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#help-19
mellow axle
vast aurora
My discrete math teacher mentioned gaussian elimination as like the way to solve systems of equations using matricies, how do you do that?
sharp oak
If you haven't seen it before at all, check out a YouTube video first imo. It's a very visual process
vast aurora
Kk
sharp oak
If you have any questions after that, feel free to ask
vast aurora
Will do
worn stump
$\begin{aligned} \lim _{n \rightarrow \infty} P\left(B_n\right) & \leq \lim _{n \rightarrow \infty} n\left(1-p_n\right)^{n-1} \ & =\lim _{n \rightarrow \infty} n\left[1-(1+\epsilon) \frac{\ln n}{n}\right]^{n-1} \ & =\lim _{n \rightarrow \infty} n\left[1-\frac{1+\epsilon}{\frac{n}{\ln n}}\right]^{n-1} \ & =\lim _{n \rightarrow \infty} n\left(\left[1-\frac{1+\epsilon}{\frac{n}{\ln n}}\right]^{\frac{n}{\ln n}}\right)^{\frac{(n-1) \ln n}{n}} \ & =\lim _{n \rightarrow \infty} n e^{-(1+\epsilon) \ln n} \ & =\lim _{n \rightarrow \infty} \frac{1}{n^\epsilon} \ & =0 .\end{aligned}$
anybody can help me this out? from the forth line
clever fjordBOT
Edison Lee
quasi sparrow
$\begin{aligned} \lim _{n \rightarrow \infty} P\left(B_n\right) & \leq \lim _{n ...
!occupied
odd edgeBOT
$\begin{aligned} \lim _{n \rightarrow \infty} P\left(B_n\right) & \leq \lim _{n ...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@vast aurora Has your question been resolved?
vast aurora
Yes
graceful willow
odd edgeBOT
graceful willow
Need help with this question
rose radish
odd edgeBOT
@graceful willow Has your question been resolved?
silent talon
Determine the canonical and expanded form of each of the functions f , g, h and p associated with the parabolas shown below.
Can anyone tell me if the G one is correct ? ( green parabola )
ember oak
Looks good
But your final result is not canonical form.
Canonical form is a(x-h)^2+k
silent talon
The first one framed isn’t ?
crude orbit
<@&286206848099549185>
odd edgeBOT
<@&286206848099549185>
long tinsel
drifting valley
no
a quadratic that is non zero can have at most two distinct real roots
if it has more than that, the whole quadratic is always zero
ie each of the coeff will be 0
drifting valley
yes
drifting valley
,rotate
clever fjordBOT
drifting valley
yes
crude orbit
thats all ?
drifting valley
yes
torpid ginkgo
Basic question here, but my prof is stating that double integrals can give areas or volumes
torpid ginkgo
This makes no goddamn sense
I thought a single integral gave us the area
Outside of a rotation or something
nocturne belfry
I thought a single integral gave us the area
you can use double integrals to get area
wooden python
integrals generally are an accumulation of tiny changes
nocturne belfry
consider like $\int_0^1 \int _0^1 \dd y \dd x$
clever fjordBOT
jan Niku
wooden python
Basic question here, but my prof is stating that double integrals can give areas...
a double integral of a function of two variables can be interpreted as the volume under its graph
in the same spirit as a single integral gives an area under the graph of a singlevar function
torpid ginkgo
Oh okay I see so a function of two variables is basically the 3rd dimension. ?
south plume
Oh okay I see so a function of two variables is basically the 3rd dimension. ?
essentially, yeah
torpid ginkgo
But if there is no function of two variables it’s an are
So I can just say Z = f(x,y) and call Z my “height”
nocturne belfry
But if there is no function of two variables it’s an are
hope this isnt confusing but i think you can interpret this case as z(x,y)=1
no interesting contribution from the height component
wooden python
Oh okay I see so a function of two variables is basically the 3rd dimension. ?
kind of meh but yes
btw we have a she/her pronoun role
boreal hamlet
(\lim_{{x \to \infty}} f'(x) = 0);
(f'(x) = f'(-x));
(f(a) > f(b)) for all (a > b);
(\lim_{{x \to 0}} f'(x) = k)
f(x) is defined and non-imaginary for all real x, k is a finite number
clever fjordBOT
padfoot9445
boreal hamlet
what is f(x)?
odd edgeBOT
what is f(x)?
