but this gives me L=L so I get nothing
#help-36
acoustic oar
fallow wren
$a_{n-1}=a_n+\frac{a_n^2}{2^{n+1}}=a_{n+1}+\frac{a_{n+1}^2}{2^{n+2}}+\frac{a_n^2}{2^{n+1}}$
soft zealotBOT
everg
fallow wren
it's no use ig
acoustic oar
yeah ig
maybe working with the original expression without squaring makes more sense
fallow wren
remark: a_0=0 is a "fixed point"
acoustic oar
yeah I saw that too
tawny hazel
acoustic oar
from here if I am not mistaken $a_n = \frac{2^{n+1}a_{n-1}+4^n-4^n}{\sqrt{2^{n+1}a_{n-1}+4^n}}$
soft zealotBOT
ω
soft zealotBOT
ω
fallow wren
$a_0=-1/2$ then $a_1=\sqrt{-2+4}-2\le -1/2$
soft zealotBOT
everg
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@acoustic oar Has your question been resolved?
fallow wren
as the function is monotone, the limit for a_0=a<b is smaller than the limit for a_0=b
fallow wren
for instance the limit for $a_0=2$ is greater than the limit for $a_0=1$
soft zealotBOT
everg
fallow wren
because the function an is monotone in a(n-1)...so if the prompt a_0s are a<b then also the limit will be .
acoustic oar
I dont see how that implies the limit is smaller
soft zealotBOT
everg
acoustic oar
oh okay yeah I get it now
fallow wren
so if you start with a_0>o then as a_0=0 is a fixed point you will get that lim a_n>=0
fallow wren
lets call b_n the sequence with a_0=0 and a_n with a_0>0
then because of the monotone argument you will get that a_n>b_n for every n
then the limit is greater or equal to zero
acoustic oar
then because of the monotone argument you will get that a_n>b_n for every n
but why
maybe for some argument it decreases faster than some other
and the a_n decreases faster at some point
fallow wren
so do you disagree with the inequality a_n>=b_n for every n right ?
acoustic oar
ye
fallow wren
assume that a_0>b_0
acoustic oar
okay
acoustic oar
yes
fallow wren
so let's try to prove that when a_n>0 then the limit is 0
acoustic oar
okay
acoustic oar
so let's try to prove that when a_n>0 then the limit is 0
thats obvious actually I see this
if it starts above 0 it wont go below 0
induction
fallow wren
yes but if it started from 2 it could end up in 1 and not 0
fallow wren
you said its 0 mb
yes I hope
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@acoustic oar Has your question been resolved?
fallow wren
Now I have to go...In the pic there is only some work about the study of the new sequence b_n... I didn't solve either the case with a_0>0 or <0
acoustic oar
bye <:girlbleak:1195548550378029117>
thank you for your contribution
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@acoustic oar Has your question been resolved?
boreal locust
solve the recursion, i think the limit is 0
let a_n = k* 2^n , using that u get k=0 or k=-1, our a_0>-1 so a_n=0 for all n
i specifically did this to get to the answer $$a_n= 2^n (\sqrt{\frac{a_{n-1}}{2^{n-1}}+1}-1)$$
soft zealotBOT
benadryl
boreal locust
Consider another sequence $$ h_n=\frac{ a_n}{2^n}$$
soft zealotBOT
benadryl
boreal locust
$$h_n+1=\sqrt{h_{n-1}+1}$$
soft zealotBOT
benadryl
boreal locust
unless $h_n=0$ (for which the limit is 0), if you assume the limit exists i think you should get the limit as -1.
soft zealotBOT
benadryl
boreal locust
so if you assume the limit is -1, you should get something like $ \lim_{n \to \infty} \frac{a_n}{2_n}=-1$
and then you might think hmm maybe $a_n$ is something like $k \cdot 2^n$ for that limit to "exist"
put that back in the recursion, and you would get k=0
soft zealotBOT
benadryl
boreal locust
all of this is just intution on why i picked a_n= k*2^n
you can just show a_n=0 is a solution to the recursion adn you are done
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hardy ledge
a matrix on the form (1 0, 0 1) can have any soultions right? meaning i can set x_1 and x_2 to whatever i wish?
final saddleBOT
a matrix on the form (1 0, 0 1) can have any soultions right? meaning i can set ...
hallow shell
a matrix on the form (1 0, 0 1) can have any soultions right? meaning i can set ...
