
They give you a hint that's basically the entire answer, no?
ik but do i not have to show why it is uncountable
little helm
Why half open?
because we only showed half opened or closed but not fully open which means that i would have to show it again
muted mural
Any open interval of the real numbers is uncountable. I guess you could show that if you want.
muted mural
because we only showed half opened or closed but not fully open which means that...
Removing one element from an infinite set does not change its size
little helm
they said that i have to show that it is bijectiv somehow
and that i have to find a function that shows that Ix has the same size as [0,1) because it is uncountable
muted mural
You don't need bijective, only injective. You only need an inequality
little helm
ah because you mean, that i can show that it is still uncountable because an uncountable intervall doesnt hit every element?
devout snowBOT
@little helm Has your question been resolved?
mighty folio
who tryna help me
devout snowBOT
who tryna help me
mighty folio
understand flux problems
tall knoll
!da2a
devout snowBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
cyan elbow
Hello , im struggling with this homework and I really need help from someone who could explain it to me … thank you❤️
devout snowBOT
Hello , im struggling with this homework and I really need help from someone who...
trail eagle
Which parts are you struggling with?
cyan elbow
I guess the basics
I literally can’t solve anything so the basics - I hope that if someone could explain on a simpler problem I could do my homework with my own knowledge
linear algebra/functions
Especially struggling with math in English so I can’t even explain well what I don’t understand 😭😭
pulsar sand
Where are you studying? These problems are weirdly obtuse for the subject matter
supple knot
Using \Gamma instead of saying graph 
pulsar sand
This is the most "I have tenure and won't teach your night class anymore" assignment I have ever seen
cyan elbow
Where are you studying? These problems are weirdly obtuse for the subject matter
ah.. its a mathematic university haha, english is not my main language and they are trying to make us get used to harder problems idk
cyan elbow
This is the most "I have tenure and won't teach your night class anymore" assign...
TELL ME ABOUT IT
and our proffesor uses the terms so WEIRDLY so we cant use chatgpt
etc..
supple knot
just do one problem at a time
cyan elbow
the classes also dont help cant lie.. i dont understand it
supple knot
do you know what 3 with overline is
cyan elbow
yes
supple knot
do you know how to find gcd of 3 numbers
cyan elbow
i have no idea what is gcd
cyan elbow
im a lost case sorry 😭
supple knot
you're probably meant to find all divisors of all 3 numbers and find the largest one of the 3
,w divisors of 264
woven radishBOT
cyan elbow
oh i think i get it
woven radishBOT
woven radishBOT
cyan elbow
so its 0.3 periodically times 12 ?
supple knot
did you finish with checking that 12 divides 312
supple knot
so its 0.3 periodically times 12 ?
yea this is a nice round number
cyan elbow
okay so i just do that with all of them
and then im supposed to do something uh
then i will get the numbers for linear functions
and idk what there, solve them or what
devout snowBOT
@cyan elbow Has your question been resolved?
devout snowBOT
@cyan elbow Has your question been resolved?
queen ravine
guys does it make sense to say that 1-1+1-1=2-2 can be 0=0 and 2=2 depending on how you manipulate it?
devout snowBOT
guys does it make sense to say that 1-1+1-1=2-2 can be 0=0 and 2=2 depending on ...
queen ravine
and 1=1
stray spade
add k to both sides you will have k = k
queen ravine
if i move the minus ones to the other side they will become positive thus 1+1=2-2+1+1
dense jay
its not saying theyre equivalent statements
but theyre all true statements
eager nova
You can deduce it, that is correct
queen ravine
so that is possible?
and it will be a true statement
since im following the rules of algebra
queen ravine
so the original equation can be 2=2 and 0=0 and 1=1 depending on how you manipulate it algebraically
eager nova
No
queen ravine
how
eager nova
The original equation is the first
Not the one you want
If my first equation is 3=3
Then I add 1 to both sides
4=4
But still the original equation is 3=3
queen ravine
1-1+1-1=2-2. but im not adding anything im just moving the numbers around by following algebraic rules
eager nova
Incorrect
queen ravine
how
queen ravine
1-1+(+1)+1-1+(+1)=2-2+(+1)+(+1)
im just moving the negative ones to the other side
right?