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
does 1 mean it goes steep in the middle and shallow on the outside?
and 3 means it's always increasing, right?
south plume
they essentially mean that the function is increasing but at a decreasing rate
boreal hamlet
log?
south plume
not defined for non-positive
boreal hamlet
oh yeah
south plume
i have to be honest, i have not solved this yet but i just have some ideas
south plume
f(x) is defined
south plume
because I made this up myself
Oh.
boreal hamlet
it should look like a s shape when we're done
and I'm certain I read about this before
but I can't find it at all
south plume
**padfoot9445**
you can also make this whole problem purely about the derivatives of functions, condition 3 implies that f'(x)>=0 for all x
south plume
and I'm certain I read about this before
integral of $e^{-x^2}$
clever fjordBOT
artemetra
south plume
,w integral of e^(-x^2)
clever fjordBOT
south plume
yeah its erf but it satisfies all of your conditions
odd edgeBOT
boreal hamlet
also, sigmoid function
wha does erf mean?
odd edgeBOT
Available help channel!
bold scroll
Hi!
Got a question that I know the answer to but need to know if theres a "correct way to calculate it.
So the question is:
During a few years, a colony of birds were reduced from 10 000 to 6000 which is on average a 4% decrease per year. How many years did it take for the colony to go from 10 000 to 6000?
I know the answer is around 12 years but I suspect that the way I found out the answer is wrong(did 10 000 * 96 = 9600 * 0.96 etc untill I was at 6127).
Is there any other way to do this where I dont have to do *0.96 12 times to get the answer?
cosmic hearth
Your intuition for solving the problem is right; generally, we're solving
[ 10000 \cdot (0.96)^n = 6000 ]
clever fjordBOT
@cosmic hearth
cosmic hearth
The way I would probably solve this is with logarithms; are you familiar with those?
@bold scroll ^
bold scroll
Hmm.. not really. But I found a chapter in my math book for it and I can see that it says logarithms among other things at the top of the homework paper
I just didnt know that it included this stuff haha.
signal yacht
cosmic hearth
Basically, yeah
bold scroll
So thank you! No need for further help. Will go throigh the chapter.
cosmic hearth
The main form of the logarithm is:
[ a^b = c \iff \log_a c = b ]
We'll probably also want to keep in mind the following rule:
[ \log_a b = \frac{\log_c b}{\log_c a} \text{ for all $a$, $b$, $c$ } ]
clever fjordBOT
@cosmic hearth
cosmic hearth
(the rule is mostly helpful for putting it into the calculator, moreso than actually solving the problem)
odd edgeBOT
@bold scroll Has your question been resolved?
bold scroll
Yes
weary tusk
Anyone knows how to find the area of a triangle by knowing it's points coordinates
wooden python
there are at least two ways
no wait, at least three
one is (relatively) low-tech but very very painful
the second is a little higher tech and moderately painful
and the third is almost painless but is very sophisticated conceptually
they are, in that order:
- compute all side lengths then apply heron's formula
- compute all side lengths, then one angle via cosine law, then find its sine and use the S = 1/2 ab sin(C) formula
- compute vectors representing two of the sides, package them into a matrix, and take half the absolute value of its determinant (works only in 2D)
weary tusk
@wooden python The problem is:
the point A(x,y) moves on the curve $ y=x^3+x $ such that $\frac {dy} {dt}$ = 2 units/s find the rate of change in the area of the triangle ABO such that O is the origin and B(0,6) at the moment that the x coordinate of the moving point is 3
clever fjordBOT
Hamdy Hisham
wooden python
dy/dt = 2 units/s?
weary tusk
**Hamdy Hisham**
Thats the final thing sorry
wooden python
this is kind of hairy
probably
it can be done but it's a bit unpleasant
can i see a pic of the original?
wooden python
the notation will be the same i am pretty sure
weary tusk
the notation will be the same i am pretty sure
Are you sure you want to see this?
wooden python
general policy is you should post originals when people ask even if it's not in english.
yes
wooden python
ok so then this is dy/dt is it
ok yeah alright
so this triangle of yours has a vertical side
(0,0) to (0,6)
whose length is obviously just 6
weary tusk
yup
wooden python
and the height, perpendicular to it, is just x
so your goal will be to find dx/dt here
it is easy from there
wooden python
wdym
you know the half base times height formula for the area of a triangle, right?
weary tusk
Yes but how the height is x
wooden python
there's nothing that stops you from considering the vertical side as the base
then the height will be horizontal
the triangle is kind of sideways but that does not really matter
wooden python
drop a perpendicular from the variable point onto the y axis.
wooden python
yes
weary tusk
Aha
wooden python
and it is equal to the x coordinate of that moving point
odd edgeBOT
@weary tusk Has your question been resolved?
robust moat
Why are the bounds different from the original function, and why is the integral a constant over regions undefined in the original function?
hasty escarp
it is a constant because the func is pres to be 0 for $x<1$
clever fjordBOT
FluffyFlareon
robust moat
is that conventional?