Technically yea
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meager pollen
hi
meager pollen
Quadrilateral ABCD is inscribed in circle w and DB is the bisector of ∠ADC
AD is 12, DC is 20
radius of the circle w is 20
find AB, BC , AC and BD
ive bneen stuck on this for 2 hours someo ne please assist me 🙏
<@&286206848099549185>
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@meager pollen Has your question been resolved?
cyan kayak
@surreal elk remember the difference between a probability mass function and a probability density function
there are an infinite number of points where the probability density is 0.25, this is not the same as the probability of each of these points being 0.25
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smoky egret
if there are 2 sets A_1 and A_2 with inf A_1<inf A_2 then inf A_2 isnt a lower bound of A_1UA_2 is this correct
final saddleBOT
if there are 2 sets A_1 and A_2 with inf A_1<inf A_2 then inf A_2 isnt a lower b...
odd rivet
yes
smoky egret
so inf(A_1UA_2)=min{inf A_1,inf A_2}?
barren hound
if all of those infima exist then yes
odd rivet
if all of those infima exist then yes
the infimum always exists?
smoky egret
she means inf A=-infinity by doesnt exist right ?
odd rivet
yeah depends on your definition I guess
well I guess the minimum of +- infinity isnt defined
smoky egret
if all of those infima exist then yes
then does the fact that either one of the 2 infima is not a lower bound of the union suffice as a proof of this statement
odd rivet
\[
\inf(\emptyset) = +\infty
\]
tobi
barren hound
there's also no infimum for e.g. the even numbers
barren hound
but yea if inf(A) and inf(B) exist then inf(A u B) should be their minimum
odd rivet
but yea if inf(A) and inf(B) exist then inf(A u B) should be their minimum
well even if its - infinity its still - infinity right?
smoky egret
but yea if inf(A) and inf(B) exist then inf(A u B) should be their minimum
i want to prove this fact
does it suffice to say that one the 2 infima isnt a lower bound to the union
so the other one must be the infimum ?
odd rivet
to find an Infimum you have to show 2 things
- you have a lower bound
- It is the greatest lower bound
odd rivet
to find an Infimum you have to show 2 things
1. you have a lower bound
2. It is...
I mean its correct, but to proof the definition you have to show these 2 things
smoky egret
since inf A_1<inf A_2 then inf A_1 is a lower bound to A_2 and inf A_2 is no longer a lower bound to A_1UA_2 but infA_1 is the least upper bound of A_1 and from the assumption about the infima it is clear that the there exist at least an element in A_1 < all elements in A_2
odd rivet
!occupied
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smoky egret
this leads to the conclusion that infA_1=inf(A_1UA_2)
odd rivet
yeah thats good
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rose orbit
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rose orbit
I tried finding delta x by doing (2 - 0) / 3 (since the amount is 3 right?)
celest crane
The number of sections is only specified as n.
Well, it's not specified, but inferred.
rose orbit
So I just... leave n at the bottom and act like I don't know it I guess?
celest crane
Yes.
celest crane
Sounds right.
rose orbit
I don't understand but I'm just following the formula I guess
Now how do I evaluate this?
celest crane
Use the limit definition.
rose orbit
I don't understands what that means, but I guess I'll just see through chatgpt
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rose orbit
.close
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icy folio
Did i do this right?
final saddleBOT
Did i do this right?
icy folio
Convergence/divergence problem using integral test
rocky tusk
yep
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@icy folio Has your question been resolved?
thorny forum
How many ways are there to arrange the letters in the word "BANANA"?
rocky tusk
ask
icy folio
...
Pass
Lol
I dont understand how its supposed to converge
Like isnt it just gettin bigger n bigger?
rocky tusk
$\frac{1}{1+\frac{x^2}{4}} \cdot \frac{1}{4} = \frac{1}{4+x^2}$
soft zealotBOT
knief
rocky tusk
I dont understand how its supposed to converge
well, what value of tan makes it go to infinity
think of it like that
icy folio
Pi/2?
rocky tusk
yep
rocky tusk
you get it?
icy folio
I think?
rocky tusk
so what’s the answer
icy folio
Like the answer to the limit?
rocky tusk
yea
rocky tusk
how about this, is arctan(1/2)/2 finite
icy folio
Yes
rocky tusk
and as b-> infinity what is arctan(b/2)/2
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rocky tusk
evolving sir
icy folio
Kinda lol
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tranquil pine
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vital crag
,rccw
soft zealotBOT
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@tranquil pine Has your question been resolved?
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@tranquil pine Has your question been resolved?
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@tranquil pine Has your question been resolved?
tranquil pine
.reopen
final saddleBOT
✅
tranquil pine
@ocean mulch
tranquil pine
.
tranquil pine
Let me see
tranquil pine
Ive learned to switch those and than take on the other way y.
@long flame
.close
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tranquil pine
.reopen
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tranquil pine
Wait... Maby..
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tepid bough
I don’t understand this question, anyone help please??
final saddleBOT
I don’t understand this question, anyone help please??
@tepid bough Has your question been resolved?
proud rock
I don’t understand this question, anyone help please??
