fading cedar
Should this not be 1?
#help-10
latent walrus
where is there a 6pi/24
latent walrus
it says to add 7pi/24 and pi/24
obtuse pebbleBOT
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loud harbor
Why is 2b) 2-(3x-1)e^-1/2x
obtuse pebbleBOT
Why is 2b) 2-(3x-1)e^-1/2x
loud harbor
Shouldn’t it be -2 if we’re setting y=2
formal junco
loud harbor
<@&286206848099549185>
obtuse pebbleBOT
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tardy epoch
Shouldn’t it be -2 if we’re setting y=2
no. draw the picture
frozen swift
how do to???
obtuse pebbleBOT
how do to???
dark stirrup
what have you tried
obtuse pebbleBOT
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sand forum
how do I show the sequence $a_n = \frac{(-2)^n}{n!}$ is convergent
obtuse pebbleBOT
how do I show the sequence $a_n = \frac{(-2)^n}{n!}$ is convergent
warm shaleBOT
donut
karmic mural
ratio test
sand forum
if the absolute value of the sequence is convergent, then the original sequence is convergent. But I still don't know how to take the limit using squeeze theorem
karmic mural
oh
sand forum
its a sequence not a series
karmic mural
ye
sand forum
I don't know how to find $\lim_{n \to \infty}{ \frac{2^n}{n!} }$
warm shaleBOT
donut
karmic mural
i mean
just think about it kind of
if it's infinity -1 * infinity -2 *infinity -3
that will always be greate than just multiplying 2 over and over
sand forum
I know it is convergent. I want to know how to show its convergent using squeeze theorem.
sand forum
ok I can't really use 3^n as a bound because I would have to show that is convergent too
and 1/n! as a lower bound isn't as good as just using 0 as a lower bound
obtuse pebbleBOT
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karmic mural
1/n! and 2^n/(1X2X3^(n-2))
next lantern
obtuse pebbleBOT
next lantern
looking at an example i wrote for composition of fns
the example had f: A -> B and g: B -> C
now my note says codomain of first must be the domain of the second
however i wrote g of f
codomain of g is C which is not the domain of f
should this have been written f of g?
warm canopy
$g \circ f$ means do f first and then do g, its convention
next lantern
oh
warm shaleBOT
ΣAC
next lantern
right
warm canopy
takes a bit to get used to
next lantern
i see
ok i thought when i wrote first i meant
in the notation
i see
ty
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split light
$$\lim_{(x, y) \to (0, 0)} \left( \frac{\sqrt{x^2 + y^2}}{\sin (\sqrt{x^2 + y^2})} \right)$$
obtuse pebbleBOT
$$\lim_{(x, y) \to (0, 0)} \left( \frac{\sqrt{x^2 + y^2}}{\sin (\sqrt{x^2 + y^2}...
warm shaleBOT
Vicoo
split light
please I need some help proving this
used polar coordinates to get that it's =1
but I don't know how to do the formal proof
obtuse pebbleBOT
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split light
<@&286206848099549185>
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rustic mantle
Hey! I've got a quick question Is 1 < x > -5 a way of saying
x are the numbers between -5 and 1
obtuse pebbleBOT
Hey! I've got a quick question Is `1 < x > -5` a way of saying
`x are the numbe...
rustic mantle
<@&286206848099549185>
rustic mantle
which is the same thing as 1 < x > -5, right?
trail cloak
Nope
rustic mantle
fak
trail cloak
That's weird notation
rustic mantle
which is the same thing as 1 < x > -5, right?
I mean, isn't this 1 is smaller than x and x is bigger than -5
severe sand
Hey! I've got a quick question Is `1 < x > -5` a way of saying
`x are the numbe...
you are saying that x is bigger than -5 and x is bigger than 1
you can just say x>1
trail cloak
Ye
Yep
But to make the x between -5 and 1, you make x bigger than -5 and smaller than 1
-5 < x < 1
severe sand
yes
undone perch
Can someone explain to me why the red working is incorrect (what I thought it would be) and why the green working is correct (what it actually is)?
obtuse pebbleBOT
Can someone explain to me why the red working is incorrect (what I thought it wo...
@undone perch Has your question been resolved?
high lily
from the working, it seems they want the volume available inside the container
not how much the bowls can hold (which was what you calculated)
undone perch
from the working, it seems they want the volume available inside the container
n...
What is the difference between those two values?
Like logically thinking through this, I think that the volume of the 4 bowls should be equal to the volume inside the container
high lily
that's the volume they're asking for
undone perch
The blue?
high lily
yes
i.e. the volume of the whole thing minus the volume of the hemi-sphere
or in your case hemi-spheres
undone perch
high lily
yeh
graceful quail
Does anyone know what this type of systems of equations is called so I can look it up?
obtuse pebbleBOT
Does anyone know what this type of systems of equations is called so I can look ...
