gritty rose
modulo as in modulo arithmetic
#help-28
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cinder wind
hello?
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visual ferry
Hi, i have list of people of how many days they attended and how many school days failed to come, what chart would be the best for this?
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visual ferry
<@&286206848099549185> <@&286206848099549185>
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frail grove
what is this asking me to solve exactly for the second problem??
frail grove
go i plug the inverse of g into f(x) or h(x)??
grim skiff
what is this asking me to solve exactly for the second problem??
It's asking you to find g(x)
Using the same process you did in part a
frail grove
It's asking you to find g(x)
.
grim skiff
Show your work
frail grove
for which part? f-1 or for the h o f-1?
grim skiff
First do you understand part a?
grim skiff
Not exactly
frail grove
oh 😦
grim skiff
Notice how $f \circ g = h$ and they do $f \circ g \circ g^{-1} = h \circ g^{-1}$
glossy valveBOT
CaptainNova22
grim skiff
Do you notice how g^-1 was applied on the right side?
frail grove
so instead, maybe it would be f o f-1 o g?
grim skiff
Like here, from the green underlined equation, to the blue one, it applied the composition of g^-1 to the right side, of both sides to the equation
frail grove
hmm yes
grim skiff
So to get the function g, from $f \circ g = h$, you do $f^{-1} \circ f \circ g $
glossy valveBOT
CaptainNova22
grim skiff
Do you see that?
grim skiff
Yes but the thing I'm pointing out is, the side it gets applied on
grim skiff
**CaptainNova22**
This, f^-1 was applied to the left side of the expression
Therefore, it should be to the left side on the other side of the equation
grim skiff
Yes
grim skiff
You mean left?
frail grove
.
grim skiff
$f^{-1} \circ f \circ g = f^{-1} \circ h$
frail grove
cuz its the opposite of g^-1
glossy valveBOT
CaptainNova22
grim skiff
So because the blue circle was applied to the left of that yellow circle, when you do it on the h side, it has to go on the left side of the h, the green circle
frail grove
ahhhhhhhhhhhhhhhh
ok that makes sense
how do i award u with a point
thanks @grim skiff
is there a thank you bot
grim skiff
Idk
frail grove
well thats lame
grim skiff
ahhhhhhhhhhhhhhhh
That's why in the example, the g^-1 was specifically applied to the right side, in the work
That's why it was not g^-1 o h
frail grove
that clicked for me
grim skiff
If you had $g \circ f = h$ and you were told to solve for f, and it gave and example, it would do something like this $g \circ f = h \to g^{-1} \circ g \circ f = g^{-1} \circ h$
glossy valveBOT
CaptainNova22
grim skiff
So because the blue circle was applied to the left of that yellow circle, when y...
It's more, if it got applied to the left side, then you do it to the left side, like with this
The blue was put on the left of the yellow hence it's where the green is
If the blue was on the right side of the yellow, then the green would have been on the right side of the h
frail grove
gotcha, so the positioning of the blue always goes next to its friend, and then on the otherside of the equation, it goes on the left or right side, corresponding where the friend is on the other side
grim skiff
Yes exactly, it corresponds to where it was placed
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@red geyser Has your question been resolved?
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visual ferry
ground beef went up 12% now it costs 448 kronas , what was the price of it before increase
torn jolt
448 x 0.88
hot herald
!status
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spice orchid
<@&268886789983436800>
Yes?
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rugged wasp
hi
flint crane
differentiate it, set df/dx = 0, find x
rugged wasp
ok
flint crane
did you do that?
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flint crane
wait i think i got it
It asks for value of x though lol
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ornate steppe
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flint crane
find y'?
ornate steppe
y prime
ornate steppe
how
flint crane
if you want to d/dx both sides, cosy * dy/dx = 1, agree?
flint crane
how to write in solution
I am proving d/dx arcsinx for you
ornate steppe
okay then prove
flint crane
if you want to d/dx both sides, cosy * dy/dx = 1, agree?