The picture isn't very clear, but what I'd do is draw a triangle for each case
So draw ABC and LKM
Draw it such that angle A in ABC = angle L in LKM
rigid verge
Cook qwaxyduck ! 🗣️🗣️💥
proud rock
Huh💀
proud rock
Draw it such that angle A in ABC = angle L in LKM
Then identify which variables you need to deduce that the triangles are congruent
tepid bough
The picture isn't very clear, but what I'd do is draw a triangle for each case
I’ll take a clear picture one second.
proud rock
Does the 3 lines mean congruent, or does it mean similar?
tepid bough
proud rock
If it means congruent, then you need sides, if it's similar, you only need angles
tepid bough
Does the 3 lines mean congruent, or does it mean similar?
Congruent yes
as in the equal sign with the dash?
it means it’s congruent
tepid bough
Why's the top one wavy like that☠️
It’s called a tilde lol
tepid bough
proud rock
Also does using the SAS postulate mean that you can only use SAS, or can u use any other methods?
tepid bough
Not the best handwriting on tablet but yeah
proud rock
If it's SAS, the u need each side next to the angle
tepid bough
Also does using the SAS postulate mean that you can only use SAS, or can u use a...
There is an missing statement
if we add a statement from the choices
The triangle would have to be congruent by Side angle side
proud rock
The triangle would have to be congruent by Side angle side
Oh ok
Then ik how to do it
tepid bough
So the angle has to be between the sides (I think)
proud rock
So the angle has to be between the sides (I think)
Yes, that's correct
tepid bough
So there is an angle at A & l correct?
proud rock
You've basically answered the whole question then. I will get flagged if I give u the answer, but u can tell me what u think it is and I'll tell u if u right
tepid bough
So there is an angle at A & l correct?
^
proud rock
So there is an angle at A & l correct?
Yes
They are the same
Ping me when you've got the answer, I'll tell u if u right. If u get it wrong I'll walk through it with u
But it sounds like you should get it
It's easier than you think
You're literally finding out what 2 sides you need in SAS
tepid bough
You're literally finding out what 2 sides you need in SAS
AB congruent to LK?
Possible answer?
proud rock
AB congruent to LK?
With that answer you've got SA
You need SAS
tepid bough
With that answer you've got SA
You need SAS
I know you need BC congruent to km
But problem is you can’t pick more than one answer I think
proud rock
I know you need BC congruent to km
Nope
final saddleBOT
proud rock
But problem is you can’t pick more than one answer I think
You are supposed to
tepid bough
.reopen
final saddleBOT
✅
tepid bough
Ahh yeah
proud rock
I know you need BC congruent to km
That gives SSA
tepid bough
correct
proud rock
Is there a vc we can join?
tepid bough
AC to LM
tepid bough
Blud guessed, but yes😭☠️
no I didn’t lol haha
It’s due to the fact
It needs to be
Between both sides
proud rock
Yes
tepid bough
If it were to be SAS
proud rock
The last side would have to be between the angle
Huh☠️
proud rock
Sorry it’s 3 AM
Dw
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worthy patio
how do i solve system of equations by using substitution
final saddleBOT
how do i solve system of equations by using substitution
vestal frigate
Do you have a problem you're working on or do you want an example problem?
vestal frigate
How comfortable are you rearranging equations?
worthy patio
i dont really understand it at all
vestal frigate
That's all right
The underlying idea in substitution is that if you have an equation with more than one variable (like x+y=5), and you know what one of the variables is equal to (say y=2), then you can figure out the other
So starting with that pair of expressions
x+y=5
y=3
What might you be able to do to figure out the value of X?
worthy patio
x=2?
vestal frigate
Exactly
Now when both expressions have more than one variable, you need to do some rearranging to be able to do that
x+y=5
x-y=1
See what you can do with that one
worthy patio
i dont know what to rearrange
vestal frigate
Start with just the bottom equation for now, let's get it to be y=something, or perhaps x=something if you prefer
worthy patio
y=2?
vestal frigate
y is equal to 2
worthy patio
x=3
vestal frigate
Yup
So you can rearrange one of them to be x=something or y=something, then you know what x or y respectively may be equal to
worthy patio
but when it is equal to more numbers like y=4x-10 i dont get it
vestal frigate
In that case you end up having to do more multiplication or division, rather than just addition and subtraction
-x+y=5
y=4x-10
Let's work with the top one first, since there's no coefficients (like the 4) to worry about
Try to rearrange it so that it's x=something
worthy patio
x=-10
vestal frigate
How'd you get that?
worthy patio
since its -x i assumed that its a negative and the only negative number is -10
vestal frigate
Not quite, here
We start with -x+y=5
We don't know what y is, and we don't know what -x is, but we know they add to 5
If we add an x to both sides of the equation, it changes it
-x+y+x = 5+x
We can add or subtract or multiply numbers into the equation as long as we do the same thing to both sides of the equal sign
Now that we have some more x's, some can cancel out. -x+x is 0, so the x's on the left go away
y = 5+x
Now we have something that y is equal to: 5+x
Following or have I lost ya?
