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Yea true
You should revise the theoretical concepts about functions, otherwise you will find dificult to solve these basic exercises
Anyway, the domain is the set of possible x values that you can give in input to the function
alright
I see
Ok, so based on that definition of domain, what would you answer for the domain of your function?
Yeah, so which of those 4 is the correct answer?
the first one?
$$\left(-\infty, +\infty\right)$$
Alberto Z.
Exact
yea that one
Now, the range is the same but in the vertical direction (in other words for the y values)
and for the range wouldnt it also be infinite because it goes endlessly?
yes
Does y = 3 have a corresponding x-value?
In other words, if you draw the horizontal line y = 3, does this intersect the red graph anywhere?
yes
Where? đ For which value(s) of x?
Noo, the y axis is the vertical axis, whereas the x axis is the horizontal axis
yes
Then why did you say this?
Nope
I mean, draw a point on the plane that has 3 as its y-coord @novel pewter
No, don't do this, follow me at each step first
btw I have to go in 15 min
alright
Ok, what is the x-coord of that red point? @novel pewter
wdym
? do you know what x and y coordinates of a point are?
yes
So what's the problem in my question?
Ahn ok alright
Now, draw the point (4 , 3) onto the previous graph (don't delete the point you did before)
Ok, now draw again on THIS graph the point you had before, (0 , 3)
the point I had before 0,3??
what was the point before that
(0, 3)
Perfect, now connect these two points (with a horizontal line)
Yes
So, what is the property of all points belonging to that red line? They all share something in common, which is...
I actually dont know.
If I pick any point in that line, what can I say for sure about its coordinates??
y = 3?
Alright
The answer for the range anyway was D, i.e. (-inf, 2] @novel pewter
Because horizontal lines abovbe y = 2 never intersect your function
And also this file can be very helpful, I suggest you to read it very carefully @novel pewter
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how do i solve for b
wildercat
$\frac{a + b}{c} = 5$
Jangler
So you are done
what did you get before moving the a
sounds like needless question, just making sure you get why to do said operation instead of just guessing just because
that is not correct
i agree with the a operation. i dont agree with what you did with c
yes thats correct. what is the right side multiplied by c
so whatâs the answer
5c. make sure whatever you do to one side, you do the exact same to the other. otherwise the sides do not equal
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this is the question
what can you do with the sinx/cosx?
i was thinking maybe multiply it to 2 sin x cos x?
but i dont know if thats a thing
ooh i didnt
but thats what i thought
let me try
i can cancel out the cosines no?
leaving me with 2 sin x * sin x
bc cos is multiplied by 2?
so if you put it into that rule what do you have?
the 2sinxcosx we can put as the "a" in this case
2 sin x cos x * (sin x/cosx)
remember b/c = sinx/cosx
@warm shale $2 sin x cos x * (sin x/cosx)$
suka
you are then multiplying by c/b
yeah
exactly
np
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To differentiate 2xy using product rule so 2x ⢠y
Then fâ = [2xâ˘dy/dx] + 2y?
yes
ok and if my original function was x^2 + 2xy = 8 it would be 2x + [2xâ˘dy/dx] + 2y = 0
yeah
yep
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should I use double or triple integral?
Or is both fine.
The projection, I imagine, is just a unit circle on the xy plane
So if I just integrate over how much the x and y changes, that would give me many circles depending on the x and y value... SO I guess that could work.
But does it work if I do triple integrals?
try and parametrise the thing you're trying to find the volume of
by that i mean you need to give intervals for x y and z that you wanna integrate over
Im not sure what the bounds should be
..
Oh, I already did the double integral
Im just trying to see if the triple integral works?
i got it
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log_7(7) = 1
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Help
so basically what add 100 and 48
148
it is one of those sorry i dont know whichđ
no, it is just 148 degrees
since QRS is QRG combined with GRS, its measure is the sum of the measures of QRG and GRS
so 100+48=148
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is this right?
@honest crystal Has your question been resolved?
I'd probably add the function f(x) itself too
or like, a graph of what f(x) could look like, since you don't know what it actually is
so y=0?