@graceful quail Has your question been resolved?
trail musk
Are you familiar with the matrix vector form of a system
Ax = b
If A is invertible we can solve for x:
x = A^-1 b
obtuse pebbleBOT
@graceful quail Has your question been resolved?
obtuse pebbleBOT
@graceful quail Has your question been resolved?
graceful quail
Are you familiar with the matrix vector form of a system
So what is contained within those two square brackets is a matrix?
kind hawk
Yes
obtuse pebbleBOT
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obtuse pebbleBOT
I'm confused about this?
rough bough
shouldn't this be r <-> p -> q as well?
brisk jackal
try writing out the truth table for iff/<=>
rough bough
try writing out the truth table for iff/<=>
and it appears that r <-> p -> q works
drifting wraith
your picture dosen't show FFFT, but your picture is not p → q anyway
p → q is gives TFTT though, so doesn;t work either
tame narwhal
how are they supposed to be grouped? (r <-> p) -> q? does that matter?
drifting wraith
yeah i'm assuming you start with →
rough bough
your picture dosen't show FFFT, but your picture is not p → q anyway
p → q is gi...
what do the columns of each of the letters refer to?
rough bough
it works if you start with ←→
yeah, but doesn't it work for not r <-> not p -> q?
drifting wraith
it works for (r <-> not p) → q
it doesn;t work for r <-> not p -> q if you argue that it means r <-> (not p -> q)
okay it's all mixed up
ignore everything i give up
rough bough
hmmm, so do you think it works for not r <-> not p -> q?
because when I tried it out, it seems to work out?
drifting wraith
that's waht your first screenshot says, don;t have to think it's marked correct
brisk jackal
the way it's written is a bit confusing, I forgot the order of operations for a moment
rough bough
that's waht your first screenshot says, don;t have to think it's marked correct
It tells me if it is wrong or not
This question is pretty stupid
I was confused what is this question asking?
tame narwhal
hmmm, so do you think it works for not r <-> not p -> q?
I think so, if you do it as (not r <-> not p) -> q
rough bough
I think so, if you do it as (not r <-> not p) -> q
I mean why doesn't it work for (r <-> p) -> q?
drifting wraith
that also works
rough bough
but why can't I have that as a solution?
drifting wraith
but you have to start with equivalence
they don't allow this order of operations
rough bough
so shouldn't it work for what I wrote?
tame narwhal
I mean why doesn't it work for (r <-> p) -> q?
I think it should, as well
rough bough
I'm applying the equivalence operator first
drifting wraith
they are marking you wrong for doing that
rough bough
yeah
rough bough
why is that the only answer?
drifting wraith
because you have to do equivalence first, which is not allowed
you must do → first
rough bough
i thought (<->) is equivalence"?
drifting wraith
yes
rough bough
because you have to do equivalence first, which is not allowed
I did do equivalence first
drifting wraith
you have to do it first, if you want this to be correct
you can't, so it can't be correct
rough bough
? Why can't you do it ?
drifting wraith
the authors of the test think → takes precedence
i also think that, so i couldn;t understand what you;re talking about in the beginning
rough bough
Is there a reasoning behind why?
brisk jackal
this exact discussion, if its not commutative then there's a problem if you interpret it left to write rather than a predefined order
rough bough
this exact discussion, if its not commutative then there's a problem if you inte...
sure
I can't seem to intuitively think why biconditional comes after implication
I get there is an order ,but why this specific ordering?
I get negation comes first, but what about the other 4?
brisk jackal
oh, I think there's a deeper reason so that it doesn't seem arbitrary
biconditional is coomposed from implication
rough bough
also what happens if we unravel biconditionals into conjunctinos and disconjuntions?
what precedes first then?
brisk jackal
p <->q expresses (p->q) ^(q ->p)
rough bough
yean and that is equivalent to (not p v q) ^ ( not q v p)
and if you have (not p v q) ^ ( not q v p) -> r
then the left of the implication would get evaluated
brisk jackal
my point is that that's why implication is evaluated 1st, because <-> is an abstraction
brisk jackal
yes, thats why not and and or take recidence over implication
rough bough
yes
so what I'm trying to say, is that if you decompose the implicatinos and equivalences, you left with elements that are in higher precedence, which thus distorts the ordering
brisk jackal
so what I'm trying to say, is that if you decompose the implicatinos and equiva...
yeah, try decomposing the above, if you don't treat it like r <-> (p ->q) when you decompose the biconditional you'll get incorrect results
you'd notice that you'd want to preserve the parentheses
rough bough
@brisk jackal Sure it is composed of implications, but how does that mean it precedes implications?
brisk jackal
did you try to decompose it?
rough bough
did you try to decompose it?
yes
equivalence = (not p v q) ^ ( not q v p)
similarly
implication = (not p v q)
brisk jackal
suppose you decomposed it the way you wanted to interpret it where <-> has equal precedence or better precedence
decompose (r <-> p) -> q and see if its equivalent to the other decomposition
rough bough
((p->r) ^ (r-> p)) -> q
brisk jackal
try the truth table on both compositions, the difference in value shows why they can't be of equal precedence
rough bough
try the truth table on both compositions, the difference in value shows why they...
hmm sure, so you are saying that equivalence is an abstraction with an additional layer, in which it precedes backwards
so although it is logically equivalent to (p->r)∧(r->p), that logical equivalence must be last
brisk jackal
hmm sure, so you are saying that equivalence is an abstraction with an additiona...
not entirely certain, I'd do research on it, because it could be the case that the precidence is arbitrary
outside the fact that we just proved the operations can't be treated with equal precidence, why we decide it comes before or after appears
for example, 2*3+5 has an order of operations, but we could interpret it differently if the order of operations wasn't set for our convenience
rough bough
hm, I think about it more
Also how would we take the converse?
nevermind
Also
I'm not really sure why this is wrong?
nevermind
.close
obtuse pebbleBOT
rough bough
thanks
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junior zephyr
HI
junior zephyr
[2:53:16 PM] <Guest13> why is definition of independence of two events in probability symmetric
[2:55:19 PM] <Guest13> im wasting my time in pointless philisophical discussions again , god please help me
lol
anyone here?
obsidian heron
Which one are you struggling
obtuse pebbleBOT
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formal prairie
Could anybody help me solve this question?
obtuse pebbleBOT
Could anybody help me solve this question?