worthy patio
how would you know if we add a x or a y to the equation
worthy patio
```
-x+y=5
y=4x-10
```
nvm but in this equation would we be solving for -x since we know what y is equal to?
vestal frigate
It depends on what variable you're looking to find an expression for
I found an expression for y there, but there are ways to find an expression for x instead
Point being, if we know that y = 5+x, we can substitute all appearances of y in y=4x-10, which gets rid of that variable
It becomes 5+x = 4x-10, which can then be solved for x
worthy patio
how would those numbers interact to solve x if they are on opposite sides of the equal sign
vestal frigate
You can move them around if you're careful about it
You can always do anything to one side of the expression, as long as you do the same thing to the other side
Let's add 10 to both sides
$5+x=4x-10 \implies 5+x+10=4x-10+10$
soft zealotBOT
m. frost
worthy patio
15x=4x
vestal frigate
Almost, the 5 and x are separate terms, they don't multiply
The 5 and 10 add to 15, but the x is added instead of multiplied
$15 + x = 4x$
soft zealotBOT
m. frost
vestal frigate
Now what could we add or subtract from both sides to get the lone x from the left to the right?
worthy patio
add another x?
vestal frigate
If we add another x we'll have $15 + 2x = 4x+x$
soft zealotBOT
m. frost
vestal frigate
Now we have more x's
worthy patio
i dont get what to do next
vestal frigate
We'll want to subtract an x from both sides instead
$15+x=4x \implies 15+x-x=4x-x$
soft zealotBOT
m. frost
vestal frigate
What happens from there?
worthy patio
15=4x-x?
soft zealotBOT
m. frost
vestal frigate
Any ideas from there?
worthy patio
x=5
vestal frigate
Exactly
If we remember from before, y was equal to 5+x
Now that we know x, what is y?
vestal frigate
Yerp y=10
worthy patio
so would it be (5, 10)
vestal frigate
It would
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glacial osprey
Hi! I need help in proving a theorem in Number Theory. Please help
final saddleBOT
Hi! I need help in proving a theorem in Number Theory. Please help
glacial osprey
The reasoning behind the last 3 rd line? Or did I make some mistake while noting down the proof?
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@glacial osprey Has your question been resolved?
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shy grove
- The function f is such that f(x) = 2x − 3 for x => k, where k is a constant. The function g is such that g(x) = x2 − 4 for x => −4.
a) Find the smallest value of k for which the composite function gf can be formed.
b) Solve the inequality gf(x) > 45.
final saddleBOT
12) The function f is such that f(x) = 2x − 3 for x => k, where k is a constant....
shy grove
guys, i don't understand how to do a
random forge
for one thing, x >= k is not written x => k, secondly for (a), make sure that the input to g(x) is within it's domain
specifically, g(f(x)) puts the output of f(x) into g(x)
final saddleBOT
@shy grove Has your question been resolved?
shy grove
for one thing, x >= k is not written x => k, secondly for (a), make sure that th...
i don’t understand the input output thing
what do you mean by input outputs?
cold coyote
final saddleBOT
cold coyote
Find equivalent resistance of the circuit
so since this is parallel circuit
(15x5x10)/(15+5+10)
= 25 ohms
2nd question, Find the supply current
Since i = v/r
is it just 24/25
obtuse matrix
Hello
cold coyote
yeah i found resistance to be 25 ohms
ok
so
the next question is
Find the power dissipated by the resistance with 15 ohms
so
formula for that is
P = V x i
so i have 24 x i
i need to find the current flowing through that resistor
obtuse matrix
Calculate I
obtuse matrix
Why 25 ohm?
obtuse matrix
It should be smt like 11/30 ohms
cold coyote
from what ive calculated if ive done it right
cold coyote
yeah
feral sail
(15x5x10)/(15+5+10)
where did you get this formula
cold coyote
right
obtuse matrix
And r1 r2 etc are the resistor values som
cold coyote
where did you get this formula
(R1 x R2 x ...)/(R1 + R2 +...)
feral sail
1/R = 1/r1 + 1/r2 … 1/ rn
the parallel equivalent resistance formula is this
cold coyote
huh
obtuse matrix
Yeah
obtuse matrix
Look
cold coyote
yeah i see
feral sail
have you perhaps heard of this one?
$R_{\text{eq}}=\frac{R_1R_2}{R_1+R_2}$
cold coyote
but i thought the formula i was using for that instance
soft zealotBOT
@feral sail
feral sail
it only works for 2 resistors
obtuse matrix
<@951897314333700186>
U can derive this from the above formula
So just use the formula to calculate the resistance
feral sail
^
feral sail
but it still is used for parallel?
