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We are given a sorted array containing elements at indices x1,x2,x3,x4,....xn.
We have to find the product ∑(xi * xj * xk) where j>=i and k>=j. For example, in an array {1,2,3,4,5}, the product would involve terms like 1*1*1,1*2*2,1*2*3 and so on.
I have found a solution by brute forcing but I ...
Expansion of a binomial gives:
$$A^3+3A^2+3A+I=0$$
We know that the matrix is regular if squared and has inverse ($detA\neq 0$).
Is it possible to determine from above equation that $detA\neq 0$?
Total ways to do it is $^{n}{\mathbb C}_3$. Java:
int[] array = new int[]{1,2,3,4,5};
ArrayList<Integers> products = new ArrayList<Integer>();
for(int i=0;i<array.length;i++){
for(int j=i+1;j<array.length;j++){
for(int k=j+1;k<array.length;k++){
products.add(array[i]*arra...
We need to solve the given first order partial differential equation :
$(y-xu)u_x$ + $(x+yu)u_y$ = $x^{2} + y^{2}$ .
I tried this :
$\frac{dx}{y-xu}$ = $\frac{dy}{x+yu}$ = $\frac{du}{x^{2} + y^{2}}$ ,
First characteristic equation : $\frac{x.dx - y.dy}{-u(x^{2} + y^{2})}$ = $\frac{du}{x^{...
If I have a gate function $x(t) = \left\{ \begin{array}{ll}
x_0 & \mbox{if $-T < x < T$};\\
0 & \mbox{elsewhere}.\end{array} \right. $
Then:
$$\lim_{T\to \infty} X(\omega) = \lim_{T\to \infty} x_0\int_{-T}^{T}e^{-i\omega t}dt = \lim_{T\to \infty} 2x_0T sinc(\omega T) = \left\{...
I did root test, but then I got stuck. In the end I got infinity/infinity ... can someone please tell me the right answer?
$$\sum_{n=0}^\infty\frac{n^n}{e^{n^2}+1}$$
According to wolfram alpha, the domain of $x^{\ln{y}}$ is $x>0$ and $y>0$ but putting $(-1,1)$ for $(x,y)$ I get a perfectly fine answer of 1?
$y>0$ makes sense, since $\ln{y}$ is only defined there. But why must $x>0$ as well. The only other problem I see is $x = 0, y = 1$ as then we get a $0^...
"Verify if both of this functions are integrable in their domains:
$g(x) = ( ||x||^2 + 1)^{frac{a}{2}}$ to all $a>n$, $domain \in \mathbb{R}^n
h(x) = ||x||^{-||x||}$, defined in $\mathbb{R}^3$
I was doing a homework problem to find the derivative of an equation and got "7" as the answer. I was trying to think about what it means if a derivative is a constant like that, is it just that the function is linear?
