No worries
#help-13
cosmic herald
If you need help
Claim a channel in the math help category
#help-16 for insatance
tribal pier
so all we have to worry about in y=2x-6 right now is the number attached to x.
that's our gradient
tribal pier
y=(2)x+(-6)
2 is our gradient, is it positive or negative?
cosmic herald
positive
tribal pier
so is the graph going to go up or down?
tribal pier
so which of our options is a straight line that is angled up?
tribal pier
what's confusing you?
cosmic herald
another says it's going to be one of the reasonsm y parents kill me
It's unexplainable
ok
deep breath
@tribal pier could we
I'm super sorry u been with me for 1 hour now
could we restart
but use
the question we're on as an example
tribal pier
yep
tribal pier
what's the equation for a straight line graph?
tribal pier
alright, so now we just need to know where to put what numbers
the gradient is the "rate of change." when x gets bigger, y should get 4 times bigger. That's what it means to have a gradient of 4
cosmic herald
do u have a website
with a 4 sided graph
so i can make an example of what ur saying
tribal pier
hmmm
try desmos
type in y=mx+c, and it'll ask if you want to make sliders for m and c
tell it yes
cosmic herald
done
cosmic herald
the gradient is the "rate of change." when x gets bigger, y should get 4 times b...
makes way more sense
and if there's a negative gradient
when x gets bigger, y gets 4x smaller?
tribal pier
precisely
cosmic herald
(if it's -4)
tribal pier
yes
cosmic herald
Sorry I been speaking English for 5 years I'm fluent at it just like I wanna make sure with words I don't use too much
tribal pier
so should the 4 replace the m or the c? try moving around the sliders and see if you can make the graph do what you want
tribal pier
sure
y is your output, it's the up/down direction of the axis
x is your input, it goes in the left/right direction of the axis
m is your gradient, it tells x how much to grow every time it gets bigger or smaller. if you move the m slider, you'll see it changes the angle the line is at
c is your y intercept, it tells the graph where it crosses the vertical axis. if you move the c slider, it shifts the whole thing up or down, but doesn't change the angle
cosmic herald
desmos too confusing
tribal pier
unfortunately I have to leave, but I hope that explanation helps a bit
cosmic herald
unfortunately I have to leave, but I hope that explanation helps a bit
Np and thx a lot
<@&286206848099549185> help pls i need to understand gradients
lost parrot
the equation of a linear graph is y = mx + c
for every point in the graph, this is true
cosmic herald
y r u deleting
lost parrot
i misread
the question
the x and y can vary, but m and c are constants
m is the gradient, c is the y intercept (the point that is at x=0)
it says m = 4, so y = 4x + c
since this equation is true for all points on the graph, you can put in (0, 3)
(-3) = 4(0) + c
so c = -3
cosmic herald
(-3) = 4(0) + c
so c = -3
I'm confused on this last part
lost parrot
so y = 4x + c
it says that there is a point (0, -3) on the graph (the y intercept because x=0)
the point (0, -3) has y = -3 and x=0
the coordinates are (x value, y value)
so you have your x value, and y value
if you put them into the equation y = 4x + c, you will get c (the y intercept)
so y = -3, and x = 0, so -3 = 4x0 + c
-3 = c
cosmic herald
so you have your x value, and y value
if you put them into the equation y = 4x +...
I understood everything you said until this point
lost parrot
(0 <-- x value, -3 <-- y value)
y <-(put y value in here) = 4x <-(put x value in here) + c
-3 = 4x0 + c
lost parrot
c = -3
y = 4x -3
cosmic herald
c = -3
y = 4x -3
okay thanks
cedar kilnBOT
Available help channel!
turbid yoke
could I get some help with this, I just cant see how one comes to the 2nd (the dr) integral, I understand the -2x^2 part but just not the other part 🤔
cedar kilnBOT
could I get some help with this, I just cant see how one comes to the 2nd (the d...
@turbid yoke Has your question been resolved?
turbid yoke
some progress has been made, i realized that the 1 could be integrated on its on and will become pi a^2 after both integrals
also seems that 2xy = sin(2 theta) => 0
dire geode
could I get some help with this, I just cant see how one comes to the 2nd (the d...
Did you try writing it out step by step
turbid yoke
think im on the right track currently
just didnt really pay attention to 0 + pi a^2 being written outside of the dr
now its just that im getting *2 too much on one term 
shouldnt -2x^2 = -2*a^2*cos^2(theta)?
ok I solved it
or err, found out how they solved it
turbid yoke
shouldnt `-2x^2` = `-2*a^2*cos^2(theta)`?
turns out I made a mistake here assuming x = acos(theta) and not x = rcos(theta)
otherwise with that fixed, integrating all the double integrals by parts made it work
.close
upper swallow
I'm confused how they went from x^2 to x^(5/2)
cedar kilnBOT
I'm confused how they went from x^2 to x^(5/2)
upper swallow
yeah
obsidian coral
$\sqrt{x} = x^{\frac{1}{2}}$
wraith daggerBOT
dldh06
upper swallow
oh yeah i know what you meant lol
obsidian coral
So distribute
$x^{\frac{1}{2}} \cdot x^2 - x^{\frac{1}{2}} \cdot x^{\frac{2}{3}}$
wraith daggerBOT
dldh06
upper swallow
oh its just 2 + 1/2?
obsidian coral
Yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
mental plaza
I need a walkthrough for this, I have about 10 of these questions relatively the same I want to do the rest on my own
cedar kilnBOT
I need a walkthrough for this, I have about 10 of these questions relatively the...