No, the inequality says f(x) is between the two functions you drew for all x
Yeah, exactly, looks good
I'd maybe label the middle one f(x) too just to be safe but I'm sure that's basically what your teacher is looking for
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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'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
I have been stuck midway
yeah what does it want me to put
You use that graph
As an example, f(4) means the function when x = 4
So f(4) just means find the y value when x = 4
So using that graph, you go to x = 4, then find what the y value is
No
Using what I said, f(-2) means the y value when x = -2
So go to x = -2 on the axis, move until you reach the graph, then find what that y value is
go to x = -2 on the axis, move until you reach the graph, then find what that y value is
The curve, that's drawn
ok once ive reached the graph what do i do
Like I'm saying first, start at the origin, move your cursor to x = -2, on the x axis, then move the cursor until you reach the curve, then move the cursor to the y axis, what's that value?
?
You move along the lines
So you reached x = -2
yes
Now you need to move until you reach the graph, the blue line
So travel vertically until you do that
so id get y= -3?
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3/4% of 200
!onechannel
Please stick to your channel.
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I'm not sure how to start proving part b?
can you write the definition of v being in Span(S)
V can be represented by some linear combinations of vectors in S?
so from there could you show that there's some linear combination of vectors in S union v that sum to 0
Yes?
If say, S is as defined for a, and V is represented by say 4x_1+2x_2+8x_k
Then -4x-2x_2-8x_k+v=0?
ya
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How to do the (b) part?
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How do u do the (b) part?
!status
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this sounds more like a 1 than a 6
anyway, consider that E, D and B are collinear means BE is a scalar multiple of BD
Oh I didn't notice it
Yeah I know that B, D and E lie on a straight line
you may write this as BE = ÎźBD, where mu is another unknown scalar
then express the equality BO + ÎťOA = ÎźBD entirely in terms of the vectors a and b
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cant find my mistake, the final value when differentiated isn't giving the same integral. can someone pls help
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@stark bay Has your question been resolved?
can i get a more clear image
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quick question, if i had like (a+b)/x=c, how could i make x the subject, is it possible?
you can multiply both sides by x, as long as x isn't zero
then do some rearrangement from there
is that the only way?
hmm, yeah basically
ok thanks
any other way will basically be this in disguise
you could take a detour, end reuslts going to be the same
you could start by adding 2 on both sides, then multiplying by 17, cube both sides, rearrange further, at some point undo the three things I listed and get the same result anyway
Desync
(again, assuming (other stuff) is non-zero)
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!status
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Add both equations, and then use the trig addition/subtraction formulae
3sinp+4sinq?
add both equations first
I did
How does adding result in that
It's cos p-q
...
it's right, but i don't think it helps you solve the problem in any way
oh, oops, I was multiplying them.
sorry
đ
yeah, my bad
I'd probably sub sinp=x , cosq=y. But I'm sure there's a more elegant method
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@rough stratus Has your question been resolved?
Little me found a way.
i think u should drop it
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!status
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4
the ans from my textbook is 1.38m
but i keep getting more than that lol-
@royal basin
are you sure you definitely meant 1.38 m (just meters) and not 1.38 m**^3** when quoting the book's answer?
your work is very sparse, but it looks like you've confused yourself as to the meaning of the letter x.
in the equation as you wrote it, x is the volume of the statue in cubic centimeters,
so once you get the value of x, you need to also convert it to the right units.
yea sorry
i did
can you show your work for the unit conversion?
your work is once again sparse,
but your mistake is thinking that 1 m^3 is 100 cm^3.
it is not.
lol it's not?đ
it's not.
lemme try again
so since it's mÂł i'll have to divide x by 100 (3times)?
sure if you wanna phrase it that way
what's the proper way to phrase it?
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I'm confused about solving some differential equations. I understand how to deal with cases where you get an absolute value of y. However, when you end up with absolute values of x, I get confused about how people are getting rid of the absolute value.
So, for example, take the differential equation dy/dx+y*(1/x)=1.
I'm getting an absolute value in my answer. However, other people don't. The reason why is that when finding the integration factor, they change e^(ln(abs(x)) to just x, whereas I change that to abs(x).
I don't see how you can just get rid of the absolute value like that.
Wolfram alpha does the same thing: https://www.wolframalpha.com/input?i=dy%2Fdx%2By*1%2Fx%3D1
You need to treat it as two different ODE
One with domain (0, infty)
Another one with domain (-infty, 0)
Though they have the same equation, but these need to be viewed as two different ODEs
Each of them you can take absolute value symbol off
I mean
x and -x respectively
What OP did was fine tbh
You mean what I did?