eager nova
You can clearly see, you are not moving
You are adding
Your visualization is thinking you moved something but you didnt
You only added to both sides
queen ravine
if you have 2x-1=0 you can move -1 to the other side by addding 1 on each side thus 2x=1
eager nova
No
You add 1 to both sides
You do not move
There is no such thing as move to the other side in an equation
misty crest
"by adding 1 on each side"
misty crest
You do not move
sure you do this is just how we speak in conversation
queen ravine
okay my point is 1-1+1-1=2-2 can be 2=2 and 0=0 and 1=1
eager nova
Whatever you do to one side you do to the other
queen ravine
if you add
eager nova
sure you do this is just how we speak in conversation
But if you read what he said
queen ravine
1 on each side
eager nova
You will understand why I am correcting him
misty crest
yea he was wrong before
misty crest
if you have 2x-1=0 you can move -1 to the other side by addding 1 on each side t...
this is fine though
queen ravine
guys obviously i know i shouldt just move stuff
stray spade
okay my point is 1-1+1-1=2-2 can be 2=2 and 0=0 and 1=1
those are statements you deduced from your original equation
eager nova
okay my point is 1-1+1-1=2-2 can be 2=2 and 0=0 and 1=1
Yes, but that doesnt change the original equation
stray spade
yes
queen ravine
so my question is:
what does it mean to get different values for the equalities since im just following algebraic rules
eager nova
Your question is not clear (or i cant read) 
misty crest
what does it mean to get different values for the equalities since im just follo...
it means you’re just demonstrating 2=2 is a true statement just as 1=1 and 0=0 is
i could for instance add 69 to both sides in each and still get a true statement
since you’re following algebraic rules you’re just maintaining equality and creating more and more true statements
queen ravine
so i can derive infinite true statements from this equation?
misty crest
yea sure
not sure how useful that is for you
but go ahead
keep adding 1 to both sides
eager nova
Since there are infinite numbers
queen ravine
alright thanks guys!
eager nova
!done
devout snowBOT
If you are done with this channel, please mark your problem as solved by typing .close
queen ravine
.close
devout snowBOT
devout snowBOT
Available help channel!
lusty sapphire
. @trail pawn ask your question here
trail pawn
how do I do inverse functions
devout snowBOT
how do I do inverse functions
warm onyx
replace x with y
soft umbra
trail pawn
am i on the right track
sharp kayak
am i on the right track
instead of g(x) just put y (since y is equal to g(x) in this case)
warm onyx
^
sharp kayak
but your first table is good
trail pawn
wait why is it 3x i thought we just multiplied it
like this
then it would get canceled out
lusty sapphire
like this, but now you must solve for y
warm onyx
then it would get canceled out
you have to multiply both sides by 3, so you get 3x = y-2
and then y=3x+2
trail pawn
why did u watch the y and the 3x and make the -2 a +2
warm onyx
only y-2 is divided by 3
trail pawn
yeah i understand that part but why did it make it switch
warm onyx
what do you mean
trail pawn
and then y=3x+2
you said this and it threw me off because the y was o the other side of the equation
on*
trail pawn
wait wouldn’t the 2 add to the 3 and make it 5
warm onyx
yeah they're not like terms
trail pawn
wait so it would just be left alone like that
warm onyx
your goal is to get Y alone
warm onyx
No that’s the final answer
devout snowBOT
@trail pawn Has your question been resolved?
wanton plume
someone please im begging LMFAO im mid timed quiz rn and i really dont know how to do this
devout snowBOT
someone please im begging LMFAO im mid timed quiz rn and i really dont know how ...