hasty escarp
if it isn't explicitly stated that the func has no val on those int / b
then it can be ass to be 0
at least I'd think
hasty escarp
OH it's so dumb x>2 is moved to seemingl wrong row. I'm not sure rn
first row x<1 makes sense to me as C
robust moat
well yes under the assumption that its constant where undefined, but also why is it $x \leq 1$
clever fjordBOT
Jason 지환
hasty escarp
except w is it $x<=1$?
clever fjordBOT
FluffyFlareon
robust moat
bahaha alright 😭
robust moat
whats that?
hasty escarp
website ?
robust moat
oh, wolfram alpha
hasty escarp
ok
robust moat
<@&286206848099549185>
odd edgeBOT
@robust moat Has your question been resolved?
robust moat
.close
pliant crest
for point normal eqn of plane or eqn of a plane standard version, why do i need the norm and a points (x,y,z) passing through it? can someone explain why these are needed
shy moth
Write out the standard eqn of a plane
mortal trench
To understand the plane equation you must understand the dot product
shy moth
Pretty much
pliant crest
can u explain the connection
mortal trench
If we have two vectors, (a,b,c) and (x,y,z), and we dot them, and set that equal to 0, we get the set of all vectors x,y,z perpendicular to a,b,c
This explains:
ax+by+cz = 0
Now to shift this, all you need to do is change the value of k
Where
ax+by+cz = k
zenith jasper
if you’re asking why a normal vector and a point defines a plane, it’s because a normal vector is normal to an infinite number of planes (along the axis of the normal vector) and a point will narrow them down to one
shy moth
I think hes more on about how we got the equations
odd edgeBOT
@pliant crest Has your question been resolved?
stiff yarrow
Did I do this correctly?
odd edgeBOT
Did I do this correctly?
stiff yarrow
.close
buoyant solstice
odd edgeBOT
buoyant solstice
apparently H is not a normal subgroup of G, but how is that determined?
drifting valley
I think you're wrong, D4 looks like a normal subgroup of S4
if you want to prove that a subgroup is not normal, either you prove it's not a subgroup or it's not normal, by contradiction with the def of normal
like you find a counterexample of a ghg^-1 which is not in H
but in general, it's way easier to try to prove it's a normal subgroup first
because if it is there are a lot of results you can use to prove it and you can construct the table at the same time
while finding a counterexample is straight up impossible if you're wrong and the subgroup is normal
if I remember correctly my algebra exercises, S4 is the only Sn with n >= 3 such that it has not only An as a normal subgroup, but D4 too so you should check that
odd edgeBOT
@buoyant solstice Has your question been resolved?
buoyant solstice
.close
proud bison
Need help understanding how to find a value of an inverse of a trig equation
The graph of f(x) = cos(3x) + 4x − 2 is strictly increasing with no horizontal tangent lines.
Is f(x) invertible? If so, find f^-1(-1)
I know f(x) is one to one, so its invertable, Im having trouble with the second part where I find f^-1(-1), feel like i tried everything lol
odd edgeBOT
Need help understanding how to find a value of an inverse of a trig equation
Th...
@proud bison Has your question been resolved?
proud bison
Need help understanding how to find a value of an inverse of a trig equation
Th...
<@&286206848099549185>
heres the question in an image
drifting valley
either you sketch in your mind, or you guess, and you use that it's strictly increasing
like you can calc f(0), if it's > -1, put something less than 0 in f
and vice versa
since they give you a function with a cos, which is a pain to invert
you can reasonably guess that's the value they ask you to find is easy to guess
proud bison
I think they want us to solve it algebraically, but then idk how to, doing it mentally i know its 0
drifting valley
cos(3x)+4x-2 = -1
so cos(3x)+4x = 1
and you can't solve it algebraically
you can only notice that x = 0 is a sol
and since the function is invertible, the sol is unique, that's f^-1(1)
and if 0 was wrong, then as I said, you take bigger than 0 or smaller
using that your function is increasing
while it's not possible to solve it algebraically, it's possible to study that with a bit more details once you'll have calculus
also you can notice obvious thing like a solution can't be < 0, nor can be > 1
but it still doesn't solve the equation algebraically because when you have cos(3x)+4x = 1 you're stuck
that's why they made the sol obv to guess
odd edgeBOT
Available help channel!
marsh sparrow
odd edgeBOT
marsh sparrow
why does the derivative not exist, if we used the power rule on the function when x = 0 then shouldnt the 0 stay as a 0?
nimble blaze
but you don't have a power function here
nimble blaze
xsin(x/9)
isn't a power function
marsh sparrow
o
so it cant have any trig functions but has to have a variable for it to be a power function
nimble blaze
you have a product of x and sin(x/9)
product rule would be applicable
and then you'll get expressions of derivatives of power functions from that
marsh sparrow
you have a product of x and sin(x/9)
product rule would be applicable
and then y...