Yes
Why?
People tend to ignore absolute values for simplicity
Doesn't that not give you all solutions?
Because R-{0} is not connected
yeah you do lose solutions I suppose
But even wolfram alpha does it.
I mean when was the last time you did $\int \frac{\dd x}{|x|\sqrt{x^2 - 1}} = \arcsec x$
NEON
For (0, infty) you have solutions , each two of them are different by a constant.
For (-infty, 0) you have some solutions each two of them different by a constant of course. Take any solution f for (0, infty) and any solution g for (-infty,0) is a solution on R-{0}
But two pairs (f,g), (fâ,gâ) no longer have to be different by one constant
It's one function just not defined at 0
You can have fâ=f+a, gâ=g+b
Thatâs why I treat it separately, on each of the connected components
I guess you will do the same when you encounter something like tan(x). This time 1/x has only two components, of its domain
I understand what you're saying I think. You would just handle the left and right sides of the coordinate plane seperately, right?
Yeah
Is what wolfram alpha did wrong then?
I was wondering if wolfram alpha assumed x>0
Based on its graphs.
(0,infty) probably.
more than 1 connected components, two different solutions are no longer different by a constant necessarily
Yeah that's what I thought. That's why I've been so confused because I thought that just adding a constant isn't going to be able to replace the absolute value.
But that's what everyone seems to think.
I guess sometimes people arenât cautious enough
Hmm
I think they need to fix wolfram alpha.
It should state that it is assuming x>0
I might report that
Hold on
It's not assuming x>0
Because on (-infty,0) the solution happens to be
Of the same form
The only issue is, you can have two different constants for each branch
For each branch of the absolute value?
Each branch of domain of 1/x
Like f(x)=x/2+5293/x for x>0, =x/2-19374/x for x<0 works
Wait what, I'm confused. But nothing is equal to anything with that equation.
The domains of both of those functions are completely seperate.
So I guess that is true, but what is your point?
f(x)=x/2+c/x for x>0, =x/2+d/x for x<0, is sufficient
It either omitted one component, or chose two constants being equal
I see...
So if you were actually doing an initial value problem and using some numerical differential equation solver or something, you would need to negate your constant as you move over the y axis?
A given value on a component , can make me fix one solution on that component
If you tell me y(1)=8, sure I now have a fixed y(x) for x>0. I canât determine y(x) for x<0, unless you give me something like y(-6)=71 too, or simply tell me the domain now is only (0, infty)
You have m components, you will need m values to determine the solution , one value for each component
Idk, I just canât determine y(x) for x<0 if (-infty,0) is part of domain and you donât provide me a value of y(x): x<0.
Any solution on (-infty, 0) works
y(x)=x/2+1/x: x doesnât equal 0, and z(x)=x/2+1/x: x>0, =x/2+5/x: x<0. There is no one of them being more special than the other one thing
But doesn't my equation work?
I could find C given some y(x) for x>0, and then have a solution for x<0.
I understand your components idea, but can't I just use my equation with the absolute value?
Then you only gave solutions whose constants are of the form (C,C)
But solutions whose constants are (C,D) are also solutions
Is that because it's undefined at 0?
It is because , again, the domain has two connected components
What is a component?
If itâs not 1/x, but 1/x(x-1) then three connected components
For now you can view it as how many parts the domain is divided into
Because it's undefined at two places?
You can say that
Because the domain is divided into three parts
(An exact definition is , for a topological space X, a subset A is said to be connected, if A is both open and closed. A connected component of X , is a maximum (in terms of inclusion) connected subset of X. Then X is disjoint union of connected components of it)
I'm a computer programmer, so I often thing about differential equations in the light of numerical approximations. If I was performing an approximation, then I could pass that undefined line fine just because I'm using finite steps.
I see. I have no idea. I only know math
Do you know about numerical approximation of differential equation solutions?
No
Ooh ok
I donât know approximation of any kind. I am only interested in pure math
Maybe it is, just looks very tedious to me personally
By comparison. I am usually interested in category theory kind of things, or algebraic geometry
I would say that the fact that sin(x) approx= x for small x is a great mathematical fact.
I see
Thatâs math
lim sin(x)/x=1
But if someone asks me to approx sin (37 degrees) , things like that
No looks like just calculation
So you care more about general cases?