^
flint crane
i dont get it
left hand side is due to chain rule
lemme write it down
@ornate steppe
flint crane
oh no thats not a solution i think
I am proving d/dx arcsinx to you
flint crane
How did you learn d/dx arcsinx then
flint crane
we learn d/dx but with arc sinx no
Then how are you supposed to find the solution lol
ornate steppe
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deft tulip
$\int\csc^5xdx$
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$\int\csc^5xdx$
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Soosh
deft tulip
hm i think this is doable with sub of tan x/2 = w but it involves multiplying a bunch of high degree polynomials, wondering if im missing a more obvious way
deft tulip
yeah that is a lot better, thanks : )
buoyant pewter
yeah that is a lot better, thanks : )
yvw:)
deft tulip
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willow oracle
Hi! Does anyone have websites where I can get example questions on algebra, Simultaneous equations, functions, financial maths and factorials on? 
coarse chasm
Hi! Does anyone have websites where I can get example questions on algebra, Simu...
khan academy should work fine
spiral vigil
I've used math-drills.com before but I don't think they have finance
willow oracle
khan academy should work fine
Everyone says Khan academy but I can't access the website 
willow oracle
I've used math-drills.com before but I don't think they have finance
Im gonna take this one too
I have my huge university entrance test on friday about maths so I want to work and get my 70% 🥲
Thank you @coarse chasm @spiral vigil 
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inner nest
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inner nest
Did I do this right?
jade radish
,rotate
glossy valveBOT
jade radish
yea
inner nest
ok I figured
jade radish
did u get 15/4 ?
inner nest
I’m not sure what to do with the 36 okay so right now I have
36(6^-1)^x+2
36(6)^-x-2
meager dew
you may be making this a little more complicated than you need to
inner nest
probably lol
jade radish
u can rewrite 36 as 1/(6^(-2))
meager dew
recall $a^{b+c}=a^b \cdot a^c$
glossy valveBOT
a disappointing son
inner nest
u can rewrite 36 as 1/(6^(-2))
can u show that in image form
jade radish
$36 = \frac{1}{6^{-2}}$
glossy valveBOT
Juke | ping me if no response
jade radish
this is kind of a roundabout way tho i think
but that's the route I took
alr, I gtg to class. close this if u ended up getting it tho
silver fern
readability?
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silver fern
im supposed to prove this for n=>2 (by induction i assume)
we´re given the hint to differentiate:
I have noticed that (a) is the derivative of the binomial theorem for x=1.
Now to prove it for n=>2 I first proved it works for n=2
and then i did n -> n+1
this is currently where im stuck. I've restructured the equation like this so far:
but im not sure where to go from here, I also dont understand where differentiation is supposed to help with this.
rapid rain
there is no induction to do here
silver fern
I think it clicked
rapid rain
we´re given the hint to differentiate:
literally you have to start from this
and differentiate both sides
silver fern
Yes, Ive done that
for x=1 u get (a)
I know how to prove it via induction now but yeah
silver fern
and differentiate both sides
after that I can say its proven because its the derivative of it? Or why
rapid rain
did you compute the derivatives?
silver fern
yes, I can type it out again
x ^k-1 and n(1+x)^n-1 I cant properly write in latex idk why zz
$\sum_{k=0}^{n} \binom{n}{k} kx^{k-1} = n(1+x)^{n-1}$
oh nvm got it
glossy valveBOT
Nox
silver fern
and for x=1 we get (a)
rapid rain
yes
silver fern
yes, Ive written that down in my answer aswell
rapid rain
and you should get rid of it asap in order to avoid troubles with 1/x
silver fern
well I argued that since k=0 and k is part of a product of the sum it has to be 0 aswell so it can be ignored
and thats how u arrive at the term given in (a)
but thats supposed to prove that it works for n=>2?
rapid rain
but thats supposed to prove that it works for n=>2?
it works for ALL n
we didn't specify which n we used here
works for all n >= 1
silver fern
under the assumption that the binomial theorem is a given I guess?
silver fern
The task description is kinda vague so I thought we´d have to 100% be rigurous in our proof, and this seems a little bit too easy to be true haha
but I appreciate it thanks
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misty cave
How do I find the period of this?
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How do I find the period of this?
misty cave
Is it just 2pi/20?
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torn jolt
For number 9, log2 is 0.43 and log3 is 0.68
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For number 9, log2 is 0.43 and log3 is 0.68
viral jasper
For number 9, log2 is 0.43 and log3 is 0.68
What is the question?