so the product of xsin(x/9) is a powerfunction but not xsin(x/9) itself?
nimble blaze
no
marsh sparrow
aw man im briandead
nimble blaze
power function
constant * variable^(some power)
buoyant maple
hey how you doing
odd edgeBOT
hey how you doing
buoyant maple
i have a fast question
how did he get
2pie 0
1 r = 0
i was abscent i just want to make sure
does he give this to us
or did he find it himself
drifting valley
he switches to polar coordinates
buoyant maple
but how did he know its 2pie
drifting valley
because you're integrating for the full turn around, he's integrating for theta = 0 to theta = 2pi
it's the whole circle
drifting valley
you have to find it but it's direct once you understand the drawing
these bounds tells you y goes from -sqrt(1-x²) to sqrt(1-x²) with x from -1 to 1
it exactly draws the circle
so when you switch to polar coordinates, your bounds have to cover exactly the whole circle too
drifting valley
r is the radius
he's integrating over the inside of the circle too, he's integrating on the whole disc of radius 1
so r has to vary from 0 to 1
buoyant maple
ok i see
do you have a video i can watch
so i can have a better understanding
because im just having issues setting it up
drifting valley
I don't know videos about it but maybe some people here do, or by looking polar coordinates double integrals you may find some
buoyant maple
can i ask you another one
this question
i know i should do e ^ r^2
ooooh never mind
i figure it out
@drifting valley thank you very much now i understand it
for this r will be
r^2 = 5
so square root of 5
and second one will be 3
and second quardent will be pie and pie/2
is that right ?
buoyant maple
yea that becomes r = 3
civic hound
@buoyant maple remeber put .close
buoyant maple
.close
odd edgeBOT
buoyant maple
<@445557486062272514> remeber put .close
My fault first time hearing about it
odd edgeBOT
Available help channel!
pale bramble
help
mellow gust
odd edgeBOT
@pale bramble Has your question been resolved?
odd edgeBOT
@pale bramble Has your question been resolved?
stuck rock
How do I apply the chain rule to 1000e^(0.3t)
odd edgeBOT
How do I apply the chain rule to 1000e^(0.3t)
stuck rock
For some reason when this textbook teaches me
it goes ok next we apply the chain rule to get
and then just skips to the answer
tropic copper
are you integrating or differenciating
stuck rock
differentiation
stuck rock
e^0.3t and then the prime of 0.3t which is 0.3
clever fjordBOT
Bettim
tropic copper
ah this
stuck rock
Ah I see what happened
I think I got it now
When you do e^(x)*g'(x) its like the chain rule basically
so then that would be 0.3 x 1000 which is 300
300e^0.3t
Okay so I am curious about removing the 1000 though
When can I do that
fringe bough
When can I do that
You can do that whenever you have a constant multiplied by your function
$\frac{d}{dx} \ cf(x) = cf'(x)$ for any constant $c$
clever fjordBOT
tatpoj
fringe bough
np 👍
stuck rock
.close
robust inlet
Why do they do x <=3 not just x = 3
Your finding the largest value of r so why would u need to find the probability that it is 0 1 2 and 3 not just 3
<@&286206848099549185>
odd edgeBOT
Available help channel!
cerulean obsidian
How to do b i do t get it
odd edgeBOT
How to do b i do t get it
cerulean obsidian
Dont'
tardy lagoon
,rotate
clever fjordBOT
tardy lagoon
combine the fractions and do the same thing in part a
odd edgeBOT
@cerulean obsidian Has your question been resolved?
wooden python
@cerulean obsidian do you know how to add fractions with real numbers?
odd edgeBOT
odd edgeBOT
Available help channel!
pine osprey
help
pine osprey
<@&286206848099549185>
pine osprey
.close
pine osprey
Anyone please?
odd edgeBOT
Anyone please?
tardy lagoon
find the maximum by letting f'(x)=0
pine osprey
.close
odd edgeBOT
jaunty summit
.close
i need help with this one
i got the equation that 0=a(x-3)^2+4.2
but can't find a or x
odd edgeBOT
Available help channel!
stray blaze
Hi there
stray blaze
Can anyone give me a general expression when an tan ( pie*x/2) will go undefined
low locust
$\pi$ is just called pi
clever fjordBOT
Denascite
odd edgeBOT
@stray blaze Has your question been resolved?