Yeah
I answer analysis problems, but I donât study them unless I need to. Like if I read Lie algebra , topological group , then analysis is not avoidable , you know, Haar measure , things like that , I guess I will read it.
I never answer PDE, or Statistic, in these channels
Ode I am okay with, PDE no, complicated
Yeah, I respect that
I definitely see the importance of computation and approximation though.
Discrete fourier transform > continuous, because it's more useful.
More general a result is, I like it more
Yep, makes sense.
Well, thank you so much for your help. I understand this way better now.
Np
I still think wolfram alpha should be more explicit about what it is doing with the constants and components.
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You tooâşď¸
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you know that (a+b)(a-b)= a^2-b^2
No
it's not about taking a square root of 14 in some way
do you even know what rationalizing means?
Wtf
did'nt your teacher taught you this?
Nope
Or you didnât pay attention in class?
then i wouldnt recommend you attempting this ques
lol
What does "More instruction" do?
Iâm in college now. Itâs been since 9th grade since I took algebra
đ
I took algebra one in 8th and 9th was 2
Gives me a terrible explanation that Iâve already tried lol
Show
This videos looks at simplifying expressions with square roots in a binomial in the denominator, also known as rationalizing the denominator. It includes 2 examples.
If it ainât Organic Chemistry Tutor it ainât right đŻ
I tried tbh but I was too lazy to find one what did conjugates, that was the first one I found that did conjugates
I got 6 + 10 to square root of 14
Show your work, and if possible, explain where you are stuck.
Ehr
nah
Itâs not correct
bruh
u got the signs wrong
đ
Howâd you do that
Your simplifying on the last line is wrong
LaTeX
$\frac{a+b}{a} \neq b$
dldh06
Meaning you can't do only -30/-5 = 6
You can't just divide one of the terms by 5
They did that math right, just the longer way
Oh damn I didnât even look at the pic right
It was the simplifying of $\frac{-30 +10\sqrt{14}}{-5}$ was wrong
dldh06
Factor 5 is better
And proceed
From the numerator
I guess
Well -5 from the numerator
Wtf
$ab + ac = a(b + c)$
dldh06
No
Bloodclat confuse wid di mathsđ
You want to simplify this
You can factor out a -5 from the numerator first
Ok
Do you see how the -5's cancel out?
$$
\frac{-5(6-2 \sqrt{14})}{-5}
$$
đ
Yes
Damn my WiFi slow đŁ
So my answer is 6-2 square root of 14
Yes
Good luck bredrin
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I guess I should say first, it's not equal to 11/25 degrees
It's equal to 11/25 radians
How do you convert from radians to degrees?
how is that in radians?
"An angle is x radians" means that "The ratio between the arc and the radius is x"
That's the definition of radian
So since the ratio between the arc and the radius is 11/25
The angle is 11/25 radians
Does that make sense?
Okay awesome
So in degrees it's 11/25 * 180/pi
And then you need a calculator to figure out what this is
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â
okay so i only
converted radian measure into degrees when it had the pi in it
and then multiply it by
180/pi
pi-pi gets cancelled
idk
you are ascribing some kind of mysticism to the conversion between degrees and radians.
when in fact it is just like any other unit conversion.
just like 1 meter = 100 cm, you have 1 rad = (180/pi) degrees
the conversion factor has pi in it but that does not really make things any different
so should it be 11pi/25?
no
11/25 is 11/25.
if we wanted to write 11pi/25 we would have written 11pi/25.
you will not have a cancellation of the kind you are used to.
okay so after multiplying 11/25*180/pi ?
,calc 11/25 * 180/pi
Result:
25.210142985756
Result:
12.60857914536
should be 25°13' if we are rounding to the nearest arc-minute, but only 25°12' is among the options, so that is probably what they want.
but is there a way i can do this without using calculator?
no
like simply putting value of pi and then solving
like 11/25*180/3.14?
i think using 3.14 for pi might already lead to too much inaccuracy.
,calc 11/25 * 180/3.14
Result:
25.222929936306
,calc 11/25 * 180/3.142
Result:
25.206874602164
,calc (11/25 * 180/3.142 - 25) * 60
Result:
12.412476129854
i dont have any option, we cannot use calculators, sorry
,calc (11/25 * 180/3.14 - 25) * 60
Result:
13.375796178344
okay so you would need at least 3 decimal digits of pi to get an accurate result ehre
in how many seconds are you expected to do this question
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Hello, I am getting two different derivs and wonder which is the correct one. Cause I need to find the extreme points.