@formal prairie Has your question been resolved?
stuck ridge
Hello any clues on how to approach part b?
obtuse pebbleBOT
Hello any clues on how to approach part b?
stuck ridge
I’m thinking maybe use the result in a and apply summation on both sides?
median dome
that is correct
whenever you have questions like this, use the results from previous parts in future parts
median dome
you just need the summation to be greater than 1/2
stuck ridge
Ohh ok
obtuse pebbleBOT
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spiral tulip
help
leaden ginkgo
i don’t see any boxes but if a line starts at x=0 and ends at x=10, you can count it’s horizontal length
leaden ginkgo
great
spiral tulip
thank you saad*
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timid silo
jolly ginkgo
What's the matter?
obtuse pebbleBOT
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jolly ginkgo
this is the matter
Yeah but you mustard tried somthing
obtuse pebbleBOT
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quartz yoke
Let ABC be an acute-angled triangle
with A = 60◦
. Let E, F be the feet of altitudes through B, C respectively. Prove
that CE − BF =
3/2*(AC − AB).
obtuse pebbleBOT
Let ABC be an acute-angled triangle
with A = 60◦
. Let E, F be the feet of alti...
obtuse pebbleBOT
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heavy frost
hello i need help with this question. we got this construction which holds water from leaking (im gonna call the black thing that holds the water the black thing :D) so when h was 0.1 meters black thing came out and water started leaking. H=0.4 meters. S of the black thing is 4SM^2. S of the white thing (thats causing black thing to come out and water to leak) is 25 SM^2. density of water is 1000kg/m^3 and g=10. note that springs dont have masses and do not calculate fraction between black thing and the floor. QUESTION: calculate the mass of the entire construction
obtuse pebbleBOT
hello i need help with this question. we got this construction which holds water...
heavy frost
use this
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latent jasper
Determine if there is any neighborhood of the point (2, 1) where the connection exists
x^4 + y^4 − 4xy = 9
define y as a function of x and then calculate dy/dx at the point x = 2
obtuse pebbleBOT
Determine if there is any neighborhood of the point (2, 1) where the connection ...
latent jasper
So this is what I did
$4x^3 + 4y^3 y' -4y + 4xy' = 0 <=> y'=\frac{y-x^3}{y^3 + x}$ And then I specifie the point $ y'(2,1)=\frac{1-2^3}{1^3 + 2} = \frac{-7}{3}$
warm shaleBOT
afeAlway
latent jasper
This is wrong and the answer is actually just 7. But how come?
median dome
why +4xy'
latent jasper
why +4xy'
because of the product rule
shit it should be minus, it is now correct. Thx for the help!
.close
latent jasper
Does the equation x^2 − y^2 + z^2 = 1 define a function z = z(x, y) in some neighborhood of (1, 0, 0)?
obtuse pebbleBOT
Does the equation x^2 − y^2 + z^2 = 1 define a function z = z(x, y) in some neig...
latent jasper
I differentiated the function with respect to z and got f'=2z. And then I did f'(1,0,0)=2*0=0
Since the value of the partial derivative is 0, I cannot draw any conclusions so what do I do?
dark stirrup
Does the equation x^2 − y^2 + z^2 = 1 define a function z = z(x, y) in some neig...
no
Because a function z(x, y) allows only one output per input (x, y).
But your equation has a z² term, so solving for z will leave you with two solutions
latent jasper
But your equation has a z² term, so solving for z will leave you with two soluti...
I don't exactly understand what you mean. Do you mean like z=sqrt(y^2-x^2+1)? In that case when I put x=1 and y=0, I get the rot of 0 which is 0. Shouldn't the answer be yes.
In any case is my first reasoning correct?
dark stirrup
$z=\pm\sqrt{y^2-x^2+1}$
warm shaleBOT
SWR
latent jasper
But at the point x=1 and y=0. It is 0
dark stirrup
Does the equation x^2 − y^2 + z^2 = 1 define a function z = z(x, y) in some neig...
Oh. Still no. Because any neighborhood at (1, 0, 0) will still have a +z and -z region, so you cannot have a function z=z(x,y) in this neighborhood.
dark stirrup
I differentiated the function with respect to z and got f'=2z. And then I did f'...