@mental plaza Has your question been resolved?
mental plaza
<@&286206848099549185>
cedar kilnBOT
@mental plaza Has your question been resolved?
south dawn
This is what I got from reading. to find how long to cut the leg. Maybe others have better idea. You can use the trig like sin or tan to find the angle. I could be totally off-from reading.
cedar kilnBOT
@mental plaza Has your question been resolved?
mental plaza
This is what I got from reading. to find how long to cut the leg. Maybe others...
I have a question, how did you get 41.5 -2, how did you get the minus 2
cedar kilnBOT
I have a question, how did you get 41.5 -2, how did you get the minus 2
@mental plaza Has your question been resolved?
gentle yacht
Matt has 4 video-game-CDs, with one of them being a Pink Panther game.
He takes 2 of the CD's to his friend, and his friend tells him that he had already played pink panther.
What's the chance that 2 of the CD's matt had brought, had the Pink Panther CD?
gentle yacht
If it was 1 CD that he had taken, then that would be 1/4 chance of Pink Panther being that CD
But that's not exactly the case here, since there are two CDs
My approach was 1/4 * 1/3 = 1/12, but that is probably incorrect
but i think there is 1/4 chance of the first CD being pink panther, and a 1/3 chance of the 2nd CD being pink panther
wicked brook
I assume it's asking without repeat. Then id use choose
$$ P = \frac{ {3 \choose 1}}{4*3} } = \frac{1}{4}.$$
wraith daggerBOT
ohNoiAmHere
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
wicked brook
cause once the panther is chosen, there's 3 to choose from
i could not be understanding the problem
gentle yacht
The answer claims to have been 1/2
gentle yacht
It says that the chance of the first Cd being pink panther is 1/4, and the chance of the second being 1/4, too
obviously, this is quite questionable
wicked brook
oh wait
i undercountd
mine should be x2
$$ P = \frac{ 2{3 \choose 1}}{4*3} } = \frac{1}{2}.$$
cause panther can be first slot
or second slot
wraith daggerBOT
ohNoiAmHere
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
wicked brook
what its saying is correct
since P(panter) = P(panther 1st) + P(panther 2nd)
cause that covers every case possible
gentle yacht
since P(panter) = P(panther 1st) + P(panther 2nd)
1/4 + 1/3
= 3+4/12
= 7/12?
wicked brook
1/4 + 1/3
= 3+4/12
= 7/12?
why is the second 1/3?
P(panther 1st) = 1/4 * 3/3
P(panther 2nd) = 3/4 * 1/3
gentle yacht
Because once you've choosen your first CD, there are 3 CD's to choose from, aren't there?
4 options to pick from first, then 3 options second
wicked brook
theyre mutually exlusive
either i choose panther 1st or i choose panther second
there arent two panthers
gentle yacht
I think it also work to calculate the chance of not getting a panther on either CD's
3/4 * 2/3 = 6/12
wicked brook
yes
gentle yacht
= 1/2 of not getting panther
wicked brook
that would be correct as well
gentle yacht
so getting a panther should be 1/2, too
I believe your way of solving this could be used for more complex problems, and that's why I am not able to fully understand it
wicked brook
yea, what im doing is theres 3 not panthers to choose from
and i can choose exctly one of them
there's two arrangments this this: namely, NP, P or P, NP
so i need to then multiply the probability by two
gentle yacht
there's two arrangments this this: namely, NP, P or P, NP
Yeah I believe i begin to get it now
it seems like just looking at your arrangments, it's two out of 4
so 1/2 of being panther, which was the solution we've initially come to
wicked brook
yea
gentle yacht
I believe I've gotten this solved, thanks a lot for the help, mate
I really appreciate it
.close
clever jewel
Hello! I know this integral is divergent:
cedar kilnBOT
Hello! I know this integral is divergent:
clever jewel
but would it be correct to say that this one is 0? since it approaches both infinities equally fast
upper garnet
both are same
under one is the right way to solve the integral
I think it's called second order improper integral
cedar kilnBOT
@clever jewel Has your question been resolved?
clever jewel
alright, thanks!
ember ether
how to find the asymptotes for a
cedar kilnBOT
how to find the asymptotes for a
ember ether
$\ \frac{ax²+bx+c}{x - \beta }$
wraith daggerBOT
megi-san
limpid meadow
Vertical asymptote is where a functions value tends to infinity / undefined. For that there's one way, when x - B is 0, the function will give an undefined value.
x - B = 0
so there's a vertical asymptote at x = B
IIRC Horizontal asymptote is the value the function approaches (if its a definite value then its an asymptote) as x tends to infinity. In this case take Lim x->0 of the function.
cedar kilnBOT
@ember ether Has your question been resolved?
ember ether
.close
modern verge
I have 0.65 and 0.95 and I want to change 0.95 to 1 while keeping the proportion between the two numbers the same. How do I do that?
modern verge
I know it must be a percentage calculation of some type. But I've never been very good at those.