The first one you have
f(x)
Differentiate like you normally do
Equate to the one below
Should get values of x
(idk how to differentiate 3x / (1+4xâ´) btw)
alright, I'll keep doing that
Only one of them should be correct as clearly one of the answer you found is 9 times the other
yes exacly but the left is the proffessors answer
Unless x = â´â(1/4) => very unlikely
but It didn't make sense even when she showed it
Hmm my knowledge too little to help you more correctly
@surreal carbon Has your question been resolved?
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Hi, I need help please. I have to graph a cubic function with the following characteristics. I'm not sure as to how to draw it.
f(-2) = 0
f(0)=8
fâ(0) = 0
fââ(x) > 0 when x > 0, and vice versa
what have you tried? how far did you get?\
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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
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6. None of the above
toki
to ki
@dry rain
he's playing fortnite rn
f''(x) tell us there's a minima for positive x and maxima for negative x (local)
f(0) tells us y intersect of graph at x=0 is 8
Ofc f''(0) is 0 when f(0) = 0 but also, slope of graph at x=0 is constant?? (Yeah ofc, it's always tangent constant)
X intersect of graph is at y= 0 when x = -2
Bro I'm ANSWERING THAT QUESTION WDYM
.
I'm not, thankyou
you definitely are
I did answer the question tho đ
@dry rain Has your question been resolved?
you should wait for them so they can work through the problem with guidance rather than listing half accurate information at them
well, i know that the x intercept is -2, and that the y is 8
but iâm not sure how to draw the graph based on the other characteristics
this is what i drew and iâm not sure if itâs right
like, because of fâ(0) =0, shouldnât the y intercept also be a turning point?
but then i donât have another x intercept
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@zenith raft @tardy epoch Help me with math lmao
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(âŻÂ°âĄÂ°)âŻď¸ľ âťââť
âŹââŹă( Âş _ Âşă)
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@tardy epoch @zenith raft @polar fossil How to find det of
$\begin{bmatrix}
1 & 1 & 2 & 4 & 4 & 0 & 3 & 0 & 8 & 3 \
7 & 1 & 8 & 9 & 7 & 3 & 2 & 3 & 4 & 4 \
4 & 2 & 9 & 5 & 7 & 4 & 8 & 9 & 2 & 3 \
1 & 3 & 6 & 6 & 7 & 7 & 1 & 9 & 3 & 1 \
4 & 4 & 1 & 8 & 7 & 2 & 0 & 3 & 2 & 8 \
5 & 8 & 8 & 7 & 9 & 9 & 5 & 5 & 1 & 6 \
8 & 5 & 7 & 0 & 0 & 9 & 8 & 7 & 2 & 1 \
2 & 8 & 0 & 9 & 2 & 8 & 3 & 6 & 1 & 3 \
9 & 5 & 4 & 5 & 9 & 0 & 1 & 1 & 8 & 7 \
2 & 5 & 5 & 2 & 1 & 9 & 2 & 5 & 5 & 6
\end{bmatrix}$? Lmao
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ti-89
â ď¸
dldh06
!show
Show your work, and if possible, explain where you are stuck.
Don't have one, how to do by hand?
U serious?
Most probably
he isn't
i will murder you
Oh goodđ
there was balance in the force
Just multiply every row by 0 and the solution is trivial
then you interrupted it with your bad Midichlorians
Mitochondria
diagonalize it
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!status
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
jezus google come on
đŞ
That's a 10 x 10....