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ivory gyro
My nephew is stuck with his homework math problem and asked me to help with the solution. I have no idea how to solve this, so I though I'd look for help here, will be real glad for step-by-step solution to show him, if possible
nova basin
https://www.wolframalpha.com/input?i=5^(2x²-1)+%3D+3+*+5^(x²%2B3x%2B2)+%2B+2*+5^(6x%2B6)
That can't be his homework
nova basin
My nephew is stuck with his homework math problem and asked me to help with the ...
this is so complicated even WA can't solve it analytically
ivory gyro
I've tried some online calculators, most of them failed
nova basin
not surprised
ivory gyro
and by the way I thought this is 5^(2*x^2 - 7)
but maybe it's actually -1, let me check
ivory gyro
wolfram shows integer answers for -1 variant
nova basin
I've tried some online calculators, most of them failed
when that happens, question whether that's actually the homework, and not something arrived at by trying to "simplify" the problem
ivory gyro
I'll ask them
it seems he's asleep already. Should I close the thread and reopen it tommorow then?
nova basin
yeah, you might as well
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wheat garden
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rapid rain
what do you need to prove?
flint dew
-1 + 1/2 - 1/3 + 1/4 ...
wheat garden
oh its a geometric series
rapid rain
oh its a geometric series
not exactly
wheat garden
isnt the ratio -1
flint dew
lets split the negatives and positives
wheat garden
and alternating
flint dew
-(1 + 1/3 + 1/5 + 1/7)... +(1/2 + 1/4 + 1/6 + 1/8)...
dont focus on the odd series
but tell me if you notice anything about the even series
wheat garden
the denominator increases by 2 per term
flint dew
what's the relation between (1 + 1/2 + 1/3 + 1/4 +1/5) and (1/2 + 1/4 + 1/6 + 1/8 + 1/10)
wheat garden
arent they both reciprocated arithmetic series
wheat garden
divide by 2
flint dew
so its safe to say that 2(1/2 + 1/4 + 1/6...) = 1 + 1/2 + 1/3 + 1/4...
wheat garden
yea
flint dew
if 1/ all of the even integers added is half of the equation then what is the other half?
wheat garden
1/all the odd integers
wheat garden
-1 + 1/2 - 1/3 + 1/4 ...
wait isnt this (-1)^n / n
flint dew
basically
wheat garden
oh then u can use AST so it converges absolutely
oh its because $\abs{\cos(\pi n)}=1$
glossy valveBOT
Jash
wheat garden
for all n
wheat garden
wgat
flint dew
for all n
0 is wrong sorry
for it to be 0 the evens would be growing at a faster rate than the odds but its not
im trying to prove what it converges to lol just realised u only need to prove if it converges
you only need to show that as n goes to infinity 1/n goes to 0 and 1/n as n increases is always decreasing to prove convergence
flint dew
you only need to show that as n goes to infinity 1/n goes to 0 and 1/n as n incr...
this is all you need to do to prove it converges
wheat garden
is it possible that a series can converge absolutely but not conditionalyl
hidden harbor
you only need to show that as n goes to infinity 1/n goes to 0 and 1/n as n incr...
1/n decreasing is not enough to prove convergence. after all, the harmonic series is not convergent
spice orchid
(Leibniz alternating series test)
wheat garden
is there a test that says if $\lim_{n\to\infty}a_n=0$, $a_n>0$ and $\dv[2]{n}a_n<0$ then the sum converges
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Jash
uneven cargo
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uneven cargo
Why is the jacobian matrix between $y^i$ and $x^i$ equal to the identity at O? In the case of the metric tensor being equal to $2I$, wouldn't the Jacobian be $\frac{1}{\sqrt{2}}I$? Is it an assumption that J=I at O?
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emil
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craggy tapir
$\int (sin^8x-cos^8x-4sin^6x)dx$
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$\int (sin^8x-cos^8x-4sin^6x)dx$
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FungusDesu
craggy tapir
the obvious step is to reduce the whole thing, but its such a sisyphean task
is there a more level headed way to approach this?
buoyant pewter
**FungusDesu**
glossy valveBOT
craggy tapir
from here how could i advance?
buoyant pewter
first two parenthesises, can be replaced with cosine of double argu,ment
craggy tapir
first two parenthesises, can be replaced with cosine of double argu,ment
come again?
