Wtf you must be an arithmetical genius or something ?
#help-13
wraith daggerBOT
tushar
earnest socket
the polar form of a complex number?
earnest socket
i see
trim crescent
So none of this is fresh sry, thus me being slow
earnest socket
the n roots you have provided can be expressed succinctly using this formula
the modulus is 1, so r = 1, and theta is the angles provided
hence the $n$ distinct roots to the equation $x^n - 1 = 0$ are $e^{i0}, e^{i\frac{1\cdot 2\pi}{n}}, e^{i\frac{2\cdot 2\pi}{n}}, \ldots, e^{i\frac{(n-1)\cdot 2\pi}{n}}$
sorry, missing e^i
wraith daggerBOT
tushar
trim crescent
Love it
earnest socket
e^{i0} is just 1,
so it confirms what you already know
1 is a root of that equation
trim crescent
Thank you so much bro
How is this free ?
You’re explanations were awesome bro
And patience too
earnest socket
we're volunteers lol
trim crescent
Love you man ❤️
earnest socket
you too, thanks
trim crescent
Hope to bump into you again someday 😘
earnest socket
you can close the channel with .close
trim crescent
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
south flume
Have I explained the viewpoints of the author correctly? Thank you
Also I want to raise Q1 and Q3 written in the screenshot. Thank you!
cedar kilnBOT
Have I explained the viewpoints of the author correctly? Thank you
Also I want t...
@south flume Has your question been resolved?
cedar kilnBOT
@south flume Has your question been resolved?
crimson sedge
cedar kilnBOT
cerulean sail
,rccw
wraith daggerBOT
cerulean sail
You're working out $\int x^{3} e^{x^{2}} dx$ and making the substitution $v = x^2$, such that $dv = 2x dx$?
crimson sedge
Yeah
I’m using u sub to set up tabular method
*u = x^2
I assume that is what u meant
cerulean sail
Thought so
wraith daggerBOT
chartbit
cerulean sail
Yeah that's what you would want to substitute
But then your integral turns into $\frac{1}{2} \int x^2 e^{v} dv = \frac{1}{2} \int v e^{v} dv$
wraith daggerBOT
chartbit
crimson sedge
Because the x^3 and 1/2x cancel right?
cerulean sail
Because the x^3 and 1/2x cancel right?
They cancel down, that's just me rewriting this for you
But then remembering that $x^2 = v$
wraith daggerBOT
chartbit
cerulean sail
I’m using u sub to set up tabular method
...what's the tabular method if I may ask?
crimson sedge
It’s a way to take integrals where u have $/int x^{a} * e^{x} dx$
wraith daggerBOT
Penguin
crimson sedge
Well that failed
It’s a way to take integrals where u have $\int x^{a} * e^{x} dx$
wraith daggerBOT
Penguin
crimson sedge
There
dire geode
Yes
dire geode
It’s a way to take integrals where u have $\int x^{a} * e^{x} dx$
you didn't follow chart's suggestions
crimson sedge
Sorry
I missed that
What was the suggestion
Is it important that x^2 happens to = u
Is that what throws my problem off
dire geode
Is it important that x^2 happens to = u
It's important because when you mix u and x variables, it's nonsense
When you change variables with u-sub, you have to replace all occurrences of x with u
So make the substitution correctly, without any x at all
crimson sedge
Ok
But that means I can’t do tabular method
Right
Or can I still
I probably still can actually right?
It would just be short
cerulean sail
It’s a way to take integrals where u have $/int x^{a} * e^{x} dx$
Do you have any further detail on the "tabular method"? Like a picture or something in notes?
cerulean sail
Is that supposed to be integration by parts?
crimson sedge
Yeah
cerulean sail
**chartbit**
Oh, then just do IBP on here then, no?
crimson sedge
“Just use a calculator” wasn’t really the help I was looking for
Unless I misunderstood
dire geode
Nobody said use a calculator
IBP is integration by parts
Tabular method is a bookkeeping version of it
dire geode
But was he telling me to just the bot to do ibp
Where exactly
crimson sedge
Tbh nvm that let me just get back to the problem
Is it possible to use tabular method on $\int ue^{u} du$
wraith daggerBOT
Penguin
cerulean sail
But was he telling me to just the bot to do ibp
I was saying to use integration by parts, or from what you're familiar with, the "tabular method" (just that I haven't heard of that name before)
cerulean sail
**Penguin**
Basically I was referring to working on this
cedar kilnBOT
@crimson sedge Has your question been resolved?