I know that if I divide both of the values with 2 and then multiply them with 2.105 I'll get 0,999875.
And with 2.106 I'll get 1.00035.
So I guess I'll keep trying some numbers to multiply with until someone has time to help me.
austere heath
find percentage of 1 over 0.95
modern verge
What does that mean?
modern verge
Oh, you mean increase percentage. Well, that's 5%, right?
austere heath
ok so
modern verge
So I think the increase should be 5.263157894736848 %
Weird number.
But what do I do with that?
austere heath
plus 1
modern verge
Why plus 1?
modern verge
Oh, shortcuts. Ok.
austere heath
then do the same on the other number
modern verge
Multiply by 1.05263157894736848?
austere heath
times the same percentage
modern verge
Okay so that should give me 0.68421052631.
If I got that right.
Yes, that is correct.
Thank you.
.close
fallen solar
cedar kilnBOT
fallen solar
I am getting x belongs to (-inf, -7-sqrt(5)] U [sqrt(5)-7, -4)
but it turns out to be (-inf, -7-sqrt(5)] U [sqrt(5)-7, -14/3)
I understood that (-inf, -7-sqrt(5)] U [sqrt(5)-7, inf) comes from the fact that the square root is defined for those values only
but why is it -14/3 instead of -4
we can only square both sides when x >= -4, right?
ok nevermind im stupid....
.close
obtuse shuttle
Could someone explain to me or point me to some explanation online on what constant functions are, what you get instead of constants when integrating a PDE?
obtuse shuttle
for example g'' = 0
and then take the integral twice to solve for g
obtuse shuttle
sometimes you get g = F(x) + G(y) instead of g = F(x) + C
violet flume
right
hollow bobcat
Interesting since i am also tryna learn DEs
violet flume
this is kind of a central thing in multivar calculus
obtuse shuttle
yea, I'm on the start of the course
violet flume
have you any partial derivative stuff?
obtuse shuttle
I can do PDEs but just don't get why sometimes you add constants like C, which is the normal
and other times functions
violet flume
I can do PDEs but just don't get why sometimes you add constants like C, which i...
do you know why you add the C
obtuse shuttle
what are those functions, why not just add constants, and how do I know when to add functions instead of constants?
yes
just never seen the functions
wraith daggerBOT
jan Niku (LinAlg Study Group)
violet flume
then $\pdv{f}{y} = 1$
wraith daggerBOT
jan Niku (LinAlg Study Group)
violet flume
so we should be able to recover f by integration
$\int \qty( \pdv{f}{y} ) \dd y = f(x,y) + ?$
wraith daggerBOT
jan Niku (LinAlg Study Group)
wraith daggerBOT
jan Niku (LinAlg Study Group)
obtuse shuttle
y
obtuse shuttle
okey let me show an example
When one is on the last step of solving a PDE by integrating, how does one know if one should add constants or functions?
Example
Determine all solutions of the form f(x, y) = g(x**2 - y) to the PDE
2 * df/dy + d2f/dx2 *+ x * d2*f/dxdy = 0
After having solved most of it one comes to this point
d2g/dt2 = 0
So we integrate twice since it's second derivative, to solve for g.
dg/dt = A , where A is a constant
g = A*t + C , where C is a constant
t = x2 - y
f(x, y) = g(t) = A**(x**2* - y) + C
That's the answer my professor has written. Now this is the part that's confusing, the next exercise he gave is this one, where there is no constants but instead functions when integrating.
Transform the PDE by using new variables u = x * e-y, v = y and then solve the PDE.
x * d2f/dx2 + d2f/dxdy + df/dx = x * e-2y
Here we arrive at a similar situation as in last problem, where we have to integrate twice but this time with regards to two different variables, u and v, to solve for g.
d2g/dudv = u
dg/du = u*v + A , where A is a constant
g = u2v/2 + Au + C , where C is a constant
now substitute back u and v
f(x, y) = g(u,v) = (x * e-y)2 ** y/2 + A*(x * e-y*) + C
if you take the derivative twice from g, then you get u, I don't see how this is different from the first example, yet professors answer is this
f(x,y) = (x * e-y)2 ** y/2 + G(x * e-y*) + H(y) , where G, H are functions
what's the difference? when to use functions and when to use constants as usual when integrating to solve the PDE?
if that's too long
look at this instead
from same example above , tldr
violet flume
the long and short of it is that partial differentiation treats functions of the other variables as constants
obtuse shuttle
then I did the next exercise and got it almost right, instead of my constants though, we got functions G and H
violet flume
you know what happens to constants under differentiation
they are lost
this creates families
obtuse shuttle
the long and short of it is that partial differentiation treats functions of the...
yea I know
violet flume
for generality you need to pick the entire family back up
when you cross through the other side
obtuse shuttle
still, why not use constants, and because constants are used sometimes and other times not, how should I know when to use constants or functions?
