Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an...
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). â Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/â¦...
Clash Royale CLAN TAG #URR8PPP up vote 16 down vote favorite 4 Hello I was wondering what was the function $f$ defines like this : Let $f(x)$ a continuous and differentiable function such that : $$f(x)=sum_k=0^inftyfracf'(k)k!(-x)^k$$ In fact can't solve it but it makes a connection between Ramanujan's Master theorem and Frullani's integral via the Fundamental theorem of calculus I explain : We have : $$int_0^inftyx^-s-1f(x)dx=Gamma(-s)f'(s)$$ Or : $$int_0^inftyfracx^-s-1f(x)Gamma(-s)dx=f'(s)$$ Now we use the Fundamental theorem of calculus to get : $$int_0^sint_0^inftyfracx^-s-1f(x)Gamma(-s)dxds=f(s)-f(0)$$ Now we take the limit to get : $$lim_stoinftyint_0^sint_0^inftyfracx^-s-1f(x)Gamma(-s)dxds=f(infty)-f(0)$$ Wich is equal to: $$int_0^inftyfracf(ax)-f(bx)ln(fracab)x$$ So my question is what is the function $f(x)$ , there exists a closed form to this ,is it trivial or not ? Thanks Ps:I know it's not very rigorous but I think it's intere...
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