cerulean sail
,w integrate x^3 e^(x^2)
wraith daggerBOT
cerulean sail
<@788085606483361802>
There you go, you got it 
ember cliff
Hello, I need to prove the continuity of a function :
If $a<b \in \mathbb{R}$, $\phi$ and $\psi$ continuous on $[a,b]$ and $\phi \leq \psi$,$f$ a function such as $\forall x \in [a,b]$, $f$ is continuous on $[\phi(x),\psi(x)]$, then prove that
$[x\rightarrow \int^{\psi(x)}_{\phi(x)}f(x)dx]$ is continuous. Apparently I need to separate the integral and focus on $[x\rightarrow \int^{\psi(x)}_zf(x)dx]$ then use Heine theorem but I am stuck with $\gamma>0,\exists \alpha > 0, \forall \varepsilon > 0, |h|<\alpha\implies |\int^{\psi(x)}_zf(x+h)dx-\int^{\psi(x)}_zf(x)dx|<\varepsilon (\phi(x) - z)$
wraith daggerBOT
Lev
cedar kilnBOT
@ember cliff Has your question been resolved?
ember cliff
Ok there was a problem with the question this is the correct one
I need to prove the continuity of a function :
If $a<b \in \mathbb{R}$, $\phi$ and $\psi$ are continuous on $[a,b]$ and $\phi \leq \psi$, I note $\Delta := {(x_1,x_2) \in \mathbb{R} \ x_1 \in [a,b], x_2 \in [\phi(x_1),\psi(x_1)]}$, $f$ is continuous on $\Delta$, then prove that
$[x_1\rightarrow \int^{\psi(x_1)}_{\phi(x_1)}f(x_1,x_2)dx_2]$ is continuous.
Apparently I need to separate the integral and focus on $[x_1\rightarrow \int^{\psi(x_1)}_zf(x_1,x_2)dx_2]$ then use Heine theorem but I am stuck with $\forall x \in [a,b], \forall \gamma>0,\exists \alpha > 0, \forall \varepsilon > 0, |h|<\alpha\implies |\int^{\psi(x_1)}_zf(x_1+h,x_2)dx_2-\int^{\psi(x_1)}_zf(x_1,x_2)dx_2|<\varepsilon (\psi(x_1) - z)$
wraith daggerBOT
Lev
dire geode
Heine Borel is most likely real analysis
rugged eagle
so maybe it's best to ask in #real-complex-analysis
cedar kilnBOT
@ember cliff Has your question been resolved?
river plank
I have another question
cedar kilnBOT
I have another question
river plank
I was using u equals sqrt(1 minus x
But like it says u have to use sqrt x
but i got answers with both Us
tropic oxide
But like it says u have to use sqrt x
what's "it"?
tropic oxide
ok, so the answer key presents a different solution method than what you did.
river plank
But I got a different answer too
tropic oxide
that by itself doesn't mean your method is wrong.
tropic oxide
But I got a different answer too
show your answer.
river plank
Ill show my owrk and idk how its wrong
I got negative 2 arcsin(sqrt 1 minus x
lus c
river plank
-2 arcsin(sqrt(1-x)) + C?
yes
cosmic steppe
That should also work
tropic oxide
i think this might differ from 2 arcsin(sqrt(x)) by only a constant.
,w simplify 2 arcsin(sqrt(x)) - (-2 arcsin(sqrt(1-x)) )
wraith daggerBOT
river plank
so i did it right and they are equivalent
tropic oxide
yes
river plank
LETS FUCKING GOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
THANK YOU SO MUCH
.thank
.uvote
.close
old hornet
Represent the following fraction as a sum of whole number and a fraction, -17/7
Why do we need to take the - common?
old hornet
Ping me
burnt leaf
Represent the following fraction as a sum of whole number and a fraction, -17/7
...
What do you mean by common?
old hornet
What do you mean by common?