The actual parallel resistance formula is
$\frac{1}{R_{\text{eq}}}=\sum\frac{1}{R_i}$
For two resistors, it becomes the following:
$\frac{1}{R_{\text{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}$
If you simplify the right hand side by doing common factor stuff, you get
$\frac{1}{R_{\text{eq}}}=\frac{R_1+R_2}{R_1R_2}$
Reciprocal both sides and you have the formula.
obtuse matrix
Uh
feral sail
yeah f
obtuse matrix
It should be 1/R eq ig
cold coyote
i see
cold coyote
U need a calculator?!!!??
well ill try solving it without one first
soft zealotBOT
@feral sail
obtuse matrix
K
cold coyote
i got 11/30
obtuse matrix
Good luck
obtuse matrix
Yeah
obtuse matrix
Corrct.
obtuse matrix
Right
cold coyote
8.79 A
obtuse matrix
Yeah
cold coyote
ok nice
so the next queston is finding the power dissipated in the first resistor with 15 ohms
so
P = VI
wait
obtuse matrix
Ok
cold coyote
i need to find how much current is going thru there first
obtuse matrix
Yeah
cold coyote
24 x 15
obtuse matrix
Yeah
cold coyote
lmao lets goo
ok so thats 1.6 A
so
p = vi
24 x 1.6
38.4W
dissipated
through the first resistor
obtuse matrix
Yeah pretty much
cold coyote
OK NICE
cold coyote
i mean i cant dm you while im in exam
but yeah ill ask you for help when i get stuck on a practice question
obtuse matrix
No cheating
cold coyote
ofc ofc
obtuse matrix
Ok
cold coyote
.close
obtuse matrix
Good luck
final saddleBOT
cold coyote
thanks man
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lapis plank
So I was given this as the equation to figure out how fast you gotta swing a baseball bat to make a ball go a certain speed, but when I plugged in my numbers I got massively way way way way faster than the ball’s speed so not sure what I did wrong
final saddleBOT
So I was given this as the equation to figure out how fast you gotta swing a bas...
runic tulip
Who gave you that formula?
$v_bat = \frac{v_{ball}}{1+ \frac{m_{ball}}{m_{bat} + m_{player}}} \cdot \frac{1}{cos \theta}$
Is that how you plugged the values? @lapis plank
soft zealotBOT
Wumpus Man
lapis plank
Maybe? The numbers are really weird
Like it’s for a really stupid calc
I think I did it wrong maybe? I don’t know
The speed of the object was 5.996e+7 m/s, weight of the object was .102 KG, and the bat+player with what mass could be put into the swing I put at 25.85 Kg
lapis plank
Who gave you that formula?
Different server
((5.996e+7/ (1 + ( .102/25.85))) * (1/cos(45 degrees)
If I do it like that I get 84462967 M/S
Which to me doesn’t make sense as that would be moving faster than the ball is
So I’m confused how that is possible
I’ve tried just using F = MA and I’ve gotten a lot less than anything remotely to that which to me makes more sense so I’m trying to figure out if his equation is wrong or if I’m using it wrong
final saddleBOT
@lapis plank Has your question been resolved?
runic tulip
@lapis plank send me the values
runic tulip
The speed of the object was 5.996e+7 m/s, weight of the object was .102 KG, and ...
Just read this msg
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lapis plank
<@674597456666820618> if you don't need help anymore then
The math isn’t making sense so a bit confused still… I’ll try later I guess
runic tulip
Ohk
runic tulip
Chat what does calc stand for?
tranquil pine
what does fx and fy mean here. Sorry but I am still learning. I think once I have enough details I can try to solve it.
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somber pollen
what does fx and fy mean here. Sorry but I am still learning. I think once I hav...
.close
hybrid heath
runic tulip
Hmm
hybrid heath
idk why but deleting the entire chat I always find so annoying
tranquil pine
I have a problem, though I am not trying to find a solution but explore instead.
hybrid heath
I have a problem, though I am not trying to find a solution but explore instead.
You should open a new channel. This one may lock soon since it just closed.
final saddleBOT
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oak nimbus
Would the highest degree and leading coefficient be the x^3 and + 1 or since the term is divided by 4 does it affect it being the highest degree?
final saddleBOT
Would the highest degree and leading coefficient be the x^3 and + 1 or since the...
atomic moon
highest degree is the biggest power of x
leading coefficient is the coefficient in front the x having the highest degree
-x^3/4 = (-1/4)*x^3
make your way
oak nimbus
thank you
atomic moon
yw
oak nimbus
.close
final saddleBOT
final saddleBOT
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zinc glen
The question is on the bottom can someone please explain it to me
final saddleBOT
The question is on the bottom can someone please explain it to me
frozen summit
do u know how to graph the functions?
frozen summit
ok these are the steps to graph
u have a function for example: f(x)=3x
and it says thats the function from 0<x<1
right?
zinc glen
Yep
frozen summit
so plug in x=0 into the function and what do u get
zinc glen
0
frozen summit
ok so ur first point is (0,0) where x=0 y=0 right?
zinc glen
Ohhhhh
frozen summit
so now just keep doing that for all the x's but keep in mind for x=2, 3 u have to use the second equation
and 4 u use the third equation
and then connect the dots
zinc glen
So for the first equation the coordinates are x=0 and y=0 and the secound one is x=1 y=3 ??