charred barn
odd edgeBOT
abstract locust
i can help with that
charred barn
using synthetic division
abstract locust
im literally right past that stage in my own work
wait can't you just make it a fraction
charred barn
its our lesson
abstract locust
ok listne
charred barn
mmm how did it become a-4
abstract locust
$2a^2 - 5a - 12 has to be OVER 2a + 3$
charred barn
man our teacher didn't taught us the other rules
clever fjordBOT
GMDennis
abstract locust
man our teacher didn't taught us the other rules
what grade are you in
charred barn
10
abstract locust
same
anyway
listen
so
idk how to draw it correctly but ill send you a pic holdup
charred barn
okii
charred barn
but our lesson is about synthetic division
abstract locust
nah but like wtf is synthetic division lmao
charred barn
lmfao 😭
abstract locust
click on the image
on the left side
it's a GIF which should demonstrate how you ought to do it
charred barn
okie
abstract locust
ight peace out
worldly robin
Oye
odd edgeBOT
@charred barn Has your question been resolved?
sand pier
M confused on how to find the cartesian limits
odd edgeBOT
M confused on how to find the cartesian limits
@sand pier Has your question been resolved?
lucid schooner
Yooo
sand pier
M confused on how to find the cartesian limits
<@&286206848099549185> just tell the limits are 0 to a for both or m i wrong somewhere
Pleasee
.-.
What's the problem I can't understand 2nd time my ques has remained unanswered...
odd edgeBOT
@sand pier Has your question been resolved?
odd edgeBOT
@sand pier Has your question been resolved?
vague torrent
.close
scarlet junco
odd edgeBOT
@sand pier Has your question been resolved?
mystic saffron
odd edgeBOT
zenith tartan
which one?
mystic saffron
Two and three
zenith tartan
do you know the expansion of $(a-b)^2$?
clever fjordBOT
!Yajat!
mystic saffron
No
zenith tartan
$(a-b)^2=a^2+b^2-2ab$
clever fjordBOT
!Yajat!
zenith tartan
use this to solve for the third one
noble ether
How Can We Factor The Sum Of Two Squares?
odd edgeBOT
How Can We Factor The Sum Of Two Squares?
zenith tartan
provide any question to work with
noble ether
Like, How To Factor (a^2+b^2) as a product?
low locust
you mean like we can factor a^2-b^2=(a+b)(a-b) ?
there is no similar formula for a^2+b^2
noble ether
Nah, The Sum Of Two Squares
mint mirage
Like, How To Factor (a^2+b^2) as a product?
a^2 + b^2 is not factorable under real numbers
You can factor it using complex numbers
noble ether
You can factor it using complex numbers
product of a complex number and its conjugate, right?
noble ether
a^2 + b^2 is not factorable under real numbers
But I’m talking about real numbers
mint mirage
And as mentioned, it's not factorable under reals
noble ether
And as mentioned, it's not factorable under reals
What about (a+b-sqrt(2ab))(a+b+sqrt(2ab))?
mint mirage
You added an extra -2ab, that expression expands to a^2 + b^2 - 2ab
noble ether
What? It would be (a+b)^2-(sqrt(2ab))^2 which is equal to a^2+b^2?
mint mirage
You specifcally asked a^2 + b^2
mint mirage
What? It would be (a+b)^2-(sqrt(2ab))^2 which is equal to a^2+b^2?
No
,w expand (a+b)^2-(sqrt(2ab))^2
Weird, website said this
noble ether
(a+b)^2 = a^2+b^2+2ab, (a+b)^2 -2ab = a^2 + b^2
mint mirage
If you want to go it that way you can, but requires more effort, if you wanted something easy like a^2 - b^2 = (a + b)(a - b) formula, then factoring a^2 + b^2 won't result into something that simple
noble ether
If you want to go it that way you can, but requires more effort, if you wanted s...
It would be (a-bi)(a+bi)?
mint mirage
Yes
full rock
I really need help with this
I just cant
odd edgeBOT
I really need help with this
I just cant
full rock
I wrote almost two pages but it got messed up both times
zenith tartan
,w 3(\sqrt{a-19}) + 4(\sqrt{b-17}) = \frac{1}{2}(a+b-11)
clever fjordBOT
full rock
,w 3(\sqrt{a-19}) + 4(\sqrt{b-17}) = \frac{1}{2}(a+b-11)
I would like the solution, I know the answer
zenith tartan
S=-b/a?
full rock
S=-b/a?
Nothing
The sum of the roots of a quadratic equation
I don't think it would work
full rock
I don't think it would work
In this particular question
zenith tartan
just take power 2 both the side, 2 times
why dont just do this?
full rock
why dont just do this?