Differentiated which function? Where did you get f from?
latent jasper
I made up a function f(x,y,z)=x^2-y^2+z^2-1. Kina like a level surface at f(x,y,z)=1
latent jasper
Oh. Still no. Because any neighborhood at (1, 0, 0) will still have a +z and -z ...
wdym here?
dark stirrup
You want to define a function z=z(x, y) that satisfies x²-y²+z²=1, correct?
latent jasper
yes
dark stirrup
And you want z to be defined in some neighborhood around (1, 0, 0) correct?
latent jasper
yes
dark stirrup
By neighborhood, I assume you mean open neighborhood. Also, do you mean an open disk around (1, 0), or an open ball around (1, 0, 0)?
latent jasper
By neighborhood, I assume you mean open neighborhood. Also, do you mean an open ...
No idea, the question I posted is all I have got to work with.
dark stirrup
okay
This sounds like an XY problem
!xy
blah, we need that macro
So my question to you, why are you asking this problem? You do not seem to have a well-defined question. So what is the root reason you are asking it?
latent jasper
I translated it from another language but that is all I got work with. That is like the entire question, no more detail is provided.
clear condor
https://xyproblem.info/
hmm
dark stirrup
Does the equation x^2 − y^2 + z^2 = 1 define a function z = z(x, y) in some neig...
So this is basically just a translation of a problem in another language? Is it a direct translation or were you paraphrasing?
latent jasper
So this is basically just a translation of a problem in another language? Is it ...
I google translated it and checked that it made sense. Except maybe when it comes to the word "neighborhood" I was sceptical at first but I googled and made sure that it actually was refering to the same thing as the word in my language.
dark stirrup
yes that's the right word
My guess is they mean open ball.
In which case, no a function can't be defined
latent jasper
My guess is they mean open ball.
yeah the answer is "No" but what difference does it make? Are you refering to the curves of z(x,y) when you said it is open ball?
dark stirrup
brb gotta change laundry
latent jasper
Wait think I might have understood it now, can you confirm this? Lets say I build a level curve at the point (1,0,0) meaning z=0. We get x^2-y^2=1. We now have two x values that give us the same answer. If I put in x=-1 and y=0 I still get it to be equal to 1. If x=1 and y=0 it will still be equal to 1.
But this doesn't sound right tho. Cause z is allowed to have different x's right?
hexed agate
brb gotta change laundry
I didn't know dogs do laundry
dark stirrup
You can choose any (x, y) and then, you're assuming that there is some z(x, y) that will satisfy f(x, y, z)=0
However, you have two possible z values:
z=+sqrt(y²-x²+1)
z=-sqrt(y²-x²+1)
But a function of z must only allow one of these.
But, a neighborhood around (1, 0, 0) will have some positive z and some negative z, so it contradicts that a function of z could exist here.
You can't a function z(x, y) in the neighborhood (1, 0, 0) because you can't define a function z at (x, y) that will map to both a positive z value and a negative z value
obtuse pebbleBOT
@latent jasper Has your question been resolved?
latent jasper
Yes, z can indeed have multiple x. It is indeed not right
I mean as in can different x's have the same z value?
latent jasper
You can't a function z(x, y) in the neighborhood (1, 0, 0) because you can't def...
So at the point (1,0,0) it is possible but in the neighborhood of it will not. Is that what you mean?
dark stirrup
But that will always happen any neighborhood around (1, 0, 0)
dark stirrup
So at the point (1,0,0) it is possible but in the neighborhood of it will not. I...
yes. exactly.
A neighborhood will always have a little more than just the isolated point (1, 0, 0)
latent jasper
However, you have two possible z values:
z=+sqrt(y²-x²+1)
z=-sqrt(y²-x²+1)
Ok in that case how does this confirm it? Didn't you agree with me that different x values meaning different planes can give the same z value?
dark stirrup
It's okay for different x to map to the same z
x is an input and z is an output. That's the difference
latent jasper
It's okay for different x to map to the same z
yeah but in that case what exactly is the reason z can't be defined as a function of x and y? What is the requirement it fails?
dark stirrup
Let's look at it in 2d
Imagine the equation is x²+y²=1 and you want a function y=y(x) for some neighborhood at (1, 0)
obtuse pebbleBOT
dark stirrup
.reopen
obtuse pebbleBOT
✅
dark stirrup
The green dashed circle is the ε-neighborhood (an open disc of radius ε)
You need a function y(x) that will essentially make this curve:
You could try y=sqrt(1-x²)
But that only defines half the curve in the neighborhood
So it's unsufficient
Same problem with y=-sqrt(1-x²)
Neither is sufficient to map the whole curve in the neighborhood
latent jasper
Neither is sufficient to map the whole curve in the neighborhood
Ok I see now, I just have to apply the same reasoning but in 3D right?
dark stirrup
yes
latent jasper
Thank you so much for the help! I think I understand now and good luck with your laundry:)
.close
obtuse pebbleBOT
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unique kettle
obtuse pebbleBOT
solar trellis
f' = g and g is diff so f' is diff. diff both sides of the first eq
this looks like a more general version of sin^2 + cos^2 = 1
unique kettle
yeah it does
unique kettle
f' = g and g is diff so f' is diff. diff both sides of the first eq
so you're saying put down that f'' = g'
unique kettle
f'' = -f
solar trellis
yep
unique kettle
g'' = -f' = -g
solar trellis
yea now you can solve for f and g explicitly
unique kettle
wdym
solar trellis
solve the ode
unique kettle
idk what ode is
solar trellis
ordinary differential equation
solar trellis
hm maybe you haven't learnt about odes
not immediately sure how else one would solve this
unique kettle
.close
lost condor
A retailer selling washing machines has found that every $20 reduction in price on the washing machine, 2 more machines are sold per month. The retailer normally sells 50 machines per month for the price of $900. Determine the optimum selling price in order to maximize revenue.