craggy tapir
yup
buoyant pewter
do it
craggy tapir
im not sure what to do with 4sin^6x here
the left side is all simplified now so thats good
buoyant pewter
i also show you my vesion:
craggy tapir
yup that seems to match with mine
buoyant pewter
yup that seems to match with mine
ok)
craggy tapir
though i prefer simplifying to the max before integrating
buoyant pewter
yvw 🙂
craggy tapir
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sick karma
does there exist a generalized form of taylor series for a function of n variables? For example it is my understanding that the taylor expansion for a function f(x,y) can be expressed as $f(x,y)|{x_0,y_0}=\sum{n=0}^{\infty}\frac{1}{n!}[\sum_{m=0}^{n}\binom{n}{m}\frac{\partial^nf(x_0,y_0)}{\partial x^{n-m}\partial y^m}\cdot (x-x_0)^{n-m}(y-y_0)^m]$ but I'm looking for something that extends to n variables, maybe some generalized matrix form is involved? I'm not entirely sure
glossy valveBOT
Triaxyz
sick karma
interesting; could you elaborate on what each variable represents? Mainly confused on what h, r, and θ represent. This appears to be an expansion for a function of r-variables? But I'm not quite sure
buoyant pewter
interesting; could you elaborate on what each variable represents? Mainly confus...
english is not my native, but let me try to show you important things:
where
is an open set
and
is function r - times differentiable in continuous way
and
sick karma
hm
sick karma
true
can you try maybe showing a slight example for how to apply this to a 3d function f(x,y,z) centered at (x0,y0,z0)?
sick karma
I'm not sure how long it would take but yes
buoyant pewter
I'm not sure how long it would take but yes
some beginnig only, 🙂
buoyant pewter
I'm not sure how long it would take but yes
that is just fwe terms, it is too much for discord, to write more 🙂
hence we use sigma notation
sick karma
I'll try to analyze the pattern and fill out the rest of the terms and check with with if you're okay with that
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sick karma
greater order of derivative, the more of terms, and thier permutations
ahh I'll need some more time to understand this but thank you for providing exactly what I was interested in finding, I appreciate the help
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calm nacelle
ahh I'll need some more time to understand this but thank you for providing exac...
BTW there's a cleaner way to write this if you look up "multi-index notation"
[f(x) = \sum_\alpha \frac1{\alpha!}\left.\frac{\partial f}{\partial \alpha}\right|{x_0}(x-x_0)^\alpha,]
where (x,x_0) are vectors. This notation makes it basically the same as the single-variable Taylor series,
[f(x) = \sum_n \frac1{n!}\left.\frac{\dd f}{\dd x}\right|{x_0}(x-x_0)^n.]
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pale pumice
Someone please tell me what the height of this is
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Someone please tell me what the height of this is
serene hazel
,rccw
glossy valveBOT
serene hazel
hmm
you can find the area of prism using SA=2B+ph formula
@pale pumice can you do that?
serene hazel
have you divided the prism's volume by the base's area yet?
pale pumice
Is the height 25
pale pumice
have you divided the prism's volume by the base's area yet?
I need the height to have the volume
serene hazel
I need the height to have the volume
honestly you could also use pythagorean theorem
$V = \frac{1}{2} \times base \times height \times length$
glossy valveBOT
アキラ (>_<)
serene hazel
do you know how this formula works
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river wave
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river wave
For my answer I got 360 L
I converted grams to lbs
Then divided 10 by lbs / liter which was 2.84 *10^(-3)
And for sig figs do I round to sig figs at end always or for every result
spiral vigil
at the end
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river wave
Is answer correct
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proper rivet
bonjour est-ce que quelqu’un peut m’aider svp ?
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bonjour est-ce que quelqu’un peut m’aider svp ?
worldly egret
Hmmmm
I would use process of elimination
The function is only defined and derivable on [0;13]
So it won't be the answers with +inf
Then it is just a matter of whether it is convex or concave on [0;4]
slate pike
Hi
slate pike
I have the following problem
warm kite
slate pike
There is a mesh of n x n squares, we will call it the board. Each side of each square will be a wall, and each such wall has an independent probability of being open or closed. Two squares forming a room will be called a chamber and each chamber contains a treasure.
Moreover the board is like the snake game, so the edge index is modulo n.