@wanton plume Has your question been resolved?
devout snowBOT
@wanton plume Has your question been resolved?
viscid rock
I dont particularly grasp the descriptions of peicewise functions, I managed to guess two of them based of my notes but if possible I need an explanation
devout snowBOT
I dont particularly grasp the descriptions of peicewise functions, I managed to ...
viscid rock
I get that when the line is parallel with the x axis I can just set the description as the lines y axis
fair juniper
do you know how to find the slope of a line?
viscid rock
yes
fair juniper
do you remember point slope form?
woven radishBOT
LocalLunatic
fair juniper
simply move the y_0 over
and distribute the m if youre feeling fancy
combine and youve got slope intercept form
viscid rock
and thats the description?
fair juniper
yup
viscid rock
Alright, thanks for your help :)
fair juniper
imagine covering the graph with your hands or something
you can make the guess that the graph is a line
but when you remove your hands, you notice its only on the interval
so you specify, that y=-2x+5 if 1<x<=6
viscid rock
This makes much more sense, thank you
fair juniper
youre welcome
viscid rock
.close
devout snowBOT
devout snowBOT
Available help channel!
heavy basalt
I have this recursion function, I need to find a general function for an
I do not know where to start
devout snowBOT
I have this recursion function, I need to find a general function for an
I do no...
urban harbor
I have this recursion function, I need to find a general function for an
I do no...
the formula doesn't seem to match up at all with the given values
heavy basalt
It does
3=2*3-3
urban harbor
nm i misread
heavy basalt
I noticed that the function is even
oh and I forgot to mention, n can be any integer
jagged harbor
oh and I forgot to mention, n can be any integer
the closed form for a_n on N u {-1} is unique, so we could hope that this closed form works for all integers. otherwise we could take the recursive relation and flip everything around
so a_(n-1) = 3a_n - a_(n+1) would be the useful bit
jagged harbor
I would
so like, there is a clean way to determine the closed form for a linear homogeneous recursive sequence with constant coefficients that involves generating functions, if you have heard of that
heavy basalt
I did not heard of that
jagged harbor
or, you may have been told to use the relation's characteristic equation or whatever it's called, and deduce that a_n is a linear combination of its roots raised to the n'th power
like, you replace each a_k with x^k and solve for x in "x^(n+1) = 3x^n - x_(n-1)"
heavy basalt
or, you may have been told to use the relation's characteristic equation or what...
I wasn't told anything, it's not a homework question, it's a recursion function from some data and I want to find the general equation for an
jagged harbor
ah, ok
jagged harbor
like, you replace each a_k with x^k and solve for x in "x^(n+1) = 3x^n - x_(n-1)...
let's just call b_n = a_(n-1), so that we have an equivalent sequence given by b_0 = 3, b_1 = 2, b_(n+2) = 3b_(n+1) - b_n
heavy basalt
so like, there is a clean way to determine the closed form for a linear homogene...
It's the first time I heard the term "linear homogeneous recursive sequence", but I googled it and found a paper about that, it says at the beggining that it will show how to solve 2nd order linear recurrence relations, if that somehow helps
heavy basalt
let's just call b_n = a_(n-1), so that we have an equivalent sequence given by b...
ok
jagged harbor
so this points to a poly eqn x^2 = 3x - 1 after some killing of the x^n's
x^2 - 3x + 1 has some irrational roots s = (3-sqrt(5)) / 2 and t = (3+sqrt(5)) / 2, so we expect b_n = us^n + vt^n to work for all n, for some u,v
we would use the initial conditions on the sequence to solve for u and v
then shift it back to the a_n world when we're done
we can check inductively that this proposed closed form works for n >= -1
but we can also verify whether or not it works for n < -1 inductively as well
heavy basalt
x^2 - 3x + 1 has some irrational roots s = (3-sqrt(5)) / 2 and t = (3+sqrt(5)) /...
Very interesting, while I'm solving this equation, can you tell me why did you write it in the first place?
jagged harbor
if it doesn't, define a new sequence c_n = a_(-n + 2) or something, and do it all again
jagged harbor
Very interesting, while I'm solving this equation, can you tell me why did you w...
so I've heard two justifications for this
the one I mentioned earlier involves generating functions
you define G(x) = sum_(n=0)^inf b_nx^n
heavy basalt
if it doesn't, define a new sequence c_n = a_(-n + 2) or something, and do it al...
