# general

1. ### How to express a cubic polynomial in general form

How to express a cubic polynomial in general form, I have a cubic polynomial as, ax3 + bx2 + cx + d = 0. How to express in general form. Suppose, If we have quadradic equation as ax2 + bx + c =0, we can express as x = -b +sqrt(b2 - 4 ac)/ 2a and -b - sqrt(b2 - 4 ac)/ 2a My question is, In...
2. ### Two general sequence summation

As shown in Chinese wikipedia "Summation" For \sum_{k=1}^n p(k) \begin{align*}\sum_{k=1}^n p(k)=\begin{pmatrix}C_n^1 & C_n^2 & \cdots & C_n^{m+1}\end{pmatrix}\begin{pmatrix}C_0^0 & 0 & \cdots & 0\\-C_1^0 & C_1^1 & \cdots & 0\\\vdots & \vdots & \ddots & \vdots\\(-1)^mC_m^0 &...
3. ### Suggestions for demonstrative speech on Trigonometry or math in general.

Hello, all. On Monday, I will be doing a demonstrative speech on Trigonometry. The speech I am doing, is for my public speaking class, and it will last around 5-7 minutes. With this in mind, I am allowed to use a powerpoint, so I am thinking of ideas or applications that are useful in...
4. ### Help with control theory and general solutions to characteristic eq.

Can somebody explain very basically the general solution to the characteristic equation below. max_u \int (-x - (1/2)u^2)e^{-2t} dt x` = x+u x(0)=1 x(T) free u(t) in +/- infinity I am fine with setting up the Hamiltonian etc but I get lost with the general solutions for the following two...
5. ### Find the General Solution (eigenvalues)

Find the general solution of the system: x' = -x+5y+4z y'= -x+5y-z z'=-6z So after setting it up in a matrix, I'm unsure of what to do next. Could anyone help? Thank you!
6. ### Recursive and General Formula Finding - not done maths for 20 years

Hi All I am new to the forum and though you may be able to help. I want to check I have the following questions correct before going any further: (a) Find, showing all working, a formula for the n-th term tn of the sequence (tn) defined byt1 = 6; t(n) = −3t(n−1)/2, n ≥ 2. (b) Find, showing...
7. ### General question in Fuzzy theory

Hello every body Please let me know , what is Ã , B~ ,.. (fuzzy fuctions)called ? These are called a-tiled , b-tiled ,... ? Thanks
8. ### General question

Hello every body Please let me know is the additive identity (0,0) means neutral member of sum operation in complex number ? And if yes why we should write identity additive because of identity mean ?? Thanks
9. ### Alleged IDENTIFICATION&CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS

Beer soaked ramblings follow. Was googling for a book title when I came across the following thread: http://www.cs.trinity.edu/rjensen/temp/DeeleyAnnuityCorrections.pdf Also found (for Sir D's benefit, says he's having problems loading pdf files) at ?IDENTIFICATION AND CORRECTION OF A...
10. ### General and Particular Solutions

Stuck on these 2 questions, I know how to find general solution but how do you find particular solution when you have both X and y in derivative? I tried using separation of variables then subbing in given value to find k then tried re-arranging to make y subject but I am still stuck [emoji20]
11. ### Simple Harmonic Motion - General Solution

(a) Show that x = a sin ωt + b cos ωt is a general solution of the equation, d^2x/dt^2 + kx/m = 0, and (b) determine the constants a and b in terms of the A and Φ of the equation, x = A cos(ωt + Φ).
12. ### General performance question

Motivation: I am to deliver an exam chemical project on pyridine at 12 noon this day. The project is about comparing geometrical (bond angles/lengths) performance differences between three different methods, namely: molecular mechanics where I use the MM2 force field and two ab initio methods...
13. ### general solution of a 2nd order ODE using substitution

The question is, by making the transformation U=Xa Y where α is a constant to be found, findthe general solution of Y''+(2/x) y'+9y=0 I'm really struggling on this I've already subbed in the new values for Y but I then became stuck. I can see that it a variation of a Bessel Equation and tried...
14. ### Find the general solution to the linear system

Hello, I got four equations from this: 1. x_1 + x_4 = 3 2. x_2 + 2x_4 = -5 3. x_3 + x_4 = -1 4. 0 = 0 Where am I supposed to go from here? I could solve for x_4. 1. x_4 = 1 - (1/3)x_1 2. x_4 = (-5/2) - (1/2)x_2 3. x_4 = -1 - x_3 I just don't quite understand what the general solution...
15. ### General form of equation of life.

So I know the general or standard form is ax+by=c I converted an answer into standard form, my professor said " ax must be positive whole number" B and C does not matter. Well in my book the answer made "C" into a whole number as opposed to how it was normally as a fraction. So does C have...
16. ### make a general formula

How do I make a general formula for k=1,2,3,... that behaves like so. If odd, the scalar is a, If even, the scalar is b, Also the binomial exponents alternately increase by 1 after each iteration, starting with the first binomial. p(1)= (1-a)^0*(1-b)^0* a^1 *b^0 p(2)= (1-a)^1*(1-b)^0* a^0...
17. ### Finding a DE from a 2nd Order General Solution

In order to find a DE from the general solution of a first order equation, we use implicit differention, so should we try implicit differentition twice to find the DE from solution to a 2nd order equation? How about y = c_{1}e^{-2x} + c_{2}e^{3x} ? Now if we had a general solution to a first...
18. ### Finding a specific solution for a general term in a sequence and a general strategy

A problem says to: Write the nth general term of the following sequence: 1, 16, 243, 4096, and 78,125......etc The answer given is n(2+n) Is that the correct answer? Also, what is a general strategy for solving such problems? Is there anything better than just guessing a pattern?(Doh)
19. ### Trig equation help, along with general question about Trig problems.

I'll start out with a question. It seems that even when I use perfect algebra to figure these questions out, I can potentially come to multiple polynomial functions. Mostly if I divide both sides, but isn't that valid when dealing with equations? I won't ramble and get to the point. What is it...
20. ### General form of an equation of a straight line

Ok this seems easy but I am little confused... I am trying to find the general equation of a straight line that does not pass through the first quadrant. Looking at y= mx +c , I realise m will have to be negative and c negative for sloping lines but I can't encapsulate the vertical lines and...