It's not as simple as it looks
zenith tartan
what have you done, could you show me your solution
zenith tartan
It's not as simple as it looks
ik
full rock
I really need help with this
I just cant
<@&286206848099549185>
cunning peak
did you square both sides?
full rock
The digits are Arabic
I tried it here
cunning peak
I really need help with this
I just cant
I'm really dumb at this kinda exercise but what I would recommend is using 19 and 17. anytime you have x and x+2, their product plus 1 is a square number
cunning peak
idk 17*19=18²-1
full rock
Oh
cunning peak
I'm going to try here
yeah squaring both sides is a bad idea I'm sorry
I'm trying by calling sqrt(a-19) = x and sqrt(b-17) = y
full rock
yeah squaring both sides is a bad idea I'm sorry
Yeah
full rock
k
cunning peak
I'm trying by calling sqrt(a-19) = x and sqrt(b-17) = y
this is the idea
I'm going to screenshot
After that you have to complete the squares of x and y
adding terms to both sides of the equation
doing that, it cancels 25/2, so all you have left is a sum of squares
and that sum is equal to 0
that means both terms NEED to be 0, since x²>=0, for all real x
full rock
Ok I did something different after this
cunning peak
full rock
Firstly I multiplied it by 2 to remove the fraction (nothing special)
Then I did:
x² - 6x = -y² + 8y -25
full rock
Firstly I multiplied it by 2 to remove the fraction (nothing special)
Then I di...
I completed the squares
cunning peak
full rock
x² - 6x + 9 = -(y² - 8y + 16)
(x-3)² = -(y-4)²
x = 3 and y = 4
And then just put in the numbers
full rock
Bro thank you
cunning peak
you're welcome
full rock
.close
odd edgeBOT
cunning peak
(x-3)² = -(y-4)²
this is not a bad idea
full rock
this is not a bad idea
It's really simple
odd edgeBOT
Available help channel!
cunning peak
made my brain thing I'm good at algebra (I'm not)
odd edgeBOT
made my brain thing I'm good at algebra (I'm not)
@cunning peak Has your question been resolved?
Available help channel!
golden orbit
im again not sure of my understanding of discrete functions
golden orbit
does the codomain of a discrete function have to be countable?
is $f:\mathbb{Z} \to \mathbb{C}$ discrete even though C is not countable?
clever fjordBOT
metnal
golden orbit
or does the codomain not matter here as long as the range of the function is countable?
where the range is a subset of the codomain is the actual set of outputs for the domain of the function
low locust
only the range matters
you can always make the codomain bigger without really changing the function
crisp wadi
And the range will be countable given that the domain is countable
golden orbit
And the range will be countable given that the domain is countable
right cuz its a function
got it, tysm
.close
gilded lodge
how would i do this question?
odd edgeBOT
how would i do this question?
gilded lodge
glass wedge
zenith tartan
<@&268886789983436800>
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
viscid flint
however you yeah that
viscid flint
let's say Liam has a chance of x to win a given game
then can you find an expression for the chance of him to win at least one game, in terms of x?
sleek falcon
im unsure if im doing, this question correct, could i show my approach?
sleek falcon
odd edgeBOT
@sleek falcon Has your question been resolved?
cedar elm
odd edgeBOT
cedar elm
based on the drawn graph are these points correct?
odd edgeBOT
@cedar elm Has your question been resolved?
odd edgeBOT
@cedar elm Has your question been resolved?
clever fjordBOT
orchid torrent
All four are wrong - do you know the definitions of the terms in the questions?
cedar elm
@orchid torrentthe graph is exactly the way the problem was presented
odd edgeBOT
@cedar elm Has your question been resolved?
odd edgeBOT
@cedar elm Has your question been resolved?
worthy peak
wouldn't this be setting the first derivative to 0?
I got 500/e^5t for my derivative, but i can't solve for 0
slow light
wouldn't this be setting the first derivative to 0?
I got 500/e^5t for my deriv...
Plugging t=0 i to the first derivative
You want the rate at t=0, not the t at which the derivative is 0
worthy peak
oh shoot
keen plover
Hi is this correct?
odd edgeBOT
Hi is this correct?
keen plover
And need guidance on how to answer number 4
fair prism
And need guidance on how to answer number 4
AxB={(x,y) | x in A and y in B}
keen plover
AxB={(x,y) | x in A and y in B}
this doesn't make sense to me yet. can you please translate it into english
fair prism
Find all combinations of (a,b) where a is in A and b is in B
For example (0,2) would be one of them
fair prism
That is the relation
If you plug x and y from an ordered pair (x,y) into that and get an integer, then it is part of the relation (the ordered pair is in the set)
fair prism
Seems like a big step up from the first problem lol
mystic saffron
Can I get some help for 48 please
odd edgeBOT
Can I get some help for 48 please
simple epoch
Is there a specific thing you’re confused about? It looks like you got it (although the last part looks it should be converges for p>=1)
mystic saffron
Is there a specific thing you’re confused about? It looks like you got it (altho...
If p=1, it diverges?
I’m redoing the whole thing right now
Feel like this makes more sense?