Like -(17/7)
burnt leaf
Ah
old hornet
Mhm?
burnt leaf
Well first off it is negative so adding numbers makes the subtracted number change in the other direction
Such as -2 + 1
Becomes -1
old hornet
Yes
burnt leaf
Indeed
dry dirge
how to find this limit
cedar kilnBOT
how to find this limit
dry dirge
y sry
crimson sedge
What would be the difference
dry dirge
how to calculate this
hasty fulcrum
it would be infinity overall
sacred grail
What would be the difference
depends on your definitions
dry dirge
hasty fulcrum
the DNE is absorbed into the positive infinity
dry dirge
how?
sacred grail
the DNE is absorbed into the positive infinity
thats not how it works 
hasty fulcrum
thats not how it works <:sully:651816820122189834>
is it really not?
that's how i was always taught
the sin just oscillates between -1 and 1 at infinity but the x 'overpowers' it
nvm that's not 1/5 then LOL
dry dirge
it is
hasty fulcrum
oh
dry dirge
but how
crimson sedge
It is 1/5 but the wording is confusing
You can just divide the numerator and denominator by x
sacred grail
🥪 it
crimson sedge
You will have sin^3(x)/x which is more or less just sin(x)/x which is obviously 0
Oh yeah u can use Sammy
tropic oxide
dry dirge
i do not know guys what are you saying
tropic oxide
your actual problem was to find $\lim_{x \to +\infty} \frac{x + \sin^3(x)}{5x + 6}$ but you asked about only the numerator.
wraith daggerBOT
Ann
dry dirge
y that was mistake
tropic oxide
y = why?
dry dirge
yes
tropic oxide
it's not a mistake so much as it is annoying
dry dirge
y = yes
tropic oxide
...
crimson sedge
What
tropic oxide
okay, that was my fault.
tropic oxide
anyway.
"the DNE is absorbed into the positive infinity" is horrendous as far as argumentation goes.
this limit can (and should) be rewritten as $\lim_{x \to +\infty} \frac{1 + \frac{\sin^3(x)}{x}}{5 + \frac{6}{x}}$.
wraith daggerBOT
Ann
dry dirge
ok after that we i guess are using limit law for summation
i am afrade to ask what is limit of sin^3(x)\x
tropic oxide
why are you afraid to ask?
also, it's /, not \
also, the limit of sin^3(x)/x is not hard to calculate on your own. you should know that sin^3(x) is bounded between -1 and 1.
dry dirge
well i spand last day to find that limit guess it is hard for me
i guess using squeeze theorem is right way
hasty fulcrum
i guess using squeeze theorem is right way
try writing the statement $-1 \leq \sin^3(x) \leq 1$
wraith daggerBOT
blanket
hasty fulcrum
mb for saying that the dne is absorbed, that was my bad
then divide both sides by x
dry dirge
how you can divide inequality by a variable ?
tropic oxide
you multiply both sides (or, in the case of an inequality chain, all links) by the same thing
in this case 1/x
we can assume x is positive since it approaches +∞
cedar kilnBOT
cedar kilnBOT
Available help channel!
hushed badger
cedar kilnBOT
south tundra
The domain of the inverse is the same as the range of the original function
jolly cape
Given: Field K, n>=1 Matrix A€K^{nxn} sucht that A * B = B * A for all B € K^{nxn}
Show that: There exists a scalar x such that A = x * Id_n
I want to consider the Eij matrices and then show that A has equal entries on the main diagonal and zeros everywhere else.
I know that A * B = B * A so A * Eij = Eij * A
1 <= i, j <= n and i =/= j
Then
$$ [ A * E{ij} ] {ij} = \sum{k=1}^{n} a{ik} * e{kj} = a{ii} = a{jj} = \sum{k=1}^{n} e{ik} * a{kj} = [ Eij * A ] {ij} $$
$$ [ A * E{ij} ] {ii} = \sum{k=1}^{n} a{ik} * e{kj} = 0 = a{ji} = \sum{k=1}^{n} e{ik} * a{kj} = [ Eij * A ] {ii} $$
$$ [ A * E{ij} ] {jj} = \sum{k=1}^{n} a{ik} * e{kj} = a{ji} = 0 = \sum{k=1}^{n} e{jk} * a{kj} = [ Eij * A ] {jj} $$
So from that the entries on the diagonal are all equal
And the other ones are 0?
I did it by hand with a 2x2 matrix but im not comfortable with the sum notation and the general case.