I already checked with the data set, this recursion function works for all integers n
jagged harbor
peel apart two terms, representing two initial conditions, and use the given recurrence relation on the rest of it
you eventually get an equation like G(x) = i + jxG(x) + kx^2G(x)
hence you can find a closed form for G(x), and if you check, it'll be 1/(x^2 - 3x + 1)
somewhat coincidentally actually, because I believe if your recursive thing was like, b_(n+2) = 3b_(n+1) - 2b_n
then G(x) = 1/(2x^2 - 3x + 1)
we do partial fraction decomp on G(x) to rewrite it back into a series as before -- this demands that you find the roots for that poly in the denominator
that's most of it
the other way is cooler
the set of all recursive sequences (f_n) satisfying the same relation -- f_(n+2) = 3f_(n+1) - f_n -- is a real vector space, and it's spanned by two sequences (u^n) and (v^n) for some u,v
I don't remember the proof for why, sorry lol
the geometric series way is more constructive but it takes a long time
heavy basalt
I see
Well I tried to solve it but I got it wrong for some reason
Can you find the mistake?
@jagged harbor please?
jagged harbor
<@191038258728140801> please?
yeah I'm staring, I think the coefficient for v on the right is -2sqrt(5), not 6
and we subtract 9+3sqrt(5) from 4, giving [-5-3sqrt(5)] / [-2sqrt(5)] = [5+3sqrt(5)] / 2sqrt(5) therefore
heavy basalt
oh shit I treated the plus sign as a minus sign for some reason
you are right
lemme fix it
It works now
thank you so much
heavy basalt
can you share where this sequence occured in nature?
Wasn't really in nature
I saw a video in my recommendations about "a hard question from India" that stated:
If x^2-3x+1=0
Then what is x^5+1/x^5 equal to?
The question looked easy to me so I tried it, then I understood I needed to take the fifth power of 3+sqrt5 and I didn't want to do that, so I plugged it into wolfram alpha, and it yielded 123.
I tried x^2+1/x^2 for the same number just because I thought for other number the result will be irrational and 5 is the only special case for which the result is integer, but I was surprised to find that for every interger power the result was an integer.
So I wrote which power yielded which number, and tried to find the relation between them.
I found the recursion function, but didn't know how to continue from here.
Now I plan to find a general formula for a number "k" to plug into x^n+1/x^n, and not just the specific case of x=(3+sqrt5)/2
heavy basalt
that sounds like a michael penn video?
MindYourDecisions's
jagged harbor
oh word
heavy basalt
I see, interesting
Bruh now I understand that it's much simpler than that, well never mind, it was nice to know how to deal with these kinds of recursion functions
Again, thank you so much
heavy basalt
Bruh now I understand that it's much simpler than that, well never mind, it was ...
Bruh I literally took a general equation then turned it into a recursion function and then asked how to turn it back into a general equation
I'm a genius
Anyway, thank you
.close
devout snowBOT
small jackal
Sub a for (2k-1)/2 on the left
winter patrol
seems to be the most simplified, can't do much more
lost laurel
I don't think it can
static raft
over what?
lost laurel
the best you can do is write it as ((18k-36)-73)/(2k-1_
static raft
you have to specify in terms of what you wanna do the simplification
icy garnet
guys how did we get the number 109 and how did we excute both number 2
restive river
You got 109 after simplifying.
icy garnet
how
sand dove
how
after multiplying the denominator and numerator by 2, you get on the numerator:
(2K-1) * 9 - 2 * 2 * 25
so 18K - 9 - 100
so 18K - 109
icy garnet
after multiplying the denominator and numerator by 2, you get on the numerator:
...
u r a hero thanks aloooot brother
cedar pike
How to do
restive river
,rotatexiasitation
woven radishBOT
restive river
Which question?
cedar pike
a
devout snowBOT
@cedar pike Has your question been resolved?
cedar pike
help pls
cedar pike
then whaty to do\
oblique mulch
Why does the answer key have a 6 and I don’t?
devout snowBOT
Why does the answer key have a 6 and I don’t?
fossil locust
Why does the answer key have a 6 and I don’t?
oh C is an arbitrary constant of integration
there's always another constant $c'$ such that $c' = 6 + c$, for all $c \in \mathbb R$
woven radishBOT
south
fossil locust
so yeah they should be collapsing that into:
answer + c'
oblique mulch
so yeah they should be collapsing that into:
answer + c'
Ok but where did they get it in the first place why didn’t I get a 6?
fossil locust
Ok but where did they get it in the first place why didn’t I get a 6?
