# computation

1. ### Card computation with a deck of 40 cards (no pictures)

Using a deck of 40 cards, I turn 6 card face up. If the only straights allowed are the ones from 8 to 10, letâ€™s say 8-9-10, what is the probability to get a straight? Iâ€™m trying to find the solution but Iâ€™m not sure of my findings. Thanks for your help. Inviato dal mio iPhone...
2. ### How to do the computation of a spiral length in a disk using college algebra?

I have found this riddle in my book and so far I've not yet come with an answer which would require the use of college precalculus. In a research facility in Taiwan a group of technicians built a new optical disk which stores information in a spiral engraved in its bottom face named "lecture...
3. ### Series Computation

What is the general method to compute an infinite sum ? I will compute one sum function of f(n,p)=n(p+1)^{-n} and see if it works Let s(n)=\sum^{\infty}_{n=1} np^{-n}\; \; for n \in N and p>1 \sum^{\infty}_{n=1} x^n =\frac{1}{1-x} \; \; \; where 0<x<1 (\sum^{\infty}_{n=1} x^n)'...
4. ### Primes, Complexity and Computation: How Big Number theory resolves the Goldbach Conje

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5. ### Nonzero solutions computation

Hi, I do not know how to start this question and what the question is asking for. Thank you so much! Please help.
6. ### Compare two sums of products without direct computation?

Say you have two sums of products and you want to know which sum is greater. All factors are positive integers. The factors in each product are generally small (< 10), but there may be many of them (in the thousands). Is there a way of determining which sum is greater without directly...
7. ### No calculator computation

Compute \sin\frac{1}{3}
8. ### Computation of matrix inverse: I + A

Let I be the identity matrix, and A be an invertible matrix. Suppose A^(-1) is given. How can we cheaply compute (A + I)^(-1) Can you help me find the right identity. Thank you so much in advance.
9. ### Determinant computation

\text{Can someone give me a hint how to compute this determinant using properties (not rule of Sarrus)?}\\ \begin{vmatrix} -2a & a+b & a+c\\ b+a & -2b & b+c\\ c+a & c+b & -2c \end{vmatrix}

11. ### Computation of an integral.

This problem was encountered here. Subject: computation of the integral \int_{0}^{\infty}\frac{\cos(x)}{\sqrt[3]{x}}\;\mathbb{d}x. \color{red}\rule{500}{2} We will integrate the function f(z)=\frac{\mathbb{e}^{\mathbb{i}z}}{z^{p}} (0<p<1) over the next figure...

Hello, I have questions about signed number representation in computer. It is about the computation of two hexadecimal number. Lets say there are two hexadecimal numbers FF_{16} and 7F_{16}. How do I compute this?? What I know is that I have to convert these two hex into binary and the hex that...
13. ### computation of pi (?)

Hi... I am fairly new to this forum... I was wondering if anyone has a good idea of how the fundamental principles can be used to compute the value of pi (?) with possible historical dates of origin. Any example also will also help. I would be really grateful for any help in this regard...
14. ### Computation of L(4)

Define L(z) = \sum_{n=1}^{\infty} \frac{1}{^z n} I am able to calculate it only for z = 2,3. Mathematica overflows if I try to calculate L(4). Any idea how to compute L(4) ? Any help will be appreciated, Balarka .
15. ### Integral Computation.

Compute the integral \int_{0}^{1}\frac{1}{(x-2)\sqrt[5]{x^2(1-x)^3}}\;dx.
16. ### Product-Series Computation

Prove that \sum_{n=1}^{\infty}\prod_{k=1}^{n}\cos\left(\frac{k\pi}{n}\right)= -0.8.
17. ### Euler Lagrange Equation Computation

Hello, I am reading a paper on evolution problems of the type u(0) = 0 u' (t) = v (t) v(t) = argmin {G (t, u(t), v(t)} The authour claims that the Euler Lagrange equation related to the last equation is dG / dv = 0 (1) I can not understand this. The Euler Equation formally can be...
18. ### Integrals computation: Help!

Hi all, can you help me to compute these integrals? \int \frac{x \sqrt{a x+b+x^2}}{d^2+x^2} \, dx \int \frac{x}{\left(d^2+x^2\right) \sqrt{a x+b+x^2}} \, dx a,b and d are real and positive. I tried with Mathematica, but the results involve logarithmic functions with complex argument...
19. ### Integral Computation!

Compute \int_{0}^{+\infty}\frac{x^{a-1}}{x+1}\;dx for 0<\Re \mathfrak{e}(a)<1.
20. ### Arithmetic mean: Why use its computation as its definition?

Why do teachers/profs and textbooks define the arithmetic mean using its method of computation? For example, they don't do it for the sine function, which they define as the length of the opposite side divided by the length of the hypotenuse of a right triangle. Then they give a method to...