@frozen summit
frozen summit
<@1000266360699494470>
yes
zinc glen
So for the first equation the coordinates are x=0 and y=0 and the secound one is...
Is this correct?
frozen summit
yep
zinc glen
Thank you I might pass my fm test now
hushed shard
So for the first equation the coordinates are x=0 and y=0 and the secound one is...
These are points that belong to the function
zinc glen
I think I’m starting to get it
frozen summit
when ur plotting, all you need to do is plug in a bunch of x's into the equation and you get your points
hushed shard
What a teacher
Introducing piecewise functions to people that are still not familiar with graphing 🤦♂️
zinc glen
It just says this will be on the test and my teacher was gone most of the year last year so I’m kinda screwed
This is what I need to know and I haven’t been taught half of it 😭
I think I’m getting it now I will close ticket if that’s ok?
Nope I need help with another thing sorry
Dw I’m just gonna fail this topic as I haven’t learnt it
.close
final saddleBOT
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tranquil pine
Locate the absolute extreme amount of of the function of the closed interval
tranquil pine
So i tried to find critical numbers but 2/3 doesn't equal zero so i got stuck there
hushed shard
Locate the absolute extreme amount of of the function of the closed interval
Do you know where to start?
tranquil pine
Do you know where to start?
Finding critical numbers
hushed shard
Finding critical numbers
Great start
So there is no critical points
What about the terminal points?
tranquil pine
What do you mean?
hushed shard
What do you mean?
Ok
So since f'(x) is a positive number, this implies that it is increasing on its domain
tranquil pine
how do you find critical numbers?
Find derivative and make it equal zero then find x
sudden python
Find derivative and make it equal zero then find x
yup, try it
grim elm
yup, try it
What>
tranquil pine
yup, try it
2/3 = 0
tranquil pine
0
sudden python
well it happens for no x lol
grim elm
I honestly cant see where are you going with this
sudden python
so thats why theres no 'critical points'
tranquil pine
well it happens for no x lol
Oh
sudden python
I honestly cant see where are you going with this
wdym
tranquil pine
Im confused
grim elm
Like it has almost nothing to do with any critical points or anything
Just being greater then 0
tranquil pine
So now how do i locate the absolute extrema
hushed shard
Just being greater then 0
Stop trolling in help channels
sudden python
Im confused
when your function is bounded, and you want to find the absolute extrema, you test the endpoints and the critical points. the endpoints occur at x=0 and x=5, and you have just verified that there are no critical points
does this make sense?
hushed shard
Now calculate f(0) and f(5)
sudden python
So that means no critical numbers
yes
the fact that
f'(x) is never 0
but there can still be absolute extrema at the endpoints, right?
hushed shard
So that means no critical numbers
Absolute min/max points have to be either critical points or terminal points
tranquil pine
Absolute min/max points have to be either critical points or terminal points
What are terminal points
tranquil pine
but there can still be absolute extrema at the endpoints, right?
Yes?
grim elm
Stop trolling in help channels
What?
tranquil pine
do you know how to test them?
Zero and five?
sudden python
Zero and five?
yes
hushed shard
What are terminal points
The function is defined on x belongs to [0,5]
The (end) points are at x= 0 and x=5
That is why if it was [0,5[ there would be no absolute maxima
hushed shard
Sub in the derivative equation?
The function itself
tranquil pine
The function itself
The original one?
hushed shard
Yes
naive spoke
Locate the absolute extreme amount of of the function of the closed interval
if u differentiate the function
u get f'(x) = 2/3 which is positive
so the function is always increasing
so maximum will be at 5
grim elm
Exactly
steel kernel
Best way to see it tbh
final saddleBOT
@tranquil pine Has your question been resolved?
zinc glen
What is meant by the limiting value
final saddleBOT
What is meant by the limiting value
grim elm
In this context its just a limit
zinc glen
?
grim elm
Limt of that sequence
zinc glen
How would that be found
grim elm
Factorise n
final saddleBOT
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night forge
number 52
night forge
is it just that if u were to do the inverse, they would still be equivalent?
i.e. B x A = D x C?
night forge
does it have to do with primes?
cartesian product
tiny gorge
A,B,C,D are sets?
night forge
nvm the answer is easy
@tiny gorge @wanton pine the condition is that they are non empty
.close
zenith kettle
Hi, i'm trying a simple Epsilon-greedy for RL, but as it tries more rounds and the choices are made better, seems the regret is actually increasing while I thought it should be shrinking to reflect the results are being optimized... so, does it look normal for regret to increase?
final saddleBOT
Hi, i'm trying a simple Epsilon-greedy for RL, but as it tries more rounds and t...