I have no idea
devout snowBOT
@oblique mulch Has your question been resolved?
long sundial
Yea
devout snowBOT
devout snowBOT
Available help channel!
median bronze
I was doing physics and got stuck on this integral
I want to integrate
2GMdx{1-x/(R^2+x^2)^1/2/[(R^2)*H]
between the limits 0 to H
median bronze
G,M,R are constants
supple knot
what's d
median bronze
differential element dx
median bronze
so should i remove the constants and just the function
supple knot
depends what you mean by "remove"
median bronze
without constants it is {1-[x/(R^2+x^2)]}dx
from 0 to H
wait
no its right
{1-[x/(R^2+x^2)]}dx
supple knot
$\int 1-\frac{x}{(R^2+x^2)^{1/2}}dx$?
supple knot
{1-[x/(R^2+x^2)]}dx
where
median bronze
on R^2 + x^2
woven radishBOT
riemann
supple knot
use $\int f + g = \int f + \int g$
woven radishBOT
riemann
supple knot
first integral will be simple. then use $u = x^2$ substitution on the second integral
woven radishBOT
riemann
supple knot
yea that works too if you keep track of limits appropriately
median bronze
oh ok thnx my problem is solved btw just a random question what is your best tip to improve in calc
as in whole maths
supple knot
do problems
devout snowBOT
devout snowBOT
Available help channel!
olive karma
The two vertices A(-10;-10) and B(6; 2) of a triangle ABC and the intersection point H(-3; 4) of its heights are given. How to determine the coordinates of vertex C?
devout snowBOT
The two vertices A(-10;-10) and B(6; 2) of a triangle ABC and the intersection p...
tame pumice
assume C to be some (x,y) then use the fact that AH is perpendicular to BC and BH is perpendicular to AC
you'll get 2 linear equations
olive karma
so we have to find vector AH and vector BH
olive karma
so the slope of AH is 2 and of BH = - 2/9
tame pumice
yes
tame pumice
m1 * m2 = -1 for perpendicular lines
find slopes of BC and AC and use this
olive karma
Slope of AC is - 1/2 and slope of BC is 9/2
olive karma
I got C(2;-16)
devout snowBOT
@olive karma Has your question been resolved?
olive karma
No I think I might have made a mistake
AC: y - y1 = m(x-x1)
y-(-10) = - 1/2(x-(-10))
y+10=-1/2(x+10)
2y+20=-x-10
x+2y+30=0
BC: y-2=9/2(x-6)
2y-4=9(x-6)
9x-2y-50=0
So
x + 2y + 30 = 0
9x - 2y - 50 = 0
10x - 20 =0
x + 2y + 30 = 0
x = 2
2 + 2y + 30 = 0
x = 2
y = - 16
Where is the mistake?!
devout snowBOT
@olive karma Has your question been resolved?
verbal beacon
You don't have to do it that complicated
The sum of all of the coordinates A B and C is equal to the orthocentre
So A+B-H gives us C.
