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The volume of a spherical cap of height and sphere radius is
I want to solve for . So I plug it into Wolfram Alpha here: https://www.wolframalpha.com/input/?i=v+%3D+pi%2F3+*+h%5E2+*+(3*r-h),+solve+h
The solution is kind of ugly but can be simplified parametrically as
where
The problem is that part under radical . It's always a negative number no matter what I plug in.
For example, if then . But plugging those values in results in a negative square root argument, .
The weird thing is, I've used this before, and it worked. I'm wondering if I made a typo that I'm just not seeing. ~ Anachronist ( talk) 00:24, 29 April 2017 (UTC)
I am a bit confused about the principal part of the PDE, and what its roots mean for the dy/dx = λ , and and how that came about. I understand that the sign of the discriminant b squared minus 4ac determines whether the PDE is Hyperbolic, Parabolic, or Elliptic, but as to the roots of from the related quadratic equation, I am a bit mystified. I understand that the roots are used to determine the coefficients of x in PDE's that might have general solutions such as f( m1x + y) + g(m2x + y ), where m1 and m2 are the roots, and therefore the coefficients of x in this form of solution, but as to stuff about the canonical form, I am confused. I see that for this, where we have the principal part of the PDE of second order being Auxx + Buxy + Cuyy, where for example, uxx is just the second partial derivative of u with respect to x, and so on, then we have a change of coordinates, letting xi = xi(x,t), and tau = tau(x,t), so that in terms of these new coordinates, by the Chain Rule, we have : ux = xix*Uxi + taux*Utau, and ut = xit*Uxi + taut*Utau, and that makes sense, but then I do not get why the second derivative of u with respect to x is what it is. I thought it would simply be partial d/dx of this ux expression, but done by the power rule, so that d/dt[xix*Uxi, would be in the form of f'g +g'f, with f = xix, and f' = xixx, being the its derivative with respect to x, and therefore that g = Uxi, and g' = Uxi,x, being the its derivative with respect to x, that is, partial d squared U over partial xi partial x. I hope this is clear, and I am sorry I have not been able as yet to master Latex, so I can only portray the derivatives in another way I hope can be understood. So what I do not understand is why the uxx has squared terms, and other things, and where it has come from. From this, also, what the Canonical Form means, and what it is meant to look like. Thank You. Chris the Russian Christopher Lilly 06:07, 29 April 2017 (UTC)
Is the following problem NP-hard:
Input:
Question: is there a multiset of indices , such that and ?
For example, on the input , we can take and thus we get and , as desired. 213.8.204.26 ( talk) 07:28, 29 April 2017 (UTC)
Let's say I want to rank Wikipedia articles by their mean pageviews (from most popular to least popular). But there are such articles as Dr. Seuss, that makes this list not so reliable (if using standart mean formula). What could you suggest to have those peaks "removed"? -- Edgars2007 ( talk/ contribs) 21:08, 29 April 2017 (UTC)
Mathematics desk | ||
---|---|---|
< April 28 | << Mar | April | May >> | April 30 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
The volume of a spherical cap of height and sphere radius is
I want to solve for . So I plug it into Wolfram Alpha here: https://www.wolframalpha.com/input/?i=v+%3D+pi%2F3+*+h%5E2+*+(3*r-h),+solve+h
The solution is kind of ugly but can be simplified parametrically as
where
The problem is that part under radical . It's always a negative number no matter what I plug in.
For example, if then . But plugging those values in results in a negative square root argument, .
The weird thing is, I've used this before, and it worked. I'm wondering if I made a typo that I'm just not seeing. ~ Anachronist ( talk) 00:24, 29 April 2017 (UTC)
I am a bit confused about the principal part of the PDE, and what its roots mean for the dy/dx = λ , and and how that came about. I understand that the sign of the discriminant b squared minus 4ac determines whether the PDE is Hyperbolic, Parabolic, or Elliptic, but as to the roots of from the related quadratic equation, I am a bit mystified. I understand that the roots are used to determine the coefficients of x in PDE's that might have general solutions such as f( m1x + y) + g(m2x + y ), where m1 and m2 are the roots, and therefore the coefficients of x in this form of solution, but as to stuff about the canonical form, I am confused. I see that for this, where we have the principal part of the PDE of second order being Auxx + Buxy + Cuyy, where for example, uxx is just the second partial derivative of u with respect to x, and so on, then we have a change of coordinates, letting xi = xi(x,t), and tau = tau(x,t), so that in terms of these new coordinates, by the Chain Rule, we have : ux = xix*Uxi + taux*Utau, and ut = xit*Uxi + taut*Utau, and that makes sense, but then I do not get why the second derivative of u with respect to x is what it is. I thought it would simply be partial d/dx of this ux expression, but done by the power rule, so that d/dt[xix*Uxi, would be in the form of f'g +g'f, with f = xix, and f' = xixx, being the its derivative with respect to x, and therefore that g = Uxi, and g' = Uxi,x, being the its derivative with respect to x, that is, partial d squared U over partial xi partial x. I hope this is clear, and I am sorry I have not been able as yet to master Latex, so I can only portray the derivatives in another way I hope can be understood. So what I do not understand is why the uxx has squared terms, and other things, and where it has come from. From this, also, what the Canonical Form means, and what it is meant to look like. Thank You. Chris the Russian Christopher Lilly 06:07, 29 April 2017 (UTC)
Is the following problem NP-hard:
Input:
Question: is there a multiset of indices , such that and ?
For example, on the input , we can take and thus we get and , as desired. 213.8.204.26 ( talk) 07:28, 29 April 2017 (UTC)
Let's say I want to rank Wikipedia articles by their mean pageviews (from most popular to least popular). But there are such articles as Dr. Seuss, that makes this list not so reliable (if using standart mean formula). What could you suggest to have those peaks "removed"? -- Edgars2007 ( talk/ contribs) 21:08, 29 April 2017 (UTC)