violet flume
you need to pick up a function involving every other variable when you integrate something you know is a partial derivative of a multivariable function
constants are included here
the only reason to use a constant is if you are integration a single variable function
which you will probably not see in PDE
well
you will see it all the time 
but that should be straightforward enough hopefully
multivariable functions get functions
when you integrate
obtuse shuttle
why is this one constants A and B and other example below it functions G() and H()?
was it because the function I integrated in the first was g(t)
and the other g(u, v)?
violet flume
ill be honest i think im too tired to track the example you posted
and is probably question for your teacher
obtuse shuttle
when I integrate a function and it has one variable = use constants
violet flume
if you understand why you might pick up a function
when to use what should be very clear
obtuse shuttle
when multiple variables = use functions instead of constants
violet flume
if i can recommend something
look up exactness methods
for ODE
this is great practice with this concept
crimson sedge
for example g'' = 0
and then take the integral twice to solve for g
Integral of g''=g'
Integral of g' = g
obtuse shuttle
am I understanding you correctly?
violet flume
im not sure that you totally understand why you might pick up a function
which is fine
or if you do and youre just confused about the example then idk if im the person to help
obtuse shuttle
I'm just asking for a rule set of how to know when to use "constant functions" instead of constants
or what it's called so I can google, can't find anything
violet flume
constant functions?
obtuse shuttle
can't see anything relevant to it when looking at exactness method, no functions in sight?
obtuse shuttle
maybe not what it's called, but the functions G() and H() you see above
which are where I got constants instead in my answer
while professor used functions instead
obtuse shuttle
when integrating or what do you mean
violet flume
in general
obtuse shuttle
don't see anything similar to my example/what I'm confused about on the page you linked
maybe we are talking past each other
violet flume
yea, im very tired
obtuse shuttle
should I close and try another group see if there maybe someone who gets my confusion?
violet flume
you could try #calculus or just wait here
#odes-and-pdes might help too but calculus is more active
not a lot of people up right now
obtuse shuttle
okey thank you anyways for trying
cedar kilnBOT
Available help channel!
formal flume
Two players, A and B, are playing an asymmetrical game. There are n points on the game board. Each turn player A targets a pair of points and player B says whether those two points are connected or unconnected. A can target each pair only once and the game ends when all pairs have been targeted. Player B wins iff a point is connected with all other points on the very last turn, while player A wins if any point is connected with all other points on any turn but the very last one OR if no point is connected to all other points after the last turn. For what values of n does either player have a winning strategy?
cedar kilnBOT
Two players, A and B, are playing an asymmetrical game. There are n points on th...
@formal flume Has your question been resolved?
golden tundra
cedar kilnBOT
deep smelt
Hey, I have a chain rule question I'm a bit stuck with. I'm not sure if I've simplified it enough, and when I plugged it into an advanced calculator it gave me something completely different.
Here's the question:
deep smelt
And here is what I tried:
lilac crane
Your first line you have a -3/4 did you mean -3/2?
lilac crane
First line is correct other than that
You know, is it ok if you make the inside to the 6th power?
Or does your prof want you to practice an unsimplified version
deep smelt
No, just as long as it's completed using the chain rule it should be okay
So I could just effectively find the derivative of this right?
And that'd be the same?
lilac crane
Yes
leaden snow
you sure you differentiated 1/(2x) correctly?
leaden snow
should be -1/(2x^2)
lilac crane
Take care
inner jay
can someone explain the first one
cedar kilnBOT
can someone explain the first one
cedar kilnBOT
@inner jay Has your question been resolved?
inner jay
yes but from the derivative I got 8,-4
inner jay
with respect to x I got 2x+y-12
to y I got x+2y
when I make them equal to zero I got 8,-4
which is minimum but idk about max
fair hare
inner jay
its probably something about the domain but I dont know what
cedar kilnBOT
@inner jay Has your question been resolved?
cold birch
What does it mean by defined range and how do I calculate it?
reef venture
frigid canyon
yes me too
bold vine
^^
frigid canyon
basically you have to ensure that all terms are defined
like there can't be a negative under a root
that type of things
dusty hazel
proud sierra
Someone dm me I need help
short token
cedar kilnBOT
short token
isnt this enough to show that sum of power series is continuous from -1 to 1 ?
or do i have to find v>0 for every e>0
s t
proud sierra
What grade is that for @short token
short token
calc 2
proud sierra
You In HS or college?
short token
what is HW
proud sierra
High school
short token
college
proud sierra
Oh what’s your major?
short token
mathematics 😄
proud sierra
Cool seems hard I’m only in the 11th grade
I want to major in software engineering any advice?
short token
be consistent
proud sierra
I’m not good at math and I don’t even know how to code
Do I wish for luck or change major?
short token
depends what is your definition of "not good"
short token
do you like math?
proud sierra
I love it but I’m not that grate at it
proud sierra
well you can design software without knowing a lot of math
Yeah but I have to pass the math classes
proud sierra
I hope so
Or else i will have to resort to other things to help me pass
Maybe one of my math teachers can help u
short token
😦
short token
sometimes
proud sierra
What kind of job do you want to have?