So C should be (-1, -12)
olive karma
So C should be (-1, -12)
You are right
But still, where is the mistake in that solution?
verbal beacon
y-(-10) = - 1/2(x-(-10))
How did you get a slope of -1/2 for AC
can I see a drawing
cuz for me im getting the slope of BC as -1/2
devout snowBOT
@olive karma Has your question been resolved?
olive karma
How did you get a slope of -1/2 for AC
I think I might have swaped the values accidentally
You are probably right
The slope of line AC should be perpendicular to the altitude BH so it's going to be the negative reciprocal of the slope BH
No, I still get different values for C
There is something fundamentally flawed with my approach
random helm
The sum of all of the coordinates A B and C is equal to the orthocentre
That's not right
random helm
https://math.stackexchange.com/questions/3779495/finding-position-vector-of-orth...
lol. You have read just part of the statement 🙂
verbal beacon
lol. You have read just part of the statement 🙂
??? bro r u high
random helm
Mind what the origin of the coordinate system is 🙂
verbal beacon
Mind what the origin of the coordinate system is 🙂
it literally doesn't matter you can translate the image?
just set the circumcenter of the circle as the origin
random helm
it literally doesn't matter you can translate the image?
it does matter. You have to find a translation vector and take it into account
verbal beacon
idk what ur talking abt
random helm
just use that formula correctly.
random helm
is that what ur saying
sure
verbal beacon
my bad sorry
i thought that if u translated it then the translation vector would cancel
thx for clarifying
random helm
The two vertices A(-10;-10) and B(6; 2) of a triangle ABC and the intersection p...
this guy here was solving a similar problem #1304507942787088506 message
in the first half(which is correct) he found a third vertex
devout snowBOT
@olive karma Has your question been resolved?
solar goblet
$\int_{-\infty}^{+\infty}xe^{-x^2}\dd x$
devout snowBOT
$\int_{-\infty}^{+\infty}xe^{-x^2}\dd x$
woven radishBOT
solar goblet
i want to determine the convergence of this integral
i first test the convergence from the bound -infty to 0
so far what i got is
$\lim_{u\to-\infty}\left(-\frac12+\frac12e^{-u^2}\right)$
woven radishBOT
solar goblet
how would i evaluate this limit without lhopital?
midnight echo
You should know the end behaviour of e^-x, right?
quaint citrus
-0.5 + 0.5 * lim 1/(e^(u^2))
lim goes to 0 and ur left with -0.5
solar goblet
oh lmfao i forgot e^-x = 1/e^x
solar goblet
You should know the end behaviour of e^-x, right?
yeah its 0
but anyway i was overthinking shit. thanks
.close
devout snowBOT
devout snowBOT
Available help channel!
knotty lagoon
I don't understand how to calculate the slant asymptote of a function correctly
acoustic leaf
what kind of function in particular?
knotty lagoon
how does it matter which
acoustic leaf
the strategy is different for rational functions vs. other types of functions
knotty lagoon
what is the difference between rational functions and other types of functions
acoustic leaf
a rational function is a fraction where both the numerator and the denominator is a polynomial
by other functions i mean anything that isn't a rational function
knotty lagoon
so where both fractions have ^2+?
knotty lagoon
by other functions i mean anything that isn't a rational function
what would be an example of a non rational function?
acoustic leaf
sin(x), sqrt(x), 10^x, log(x)
acoustic leaf
for rational functions, there is a slant asymptote only if the numerator has a degree 1 higher than the deniminator
acoustic leaf
you can find it by performing polynomial long division/synthetic division
knotty lagoon
what are the steps to this
sage burrow
what are the steps to this
acoustic leaf
if you look up polynomial long division you will find many guides to this. here are a couple:
https://www.mathsisfun.com/algebra/polynomials-division-long.html
https://www.khanacademy.org/math/algebra-home/alg-polynomials/alg-long-division-of-polynomials/v/polynomial-division
knotty lagoon
if the remainder is negative do you include it
acoustic leaf
the asymptote is the quotient you get. the remainder is not relevant to the asymptote
knotty lagoon
okay so for 16x^2 + 12x -2/8x + 10 i got 2x+4 with a remainder of -38
so y = 2x+4?
acoustic leaf
$$\polylongdiv{16x^2+12x-2}{8x+10}$$
woven radishBOT
cloud
knotty lagoon
how is 20x still -20x and not +20x
acoustic leaf
they are subtracting it
devout snowBOT
devout snowBOT
Available help channel!
surreal shell
trig identities
devout snowBOT
trig identities
lost laurel
I'd suggest you multiply each term by the conjugate of the denominator
surreal shell
for which side?