@simple epoch
simple epoch
Oh wait yeah I’m dumb
mystic saffron
Tried to make it as clear as possible
simple epoch
Working through it now, your work looks correct to me
mystic saffron
Working through it now, your work looks correct to me
All good right
I feel like separating different cases for p is easier
simple epoch
Alright I worked through it and got what you got so you should be good. Your reasoning looks sound and I don’t see any errors
mystic saffron
Appreciate it
Was wondering if you could help me with one improper integral
@simple epoch
simple epoch
Sure
mystic saffron
My integral of choice doesn’t help me at all
Is there something better
That I can use
simple epoch
Make sure you wrote that problem down correctly lmao that’s an ugly integral
mystic saffron
Make sure you wrote that problem down correctly lmao that’s an ugly integral
They want me to compare it to another improper integral
Which makes sense I guess
mystic saffron
Is (the integral of) x^3/x^5 convergent or divergent?
Divergent
Wait
Hold on
Convergent
simple epoch
Your first guess was right it’s convergent
simple epoch
Is that always less than or greater than your main integral
mystic saffron
Let me do this
simple epoch
You got it
earnest raft
its convergent
mystic saffron
You got it
simple epoch
LGTM
rose harness
How do I find out angle C? Circle theorem maths
odd edgeBOT
How do I find out angle C? Circle theorem maths
swift rock
How do I find out angle C? Circle theorem maths
to find angle c cant u just do this ?
sum of angles in a triangle = 180
odd edgeBOT
@rose harness Has your question been resolved?
mystic saffron
odd edgeBOT
mystic saffron
is it 0.55?
clever fjordBOT
Result:
26.708225867668
i already answered that one can you help me with this one?
<@&286206848099549185>
odd edgeBOT
@mystic saffron Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
distant spoke
How to solve this question? (i forgot 😦 )
odd edgeBOT
How to solve this question? (i forgot 😦 )
clever fjordBOT
distant spoke
I know, but i cant simplify the sqrt after simplify the Numerator
mystic saffron
what do you mean? can you elaborate?
clever fjordBOT
mystic saffron
that's actually all you need tbh
like try to plug in the value the limit approaches
you will get something that is 1/0
that is undefined and not indeterminate
which implies...
odd edgeBOT
odd edgeBOT
Available help channel!
blissful nimbus
hi, just a quick q _ what does the A represent here. is there a specific mathematical term
regal moss
odd edgeBOT
regal moss
How do I do parts e and f
odd edgeBOT
@regal moss Has your question been resolved?
odd edgeBOT
@regal moss Has your question been resolved?
eager void
How do I do this improper integral?
odd edgeBOT
How do I do this improper integral?
eager void
I know the limit part, but dont know how to actually do the integral
drifting valley
your fraction is just sin(4x)(1-cos(4x))^-1/5, they write it as a fraction just to make it complicated
eager void
yeh
drifting valley
look how (1-cos(4x))' = 4sin(4x)
eager void
substituion?
drifting valley
yes, it's a way to do it
drifting valley
take u = 1-cos(4x)
eager void
yep
but why is this improper integral?
because I get the integral is 5/ 16 * (1-cos(4x))^4/5
is it becuase you cant take sqrt(0)
so we have to do the limit
drifting valley
because at x = 0 the function is not defined since the denom cancels, however, the function still has a finite limit at 0, which lets the integral to converge
eager void
because at x = 0 the function is not defined since the denom cancels, however, t...
what u mean it cancels out?
drifting valley
I mean denom = 0
drifting valley
at x = 0, 1-cos(4x) = 0
eager void
yes
drifting valley
but you can't divide by 0
odd edgeBOT
odd edgeBOT
Available help channel!
gritty orchid
i really need help
odd edgeBOT
i really need help
zenith edge
!status
odd edgeBOT
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
Okay, how familiar are you with quadratic functions?
cold viper
An example of a quadratic function is anything that goes up and down
gritty orchid
i have to write it my paper
i really have no idea how to do this
and im sleepy as heck
cold viper
Example: a ball if you forget about friction qnd air resistance
gritty orchid
mhm but how do write it in the 2nd box and etc etc?
zenith edge
We're not gonna be able to just do the task for you so we'll need you to work with us a bit here. Have you worked with quadratic functions at all? Do you know how they look and how to calculate important values like intercepts and top/bottom points?
gritty orchid
no 0%
zenith edge
Alright
zenith edge
A quadratic function is a function on the form $f(x) = cx^2 + bx + a$, or $ax^2 + bx +c$, this often varies from country to country which way you write it
clever fjordBOT
Joachim
zenith edge
,w plot x^2 + 4x + 4
clever fjordBOT
zenith edge
They tend to look like something like this
gritty orchid
i see i see
zenith edge
,w plot -x^2 + 10
clever fjordBOT
zenith edge
or this
See how the sign of that first x^2 decides if the graph is "smiling", positive x^2 = smiling graph
gritty orchid
yes yes
zenith edge
A real world example like animelover mentioned is throwing a ball into the air
gritty orchid
how do i write a table that represents quadratic function?