Im not sure how to solve I initially would do
R=(900-20x)(50+2x)
and then I would solve but the answer is incorrect
obtuse pebbleBOT
A retailer selling washing machines has found that every $20 reduction in price ...
obtuse pebbleBOT
@lost condor Has your question been resolved?
obtuse pebbleBOT
@lost condor Has your question been resolved?
lost condor
Can someone please help?
obtuse pebbleBOT
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obtuse pebbleBOT
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knotty nebula
What is the answer for part b regarding the form?
obtuse pebbleBOT
What is the answer for part b regarding the form?
@knotty nebula Has your question been resolved?
obtuse pebbleBOT
@knotty nebula Has your question been resolved?
obtuse pebbleBOT
@knotty nebula Has your question been resolved?
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uneven night
@royal basin my internet disappeared
obtuse pebbleBOT
<@183668144404037632> my internet disappeared
uneven night
But you said I was on right path
Then I canceled out sin x on both sides
I got sin x=2cos x
Then I did tan x= 2
Then I got x=arctan 2
But I think it’s wrong
This was the original question (1-cos x) (1+cos x) = sin (2x)
Can someone help solve this
idle thunder
@uneven night post the original problem
unreal musk
Then I canceled out sin x on both sides
Did you account for the fact that sin(x) could be zero?
uneven night
This is the original question
uneven night
This was the original question (1-cos x) (1+cos x) = sin (2x)
Solve this
uneven night
All solution
unreal musk
Well the steps you’ve suggested should get you some solutions
unreal musk
Did you account for the fact that sin(x) could be zero?
But you have to be careful if you divide by something that can be zero as you can lose solutions
obtuse pebbleBOT
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uneven night
But you have to be careful if you divide by something that can be zero as you ca...
I but I got x= arctan 2
And it seems so wrong
unreal musk
How comes? Were you expecting nice numbers or something?
obtuse pebbleBOT
timid silo
.reopen
obtuse pebbleBOT
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tame narwhal
dapper venture
dapper venture
Why is it u0 = u1 -5^1
Shouldn't it be u0 = u-1 - 5^0
Since the original reccurence relation was un = un-1 + 5n and with u0 = un we know n = 0
tame narwhal
because n=1 there
tame narwhal
they're just rearranging from $u_n = u_{n-1} + 5^n$ for n=1
warm shaleBOT
cwatson
tame narwhal
so $u_1 = u_0 + 5^1 \Rightarrow u_0 = u_1 - 5^1$
warm shaleBOT
cwatson
dapper venture
Oh tysm that makes sense now
obtuse pebbleBOT
@dapper venture Has your question been resolved?
ripe violet
what do I do from here? I'm lost
obtuse pebbleBOT
what do I do from here? I'm lost
clear condor
are you sure du is correct
jolly ginkgo
Why the question format so horrible
ripe violet
yeah, Im using a software called infinite calculus from kuta software
it generates calculus problems
lol
jolly ginkgo
The -3x must be in ()
summer salmon
Can someone tell my the antiderivative of x^3/5 becomes 5x^8/5 / 8
obtuse pebbleBOT
Can someone tell my the antiderivative of x^3/5 becomes 5x^8/5 / 8
timber island
!status
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
missing a crapton of parentheses
timber island
missing a crapton of parentheses
well..ur right
high lily
$\int x^{\frac35} \dd{x}= \frac58 x^{\frac85} + c$
warm shaleBOT
ℝamonov
high lily
(reverse) power rule
summer salmon
How
high lily
would you be able to integrate x^2
high lily
yes,
summer salmon
- C
high lily
can you describe the steps you took to obtain that
summer salmon
The x^n+1 formula thing
high lily
and what's stopping you from doing that same thing for
x^(3/5)
high lily
missing a crapton of ()
summer salmon
Yeah mb
high lily
i'm insistent as its important in communicating what you have
and trains your understanding of the order of operations
$\frac{x^{\frac35 + 1}}{\frac35 + 1}$
warm shaleBOT
ℝamonov
high lily
simplify, combine terms
summer salmon
Are the exponents values and the ones at the denominator similar terms?
summer salmon
Im having troubles on which values should i combine
obtuse pebbleBOT
@summer salmon Has your question been resolved?
high lily
the 3/5 + 1
ashen perch
Help, what do I do here? Do I just give an angle that can be added to the given angle that can make it complement and/or supplement?
obtuse pebbleBOT
Help, what do I do here? Do I just give an angle that can be added to the given ...
timid silo
Help, what do I do here? Do I just give an angle that can be added to the given ...
I guess so
daring fiber
Hey
daring fiber
Can someone help me with this?My question is basically the numbers losted there 1 3 5 are all odd,should i still take 2k+1 as inductive step and k as base step?
kind hawk
well for k+1 you get 2(k+1)+1=2k+3
daring fiber
So i just use 2k+1 right
kind hawk
yes
kind hawk
do you have the eps delta definition of the existence of a limit?
daring fiber
Yeah i do,i learned them back in calculus 1
kind hawk
negate that
daring fiber
I am guessing i just have to negate the formula?