proud sierra
I was about to say you can do math for them
Ik people that do math for them
But they retired
GL
cedar kilnBOT
@short token Has your question been resolved?
short token
.close
dire wedge
how do I do question B?
by subtracting 5 from the 1.1 and making it
-4.9t^2 + 10.8t -3.9
somber belfry
okay so what does B mean
dire wedge
okay so what does B mean
I need to find the 2 spots where the ball reaches 5 meters and choose the correct one
I think
somber belfry
you need to find the time where the ball is 5 meters high
somber belfry
I need to find the 2 spots where the ball reaches 5 meters and choose the correc...
this is basically it yes
where would you begin
gleaming cloud
I need to find the 2 spots where the ball reaches 5 meters and choose the correc...
what makes a spot "correct"?
somber belfry
well if its a negative t its none sense
dire wedge
what makes a spot "correct"?
the point closest to the left
gleaming cloud
fair
somber belfry
it could be 2 points by the way
dire wedge
since the ball it being thrown left to right?
gleaming cloud
it could reach the height of 5m twice
gleaming cloud
it could reach the height of 5m twice
(once while going up, once while coming down)
dire wedge
<@700802265430360134> but okay where would you start now ^^
at y intercept 1.1
wraith daggerBOT
Eichhorst
somber belfry
its basically task A but the other way around
dire wedge
cause that's the only way Ik
somber belfry
then we move the h to the otherside to make 0 or nah
you dont need to and whenever I did quadratic formula I want to have a postive integer on the left anyway
but you could do it to have a starting point
somber belfry
u making this really complicated man
sorry 😦
somber belfry
is the starting point necessary?
what do you mean with starting point?
dire wedge
but you could do it to have a starting point
this
somber belfry
oh sorry my bad English, I meant it in a more work wise way. if it helps you to solve the task go for it. So you find a beginning
dire wedge
oh sorry my bad English, I meant it in a more work wise way. if it helps you to ...
I wanna be able to do it quickly
are there no shortcuts
turbid yoke
I mean, its really just solving 1 equation
somber belfry
I wanna be able to do it quickly
are there no shortcuts
how do you solve this?
turbid yoke
if h = <the expression i cant remember> and h = 5, then what does that imply?
somber belfry
like p/q formula?
dire wedge
I mean, its really just solving 1 equation
what equation?
the only one I can think of is the one I put above
-4.9t^2 + 10.8t - 3.9
dire wedge
like p/q formula?
I don't know that
somber belfry
I don't know that
okay
turbid yoke
what equation?
the only one I can think of is the one I put above
-4.9t^2 + 10.8...
-4.9t^2 + 10.8t - 3.9 isnt an equation on its own
somber belfry
well you just solve a quadratic equation
dire wedge
h = -4.9t^2 + 10.8t - 3.9
there
somber belfry
if you want a method for that I can prove you one
dire wedge
if you want a method for that I can prove you one
show me the method
somber belfry
okay so you are familiar with binomial formulas?
dire wedge
okay so you are familiar with binomial formulas?
I think so?
somber belfry
h = -4.9t^2 + 10.8t - 3.9
there
so yeah we want to write this as a binomial formula so we can just pull the root and izi
dire wedge
would (b/2)^2
be one?
somber belfry
no its an pretty easy method once you get the hang of it
and it REALLY helps understanding quadratic equations
dire wedge
and it REALLY helps understanding quadratic equations
lemme find a utube vid for it
somber belfry
lemme find a utube vid for it
I can write you down a guide if you want lol
dire wedge
I can write you down a guide if you want lol
pls do
it looks mad hard
somber belfry
but try a youtube video sure
@dire wedge we can go through this if you wish to
thats how I do it 😅
dire wedge
I needa go for now
thx for your help, ima study up this
somber belfry
I needa go for now
thx for your help, ima study up this
didnt you teacher give you a method of solving quadratic equations?
but sure come back when you have more questions
dire wedge
didnt you teacher give you a method of solving quadratic equations?
I think he did but it wasn't the binomial formulas i'll check with him tmrw
or ig on monday
somber belfry
I think he did but it wasn't the binomial formulas i'll check with him tmrw
there are a lot of different methods to solve quadratic equations this is just one of them
cedar kilnBOT
Available help channel!
crimson sedge
Transforming r=theta into the cartesian plane as a single function
crimson sedge
I'm pretty close but I need some help
flint plinth
Transforming r=theta into the cartesian plane as a single function
function of what variable?
crimson sedge
Assume f(x) = x cos (x), g(x) = x sin(x)
flint plinth
ah
flint plinth
and is the range of theta constrained?
crimson sedge
(f(t), g(t))
flint plinth
Assume f(x) = x cos (x), g(x) = x sin(x)
so what's wrong with this parameterization?
crimson sedge
If n is a constant,
The intersection of
x = f(n)
y = g(n)
form the fibonacci spiral
But to get it in a single equation Id have to say
x = f(g^-1(y))
crimson sedge
But to get it in a single equation Id have to say
x = f(g^-1(y))
I think, atleast
But I cant find the inverse function of x sin(x) and even wolfram's not digging up anything
If h(x sin(x)) = x,
r = theta
is the same as
x = h(y)cos(h(y))
Could it be non elementary?
crimson sedge
and is the range of theta constrained?