@zenith kettle Has your question been resolved?
final saddleBOT
final saddleBOT
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shadow karma
Hello, what condition is needed so that the condition $|Ax| = 1$ defines a bounded set?
final saddleBOT
Hello, what condition is needed so that the condition $\|Ax\| = 1$ defines a bou...
soft zealotBOT
DAILI
shadow karma
Is A being full rank sufficient?
final saddleBOT
Available help channel!
daring cloud
how to disprove this :
4 divides 14 without a remainder
like i know 14/3 is 3.5 but thats not a disprove
my doc told me to disprove something u need to porve that its wrong
so how to do this
final saddleBOT
how to disprove this :
4 divides 14 without a remainder
like i know 14/3 is 3.5...
hybrid heath
how to disprove this :
4 divides 14 without a remainder
like i know 14/3 is 3.5...
It's actually a little difficult to prove by itself
Basically, this question is just an application of the division theorem
Division theorem states that the remainder of a division is unique
daring cloud
so should i just write 14/4 = 3.5 and 3.5 is not in Z
daring cloud
college
daring cloud
what do u mean class
like in school ?
or what course ?
the name of the course ?
daring cloud
i don't know in english but i translated it and they say its The theory of reasoning xD
but we learn how to prove things
like for example there were a question that asked if 13 divides 143 so my answer was :
we pick k = 11 and k is in Z and we get 143 = 13 * 11 , and this proves that there's an integer k =11 such that 143 = 13 * 11 , then according to the definition 13 divides 143 without a remainder
final saddleBOT
@daring cloud Has your question been resolved?
daring cloud
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final saddleBOT
final saddleBOT
Available help channel!
gray wasp
final saddleBOT
final saddleBOT
@gray wasp Has your question been resolved?
final saddleBOT
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unique cliff
I would like help with this..
final saddleBOT
I would like help with this..
unique cliff
The steps I took so far were primarily just to use the chain rule
For instance, (w^2-2)^4 with the chain rule would end up as
4(w^2-2)^3 and when we multiply by the derivative of the inside
and the derivative of w^2 is 2w
so after using the chain rule I get to
3 / 8w(w^2-2)^3 and get stuck
oh nvm I think I can get it
.close
final saddleBOT
final saddleBOT
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gleaming spear
Matrix question! Exists there a matrix $T\in\mathbb C^{n\times n}$ such that
$$T^* \begin{pmatrix}
I_{p\times p} & \Sigma_{p\times q} \\
(\Sigma^*)_{q\times p} & -I_{q\times q}
\end{pmatrix}T = \begin{pmatrix}
I_{p\times p} & 0 \\
0 & -I_{q \times q}
\end{pmatrix}$$
where $p+q=n$ and $\Sigma$ is diagonal (row echelon? as it is rectangular) of any rank (basically result of SVD).
π=√g
gleaming spear
Basically looking for a congruence
Explicitly the matrix looks like this for example:
primal loom
Basically looking for a congruence
hello
gleaming spear
hello
gleaming spear
Explicitly the matrix looks like this for example:
\begin{pmatrix}
1& & &a& & & \\
&1& & &b& & \\
& &1& & &c& \\
a^*&& &-1&& & \\
& b^*&&&-1& & \\
&&c^* &&&-1& \\
&&&&&&-1
\end{pmatrix}
π=√g
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
gleaming spear
Where i want to remove the off diagonal entries
final saddleBOT
@gleaming spear Has your question been resolved?
final saddleBOT
@gleaming spear Has your question been resolved?
gleaming spear
Any ideas🥺
grim nebula
,, \mat {I_{p\times p} & \Sigma \ \Sigma^* & -I_{q\times q}} = \mat {I_{p\times p} & 0 \ \Sigma^* & I_{q\times q}} \mat {I_{p\times p} & \Sigma \ 0 & -I_{q\times q} - \Sigma^*\Sigma}
oops wrong spots
soft zealotBOT
grim nebula
you should get this using row reduction
final saddleBOT
@gleaming spear Has your question been resolved?
gleaming spear
,, \mat {I_{p\times p} & \Sigma \\ \Sigma^* & -I_{q\times q}} = \mat {I_{p\times...
Thanks, but i dont rly see how I can get this in the form T*AT
grim nebula
Thanks, but i dont rly see how I can get this in the form T*AT
well it shows that your matrix is full rank
so then because it's symmetric, the spectral theorem gives existence of T
gleaming spear
Hmm ok thanks a lot! I can work with this i think
final saddleBOT
@gleaming spear Has your question been resolved?
teal solar
final saddleBOT
teal solar
Helloo, I am able to find the derivative for the area of the rectangle, which I found to be 8cos(0.5x)-4xsin(0.5x)
the problem then requires me to find the critical point to find the max (largest area)
it wants be to use the calculator to solve for the critical point but when I do I get x =999,999 which can't be right since x can only be between (-pi,pi)
tacit fractal
I think you might've done something wrong on the calculator.