Okay perfect
Okay this is actually just a last quick question but here in question c
What does S mean?
kind hawk
I dont know the notation your course uses
could be the partial sum
but that's just a guess
daring fiber
Yeah I understand,thanks a lot for your help though 🙏🙏🙏
obtuse pebbleBOT
@daring fiber Has your question been resolved?
deft hazel
Yeah I understand,thanks a lot for your help though 🙏🙏🙏
Which q
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
silk basin
I need to rewrite the first fuction into the second
obtuse pebbleBOT
I need to rewrite the first fuction into the second
silk basin
I have no idea where to even start
silk basin
i mean how, we cant divide it, cuz its a 0 on the other side
spring trail
huh
who told you you cant
you can
but by doing that it ignores some possible values of the variable
but if the question asks you to show thta
dont worry abt it
silk basin
so we'd get 0/ke-kt=1-kt
obtuse pebbleBOT
timid silo
.reopen
obtuse pebbleBOT
✅
royal basin
timid silo
how sorry im new to discord
timid silo
ok
trim portal
.close
cosmic acorn
AD=?
wary vigil
could you translate the question to english?
cosmic acorn
|AB|=|AD|
|AC|=10
|BD|=10
if |DC|=3 find |AD|
cosmic acorn
yes
weak valve
Let angle ABD = x
AB=AD implies angle ADB = x
angle ADC = pi - x
angle DAC = pi - 2x
Use sine rule on triangle ADC, then u can find x then find AD
@cosmic acorn
rugged locust
Hi, I need a help with this exercise
obtuse pebbleBOT
Hi, I need a help with this exercise
rugged locust
I was only able to work out the inverse function and then I am completely clueless
warm canopy
you need to figure out what a,b,c,d should be to make f(x) = f^(-1)(x) for all x
rugged locust
so for example ac=-dc?
weak valve
yea, and more conditions
mellow wave
Dealing with money math specifically USD
Say I sell things for 1 dollar and for some reason (Tax or another thing)
says I need to charge 1/3rd of said price for that reason
thats 0.33333~ cent repeating.
If I only do 33cent I lose out on a cent if I say 34 cent I'm charging 2 cent to many.
Knowns We don't know how many someone is going to order so it could be 1$ worth of items or millions.
Over the course of our relationship I would like to have a fair charge between us without anyone paying/losing more then 1 cent (overall) but be able to explain how the invoices are calculated.
obtuse pebbleBOT
Dealing with money math specifically USD
Say I sell things for 1 dollar and for...
mellow wave
My best solution so far is to keep track of the additional cents after the 100th place and as that gets to 1 add the cent onto the invoice. To me that means we're only out maximum (basically) a cent
clear condor
or you can just sell things in 3's
mellow wave
Not an option
Prices are based on work done not static items
So this situation can pop up as much as it does
drifting wraith
that's the only solution
like the only problem would be that maybe you track it with precision of 0.001 of a cent and in the end, it turns out you made 10 thousand transactions so you weren't tracking it precisely enough
so you use rational numbers, they're infinite precision
or if every time you reach these special numbers of transactions, you recalculate, that would work but i can't even tell what these numebrs are
so rationals is easier
rational just measn common fraction or whatever you call it
and you always divide by 3...
so the balance is always −2/3, −1/3, 0, 1/3 or 2/3
both what you add and what you end up with
obtuse pebbleBOT
@mellow wave Has your question been resolved?
tawny briar
how do i calculate k in 2^(k-2)+3^(k-3) = k^6
obtuse pebbleBOT
how do i calculate k in 2^(k-2)+3^(k-3) = k^6
barren estuary
how do i calculate k in 2^(k-2)+3^(k-3) = k^6
At a quick glance it looks like it probably doesn't have a simple analytical solution. You'll probably need to use a root finding algorithm like newton-rhapson
tawny briar
that sounds way too difficult
kind hawk
then just throw wolframalpha at it
daring burrow
obtuse pebbleBOT
daring burrow
I used my textbook example as a reference but I guess I went wrong somewhere along the way
would i write my 8/10^2 as 80/10^2? I originally read it as 0.0819
obtuse pebbleBOT
@daring burrow Has your question been resolved?
obtuse pebbleBOT
@daring burrow Has your question been resolved?
distant sphinx
I started it for you you should be able to do the rest.
obtuse pebbleBOT
@daring burrow Has your question been resolved?
prisma notch
The scale factor of two similar polygons is 3:8. What is the ratio of their areas?