Let $X$ be a random variable denoting number of treasures in a board. Calculate the expected value of $X$, $E(X)$.
glossy valveBOT
szahu420
slate pike
Example: n x n board with 5 treasures
Generally my attampt would be to create a new random variable $T_{xy}$ which is equal to one if the edge under $x,y$ has a treasure but these won't be independant right
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szahu420
slate pike
<@&286206848099549185>
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slate pike
<@&286206848099549185>
cunning vessel
Example: n x n board with 5 treasures
slate pike
That's the same one
slate pike
no, it has to be exactly two
so the picture contains all possible chambers
which is vertical and horizontal
slate pike
<@&286206848099549185>
pulsar thistle
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tardy pine
hi
tardy pine
help me out
it should be 2(n-1) instead of 2n-1 correct? For the penultimate sum
there should be another problem ig
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dim pumice
A triangle ABC is equilateral. Find the angle between the vector 7u+v and 7u+2v if u =AB and v=AC.
dim pumice
I know I am supposed to use the formula u•v = |u| |v| * cos °
But I don’t understand how
open igloo
Right, now note that it's |u|² and |v|², so it's just
49x²+21u•v +2x²
u•v can be found out since we know the angle between u and v
(7u+v)•(7u+2v) can also be found out using
|7u+v| |7u+2v| cosθ(let θ be the angle we have to find between these two vectors)
Now you can equate the above term to
open igloo
This
dim pumice
Okay so I take |7u+v||7u+2v| and do square rot of that?
open igloo
Why the sqrt again?
open igloo
Wait
Just find the |7u+v| and |7u+2v| for now
Coz I'm not quite sure what you mean by taking square root of |7u+v| |7u+2v|
dim pumice
Yes I know but I just calculated |7u+v| and |7u*2v| now
open igloo
$|\vec{a} + \vec{b}| = \sqrt{|\vec{a}|^2 + |\vec{b}|^2 + 2|\vec{a}||\vec{b}| cos\theta}, \theta$ is the angle between them
dim pumice
glossy valveBOT
Lorentz
dim pumice
That’s not the formula I have
open igloo
What do you have then
dim pumice
dim pumice
Okay so what do I do now
open igloo
But then |7u+v| would be sqrt((7u+v).(7u+v))
open igloo
You can combine all terms into a single one within the sqrt actually
Note that in 14uv, it's actually 14(u.v)
And |u|=|v|=x
dim pumice
Okay how do I do that
open igloo
14(u.v)?
What I mean is
49u^2 + 14(u.v) + v^2 = 49u^2 + 14(uv cos60⁰) + v^2
= 49x² +7x² + x²
dim pumice
Oh okay
open igloo
Similarly find |7u+2v|
dim pumice
Okay thank you for the help but I don’t really understand so I think I will continue tomorrow but thank you for the help!
.close
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open igloo
Aight
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indigo stream
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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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
i need to solve this using these
indigo stream
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
2
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indigo stream
so i think i have to use product to sum identity
but i cant since
the sins have a minus beetween them
robust slate
Consider ||multiplying both sides by 2||
robust slate
I meant with the product to sum identities
robust slate
just do it and it becomes obvious
indigo stream
just do it and it becomes obvious
i dont get it
robust slate
well you have smthn of the form sina - sinb
indigo stream
robust slate
which of the identities has something like that
indigo stream
sum to product?
robust slate
out of these 4.
robust slate
sina - sin b
indigo stream
ph the 4th
indigo stream
hmm lemme cook
because E=mc^2
i can do
2cos(x+3x/2)sin(x-3x/2)=0
4x/2 = 2x
and
2x/2
is just -x
x bieng theta
so i end up with 2cos(2x)sin(-x)=0
@robust slate but what now
robust slate
Well when is a product equal to zero?
indigo stream
ahhhh the zero product property
cos(2x)=0
and
sin(-x)=0
now i use the unit circle
but this is the part i know nothing abt
robust slate
Do yk about how cos and sin are represented on the unit circle
indigo stream
yesno
u got a khan academy link?
i think something to do with sin being x axis
and cos is y axis?
maybe ..
robust slate
u got a khan academy link?
indigo stream
oh thanks
ok got it
so do i just subsitute values for theta
like 90 180?
@robust slate
robust slate
For what?
indigo stream
for the solutions
robust slate
,w cos(2x)sin(x)=0
glossy valveBOT
robust slate
There’s more (also, don’t forget periodicity)
halcyon bobcat
Hallo does anyone know what element-wise power mean?
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Hallo does anyone know what element-wise power mean?