Its not really considered
crimson sedge
so what's wrong with this parameterization?
Nothing, but I don't want it in vector form
<@&286206848099549185> I am in over my head
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
Any approximations atleast?
Something that has a spiral shape
My standards are on the floor
If anyone sees this after the question closed and knows or is close to the answer please dm me
cedar kilnBOT
@crimson sedge Has your question been resolved?
amber ridge
Transforming r=theta into the cartesian plane as a single function
it won’t be a function
crimson sedge
it won’t be a function
so its non elementary?
crimson sedge
a function can only have one output per input
yk what I mean
a relation
I want something that can be graphed in terms of x and y in a single equation
dire geode
I want something that can be graphed in terms of x and y in a single equation
does $y = x\tan\sqrt{x^2+y^2}$ count
wraith daggerBOT
riemann
crimson sedge
does $y = x\tan\sqrt{x^2+y^2}$ count
Is there a way to graph only the positive part of the spiral?
dire geode
what does that mean?
crimson sedge
https://math.stackexchange.com/questions/2622447/archimedean-spiral-in-cartesian...
Ive been searching up "fibonacci spiral" this whole time
crimson sedge
alright, well thats one part of what Im trying to find done
thanks a lot
I fucked up going from theta to x and y so I tried to do it another way
.close
cedar kilnBOT
crimson sedge
.reopen
cedar kilnBOT
✅
dire geode
oh right
crimson sedge
even arctan(y/x)
I dont get how that works though
I want a positive angle, not a negative one
dire geode
send me a desmos link
dire geode
positive angle means y/x > 0. but that just means x and y have the same sign. so maybe in addition to x > 0, you want y > 0. then separately add x < 0 and y < 0
crimson sedge
positive angle means y/x > 0. but that just means x and y have the same sign. so...
wouldnt that just give me the 1st quadrant?
dire geode
fuck
crimson sedge
agreed
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
warm vector
cedar kilnBOT
warm vector
My first step was finding the gradient
I’m up to here
How would I further proceed this?
I’ll be back soon.
.close
warm vector
cedar kilnBOT
tropic oxide
no
bad notation strikes again
x^-2 is not 1/sqrt(x), it's 1/x^2
and also you cannot just write a function, followed by an equals sign, followed by its derivative
warm vector
Ok
tropic oxide
it appears you're trying to be as terse as possible in your working
warm vector
Yes
tropic oxide
you should NOT do that
tropic oxide
that is better so far
warm vector
Ok now I’m trying to find the gradient
tropic oxide
yes, and it should be less "trying" and more "doing" imo
warm vector
True
tropic oxide
evaluating a function at a point, especially when the function has a known formula, should be practiced until it is as automatic as doing an arithmetic problem
loud flare
confused
crude scroll
if im not trippin, the top and bottom length should be the same, no?
93 = 5y+3
Same thing for the sides
-5x-3=62
south dawn
if im not trippin, the top and bottom length should be the same, no?
not trippin
south dawn
https://ocw.mit.edu/courses/18-01sc-single-variable-calculus-fall-2010/
No. I just like to promote because I love MIT.
crude scroll
nice ok
cedar kilnBOT
@loud flare Has your question been resolved?
upper swallow
Solve for b. The answer sheet says the answers are 1 and -1 but I'm not sure how they got there
livid hound
did you make an attempt?
evaluate the definite integral like any other and solve for b
upper swallow
I did that, then i ended up with sqrt(-7) which isnt possible
upper swallow
upper swallow
-2^2 = 4 then -(-b) is pos b
livid hound
-2^2 isn't 4
upper swallow
it is according to my calc
livid hound
your calc is wrong and/or you aren't entering stuff into your calc properly
and also you shouldn't be using a calc for that
upper swallow
livid hound
from order of operations, the power applies to the 2 only
$-2^2$ is NOT the same as $(-2)^2$
wraith daggerBOT
ℝamonov
upper swallow
worked for me like that before
sharp lotus
livid hound
worked for me like that before
i highly doubt that
upper swallow
no need to be rude.
sharp lotus
-2^2...if you have the minus sign outside of a paranthesis then it isnt part of the quantity getting squared
livid hound
rudeness was not my intention
upper swallow
yeah I know what it means, my calcs not let me down like this before :/
sharp lotus
if there is a parenthesis around it then (-2)^2 means you are squaring -2
mortal raptor
worked for me like that before
can you type -2^2 without the brackets on your calculator
upper swallow
it gives -4
sharp lotus
well why are you putting paranthesis on the calculator around the quantity you are squared, that isnt the calculators mistake
mortal raptor
type 2, press square, then press minus
mortal raptor
lol true
cedar kilnBOT
sharp lotus
and when you have - times a square on your paper you dont need to type that in your calculator
livid hound
it might be because you're pressing the ${\boxed{}}^{\boxed{}}$ button before the -
wraith daggerBOT
ℝamonov
cedar kilnBOT
Available help channel!
sharp lotus
if you have -678.5^2 on paper or something you really need a calculator for..just square the 678.5 number on the calculator then add a minus on the paper, this is simpler @upper swallow
sharp lotus
.close
silk fjord
The power advantage gained by suppressing the carrier is equal to how many decibels?
cedar kilnBOT
The power advantage gained by suppressing the carrier is equal to how many decib...