I just need a reminder of how to do this
obtuse pebbleBOT
The scale factor of two similar polygons is 3:8. What is the ratio of their area...
dark vector
9:64 would be my guess, but i'd like to be double-checked on that
prisma notch
That was one of my few guess, so I think that might be correct. Thank you
fickle turret
Yes, it is
prisma notch
.close
proven zealot
hey a I had a question, a tringular matrix had alot of like characteristics, but I keep messing them up. so if I got them all correct it's like the eigenvalues of a tringular matrix is the diagonal from left top to right bottom, the trace of it is the summation of that diagonal the determinant is the multiplicaiton of that diagonal and this counts for all upper tringular matrix right?
obtuse pebbleBOT
hey a I had a question, a tringular matrix had alot of like characteristics, but...
frosty spoke
the eigenvalues are given on the diagonal of a triangular matrix, yes
the trace is always the sum of the diagonal, for any matrix
proven zealot
the trace is always the sum of the diagonal, for any matrix
oh
so even
uhm
non square matrix
frosty spoke
the determinant is the product of the eigenvalues, so it would be the product of the diagonal
frosty spoke
non square matrix
not sure if I've ever heard of trace for non-square matrices
proven zealot
the determinant is the product of the eigenvalues, so it would be the product of...
so in general the determinant is the product of eigenvalues and in a particular case for tringular matrix it is the diagonal ofcourse
proven zealot
not sure if I've ever heard of trace for non-square matrices
uhh so trace is only for square matrix?
well me neither tbh cuz the concept of eigenvalues and eigenvectors are only applicable for square matrix and trace is also used in these concept
proven zealot
the eigenvalues are given on the diagonal of a triangular matrix, yes
btw does this count for upper and lower tringular matrix too
am I asking too many questions now?
frosty spoke
yes it's the same for lower and upper triangular matrices
frosty spoke
uhh so trace is only for square matrix?
yes
frosty spoke
so in general the determinant is the product of eigenvalues and in a particular ...
yes
proven zealot
yes it's the same for lower and upper triangular matrices
oh wait I just visualized it with the co factor expansion
proven zealot
the trace is always the sum of the diagonal, for any matrix
and is this also the case if it's not a tringular matrix so the eigenvalues are not the diagonal
if I remember correctly the general formula for trace was the summation of eigenvalues right so in that case will it still be the diagonal
frosty spoke
and is this also the case if it's not a tringular matrix so the eigenvalues are ...
yes it is
frosty spoke
no it's not
proven zealot
oh
frosty spoke
do you understand that something can be simultaneously equal to multiple things?
proven zealot
yes
but in our case u say the summation of a diagonal will be the same to teh summation of the eigenvalues
even for non tringular matri
for every n x n matrix btw
proven zealot
uh so the eigenvalues are always the diagonal ?
or is that not true
for n x n matrix
nvm that's not ture
proven zealot
but it's true
but it's a bit hard to visualize so I can uhm just get any n x n matrix and I know that the summation of the diagonal is the same as the summation of the eigenvalues?
frosty spoke
uh so the eigenvalues are always the diagonal ?
no
bruh
how did you conclude that
frosty spoke
but it's a bit hard to visualize so I can uhm just get any n x n matrix and I kn...
yes
proven zealot
yes
oh 1 more thing the algebraic multiplicity is always less the the geomtric multiplicity right
frosty spoke
oh 1 more thing the algebraic multiplicity is always less the the geomtric multi...
geometric multiplicity is less than or equal to algebraic
proven zealot
ye
I actually meant that
mb
is there btw a intuitive explkanation for it?
that I understnad
I know how to calculate both of them btw
proven zealot
geometric multiplicity is less than or equal to algebraic
I assume there isn't?
frosty spoke
is there btw a intuitive explkanation for it?
this follows from the fact that the geometric multiplicity relies on Av = lambda v
and this is a stricter condition that (A-lambda I) is not invertible or something
or rather
hmm idk how to explain it lol
that's a terrible explanation btw
proven zealot
ah okay I guess it comes later then
frosty spoke
basically there's no proof that they're equal
because they're not
and it wouldn't be greater, because that would mean the characteristic polynomial have a higher degree
proven zealot
so it's always equal/less then therefore?
proven zealot
and it wouldn't be greater, because that would mean the characteristic polynomia...
I think I understand this part because an eigenvalue always has an eigenvector right
frosty spoke
yes
proven zealot
so if there is an eigenvalue with an higher dimension then the algebraic multiplicity then uhm
frosty spoke
I'm probably not great at explaining something like this
basically suppose you have an eigenspace
proven zealot
I'm probably not great at explaining something like this
I feel like you are doing great
frosty spoke
suppose it has a basis of k elements
you can do a transformation so that this basis becomes the standard basis of k elements
frosty spoke
basically you'd get the change of basis matrix and look at
proven zealot
since it is only 1 base
frosty spoke
UAU^-1 or something like that
this would give you a matrix with the same characteristic polynomial
but this matrix is also block-diagonal
proven zealot
this would give you a matrix with the same characteristic polynomial
so what would happen if u have an geomtric multiplicty higher then algebraic multiplcity
frosty spoke
so you can compute the characteristic polynomial as just the product of characteristic polynomials
frosty spoke
so what would happen if u have an geomtric multiplicty higher then algebraic mul...
you can't
proven zealot
why would that lead to a characterstic polynomail higher then n degree
frosty spoke
it's just logically not possible
because this procedure calculates that the multiplicity of (x-lambda) root in the characteristic polynomial of this transformed matrix is at least the dimension of the eigenspace
proven zealot
because this procedure calculates that the multiplicity of (x-lambda) root in th...
