# explanation

1. ### Need assistance with solving and explanation of expressions

I came across this equation and not familiar with the expressions and the result. Please provide input for both. Thank you.
2. ### need explanation for integer part

Is this statement true ? \lfloor n/2 \rfloor \approx \frac{n}{2}+ \frac{1-(-1)^n }{4}. \; n\in \mathbb{N} and n\neq 1.
3. ### Need explanation on 2nd DE

Cannot find explanation for this : Why e^{rx} satisfies the equation yâ€™â€™+pyâ€™+qy=0 ? p,q-constants. How to prove it and how to derive it , where it comes from ? My thoughts are to substitute for y=\sum_{}^{\infty} c_n x^{n} and see the results. Method required !
4. ### z-transform example explanation

Hello everyone, I wanted to ask if anyone can explain this task to me, I tried to understand how to get this f(nTs) and I tried to apply some knowledge from Laplace transform but I don't get the same result. What is the step coming to this f(nTs), because afterwards everything is clear and...
5. ### Explanation for factorial !

Why gamma(1/2) is 1/2 \cdot sqrt(\pi) ? Does (1/2)! make sense or applied in physics? If so , then is (1/2)! the product of all real numbers in interval (0,1]?
6. ### PDE solution explanation

Given equation : zâ€™_{x} a(x) +zâ€™_{y} b(y)=c . Why the solution is found by dx/a(x)=dy/b(x)= c/dz ?
7. ### Need explanation

Just give the hint . (1) If a+b+c=0 \; and a\neq b \neq c\; a,b,c real numbers . Show that \frac{a^2 }{bc +2a^2 } +\frac{b^2 }{ac+2b^2 } +\frac{c^2 }{ ab+2c^2 }=1 . (2) Factorize the polynomial : x^7 +x^5 +1 .
8. ### Need explanation on probability

x+y=10 \; \; , x and y are natural numbers. Find probability such that xy\leq 24 .
9. ### Need explanation

Let A denote the largest of the numbers a_1 , a_2 , ... , a_p for p,n \in N Need explanation for \frac{A}{\sqrt[n]{p}}\leq \sqrt[\displaystyle n]{\frac{a^{n}_1+a^{n}_2 +...+a^{n}_p } {p}}\leq A how to show it is true (how to derive?)
10. ### Explanation on Similar Triangle

...I want users of this forum to explain the CONCEPT OF SIMILAR TRIANGLE...finding the unknown sides of similar triangle and about finding the area of trapezium in similar triangles (CLEAR DIAGRAM INCLUSIVE).
11. ### Algebraic explanation of Division

As an elementary student, I've always struggled with arithmetic, in particular, division and multiplication. This had to do with my lack of interest, as I didn't know why we multiplied and divided the way that we did. (why it worked). Having learned algebra, I now fully understand...
12. ### requesting for explanation of surface integration

Evaluate âˆ«âˆ« < x, y, -2 > * N dS, where D is given by z = 1 - x^2 - y^2, x^2 + y^2 <= 1, oriented up. Official Answer: - pi Cross Product: \int_{0}^{2\pi} \int_{0}^{1} ( r cos \theta , r sin \theta , -2 ) * ( 2r^2 cos \theta , 2r^2 sin \theta , r ) ~ dr d \theta \int_{0}^{2\pi}...
13. ### sin(z) = -1 - i with solutions (need explanation)

So I look at the prof's solutions - see attached. I dont understand how he got from (coshy)^2 + (sinhy)^2 = (sinhy)^2(coshy)^2 to cosh2y = 1/4(sinh2y)^2 Then cosh2y = sqrt(5) +2 y = (1/2)ln(sqrt(5)+2 +/- sqrt(8+4sqrt(5)) Then sinx = 2-sqrt(5) x= 2pi - sin(sqrt(5)-2)^-1 +...
14. ### My "P=NP" Explanation

Question: "If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? this is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city...
15. ### Inverse of Percentages - Explanation

Hi Guys, I'm trying to understand something I've come across regarding percentage weights. I have five people with percentages that add up to 100% (n = 5) A = 0.75 A' = 0.0625 A' = (1 - A)/(n-1) B = 0.07 B' = 0.2325 C = 0.06 C' = 0.2350 D = 0.02 D' = 0.2450 E...
16. ### need some explanation about square roots

I know about roots and the quadratic formula, but I need some explanation about what was done here from the part where the square root of 8 became the square roots of 4 and 2 to the end of this, especially the third line.
17. ### triangular membership function equation explanation?

Although I know the equations for triangular membership function but I can't figure out how they are derived. Are they derived from slope of line concept or by some other concept. Need your help guys.
18. ### easy explanation about definition of p-value

Hi, please, I would want to know an easy and linear explanation of the following statement about the definition of the p-value: So let H_0 be the null hypothesis, "the p-value of the test is the probability that a value of the test statistic in the direction of the alternative hypothesis...
19. ### Tensor product - explanation

Hi, can someone please explain me what "intuitively" means "tensor product" and what it is "good for"? As I understand it, tensor product of two vector spaces U,V is the set of all formal linear combinations of elements (ui,vj) where ui (vj) is element of a basis of U (V). Thank you for any...
20. ### I need explanation

[/url][/IMG] http://s30.postimg.org/y6jgjhxb5/angle.png I subtract 121 to 180 degree and got 59 but I am wrong Can someone explain how is this 61?