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The Math Help Thread
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oreomunsta
Banned
I think you want the formulae for the perihelion and the aphelion.
With such a small eccentricity, the center and the focii are really close together. It's superfluous information, but a star does not stay put when a body rotates it
Center doesn't matter in general but it is the distance of the semi-major axis. The Sun will be one of the two foci, with the other foci being empty space. As oreomunsta said you are trying to solve of the aphelion and perihelion of the orbit.
I'm getting ~90,986,849 for minor vertex. And webassign says 90,987,000 is wrong :/
Set it up as an ellipse basically with major vertex being (-91,000,000,0) and (91,000,000,0) assuming "center" is (0,0). But webassign did accept my 92,547,000 as the aphelion, so I dunno where I'm going wrong on the perihelion.
Edit: Oh wait, 90,986,849 is, I believe, the distance from center to minor vertex. Doh.
Set it up as an ellipse basically with major vertex being (-91,000,000,0) and (91,000,000,0) assuming "center" is (0,0). But webassign did accept my 92,547,000 as the aphelion, so I dunno where I'm going wrong on the perihelion.
Edit: Oh wait, 90,986,849 is, I believe, the distance from center to minor vertex. Doh.
Got that last one, but now this one elludes me :/
Find an equation for the ellipse that has its center at the origin and satisfies the given conditions.
eccentricity= 1/2, vertices on the x-axis, passing through (1, 3)
I came up with (x^2)/4 + (y^2)/3 = 1. Wolfram also says this, webassign says we're wrong
Edit: Whoops, double post. But now I see that cannot be right, since it passes through (1,3), the point above origin would have to be > 3
Find an equation for the ellipse that has its center at the origin and satisfies the given conditions.
eccentricity= 1/2, vertices on the x-axis, passing through (1, 3)
I came up with (x^2)/4 + (y^2)/3 = 1. Wolfram also says this, webassign says we're wrong
Edit: Whoops, double post. But now I see that cannot be right, since it passes through (1,3), the point above origin would have to be > 3
Biggest-Geek-Ever
Member
Maybe a little late to the party, but if you know the eccentricity is 1/2, then you can solve for c^2 in terms of a^2. You can then solve for b^2 using a^2 - b^2 = c^2 and be on your way to finding the equation of the ellipse.Got that last one, but now this one elludes me :/
Find an equation for the ellipse that has its center at the origin and satisfies the given conditions.
eccentricity= 1/2, vertices on the x-axis, passing through (1, 3)
I came up with (x^2)/4 + (y^2)/3 = 1. Wolfram also says this, webassign says we're wrong
Edit: Whoops, double post. But now I see that cannot be right, since it passes through (1,3), the point above origin would have to be > 3
chain rule, try differentiating the latter expression.
the dt in the equation says what variable you will be deriving or integrating, so in this case "s" is just some constant.
RazorbackDB
Member
A little help with something basic, i'm doing a cross product between two vectors, and I end with
i(3 - 5sqrt(3)) - j(-6) + k(-10)
what can i do with the subtraction inside the i?, currently I'm just writing it as
3i - 5sqrt(3)i + 6j -10k.
i(3 - 5sqrt(3)) - j(-6) + k(-10)
what can i do with the subtraction inside the i?, currently I'm just writing it as
3i - 5sqrt(3)i + 6j -10k.
FortuneFaded
Member
I would leave it in the bracket i.e. (3 - 5sqrt(3))i. Separating the coefficients of i could lead to issues if you then have to, for example, dot product this with another vector.
RazorbackDB
Member
Seems reasonable, I tried to take the magnitude of that vector, solved i as a binomial and ended with
sqrt(38-30sqrt(3))
I guess there just isn't another way. thanks for the help.
spelltropy
Member
Can anyone give me some help with some (likely very basic...) abstract algebra? I missed a few weeks and I've no idea what I'm doing...
There's a ton of other questions, really confused right now
There's a ton of other questions, really confused right now
I'm going to assume that you know what each of those groups is. In particular, you need to know the group operation. In any group, the cyclic subgroup generated by g (which I will denote <g>) is the set of elements g^n for all integers n (which you can prove is indeed a subgroup). So in the case of the integers with the addition operation, <1> is the subgroup of all integers (i.e. the subgroup is the entire group), <2> is the subgroup of all even integers, and <10> is the subgroup {..., -20, -10, 0, 10, 20, ...}.Can anyone give me some help with some (likely very basic...) abstract algebra? I missed a few weeks and I've no idea what I'm doing...
There's a ton of other questions, really confused right now
So I'm not entirely sure what the group is in part a or what rho_3 is in part e (maybe a 270 degree rotation?) but in b you have a group that is essentially the set {0, 1, ..., 11} with addition modulo 12. So <8>={8, 2*8, 3*8, 4*8, ...} (mod 12) = {8, 4, 0}, after which point the elements repeat themselves. I won't attempt to write matrices here, but for part c you should also find that the terms repeat after only a few iterations. Part d should be a case where the subgroup is infinite, as in the first example I gave.
hm... I think I have an equation however I'm not sure how exactly it'll work with the second part:
How long will it take to decay to 25% of its original value? Show algebraically.