ye I understood that part
the algebraic multiplcity of all the things together is the degree
frosty spoke
and since this transformed matrix has the same characteristic polynomial as the original one
the algebraic multiplicity has to be >= the geometric multiplicity
proven zealot
the algebraic multiplicity has to be >= the geometric multiplicity
btw in the lecture he was trying to proof the determinant is the multiplcation of eigenvalues and the trace is the summation and he came to this but I don't understand the last step and he says it's a difficult step
spoor stands for trace btw
frosty spoke
I believe if you do cofactor expansion it follows
proven zealot
I believe if you do cofactor expansion it follows
he says btw u can do hard core co expansion and it will work or there is an smarter way
he also said the dots here it doesn't even matter what there is
frosty spoke
yeah the dots there are messy
uh the way I always learned that the trace is the sum of the eigenvalues is proving this weird thing about the trace operator
proven zealot
so I assume what the dots are will be canceling each other out?
frosty spoke
no
frosty spoke
they're just not relevant
proven zealot
oh
frosty spoke
you're basically going to match the coefficients of the powers of lambda
proven zealot
is that the way to proof it?
proven zealot
you're basically going to match the coefficients of the powers of lambda
but I still don't see how he got taht expression
but he said u gotta believe me it's true
proven zealot
you're basically going to match the coefficients of the powers of lambda
btw this was indeed the way
frosty spoke
but he said u gotta believe me it's true
yeah honestly this is probably one of those things I'd just believe lol
proven zealot
yeah honestly this is probably one of those things I'd just believe lol
oh okay xd I think I should be able to undersatnd this someday right
frosty spoke
it's one of those things that I'm sure there's some proof on the internet for
restive wharf
A proof for what?
proven zealot
it's one of those things that I'm sure there's some proof on the internet for
how is this thing called idk the name or what to search for
frosty spoke
it's a pretty standard proof, though not nearly as elegant as rotating things around a trace
if you just look up proofs that the trace is the sum of the eigenvalues
im sure you'll find the Laplace expansion worked out
maybe there's a neater way for it idk
proven zealot
maybe there's a neater way for it idk
I watched this one and he explained it pretty good I think
obtuse pebbleBOT
@proven zealot Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tepid urchin
find a power series that is to the sum of x
x/inf +0n^n
how is this wrong
tepid urchin
.close
broken hare
nocturne minnow
Factor it fully
nocturne minnow
No
broken hare
what part is wrong
broken hare
You just have 5 + i and 5 - i
nocturne minnow
Those are the solutions, not the factors
nocturne minnow
Yes
nocturne minnow
I guess because the complex solutions technically isn't factorable under real numbers
broken hare
at least i know the form now
nocturne minnow
Meaning it wants factors that doesn't have i
broken hare
.close
timid silo
i think im missing 2 cases
obtuse pebbleBOT
i think im missing 2 cases
clear condor
on
timid silo
obtuse pebbleBOT
@timid silo Has your question been resolved?
viral blade
n(n-1) = 0 mod 10000 does not imply n=0 or n=1 mod 10000
timid silo
why
viral blade
because Z10000 does not have the zero product property
for example, 16*625 = 0 mod 10000
only for mod a prime number would that work
timid silo
yikes then how do i prove this
obtuse pebbleBOT
@timid silo Has your question been resolved?
ruby elm
Find the domain of y = √(log base3 ( cos ( sinx)) )
obtuse pebbleBOT
Find the domain of y = √(log base3 ( cos ( sinx)) )
ruby elm
frigid sail
for square root to be valid inside function must be greater or equal to 0. Which means that cos(sinx) must be greater or equal to 1. As cos value can't be greater than 1. we can look for all x such that cos(sinx) =1
hasty anvil
obtuse pebbleBOT
hasty anvil
Can someone help me with this ?
dark stirrup
!status
obtuse pebbleBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
3
dark stirrup
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
hasty anvil
viral blade
,rotate
warm shaleBOT
viral blade
no idea what happened here after the first step
but i think going from the inside out on this one makes the most sense
at each step writing the inner part as 2^(some fraction)
hasty anvil
What's ur answer ?
wide salmon
obtuse pebbleBOT
wide salmon
I just asked a question about this, but have another
My teacher simplifies to get this
Is this a possible typo?
Because how do you factor out a 2x with 1 on the inside
When there is only 1 x left on that side after canceling x^2 with 1/ax
timid silo
this is not correct
wide salmon
ok thanks, i believe the 2 is just a typo then
wide salmon
yes that's what I was thinking
but with the 1 on the inside I didn't understand how that would be possibe
thanks!
wide salmon
if you dont mind me asking
wide salmon
Do you know how to take the zeros of the right side of this expression
I’m not sure what to do with the ln
timid silo
u mean it equals to 0
wide salmon
Yes
timid silo
and 2ln(ax)+1 =0
wide salmon
Yeah
timid silo
lemme think
timid silo
i think it can
so
move 1 to the other side
so its 2ln(ax)=-1
the devide
ln(ax)=-1/2
then raise both sides as a power to e
so e^ln(ax)=e^-1/2
then ax=e^-1/2
then x =1/ae^-1/2
timid silo
yes
timid silo
now u can plug it in the ln and try
bleak storm
Hey! i really need help for something really simple
obtuse pebbleBOT
Hey! i really need help for something really simple