Let me know if I have a mistake somewhere
wraith daggerBOT
aabb
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
jolly cape
man for some reason I fucked up the latex, let me retry
jolly cape
Im very new to using Latex. I copy pasted it to the bot before and the single parts came out fine
but now even the single parts come back skewed
jolly cape
$$ [ A * E{ij} ]{ij} = \sum{k=1}^{n} a{ik} * e_{kj} \ = a{ii} = a_{jj} = \sum{k=1}^{n} e_{ik} * a_{kj} \ = [ Eij * A ]{ij} $$
$$ [ A * E{ij} ]{ii} = \sum{k=1}^{n} a_{ik} * e_{kj} \ = 0 = a_{ji} = \sum{k=1}^{n} e_{ik} * a_{kj} \ = [ Eij * A ]{ii} $$
$$ [ A * E{ij} ]{jj} = \sum{k=1}^{n} a_{ik} * e_{kj} \ = a_{ji} = 0 = \sum{k=1}^{n} e_{jk} * a_{kj} \ = [ Eij * A ]_{jj} $$
wraith daggerBOT
aabb
sacred grail
bruh
jolly cape
here <@697745796929552414>
very much appreciate it
crimson sedge
works 
jolly cape
yeah looks much better, to the point its clear whats going on I guess
Anyway, did I got the sum notation and general Idea correct?
crimson sedge
im gonna use \hphantom ngl because figuring out the correct measurment is pain
oh okay lol
crimson sedge
OP check your work i am just fixing ur latex
jolly cape
thanks haha
I was just making the Latex up on the go just googling everything, can you recommend a good enough resource to get the basics down?
jolly cape
aight, thanks for the help
wraith daggerBOT
cedar kilnBOT
@jolly cape Has your question been resolved?
jolly cape
tagging <@&286206848099549185> once
jolly cape
.reopen
cedar kilnBOT
✅
jolly cape
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azure dock
when doing bitwise arithmetic is there a quick way to find out how many possible values of X there are other than just going bit by bit and seeing what the combinations are
tropic oxide
this is kind of hard to read 
are we to assume AND has higher priority than OR?
i would try to clean up this expression
azure dock
are we to assume AND has higher priority than OR?
yes
azure dock
i would try to clean up this expression
how do you clean it up, i know hoow to simplify normal boolean algebra but in this case i dont know
tropic oxide
right
tropic oxide
yeah this should yield to normal Boolean algebra
(X AND 101110) OR X should just be X
azure dock
then the part after or in 2nd parenthesis is just 0
tropic oxide
yeah
azure dock
so it would be x*(x*101101)
tropic oxide
i got this simplified all the way down to X AND 101101 = 001100
minor crag
Translate: with using the derivative of function (you can choose y whatever u want ) show that :
gleaming cloud
Write f using the binomial formula
cedar kilnBOT
@minor crag Has your question been resolved?
minor crag
and how do i get the k/n and cnk
cedar kilnBOT
@minor crag Has your question been resolved?
iron cipher
le cnk vient du dvlp avec la formule du binome, le k/n devrait venir apres derivation et reindexation de la somme avec une petite manipulation des coefficients.
digital bloom
cedar kilnBOT
digital bloom
Just to check, they seem to have messed up on the a0 term
cedar kilnBOT
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digital bloom
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cedar kilnBOT
cedar kilnBOT
Available help channel!
novel stone
I need to prove that vectors p and a are ortogonal for any a,b,c vectors, where p = (a * c) * b - (a * b) * c
red pumice
p is a vector?
novel stone
yes
red pumice
looks more like a number if p = (a * c) * b - (a * b) * c
and sure numbers are vectors but this seems wrong
novel stone
I see
red pumice
a dot ((a dot c)b - (a dot b)c) = 0 is what you need to prove
$<a, <a, c>b - <a, b>c> = 0$
wraith daggerBOT
Gijs
novel stone
so I need to prove that p's expression is equal to 0
red pumice
no
just that p's dot product with a is 0
just use the algebra rules for dot products
novel stone
is "dot" asociative for vectors
red pumice
no
it cant be
because the dot product between 2 vectors is a number
and there is no dot product between a number and a vector
novel stone
I got ab(ac) - ac(ab)
is it ok to say that it is equal to 0
or am I doing it wrong
novel stone
a dot b dot (a dot c) - a dot c dot (a dot b)***
red pumice
you cant take the dot product between numbers
and writing ac implies ordinary multiplication, which cant be since a and c are vectors
you have the right ideas
novel stone
sorry, my bad
red pumice
but your notation is a mess
novel stone
yeah
red pumice
youre almost there
novel stone
should I use distributivity between dots?