I'm getting a totally different result which actually makes sense. Hence check your calculator work
teal solar
I think you might've done something wrong on the calculator.
yeah I thought so too, so I solved a previous example but got the right value
tacit fractal
hmm what calculator is it and what are you inputting?
tacit fractal
the calculator step doesn't look wrong. I had a look at using degrees instead but that didn't make a difference. Honestly I'm not too sure. I would rearrange it or try restricting the domain of solutions (if your calculator can do that).
final saddleBOT
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Available help channel!
rugged merlin
Can someone tell me where the negative sign comes from in (3.32) for the second term?
final saddleBOT
Can someone tell me where the negative sign comes from in (3.32) for the second ...
@rugged merlin Has your question been resolved?
short prairie
How am I supposed to factories this
final saddleBOT
How am I supposed to factories this
final tangle
do you know how to factorise
a^2 + b^2 + 2ab
or written in a more recognisable form,
a^2 + 2ab + b^2?
short prairie
do you know how to factorise
a^2 + b^2 + 2ab
or written in a more recognisable f...
Thanks I got it
final saddleBOT
Available help channel!
full halo
final saddleBOT
final saddleBOT
@full halo Has your question been resolved?
full halo
<@&286206848099549185>
hallow shell
Should be 2x-8<=y<=2
You saying 2x-8<2?
full halo
Wym
hallow shell
2x<10
x<5??
full halo
Mhh ok?
hallow shell
But isn’t (5,2) a valid point
hallow shell
Should be 2x-8<=y<=2
this
hallow shell
Sorry, I don’t understand which third part u asked about
Oh yea
Think it’s typo
Last part should be y I think
full halo
Last part should be y I think
But like i wrote it?
full halo
Should be 2x-8<=y<=2
.
hallow shell
Technically doesn’t matter since it’s >= (inclusive inequality)
But with the setup 0<= y, I think it’s better to just use y <= 2x-8
final saddleBOT
@full halo Has your question been resolved?
full halo
But with the setup 0<= y, I think it’s better to just use y <= 2x-8
But its wrong its the ys that are >= of 2x-8
hallow shell
yea, i think "x" was a typo.
If it wasnt a typo, then you would have:
x ≤ 2x - 8
x - 2x ≤ -8
-x ≤ -8
x ≥ 8
Which is obviously wrong since they said x ≤ 5
flint summit
they want to know
final saddleBOT
they want to know
flint summit
during the first cycle
when we are at 6 meters
i had sin (-0.5)
and the two values i got was 7pi/6 and 11pi/6
but apprently its 7pi/6 and -pi/6
why is it minus pi
and not the 11pi
spring haven
Because there is a positive value of t so that that expression inside the sin equals -pi/6
The constraint is that t must be positive
Thats how you define the first cycle
flint summit
i dont get it
it must be positive in the first cycle
yes
so how did we go back to a negative cycle to get -pi/6
rocky tusk
so how did we go back to a negative cycle to get -pi/6
brother the input for the sine function you have isn’t just t
set the input equal to those values
flint summit
i dont get what you mean by that
rocky tusk
the input of sine here is pi/20 (t-10)
rocky tusk
sorry what even is the question?
flint summit
they want to know when it is at 6 meters during one cycle
its a Farris wheel spinning
rocky tusk
can you show the wording
rocky tusk
also does it state a range for the parameter
flint summit
during its first turn, after how much time is the person at 6 meters
flint summit
also does it state a range for the parameter
if i understood that properly its one turn (cycle)
rocky tusk
so t is time so 0<= t
flint summit
yes
rocky tusk
and h is height?
flint summit
yes
rocky tusk
ok and you got what?
flint summit
i had sin (-0.5) = pi/20 (x-1)
flint summit
then i drew this
and i took the 7pi/6 and the 11pi/6
but the correction takes the 7pi/7 and the -pi/6
rocky tusk
i had sin (-0.5) = pi/20 (x-1)
where did you get this
flint summit
6 = 9 sin (pi/20)(x=-10) + 10.5
6 - 10.5
-4.5 / 9
0.5
0.5 = sin bla bla
then sin to the other side
rocky tusk
ok $\sin(\frac{\pi}{20}(t-10)) = -0.5$
soft zealotBOT
knief
flint summit
yes
rocky tusk
ok so you’re confused why they set the inside equal to -pi/6?
rocky tusk
well yes because there are multiple answers
flint summit
you send sin to the other side, and find what rad values are equal to -0.5 right
sin(-0.5) = 7pi/6 etc etc
by drawing it out
flint summit
idk what that is
rocky tusk
sin^-1