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misty
halcyon bobcat
torn jolt
Hallo does anyone know what element-wise power mean?
is this in context of matlab or something lmao
halcyon bobcat
is this in context of matlab or something lmao
nope
wintry cypress
how to find the distance between two straight lines given their equations?
vivid snow
Do you mean the distance between two points?
silk flame
In 3D I assume, and shortest distance if the lines are skew?
broken tide
how to find the distance between two straight lines given their equations?
you mean perpendicular distance between two parallel lines?
wintry cypress
Do you mean the distance between two points?
between a point and a straight line, i know the forumula, i just don’t know how to set the problem
wintry cypress
you mean perpendicular distance between two parallel lines?
yeah
wintry cypress
a point and straight line?
yeah, but i don’t remember how to find the point
wintry cypress
the problem says “hint; you can find it using the distance between a point P and the other line”
i don’t remember how to find the point P
i know the formula tho
broken tide
oh for a point
wintry cypress
the two lines are:
r: x+3y+7=0
s: x+3y+2=0
wintry cypress
this is the forumula i should use
but for x0 and y0 i need a point p from the line
i don’t remember how to find it
broken tide
this is the forumula i should use
that formula is derived from this
if you want to use this formula you can connect the two lines using a perpendicular
wait ill write it out
wintry cypress
the problem is that it says that i should use a point p from one line, but how do i find that random point p? i put a random value on the x and find its value on the y?
broken tide
the problem is that it says that i should use a point p from one line, but how d...
welll you can get the slope
using m1m2 = -1
and you can choose any random point on the line
lets say for instance in eq 1 put y = 0 and you get x = -2
so you can use this point (-2,0)
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broken tide
wintry cypress
tysm
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pine spear
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pine spear
I know that a) The other root is 2+3i because it's its conjugate
upper anvil
I know that a) The other root is 2+3i because it's its conjugate
apply the same for b
pine spear
Yes
But c) is where i'm stuck
Why does it matter that the coefficients are real to imply the other root is conjugate?
pine spear
I think that if I don't know if the coefficients are real, I can have 2+3isqrt3 s a root and something different from 2-3isqrt3 as the other
pine spear
i is certainly a root
A simply counter example like this explains it?
upper anvil
it's just to disprove that the cojugate is a root for a quadratic with nonreal coefficients
it's not meant to "explain" why that is, but an example might clear up some ideas
pine spear
Ok, the general approah of the question that is bugging me.
upper anvil
say one root of the quadratic is 2+3i sqrt 3
pine spear
I understand your explanation and have found other counter examples.
upper anvil
say one root of the quadratic is 2+3i sqrt 3
this means that the quadratic
is in the form of
$a(x-(2+3i\sqrt 3))(x-k)$
and you can see that k can be anything really
pine spear
How did you get this form for the equation?
And a and k are complex or real? Can i know that?
glossy valveBOT
znsn
pine spear
Ah
upper anvil
without more information, that's the only thing we can get
we cannot know what a and k are
upper anvil
no not parametric
tbh idk what the name is
but
the idea is to use the roots of the quadratic
and turn it into a form of constant*(x-root1)(x-root2)
pine spear
Yes, I think I get you. Very helpful. I'm just thinking if I grasped it all
Because I rarely use this alternate form.
upper anvil
parametric is if we have x=f(t), y=g(t), with t in a certain set
pine spear
Only when I factor a polynomial and it's usually (x-r)(x-s) without the a
upper anvil
oh
upper anvil
it depends on the leading coefficient
like if we have x^2+nx+m
then it's going to be like (x-a)(x-b)
but if we have 2x^2+nx+m
it's going to be 2(x-a)(x-b) (im using different a and b from previous example)
pine spear
It makes sense.
But just to clarify.
If I use the discriminant to analyse if the roots will be real or complex
upper anvil
discriminant (not trying to be pedantic, but be careful because you'll have to encounter determinants at a later date)
upper anvil
In the case discriminant <0 the root is complex
yeah
pine spear
If I hae complex coefficients, I can't say uch about the discriminant
Because there can be a combinations of a b and c that make the discriminant, for example real and positive, but the other terms in the root imaginary, making the root complex
upper anvil
using the discriminant may not work well
because
there is no ordering of complex numbers
upper anvil
like we cant truly compare i with 1
(you could prove that theres no good ordering, and issues basically stem from i^2 being -1)
but you dont need that now, just know that you cant compare complex numbers
oh yeah besides equality
pine spear
Thank you very much, you were very helpful.
upper anvil
np
pine spear
.close
clever turret
Bolzano-Weierstrass
Proof:
in the proof I got to the point of obtaining the two sequences Ak,Bk, one strictly increasing and the other strictly decreasing, and I obtained the respective intervals [ak,bk], each containing infinite terms.