I got
(a dot b dot a)(a dot b dot c) - (a dot c dot a)(a dot b dot c)
(a dot b dot c)(a dot b - a dot c)
red pumice
a dot b dot c is incorrect notation
it doesnt mean anything
a dot b is a number
a dot c is a number
dot product is for vectors
not numbers
red pumice
a dot b dot (a dot c) - a dot c dot (a dot b)***
funny thing is this is exactly the right way to prove it
so youre doing well
its just notation
novel stone
so I need to figure out why it equals to zero?
red pumice
well yes thats been the question from the start
novel stone
I am not sure what to do next
red pumice
alright so
a dot ((a dot c)b - (a dot b)c) = a dot((a dot c)b) - a dot ((a dot b)c) \
thjats the first step
which is using the distributive property
novel stone
a dot ((a dot c)b - (a dot b)c) = a dot((a dot c)b) - a dot ((a dot b)c) \
= a dot( (a dot b) dot (b dot c) ) - a dot( (a dot c) dot (b dot c) )?
red pumice
multiplication is not the same as dot product 
cedar kilnBOT
@novel stone Has your question been resolved?
novel stone
multiplication is not the same as dot product <:blobcry:971797574916907028>
I am tired now, I will try to get through it tomorrow
thank you a lot for the help
also, one more question
just to be sure I understood correctly
so (a dot b)c is different from (a dot b) dot c?
minor crag
cedar kilnBOT
minor crag
Translate: by using the derivative of the function ( u can take y whatever u want) show that :
upper garnet
still stuck on same exercise? rip
cedar kilnBOT
@minor crag Has your question been resolved?
crimson sedge
mais je te l'ai pas déjà expliqué ce truc ?
Oh tu parles français aussi?
c'est bien
foggy merlin
Oh tu parles français aussi?
yep, t'avais jamais remarqué ? mdrrr
crimson sedge
yep, t'avais jamais remarqué ? mdrrr
non hahaha
wooden pasture
cedar kilnBOT
steady fossil
is the double dots /?
wooden pasture
Yea
crimson sedge
The : is division right
?
patent cape
Flip the fraction to turn it into multiplication
crimson sedge
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$
wraith daggerBOT
♡Lex♡
crimson sedge
First and only time I will ever use the division symbol
gleaming cloud
Suiii
latent bloom
First and only time I will ever use the division symbol
Wow lmao
wooden pasture
patent cape
After you do that factor out 5x from the denominator
wooden pasture
That’s the solution
patent cape
Why use stacked fractions it's a pain to look at
Personally I just simplify what I can and keep it in product form
patent cape
Isn't it 5x+25 in the first fraction
Since you distributed the 5
Also you could have canceled it with the 5 from 5(x²-25)
wooden pasture
Oh lemme try again
patent cape
And hint for the next part: ||difference of squares||
patent cape
Yeah but you didn't really do what I said
wooden pasture
patent cape
$5 \cdot \frac{x+5}{x-1} \cdot \frac{x}{5(x²-25)} = \frac{x+5}{x-1} \cdot \frac{x}{x²-25}$
wraith daggerBOT
Kel.plush
patent cape
You can't simplify like that man
wooden pasture
Why
patent cape
Properties of fractions
patent cape
I apologize if I mispelt it, English isn't my first language
cedar kilnBOT
@wooden pasture Has your question been resolved?
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@wooden pasture Has your question been resolved?
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cedar kilnBOT
@ashen vapor Has your question been resolved?
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@ashen vapor Has your question been resolved?
tidal knoll
cedar kilnBOT
tidal knoll
anyone know whats wrong with this
soft owl
,w distance between (8,3,-1) and (2,5,5)
wraith daggerBOT
earnest socket
you know (2,5,5) must satisfy the equation
so just adjust the RHS to make sure it is
no need to work with distances if you have the center correct and a point on the sphere
soft owl
diameter² = 76 = 4R²
earnest socket
this uniquely determines the sphere (and the equation)
tidal knoll
diameter² = 76 = 4R²
so its 38?
earnest socket
no
tidal knoll
ah so 2 sqrt 19?
soft owl
ah so 2 sqrt 19?
this is the length of the diameter
divide it by 2 to get R (which is R = sqrt 19)
earnest socket
or substitute 2,5,5 or 8,3,-1 into the LHS, and whatever you get, make that the RHS
this automatically gives you the square of the radius
earnest socket
.close
cedar kilnBOT
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soft owl
.close
raven bough
can anyone help?
cedar kilnBOT
can anyone help?
raven bough
how do i know what is AB?
livid hound
well you have an equation giving you the relations between AC and AB
sub the given expressions into that equation
raven bough
yes
raven bough
like this?
dull dawn
dont even worry about CB here
livid hound
CB will be 3x yes, but that didn't seem to be what you wanted
livid hound
it's technically not incorrect, but writing 4x + 3 over the 5x doesn't really help
you have the equation
AC + 3 = AB
right?
raven bough
yes
livid hound
and from the diagram you have expressions for AC and AB right?