I wanted this one
2 & 3 & 5 & 3 & 8 & 2 & 1 & 4 & 4 & 9 & 0 & 3 & 3 & 4 & 8 & 6 & 3 & 9 & 1 & 3\
9 & 2 & 4 & 8 & 0 & 7 & 0 & 7 & 1 & 3 & 0 & 8 & 0 & 1 & 1 & 2 & 4 & 5 & 7 & 2\
3 & 6 & 4 & 4 & 6 & 8 & 1 & 6 & 9 & 4 & 3 & 1 & 5 & 8 & 3 & 3 & 0 & 6 & 1 & 5\
2 & 8 & 2 & 1 & 4 & 0 & 6 & 3 & 4 & 0 & 4 & 5 & 9 & 1 & 9 & 1 & 0 & 0 & 4 & 1\
2 & 3 & 1 & 2 & 7 & 0 & 2 & 6 & 4 & 6 & 0 & 9 & 5 & 2 & 2 & 8 & 2 & 9 & 7 & 7\
0 & 7 & 8 & 2 & 7 & 6 & 2 & 1 & 6 & 7 & 8 & 1 & 4 & 9 & 0 & 2 & 2 & 3 & 6 & 3\
2 & 1 & 2 & 5 & 9 & 2 & 2 & 3 & 1 & 8 & 2 & 1 & 3 & 7 & 1 & 6 & 8 & 4 & 8 & 2\
3 & 2 & 2 & 7 & 0 & 1 & 5 & 3 & 5 & 3 & 0 & 0 & 9 & 7 & 7 & 0 & 1 & 5 & 0 & 5\
4 & 7 & 6 & 4 & 3 & 0 & 0 & 7 & 6 & 3 & 3 & 9 & 7 & 9 & 9 & 2 & 7 & 7 & 2 & 6\
7 & 7 & 0 & 5 & 5 & 2 & 0 & 4 & 1 & 6 & 7 & 2 & 3 & 1 & 9 & 3 & 0 & 4 & 2 & 5\
2 & 6 & 9 & 9 & 4 & 3 & 7 & 8 & 5 & 6 & 1 & 8 & 2 & 1 & 9 & 1 & 2 & 6 & 1 & 6\
5 & 0 & 3 & 9 & 7 & 0 & 2 & 6 & 3 & 4 & 8 & 2 & 7 & 6 & 8 & 1 & 6 & 4 & 2 & 6\
3 & 8 & 1 & 1 & 4 & 7 & 1 & 0 & 7 & 0 & 7 & 9 & 8 & 7 & 8 & 9 & 6 & 6 & 5 & 2\
1 & 2 & 0 & 2 & 7 & 5 & 5 & 8 & 5 & 0 & 0 & 4 & 7 & 7 & 5 & 4 & 1 & 7 & 5 & 3\
7 & 9 & 9 & 3 & 8 & 1 & 5 & 6 & 8 & 4 & 6 & 6 & 5 & 0 & 4 & 8 & 0 & 3 & 4 & 6\
4 & 2 & 8 & 0 & 5 & 5 & 6 & 5 & 1 & 8 & 9 & 4 & 7 & 7 & 2 & 1 & 2 & 2 & 3 & 9\
2 & 8 & 8 & 0 & 5 & 4 & 1 & 5 & 6 & 2 & 1 & 9 & 5 & 1 & 0 & 3 & 6 & 5 & 9 & 2\
2 & 0 & 5 & 9 & 1 & 1 & 1 & 6 & 5 & 5 & 3 & 6 & 2 & 5 & 2 & 8 & 9 & 8 & 8 & 8\
7 & 8 & 2 & 1 & 3 & 2 & 0 & 4 & 2 & 7 & 8 & 4 & 4 & 1 & 6 & 9 & 2 & 2 & 7 & 4\
6 & 5 & 0 & 3 & 5 & 8 & 5 & 5 & 9 & 5 & 7 & 8 & 8 & 8 & 0 & 0 & 7 & 6 & 9 & 5\
But I couldn't format it

@tardy epoch Help me with this instead
i will double murder you
Is it W?
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how does the area of a polygonal face be generalized to $\frac{nl^2}{4tan(frac{180}{n}}$
Aâ¤Ă
rk.macharia
Compile Error! Click the
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what's n and l here
n is the number of sides and l is the side length
is this a regular polygon
yes
think of it as splitting the polygon into n different triangles
with the vertices being, the center of the polygon and 2 adjecent vertices of the polygon
like this for a regular hexagon
or this for a heptagon
you can calculate the area of 1 triangle and multiply by n
so the area of one triangle will be 0.5 s^2 sinX given that angle x is the one where one of the vertices is in the center of the triangle and s is the side(s) adj to angle x
but the formula uses l which is the side opp angle x
so s is the length from the center of the polygon to one of the vertices?
yes
I found that the base angles of the triangle will be (n-2)*180/n
you have to divide by 2 because thats the angle formed at each vertex
and the base angle is half of that
if you sub l/2=s*sin(x/2) into your equation, we get l^2cos(x/2)/4sin(x/2)
simplifying gives us the formula l^2/4tan(x/2)
but x=360/n so we can sub that into the equation to get l^2/4tan(180/n)
and then multiply by n to get our equation for the area of the whole polygon
thanks vv much.... I was forgetting to half the angle.... I was getting some vv weird stuff
no problem
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i need help
what about it?