What I didn't understand in the demonstration is this:
the interval [a1,b1] contains the terms of the sequence an; therefore the first integer n1 exists, such that an1 ∈ [A1,B1]. For the same reason there exists a first integer n2, among all natural numbers larger than n1, so an2∈[A2,B2]. So as to create n1<n2....<nk...<...
so ank ∈[Ak,Bk] . Since Bk-Ak =(B-A)/2^k . That is, Ak<=ank<=Bk = Ak +(B-A)/2^k
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Bolzano-Weierstrass
Proof:
in the proof I got to the point of obtaining the two...
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clever turret
<@&286206848099549185>
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ebon glen
If you were to use base infinity (ie. every integer has its own symbol) how would you write non-integer numbers?
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mossy robin
aren’t rational/irrational numbers just [integer].[integer]?
it won’t be easy especially irrational numbers though
uncountable amount of numbers to be represented by countable symbols
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dusty scaffold
the obvious thought would be that each number gets its own symbol
numerals like [number][number] or [number].[number] don't mean anything without specifying what it means to multiply by "infinity"
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tidal citrus
yeah no
azure jewel
Also you're allowed to ask about homework anyways
It's just tests you can't
homework you have access to computers anyways, you could just check this in wolframalpha
<@&268886789983436800> spam
floral spear
calm nacelle
It lags sometimes, I just manually deleted
azure jewel
yeah if it's homework, just use something like wolfram alpha to check.
Do the work yourself the first time around, for practice
but there's no point submitting work without knowing it's right
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torn jolt
yeah if it's homework, just use something like wolfram alpha to check.
If wolfram alpha a sort of graphing calculator
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supple jay
Rate of growth of GDP per year is 1%, how much will GDP change relative to its current state in 10 years? Answer: 1.01^10
supple jay
Can someone explain to me this
Why rate of change added to decimal of 1 and ^(number of years)
hot knoll
Consider this situation
You invest $100 with 10% interest every year
This means you get 10% more than what you started with every year
10% growth means that
In addition to the 100% that you started with, you also get 10% more
So overall you have 100% + 10% total after 1 year of growth
hot knoll
Then to calculate the amount after 1 year i would need to multiply
100 * (100% + 10%)
Let's just start with year 1
supple jay
ye
hot knoll
Then to calculate the amount after 1 year i would need to multiply
100 * (100%...
This would be 100*(1+0.1)
As a decimal
This is where the (1 + rate) part of the formula comes from
Does that make sense?
supple jay
aha
hot knoll
In your problem you get 100% + 1% after 1 year
supple jay
so that would amount to 110?
hot knoll
This would be 100*(1+0.1)
For this yes
So that's one year of growth
So tell me how much total money do you have invested now?
supple jay
next year is 121?
hot knoll
Yesss
supple jay
damn
oh so
it just keeps rising
interest applies to the 110 then again
like compounding?
hot knoll
Nice lol
supple jay
ye thanks
hot knoll
Yw hope that clarified
supple jay
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compact salmon
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compact salmon
y'all how did this turn to this
im doing integration but i've always struggled with applying trig identities
idk what they did
is it change (cosx)^2 to 1 - (sinx)^2
idk what to do after or how to expand it so that it turns into the thing below
eager obsidian
y'all how did this turn to this
first use sin(x)cos(x) = (1/2)sin(2x)
then convert sin^2(2x) in terms of cos(4x)
deft tulip
oh shit i never saw that
it's just using the identities for cos^2 1/2t and sin^2 1/2t in terms of t then simplifying i think
compact salmon
it's just using the identities for cos^2 1/2t and sin^2 1/2t in terms of t then...
im doing ib math this was not available in my formula booklet 😭
deft tulip
theres probably a bunch of ways to reach that but yeah the solution just skips steps and doesnt show it i guess
what nebula said should work also
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nova sigil
What have you tried?
barren radish
i dont mind u can help the other guy first
torn jolt
What have you tried?
no idea on how to figure this problem out
torn jolt
no idea on how to figure this problem out
What is the first second fundamental theorem of calculus?
nova sigil
no idea on how to figure this problem out
What's the inverse of differentiation
nova sigil
i dont mind u can help the other guy first
Ah my bad I see
torn jolt
if f is a continuous function and c is any constant, then A(x)=∫xcf(t)dt is the unique antiderivative of f that satisfies A(c)=0.
barren radish
if you derive velocity you get acceleration
if you integrate acceleration you get?
torn jolt
if you integrate acceleration you get?