(those are 4x and 5x respectively)
raven bough
yes
livid hound
sub 4x for AC
sub 5x for AB
livid hound
(you should end up with something that's still an equation)
raven bough
it says one side is greater than another by 3
livid hound
does it say which side?
raven bough
and hypotenus : biggest side equals 5:4
livid hound
do you have the original question
raven bough
yes but it is in Georgian
basically it says this
and hypotenus : biggest side is same as 5:4
livid hound
in this context it seems the word you want is
leg
which refer to non-hypotenuse sides of a right triangle
raven bough
yes
so one leg is bigger than another by 3
and hypotenuse : biggest leg is same as 5:4
you know what i mean?
livid hound
yes
livid hound
yeh, that's fine
raven bough
i don't know how to continue from here
livid hound
you can use the ratio between the hyp and longest leg to get an express for AB in terms of x
livid hound
it's fine, just find the ?
livid hound
no
the ? was representing something you wanted to determine, but then just dissapeared
I'll give you something less tedious
actually it's easier to first express CB in terms of y
(which from pythag you implied you know will be 3y)
livid hound
still wrong
raven bough
😩
livid hound
you essentially divided the left by y while multiplying the right side by y
livid hound
from here you can apply pythag
cedar kilnBOT
@raven bough Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Trying to do this interesting question
cedar kilnBOT
Trying to do this interesting question
crimson sedge
From the definition of the matrix product, describe an algorithm in English for computing the product of two upper triangular matrices that ignores those products in the computation that are automatically equal to zero.
Like
Upper triangle matrices are square $n \times n$ matrices and their product is also $n \times n$
wraith daggerBOT
♡Lex♡
crimson sedge
describing an algorithm for that 
long swan
Frame it in terms of dot products
crimson sedge
oh i actually did it in python haha
i basically said this
well
okay i am not done yet
Okay whatever
ignore python
lets just define it normally
sacred grail
foggy merlin
sacred grail
for i in range(n):
for k in range(n):
for j in range(i, k+1):
c[i, k] += a[i, j]*b[j, k]
but more efficient
crimson sedge
yeah basically what i wrote
actually lemme try finishing that
yeah okay
what
it got deleted?
wtf
sacred grail
crimson sedge
okay this server is deleting my code
sacred grail
got marked as spam 
sacred grail
does it have banned words in it
sacred grail
cerulean talon
5x-35-(4x-9)=-3x(2x+4)
cedar kilnBOT
5x-35-(4x-9)=-3x(2x+4)
cerulean talon
Why does 4x-9 become 4x+9?
Is it because the parentheses?
And why we don't subtract x-6x but add it, is it because inverse operations?
tropic oxide
it's not "4x-9 becomes 4x+9"
if anything becomes anything else, it's -(4x-9) becomes -4x + 9
And why we don't subtract x-6x but add it,
are you looking at some worked solution here?
cerulean talon
> And why we don't subtract x-6x but add it,
are you looking at some worked sol...
Yes
cerulean talon
if anything becomes anything else, it's **-(4x-9)** becomes **-4x + 9**
Is it because the parentheses?
Oh i got it
-
-
- = + right?
-
Still need answer
undone sage
Answer to what bro
cerulean talon
Does -(4x-9) become -4x+9 because - * - = + ?
foggy merlin
-(4x-9) = (-1)(4x-9) and you expand
cerulean talon
why we don't subtract x with -6x when solving an equation, is it because inverse operations?
x=-6x+14
Oh I got it
Because we need to eliminate -6x to 0 right?
by adding +6x
.close
cedar kilnBOT
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digital bloom
For part 5
Why is their marginal density function for y like that?
I got this instead
cedar kilnBOT
@digital bloom Has your question been resolved?