<@&268886789983436800>
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I have this sprite and I want to find where the green dots are. The players origin us half the width and 9/13 of the height (going from top to bottom and left to right.) How do I find the x and y position of the green dots if the player spins around the origin. right green dot is 11 / 13 of the width and 3 / 13 for the height. left green dot is 3/13 width and height. Never done trig or geometry before because I am a sophmore what formula or whatever do I need?
My player is on a large screen and I have the player x and y which is located at half the width and half the height
Oooo, a CS-related question! We rarely get those
yea most cs guys are good at math lol
What information do you have? The player's angle?
yes
In the picture you sent, is the angle 90° or 0°?
0
You could precompute the distance from the origin and angle of the 2 green dots when it is at 0°
Then you can calculate their current angle at any time by adding the player's angle to the precomputed angles
After which you can use cos of angle times magnitude and sin of angle times magnitude to get their offset from the origin
Then just add that to the origin's coordinates
ok thanks a ton I'll get back to you when I program all of that đ
probably not today it's pretty late
I'm honestly not sure if that's the most elegant way to do it
It's probably the most efficient though
eh I have no idea how this stuff works so as long as it works thanks
CS grindset
More seriously though try to understand it
ok thanks
@pulsar grail By the way, if you're planning on messaging me back in DMs you can .close this channel
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What would be the best way to write this $$\abs{\vec{v_2}}$$ term?
One person
huh, you have a text channel before this
Basically it would be the square root of the vertical velocity of the foot ball at t_0 and the horizontal at t_0... i should've made t_0 t_1
No i don't?
Yeah, because Different question
different not all you can cut it into another channel
Green leaf
wait why im not active?
Hmmm
you can wait the other, im lazy
One person
It only gives one value
But i need two from it
how do i get the 2nd one
the
highest/minimum angle to reach the distance $$R- \Delta x$$
One person
@timid silo Has your question been resolved?
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Lets say I have some function that is $g(x) = \frac{-1}{f(x)}$
SubsonicSpraak
Is the global/local minimum of f(x) also a local/global min of g(x)?
,w graph -1/x^2
Hmm, yeah, fair point. but a local minima for sin(x) is a local minima for -1/sin(x) (as per your graph)?
First of all,
g'(x) = f'(x)/(f(x))^2, so g' has the same critical points as f' whenever f is not zero
g''(x) = [f(x)^2 f''(x) - 2 f'(x)^2 f(x)]/(f(x))^4, so at any critical point where f is not zero, g'' has the same sign as f''
From these we can basically conclude the property about local minima/maxima of f transferring to local minima/maxima of g, but global minima/maxima are not similarly well behaved, as demonstrated by Frosst
If we assume that f is smooth and nowhere zero though, then I think you do get that g and f share the same local/global minima/maxima
ah there's the 2 parts, x^2 shows the f is 0 situation and sinx shows the global situation
Since -1/x is a strictly increasing function if you restrict to x>0 or x<0
In fact you don't even need the criterion that f is smooth tbh
Just that it stays either above 0 or below 0 the entire time
To be honest this is to do with the breaking time for PDEs (the first time (t) a shock forms), and I'm trying to word how I'm analytically exploring that above function to reason when we get the minimum positive value of:
$\frac{-1}{f(x)}$
SubsonicSpraak
those are definitely words i've seen in my pdes class but i dont understand them
Asking about your attempted solution rather than your actual problem
You're going to have to post more context
If you want help with it
Unless you're satisfied with what you already got
I just needed to grapple with the initial problem I posted. I have values and everything working, I just wanted to explore some properties of my initial function
to make my logic make sense
So thanks everyone!
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no problem!
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for question 8
,rotate
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is this number 8?
yeah
should be correct
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Hi. How to you solve this type of systems?
I managed to get this:
themathboi #2137
How am I supposed to proceed?
