doubt

1. Why is discriminant taken to be zero when finding the range of y?

So, I was given a question which went like this y=Quadratic/Quadratic, find range of y. So, my teacher said that I needed to make a quadratic in x by taking all the terms in one side and then I had to make the discriminant greater than or equal to zero since x is real. But, discriminant is...
2. Chi square test doubt

Good evening, I have this problem: I have several groups of type individuals, from A to F let's say. For a given condition, I have my observed values that comply with the condition (in a sample that sums N1 subjects) and a control value (the same type of group) but that does not complies that...
3. comparing power series doubt

suppose I have two power series. e^x-x=1+\frac{x^2}{2!}+\frac{x^3}{3!}+\frac{x^4}{4!}+ \frac{x^5}{5!}+... e^{x^2}=1+\frac{x^2}{1}+\frac{x^4}{2!}+\frac{x^6}{3!}+..... can I say e^{x^2}>e^x-1 because \frac{x^2}{2!}<\frac{x^2}{1} ,\frac{x^3}{3!}<\frac{x^4}{2!} and so on term-by-term.... will this...
4. Beginner Linear Algebra doubt

consider the two vectors y and z: \begin{align} z &= \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix} \end{align} \begin{align} z &= \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \end{align} I know that these vectors span a 2 dimensional space(A plane). Does that mean the vectors span...
5. Doubt on the definition of the inverse of a group element

The following is an excerpt from Milne's Group Theory lecture notes handed down on Winter 1994 at the University of Michigan. Could somebody please explain me the highlighted passage in the document? It's very small.
6. doubt in differentiation

Hi all, I am new to this forum, I wanted to differentiate the with respect to vk. I attached my file. Can any one help me in this. Thank you in advance
7. doubt in equation

what does mean that delta equal to SIXTH DEGREE.how delta become a^2*b^2*c^@(i.e product of leading diagonal element).Thank you in advance
8. M / M / 1 Queue, doubt about the output

Hi, guys. I'm starting my studies about queues and I wanna know if in a M / M / 1 wait queue with rate lambda (poisson) as the input, the output is a poisson process too. It's like below: input (lambda tax) ---> wait queue ---> output (what i wanna know) ---> server (mi tax)...
9. M / M / 1 wait queue with rate lambda (poisson) as the input, doubt about the output

Hi, guys. I'm starting my studies about queues and I wanna know if in a M / M / 1 wait queue with rate lambda (poisson) as the input, the output is a poisson process too. It's like below: input (lambda tax) ---> wait queue ---> output (what i wanna know) ---> server (mi tax)...
10. Bounded Lattice doubt

Hello R--> means is related to E --> means is an element of Let L be a lattice Upper Bound : i E L such that a R i for all a E L. Lower Bound : o E L such that o R a for all a E L. A bounded lattice is one which has both upper and lower bounds. The above definition does not seem to be...
11. Set theory doubt: intersection and union

We can define Union, within sets A within a set P, by the expression: {x| x E A for some A E P} The expression for intersection goes as: {x |x E A for all A E P} Why does union use the operator "for some" and intersection use the operator "for all"?
12. Easy doubt on second-order logic

Why does the negation of the operator "For all" results in the operator "There exists", and vice-versa?
13. Doubt on the Axioma of Separation (Russel's Paradox)

How can this evade Russel's Paradox? If p is a property, for any X, there exists a set Y = {x E X;P(x)} If P(x) = x ~E x (a set x cannot contain itself) ^ Y = x Then Y E X ^ Y ~E Y A paradox: Y E X and Y ~E Y cannot coexist
14. doubt

Virtually every business can benefit from expert SEO services. It is common for business owners to neglect this important marketing piece, particularly those that are not Internet savvy themselves. However, regardless of your own web usage, there is not doubt that you have potential customers...
15. Doubt

differentiate respect to (x) 2^x In this case my friends do like this y=2^x lny=xln2 Then differentiate both side respect to x In the second step how we take a variable in front of log,we only take a constant to the front of log.. please give me a solution
16. complex number in polar form argument and modulus doubt

Pls share ur ideas i wish to knw were i have gone wrong or is the text answr is wrong pls help(Headbang)(Headbang)(Headbang)
17. Fixed point iteration doubt

Hi! I was asked to find an approximation for a root of f(x)=2sin(x\pi)+x=0 on the interval [1, 2] using the fixed point iteration method, with p0=1. So, I got g(x)=x=(\arcsin(-x/2))/\pi However, that way I just get numbers very close to zero (which is a solution for the equation, but it's not...
18. A doubt on stastical independence , orthogonality and uncorrelatedness ?

Hi friends, I wanted to make my concepts on statistical independence, uncorrelatedness and orthogonality clear. Suppose I have 2 random variables x and y. I have 2 pictures on the above concepts, which is more general picture? If you finds any mistake in the picture , please...
19. Matrix multiplication doubt

I have to do a matrices operation given as A.X=B where A is an 1X1 matrix, x is a 3X1 matrix and B is a 3X3 matrix with elements of 3rd column zero. here A is unknown term and i wish to find the value of A. please guide me on how to solve this problem?
20. Compond Interest and Annuity doubt!?

1)Mr. Paul borrows 20000 on condition to repay it with C.I. at 5% p.a in annual installments of .2000 each. The number of years for the debt to be paid off is? 2)A person invests 500 at the end of each year with a bank which pays interest at 10% p.a C.I. annually.The amount standing to his...