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vital delta
cedar kilnBOT
vital delta
ive calculated a) and b) but for c) i really dont know
tropic oxide
work backwards along the week
tropic oxide
does your teacher penalize you for writing nP1 as n?
vital delta
no ig
tropic oxide
there are only 3 options for Fri (study, football, hike)
afterward, there are only 3 options for Thu (study, football, hike, cycle, minus whatever he did on Friday)
and the remaining 3 activities can be distributed among Mon, Tue and Wed any way we want.
rose rose
You take a 4 out of it
Nope, wrote that wrong. Sorry bad with latex
But I guess you get the idea
We are going for arctan, which has derivative 1/(x^2 + 1^2)
winged jewel
surely the last part would have 4 removed from the denominator as its taken to the outside to make 1/2?
rose rose
The u sub will be x/2
An x square at the denominator and no x term in the numerator is a good sign you want arctan
(or arctanh)
vital delta
cedar kilnBOT
crimson bobcat
how do i solve this integral
cedar kilnBOT
how do i solve this integral
runic garnet
$\int_{0}^{1} {\sqrt{x-x^2}}dx$
this?
except with bounds 1 to 0?
or is it 0 to 1?
flint plinth
haven't tried working it out, but how about completing the square and trying a trig substitution
crimson bobcat
except with bounds 1 to 0?
1 to 0
crimson bobcat
haven't tried working it out, but how about completing the square and trying a t...
trying that rn
runic garnet
this?
runic garnet
then its 0 to 1
wraith daggerBOT
Stephen
crimson bobcat
i completed the square
and got sqrt (1/4 -u^2), where u=x-1/2, and its 1/2 on the top and -1/2 on the bottom
crimson bobcat
now u=1/2 sin theta
crimson bobcat
And itll be between 90 to -90
flint plinth
yep (or -pi/2 to pi/2 if using radians)
crimson bobcat
ahh
flint plinth
(which you probably should be doing)
flint plinth
yea
crimson bobcat
okay thx
flint plinth
there a missing close-paren in the sqrt part
i guess you mean $$\sqrt{\frac{1 - \sin^2(t)}{4}}$$
wraith daggerBOT
Bungo
crimson bobcat
Ye but i think yk what i mean
flint plinth
crimson bobcat
huh?
flint plinth
you use that to integrate cos^2
flint plinth
sure
crimson bobcat
should i expand the brackets
flint plinth
yeah you can integrate the two terms separately if you like
flint plinth
on the rhs it should be cos(2t) not cos^2(t)
flint plinth
then yeah you can just integrate that as $$\int_0^1 \frac{1}{8}\ d\theta + \int_0^1 \frac{1}{8}\cos(2\theta)\ d\theta$$
wraith daggerBOT
Bungo
crimson bobcat
from pi/2 and -pi/2
flint plinth
yep
crimson bobcat
and i sub in pi/2 and then -pi/2 and then subtract
okay
so i got pi/8
fro the first bit
flint plinth
right
flint plinth
integral of cos(u) is sin(u) right?
crimson bobcat
-sin
flint plinth
nope, integral not derivative
flint plinth
so integral of cos(2t) = (1/2)sin(2t)
crimson bobcat
ye
flint plinth
(quick var substitution or just do it in your head)
crimson bobcat
whats that
crimson bobcat
ugh more sub
flint plinth
otherwise just mentally do it
crimson bobcat
this is difficult
flint plinth
and check that the derivative of (1/2)sin(2t) is indeed cos(2t)
crimson bobcat
the 1/8 turns into t/8 right
flint plinth
this is difficult
the hard stuff is done, this part is easy 😀
crimson bobcat
lol
flint plinth
the 1/8 turns into t/8 right
wait, in the second integral?
crimson bobcat
yes
the 1/8 at the btoom
bottom
im doing it in two parts like that
so its (sin(2t))/2/8t
flint plinth
$$\int\frac{1}{8}\cos(2t)\ dt = \frac{1}{8}\int \cos(2t)\ dt = \frac{1}{8}\left(\frac{1}{2}\sin(2t)\right)$$
wraith daggerBOT
Bungo
crimson bobcat
my brain is dying
flint plinth
haha
crimson bobcat
oh yh the 1/8 is a constant so you can take it out
flint plinth
don't die yet, this is the very last step haha
flint plinth
yep
flint plinth
because the second integral is zero
flint plinth
btw, short cut:
crimson bobcat
because the second integral is zero
yes
crimson bobcat
btw, short cut:
ye?
flint plinth
$$\int_{-\pi/2}^{\pi/2}\cos(2t)\ dt$$
wraith daggerBOT
Bungo
flint plinth
the period of cos(2t) is pi
you are integrating over one period
so the integral is zero
wraith daggerBOT
flint plinth
wolfram agrees!
cedar kilnBOT
@crimson bobcat Has your question been resolved?
radiant prairie
cant i just use the root test and then write it converges against 1?
radiant prairie
so the task is i have to show that it converges btw
modern compass
the root test is inconclusive if it converges to 1
radiant prairie
oh you right
modern compass
are you showing the series converges or the sequence?