@silk fjord Has your question been resolved?
cedar kilnBOT
halcyon swan
<@&286206848099549185>
Why did you ping the role, and then proceed to close...?
Please don't do that
crimson sedge
cedar kilnBOT
crimson sedge
part c
i want to know why my answer is rong
i found the vector line equation of AB ; r = a + λ (b - a) and I set it equal to OC vector = λ (OC)
AB = (2 2 1) + λ (-1 -1 -5) = λ (3 3 -3) ---> λ= -1
and so i get (-3 -3 3)
dawn jetty
i want to know why my answer is rong
i found the vector line equation of AB ; r ...
The line equation for AB is wrong
Notice that the diagonal AB is given directly by (b-a)
Instead, you can use the property of rectangles, which states that the diagonals of a rectangle meet at their midpoints
So if you have the position of C, and O (O being the origin) you can easily find the vector AC, and compute its midpoint
lament kraken
IB question?
crimson sedge
IB question?
no edexcel
crimson sedge
The line equation for AB is wrong
why?
crimson sedge
Notice that the diagonal AB is given directly by (b-a)
that would be the vector AB but not vector line equation right?
crimson sedge
Instead, you can use the property of rectangles, which states that the diagonals...
yep that way is alot easier and true it is wat is expected but; im jst dont get what hav i done wrong
crimson sedge
huh...i dont get it...bit more elaboration please
doesnt the first coordinate not matter when it is collinear?
dawn jetty
that would be the vector AB but not vector line equation right?
you know what
this is my bad
I was wrong, you're equations were right
crimson sedge
eqn of vector line between 2 points C & D is given by
r = c + λ ( d -c) right? so i used tht
dawn jetty
go back to your original equations , re calculate them
you're supposed to get lambda=0.5
crimson sedge
....i did 😭 but i stil get same
dawn jetty
(2,2,1) + a(-1,-1,-5)=a(3,3,-3)
=> (2,2,1)=a(3-(-1),3-(-1),-3(--5))=a(4,4,2)
a=1/2
which is exactly the midpoint for both vectors
Im sorry about my earlier answer leading you astray, its been a while since I actually saw vector line equations (despite taking LinAlg2....)
crimson sedge
Im sorry about my earlier answer leading you astray, its been a while since I ac...
no probs at all abt it
crimson sedge
(2,2,1) + a(-1,-1,-5)=a(3,3,-3)
=> (2,2,1)=a(3-(-1),3-(-1),-3(--5))=a(4,4,2)
wow so my mistake was an arithmetic error 😐
pain 😭
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Ngl I'm quite proud of myself for getting this haha
Thank you very much
cedar kilnBOT
Thank you very much
crimson sedge
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cursive turtle
I need help
cedar kilnBOT
I need help
wraith daggerBOT
Poni
cursive turtle
Okay
cedar kilnBOT
@cursive turtle Has your question been resolved?
frigid fox
<@328765192173256704>
Ok, Do you know about Sum of roots and Product of roots of a Quadratic
cursive turtle
Yes
frigid fox
Ok then let them be x1 and x2
So can you tell me what is x1 + x2 and x1x2
cursive turtle
I already found, $$x1 + x2 = 3$$
wraith daggerBOT
Poni
cursive turtle
and $$x1*x2 = 29$$
wraith daggerBOT
Poni
cursive turtle
Why 7x + 39?
Could you show me the paper you did it, or simply do it in discord?
@delicate patio
delicate patio
I did it by normal method
cursive turtle
The quadratic formula
delicate patio
I'll go by that too
cursive turtle
As @frigid fox said.
frigid fox
Then, the new roots are x1-2 and x2-2 ,
So the quadratic will be $x^2 - (x1-2 + x2 -2)x + (x1-2)(x2-2)$
wraith daggerBOT
Trystnest
cursive turtle
Are the first roots I found correct
wraith daggerBOT
Trystnest
frigid fox
Yes
wraith daggerBOT
Poni
cursive turtle
What should I do next?
frigid fox
**Trystnest**
This
We can find the Sum and Product of new roots with out finding the exact previous roots
cedar kilnBOT
cedar kilnBOT
Available help channel!
cursive turtle
$$x^2 - (x_1 + x_2 - 4)x + (x_1 - 2)(x_2 - 2) = x^2 - (3 - 4)x + (x_1* x_2 - 2x_1 - 2x_2 + 4)$$
wraith daggerBOT
Poni
cursive turtle
$$ x^2 + 1x + [29 - 2(x_1 + x_2) + 4]$$
wraith daggerBOT
Poni
frigid fox
I think you got it
cursive turtle
$$x^2 + x + [29 - 2(3) + 4] = x^2 + x + (29 - 6 + 4) = x^2 + x 27$$
wraith daggerBOT
Poni
cursive turtle
So the final answer of the equation is: $$x^2 + x + 27$$
wraith daggerBOT
Poni
frigid fox
👍
frigid fox
Yes, Done
cursive turtle
thank you very much
im sorry, @frigid fox but why did we substract twice with -2
shouldn't we do it just once
frigid fox
im sorry, <@975821214796894230> but why did we substract twice with -2
Both the roots are subtracted by 2
cursive turtle
ye, sorry confused that
cedar kilnBOT
@cursive turtle Has your question been resolved?