Anyone?
MisterLuffy
Member
I need help on this question. I have to use Kruskal's algorithm to find the minimal spanning tree for this weighted graph.
Just google the algorithm. It tells you exactly what to do and it's pretty much trivial.
teh_J0kerer
Member
Ok guys, here's a cute little math problem that has come up in a physics research project that I'm working on, and I actually have no idea how to approach it! Maybe this is too hard I dunno, but it's easy to state:
Let f(x) be a positive function defined on [0, 2 Pi]. i.e. f(x)>0 for all x.
Given: Integral from 0 to 2 Pi of f[x] = 1.
Also, integral from 0 to 2 Pi of f[x]Sin[x] = r. (some given real number r, r is necessarily between -1 and 1.)
Question: What is the maximum possible value of the integral from 0 to 2 Pi of
f(x) Cos[x]? (the maximum is to be taken across all functions with the above properties)
Let f(x) be a positive function defined on [0, 2 Pi]. i.e. f(x)>0 for all x.
Given: Integral from 0 to 2 Pi of f[x] = 1.
Also, integral from 0 to 2 Pi of f[x]Sin[x] = r. (some given real number r, r is necessarily between -1 and 1.)
Question: What is the maximum possible value of the integral from 0 to 2 Pi of
f(x) Cos[x]? (the maximum is to be taken across all functions with the above properties)
There's no other information about f? Does it need to be differentiable, continous or something?
Hmm, nice problem...
Notation: F(x) = Int[f(x),x] is the indefinite Integral over f
Int[f(x),x,0,2*pi] is the definite Integral over f between 0 and 2*pi
Partial Integration yields the following:
Int[f(x)*cos(x),x,0,2*pi] = F(2*pi)*cos(2*pi) - F(0)*cos(0) - Int[F(x)*(-sin(x)),x,0,2*pi] = 1*1 - 0*1 + Int[F(x)*sin(x),x,0,2*pi] = 1 + Int[F(x)*sin(x),x,0,2*pi]
F(x) is monotonically increasing, since f(x)>0, also we know that F(0)=0 and F(1)=1
Now we "just" need to find an F(x) so that the Integral Int[F(x)*sin(x),x,0,2*pi] becomes maximal. I need to sleep over this, but maybe someone has a bright idea (I'm also pretty sure that is a known problem)...
FortuneFaded
Member
I did the same also partial integration of f(x)sin(x) yields:
Int[f(x)*sin(x),x,0,2*pi] = F(2*pi)*sin(2*pi) - F(0)*sin(0) - Int[F(x)*(cos(x)),x,0,2*pi]
so Int[F(x)*(cos(x)),x,0,2*pi] = -r
I think it should be F(2pi) - F(0) = 1 by FToC.
Is the bolded necessarily true? Do we not only know that F(1)-F(0) = 1?
No, you are right, it's not.
But since we only ever integrate between 0 and 2*pi anyway, we can ignore whatever happens to f(x) and F(x) outside those bounds without loss of generality and only consider functions with F(0)=0 and F(1)=1.
I admit I'm a bit sloppy with these things, since I'm a physicist and not a mathematician.
teh_J0kerer
Member
Well, just define F[x] = Integral from 0 to x of f[x]. Then you do have F[0] = 0 and F[2 Pi] = 1.
I have also considered approaching the problem this way, but I don't know how to deal with the restriction that F[x] is monotonic.
Well, ok to be precise, f[x] may be assumed to be differentible, and moreover, when I ask for Max[Integral[f*Cos]], I really mean, "Least Upper Bound" rather than "Max", because the actual maximum may not be realized within the set of differentiable functions.
I have also considered approaching the problem this way, but I don't know how to deal with the restriction that F[x] is monotonic.
Well, ok to be precise, f[x] may be assumed to be differentible, and moreover, when I ask for Max[Integral[f*Cos]], I really mean, "Least Upper Bound" rather than "Max", because the actual maximum may not be realized within the set of differentiable functions.
Maybe we could express F(x) as a Fourier series. When the function is bounded and monotonic, the fourier coefficients are bounded as well.
The Riemann-Stieltjes integral mentioned in this Stackexchange discussion could be very hepful in general:
http://math.stackexchange.com/questions/129579/bounded-fourier-coefficients-for-monotonic-functions
teh_J0kerer
Member
Actually, someone on stack exchange just answered the problem!
http://math.stackexchange.com/quest...een-fourier-components-of-a-positive-function
Funny, it's actually obvious when you see the answer, making this a pretty cool little puzzle.
http://math.stackexchange.com/quest...een-fourier-components-of-a-positive-function
Funny, it's actually obvious when you see the answer, making this a pretty cool little puzzle.
It was answered already, but I asked because I was thinking of using the dirac function too!
MisterLuffy
Member
For this problem, I have to find all possible spanning tree for this graph.
Do I just have to draw variety of graphs with the same vertices and edges as this one?