radiant prairie
sequence
or wait my task is in german
i have to look it up xD
should be series
modern compass
ok, then yeah. The root test would be inconclusive
radiant prairie
the teacher suggested to use the Bernolli's inequality and sandwich set but i dont really know how to use them here
crimson sedge
cant i just use the root test and then write it converges against 1?
you are just trying to check for the sequence's convergence right?
oh wait series?
modern compass
so they said to use these?
radiant prairie
yeah
modern compass
the first one should work, letting x = -1/n^2 and r = n
radiant prairie
thanks im going to try it out
cedar kilnBOT
@radiant prairie Has your question been resolved?
radiant prairie
i dont understand why we have to use this test how can i show with that that it converges
radiant prairie
.close
cedar kilnBOT
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glad berry
Hello guys i need help with my exam in university on 9th january on this topics
glad berry
systems of linear equations Gauss method
feature limits with Lopital
function study
indefinite integral
definite integral
finding a region of convergence of a power series
matrix rank Gaussian method
gleaming cloud
Ask a question
frosty thicket
did you read the rules and guidelines
gleaming cloud
No cheating
cedar kilnBOT
@glad berry Has your question been resolved?
dull oxide
Studying or needing answers?
crimson sedge
cedar kilnBOT
crimson sedge
can someone help me do part C i cant figure out how to get the coordinates with constant K around
grand forge
can someone help me do part C i cant figure out how to get the coordinates with ...
since they intersect
u can just solve
k - 1/8x = 1/2(12x^2)-10x+22
get k in terms of x
yk
crimson sedge
That gives the answer in terms of k
grand forge
True but we know
the gradient of line l is -1/8
so therefore getting the derivitive of line c
and making it equal to the neg recipricol of -1/8 (which is 8) u can find k coz u will the x coord
crimson sedge
bruh we haven't started on derivatives yet
grand forge
LOL
than i have no clue how u would do this
is that 1/2 infront of all the expression or just 12
crimson sedge
infront all i think
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
no
teal grotto
cedar kilnBOT
teal grotto
for ii) i got to 6+6s-3t = 0
it says find the relationship between s and t tho
so do i have to rearrange or what?
long arrow
I think they want smth like s = f(t) or the other way around, so yes
teal grotto
so i should do 6s = 3t -6
long arrow
which gives s = t/2 - 1
teal grotto
are we allowed to do that with vectors?
cosmic marten
I have the following smiley down below. If have a linear function f(u) = ({0,1},{1,0})u and the input is the smiley face, is the red version a correct depiction of the transformation?
cosmic marten
i.e the smiley gets turned sideways?
dire geode
Nah yes
Find where the top right corner gets mapped to
You can assume the coordinate is (1,1) just to get a feel
cosmic marten
Is it just upside down then?
Went with your tip and quickly realized that all points of the smiley stay in the same place, just that the axises swapped places
dull oxide
~~Nah~~ yes
You sure?
The change of base should end up making it symmetric about y=x, right?
cosmic marten
oh
So, is it correct to think about these types of mapping as some sort of rotations, in general?
cosmic marten
Ahh
dire geode
Rotations aren't the same as reflection
I thought it was a rotation at first glance but that was wrong as SWR pointed out
cosmic marten
Thank you for the comprehensive picture :). I'll print that and use it for revision tomorrow.
cedar kilnBOT
@cosmic marten Has your question been resolved?
cedar kilnBOT
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ionic kindle
Why do I keep getting banned from Discord servers?
cedar kilnBOT
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upbeat pond
how u do this
cedar kilnBOT
how u do this
opal sierra
how do I do this using the way shown in the video?
upbeat pond
.close
cedar kilnBOT
opal sierra
.reopen
opal sierra
oh!
opal sierra
Already closed by OP, try getting a new one <:catThimc:732011802459635713>
oh yeah
cedar kilnBOT
Available help channel!
mossy mango
cedar kilnBOT
mossy mango
can someone explain why the average here asking is not (150+25*4) / 5
deft gull
average per student
this is interesting
think about what that means
so think about this
lets say there is a class of 10 and a class of 5
the average CLASS SIZE is 7.5 students
but in the eyes of the students, there are more students in the class of 10 than in the class of 5
so like the average per student
would be like if each student wrote how many people are in their class on a paper
then you average those numbers
yes
then take the average
yep
so do something similar for the problem
yep
there was an AMC 10 question similar to this
that’s how i learned it 💀
no
stats is my weak area