?
barren radish
lets see
acceleration of is the rate of change of velocity
if you graph it out then what does the area mean
barren radish
im not a good teacher lmao
torn jolt
If you dont know look it up
Its fundamental so you should know
I switched back between first and second like four times. Just look at both of them and you'll figure it out
barren radish
the opposite of a derivative is the antiderivative/integral
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next basalt
Could someone explain what the purpose of the crossing between vectors is?
next basalt
Also a quick summary of the projection formula :(
fair oracle
let’s first discuss, dot products
Given two vectors, a and b
We define $a \cdot b = |a| |b| \cos \theta$
glossy valveBOT
.doc
fair oracle
right?
Intuition is that, given two vectors, a dot product gives the notion of how much one vector lies in the direction of another
The notion is captured more in the projection
Notice, the projection of vector a on to b is |a| cos theta ( this can do found using basic trig)
fair oracle
We define $a \cdot b = |a| |b| \cos \theta$
ie from this definition, dividing both sides by |b| gives us the projection
to get more feel, if two vectors have zero angle between them then cos(0)=1, ie the projection is |a| itself, if they are perpendicular, no projection at all
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viscid haven
the area of a courtyard is 3750 msq . find the cost of covering it with gravel to a height of 1 cm if the gravel costs rs 6.40 per cubic meter ?
deft tulip
what's giving you trouble?
deft tulip
well you are given the cost per some unit of volume, so start out by finding the volume of the gravel to be used
viscid haven
area is given we only have to multiply it with 0.1 m ?
upper skiff
deft tulip
you have area in cm^2 so start out by just working in cm, multiply by 1
we can convert cm^3 to m^3 afterwards
deft tulip
oh so A = 3750m^2? ok then convert height of 1cm to m units, what would that be?
viscid haven
375
deft tulip
1 cm = ? m
viscid haven
0.01
deft tulip
yes
so your height is 0.01 cm
so area x height = 37.5 yes?
(3750 m^2) (0.01 m) = 37.5 m^3
viscid haven
yes
deft tulip
what next?
viscid haven
multiply it with 6.40 ?
deft tulip
yes
viscid haven
240
deft tulip
and what are the units on that?
viscid haven
for what ?
deft tulip
for 240
viscid haven
rs
deft tulip
yes, so that's it
deft tulip
!done
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viscid haven
.close
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distant grove
why are they not both false
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why are they not both false
distant grove
for the first one i gave counterexample with A matrix [-2,1] and B with [2,-1] on the diagonals
and then it gives a zero matrix
distant grove
zero matrix is diagonal?
wise wyvern
zero matrix is a lot of things lol, diagonal being one of them.
vast fossil
Being diagonal only requires every entry that's not on the diagonal to be zero
distant grove
oh, okay
vast fossil
That does not imply every entry on the diagonal to be nonzero for diagonal matrices
distant grove
but then the second statement is false regardless, isn't it?
wise wyvern
It is.
nimble crane
but then the second statement is false regardless, isn't it?
correct
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chrome cedar
Hi I need to solve the following integral: Ci = \delta M / Q
chrome cedar
I believe the result should look like a heavisde, I'm just not sure how to obtain it
the result for cf will be Ci if 0 <= x <= vij*t
and 0 if x its outside those bounds
right?
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torn jolt
yo guys
torn jolt
hella simple question
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hella simple question
torn jolt
i just forgot need someone to remind me
how do i integrate xsinx for example
cuz i know its not just x2/2 * -cosx theres more to it
like u substitution
if anyone can help remind me pls @ me
spice orchid
you need to integrate by parts
torn jolt
you need to integrate by parts
i never did it that way isnt there another way
spice orchid
not anything that is easier no