zenith edge
Now we can either graph the ball travelling in the x and y direction, or just think about the y direction(height) and say the x direction is time
The table for the qudratic equation could include stuff like starting position, top position, when it hits the ground etc
gritty orchid
i see i see
zenith edge
You should probably watch a video or two on the subject though to be able to do all the required tasks here
You should also probably solve these in the order 1 - 4 - 2 - 3
Decide what you want the graph to represent, then figure out an equation for it, then calculate important values, then use those values to draw it
cold viper
I just did a quick Google search. There are so many real life examples. U just have to chose one
gritty orchid
oh okay i see i see
thank you so much guys
but im really struggling to do all these im really sleepy lol
i have to submit it by tom
zenith edge
Watch this video series, everything by Khan Academy is very good in general
The videos are pretty short and informative
gritty orchid
THANK YOUUUUUU
zenith edge
Happy to help
You might want to .close this channel in the meantime, but feel free to open a new one and ask for help later if you're struggling with particular points in the task
odd edgeBOT
@gritty orchid Has your question been resolved?
gritty orchid
how to i make table value for y=x^28x+7?
lone zinc
Can someone explain 7 a) i dont understand the solution at all
lone zinc
what does Z x Z mean? Ik Z represents integers but why is it multiplying integers by integers
latent scaffold
ZxZ are pairs of integers
So any pair (m,n) where m and n are integers
The x is called a Cartesian product
lone zinc
ZxZ are pairs of integers
ah ok so then why do they sub in y, 0 for m and n then?
latent scaffold
To show surjectivity, you need to show that for any integer y in the codomain Z, you can find some ordered pair (a,b) in the domain Z x Z such that f(a,b) = y
But this is fairly simple since f(a,b) = a - b
So if we let b = 0 and a = y, we get f(y,0)=y
So the pair (y,0) maps to y
lone zinc
so since any value you sub into y will give itself then its surjective?
latent scaffold
Yes
vagrant saddle
odd edgeBOT
low locust
the gap from P_n to P_(n+1) is not good enough (like you noticed). however what about the gap from P_n to P_(n+2) ?
low locust
yes you need to consider P_(n+2)
odd edgeBOT
Available help channel!
untold kayak
odd edgeBOT
reef sandal
Okay so because dy/dx is defined implicitly, it's basically a multivariable function, like f(x,y)
So I'd make a note that you let dy/dx = f(x,y) = whatever
Then the slope of the tangent line at (a,b) is simply f(a,b)
reef sandal
Looks like it
untold kayak
Are you talking about 6
reef sandal
The process is the same for both questions
untold kayak
I’m confused isnt the vertical tangent when you make the equation equal zero
The bottom of the equation equal zero
reef sandal
Typically if you get something like C/0 where C is some random ass number, that's an indicator of a vertical tangent
As long as C ≠ 0
odd edgeBOT
@untold kayak Has your question been resolved?
umbral hawk
i have a question, lets say i have a sequence.
i want the first number to be x, x is a fraction
the second number is 2x
the third number is 3x
lets say infinite is n, so nx < 1
odd edgeBOT
@umbral hawk Has your question been resolved?
umbral hawk
okay
for example
1/2 2/3 3/4 -> works
but 1/2 starts too big
thats a good sequence, just not good enough
static totem
to big for what
static totem
1/10 2/11 3/12
umbral hawk
1/10 2/11 3/12
i think i've got it
so
starts at 1/5
and every step it gets 1/5 closer to 1
so like
1/5 which is 0.2
then 0.2 of 0.8 which is 0.16, so 0.36 is next
how would u do it as a sequence?
static totem
1 − (4/5)^n for example
umbral hawk
1 − (4/5)^n for example
ooo thats neat
how did u get to it
if i may ask
ok i got it:
1st term: 1 - 4/5
2nd: 1 - 4/5 + (1 - 4/5) * (1 - (1 - 4/5)) = 1 - 4/5 + (1 - 4/5) * (4/5) = 1 - 4/5 + 4/5 - (4/5)^2 = 1 - (4/5)^2
3nd: 1 - (4/5)^2 + (1 - 4/5) * (1 - (1 - (4/5)^2)) = 1 - (4/5)^2 + (1 - 4/5) * ((4/5)^2) = 1 - (4/5)^2 + (4/5)^2 - (4/5)^3 = 1 - (4/5)^3
summary -> 1 - (4/5)^n
thanks @static totem
lone zinc
For question 11c what do i do next here?