One more question, does a tree exist if it has 8 vertices and 8 edges? If I go by the theorem that tells me for any positive integers n, any tree with n vertices has n-1 degree. 8 - 1 = 7 edges
Does that mean the tree exist if I draw out the tree that has 8 vertices and 7 edges?
Do I just have to draw variety of graphs with the same vertices and edges as this one?
One more question, does a tree exist if it has 8 vertices and 8 edges? If I go by the theorem that tells me for any positive integers n, any tree with n vertices has n-1 degree. 8 - 1 = 7 edges
Does that mean the tree exist if I draw out the tree that has 8 vertices and 7 edges?
You could draw a couple of graphs with a subset of the vertices of the pictured graph, but you could also choose a different notation like G = (V, E \ {a,b})
You should probably trust the theorems.
Your last question seems a bit too unclear. 'the tree that has 8 vertices and 7 edges'?
MisterLuffy
Member
Here's the question, it's vague.
Either draw a graph with given
specifications or explain why no such graph exists.
Tree: with eight vertices and eight edges.
That's all the question is given me.
This is probably a no-brainer to y'all, but I can't wrap my head around this and my teacher didn't go over the Fundamental Theorem of Calculus in class. :/ I understand how to do it with single variable Calculus but I'm not sure if I'm doing this correctly. I'm guessing doing the partials first is unnecessary, but it seems to check out?
I'm probably gonna be posting a lot of dumb questions in the next few days so I apologize in advance.
I'm probably gonna be posting a lot of dumb questions in the next few days so I apologize in advance.
So you know from the theorem that this is not possible. Not you just have to show/prove it.
Simply drawing a tree with 7 edges won't suffice.
Biggest-Geek-Ever
Member
When I've seen Df(a,b,c,...), it's referred to the matrix of partial derivatives evaluated at that point (it's actually a linear transformation, but I'm not sure that's relevant to you). In your case that matrix would beThis is probably a no-brainer to y'all, but I can't wrap my head around this and my teacher didn't go over the Fundamental Theorem of Calculus in class. :/ I understand how to do it with single variable Calculus but I'm not sure if I'm doing this correctly. I'm guessing doing the partials first is unnecessary, but it seems to check out?
I'm probably gonna be posting a lot of dumb questions in the next few days so I apologize in advance.
[∂f/∂x , ∂f/∂y] = [sin(π/2•1)/π/2•1 , sin(π/2•1)/π/2•π/2] = [2/π , 1]
Since your linear transformation is going to ℝ, this is actually the gradient of f.
You seem to be solving for the tangent plane at that point. I don't think that's what the question is asking for, but I might be wrong.
That's how he's taught us to write total derivatives. It's kind of confusing because even he doesn't follow it all the time and he'll just say that it's the same thing? I dunno. D:
Otherwise, the matrix you got would be multiplied by the matrix (x y) (don't know how to get it vertical) to get:
Df(x,y) = (2/π
x + yI'll try to ask him in class what it is he's looking for. But thank you!
MisterLuffy
Member
The only way to show it I guess is to draw a tree with 8 vertices, and draw out the edges. I just drew the tree with 8 vertices, and it gave me 7 edges.
Well, you already have the theorem that tells you exactly that. Drawing a tree is not much of a proof. At that point you are talking about a specific tree, even though multiple trees with eight nodes exist.
You could start with the hypothesis that the graph with eight edges exists and show that it can't. E.g. By removing one node/edge at a time arguing that what remains is still connected and acyclic -- until it can't be.
Is anyone here good with statistics?
Suppose X has a normal distribution with mean u1 and known standard deviation 7.
Suppose Y has a normal distribution with mean u2 and known standard deviation 9.
Suppose we have a random sample of size 6 from the X distribution. The sample mean xbar is 24.
Suppose we have a random sample of size 8 from the Y distribution. The sample mean ybar is 27.
Calculate the variance of Xbar - Ybar
I have absolutely no clue how to solve this. Can someone offer me some help? Does anyone know the formula I can use to solve this and walk me through it?
Suppose X has a normal distribution with mean u1 and known standard deviation 7.
Suppose Y has a normal distribution with mean u2 and known standard deviation 9.
Suppose we have a random sample of size 6 from the X distribution. The sample mean xbar is 24.
Suppose we have a random sample of size 8 from the Y distribution. The sample mean ybar is 27.
Calculate the variance of Xbar - Ybar
I have absolutely no clue how to solve this. Can someone offer me some help? Does anyone know the formula I can use to solve this and walk me through it?
I'm no stats guy, but google gave me this site, which seems to answer your question in pretty decent detail. I think it has more than necessary for your problem, but the first half of it gives a good explanation of what you'll need.
Permanently A
Junior Member
Probably missing something absurdly simple. I don't understand what he did here to simplify the equation. Thanks in advance
1−​2/ (√​(x+1))​​​​​​​=0
√​(x+1) ​​​=2
x=3
1−​2/ (√​(x+1))​​​​​​​=0
√​(x+1) ​​​=2
x=3
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