obtuse shuttle
when getting the slope for a tangent line, or anything for that matter, it's rise over run, delta y/delta x
obtuse shuttle
then wtf is this
if you solve for m in that equation you get m = (y - y1)/(x - x1)
question is, why is it m = -a/b, where (a,b) is the point of the tangent
frigid fox
question is, why is it m = -a/b, where (a,b) is the point of the tangent
a,b here are not points of contact, they are the coefficient of x and y in the equation of line
obtuse shuttle
sorry, looks like he means (a,b) is not the point
yea
so he takes the coefficients of x and y of the tangentplane
still, why x coefficient/ y coefficient
in all other cases, it's opposite, rise/over, y/x
and why minus a/b
where is this coming from
frigid fox
express ax+by+c=0 in slope intercept form
obtuse shuttle
express ax+by+c=0 in slope intercept form
thank you
and we use it here because we want to find the tangentline at the given point to the level curve of the function, level curve is R2 here, so we can express the level curve by polynomial with two variables
?
frigid fox
yes
obtuse shuttle
or is it better to view it as, the gradient vector in that point gives the slope of the tangent in that point by making it a scalar by a/b
okay thanks
.close
cedar kilnBOT
grave jay
cedar kilnBOT
grave jay
Why is my method wrong? (First picture)
cedar kilnBOT
@grave jay Has your question been resolved?
steel ember
where did .125 and .353 come from?
cedar kilnBOT
where did .125 and .353 come from?
steel ember
is the answer key even correct?
cedar kilnBOT
@steel ember Has your question been resolved?
steel ember
<@&286206848099549185>
dark frost
where did .125 and .353 come from?
the answer will be
homozygous dominant = 125
heterozygous = 250
as far as my knowledge on the punnet square goes
steel ember
the answer will be
homozygous dominant = 125
heterozygous = 250
so the answer key is wrong?
it says 41, 46, and 13%, none of which equal 125 or 250
dark frost
so the answer key is wrong?
I'm prolly wrong here
steel ember
I'm prolly wrong here
why??
dire geode
where did .125 and .353 come from?
It came from your notes or text
dark frost
why??
nvm
it's the hardy weinberg law 
p^2 + 2pq + q^2 = 1
dominant homozygous frequency is p^2
heterozygous frequency is 2pq
homozygous recessive is q^2
steel ember
is p^2 homozygous dominant?
dark frost
yes p^2
steel ember
It came from your notes or text
these arent my notes
ok why isn’t q equal to .25, the percentage of homozygous recessive?
dire geode
it's the hardy weinberg law <:rofl:829718266037141565>
This is
steel ember
shouldn’t p and q be equal to the percentage of homozygous dominant and recessive in decimal form?
dark frost
ok why isn’t q equal to .25, the percentage of homozygous recessive?
q^2 should be equal to .25
dark frost
shouldn’t p and q be equal to the percentage of homozygous dominant and recessiv...
there's something wrong with either the question or the answer key
definitely
dark frost
isn’t q the frequency?
q^2 is the frequency
steel ember
q^2 is the frequency
so is this correct?
dark frost
where did .125 and .353 come from?
yes
steel ember
ok i’ll tell the teacher the answer key is wrong
thanks @dark frost @dire geode
.close
quasi marsh
Hi, i wanted to ask; The other day, i got this one idea on a definition of a number. My question is if it's right, or does it not make sense, thanks.
crimson sedge
Anyone know the formula for the nth integral of e^x
Im too lazy to calculate it and google is shit with math questions
elder pewter
It integrates to itself
crimson sedge
It integrates to itself
the constants though
tidal kernel
In the time it took you to ask the question and wait for an answer you could have worked it out
You cannot expect to receive help if you cba to put in any effort yourself
livid garnet
livid garnet
<@&286206848099549185>
cedar kilnBOT
@livid garnet Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
upper abyss
What are we trying to show is true?
fluid grove
upper abyss
We can look for saddle points in 10x + y - xy
We'll take the partial of both variables to get a system:
10 - y = 0
1 - x = 0
We find that there's a potential minimum at (1,10)
But that's still 10
Worth checking all the endpoints, but this is looking true.
cedar kilnBOT
cedar kilnBOT
Available help channel!
cold oasis
cedar kilnBOT
cedar kilnBOT
cedar kilnBOT
Available help channel!
rugged tusk
cedar kilnBOT
rugged tusk
any idea how to calculate sum of this series ?
tropic oxide
this series equals $f(1)$ where $f(x) = \sum_{n=1}^{\infty} \frac{(-1)^n nx^{n-1}}{(2n+1)!}$
wraith daggerBOT
Ann
rugged tusk
but then how to deal with factorial ?
tropic oxide
you should know some taylor series for standard functions that contain factorials