# coefficients

1. ### How do I find the minimum force done by a person pushing a box when two coefficients?

The problem is as follows: A box of $320\,N$ is at rest over a horizontal terrain. The coefficients of friction between the box and the terrain are $0.36$ and $0.48$. A girl is pushing the box with her arms making an angle of $37^{\circ}$ with the horizontal. Find the magnitude of the minimum...
2. ### Lotka-Volterra with periodic coefficients differential inequality

I would like to ask which transformation should I use to recive from this Lotka-Volterra inequality xâ€²=x(aâˆ’bxâˆ’cy)<x(aâˆ’bx), this differential form x(t)\leq \frac{x(T)e^{A(t)}}{1+x(T)\int \limits_{T}^{t}e^{A(s)}b(s)ds}, \text{where} A(t)=\int_T^t a(s)ds.
3. ### Undetermined coefficients

Hello everyone, In this equation what will be the answer guess for 12t^-2e^(-3t/2) I know polynomial guess Trigonometric guess Exponential guess But didnâ€™t come across t^negative power :( Thanks
4. ### I would like some help with factoring quadratic equations with leading coefficients.

Hello. I seem to have some problems factoring quadratic equations when the leading term has a coefficient. Here is an example 3w -7 = sqr(8w -7) (3w -7)^2 = (sqr(8w -7))^2 9w^2 -42w +49 = 8w -7 9w^2 -50w +56 = 0 Ok so here we have a standard form quadratic equation with a leading...
5. ### Polynomials with integer coefficients

Hello, I want to prove that for P, Q two unitary polynomials with rational coefficients, if PQ's coefficients are integers then both P and Q are of integer coefficients. I'm trying to look for a starting point. Any advice? Thanks!
6. ### Method of finding polynomial series coefficients?

Recently, at work, an application came up where I had a series that I suspected was generated by successive terms of a polynomial and I needed to find the coefficients of that polynomial, similar to the problem in this thread (Reference 1). I give another sample calculation in Reference 1, with...
7. ### Method Of Undet. Coefficients question

Hi everyone! I'm really struggling with this problem Solve X' = AX + F(t) with A = ( 1 2 , 2 4) and F(t) = ( t , 2e^(5t) ) A and F(t) are both matrices, I'm not sure if there was a better way for me to write them. I think I need to use method of undetermined coefficients, and I...
8. ### Linear Ordinary Differential Equation with Constant Coefficients

Linear Ordinary Differential Equation with Constant Coefficients. This is a concise outline and summary of a solution paradigm for the topic, ie, just follow the steps, and do and interpret the resulting algebra. L(y) = a_{0}y^{(n)}+...+a_{n-1}y'+a_{n}y = 0 By substitution, e^{rx} is a...
9. ### sum containing binomial coefficients

Prove that prove that $\displaystyle\binom{2n}{n}>\frac{4n}{n+1}$ for all $n\geq 2$
10. ### pascal's triangle proof with binomial coefficients

Hey I wasn't sure exactly where to put this, but since here in the states you normally start to use binomial coefficients in stats I put it here. So I was doing a problem in a book were I had to prove that (n + 1 choose k) equals (n choose k - 1) + (n choose k). I came up with the...
11. ### Linear first ODE with variable coefficients

Hi! I used to go about solving linear ODEs with constant and variable coefficients. Upon my knowledge all the times the ones with variable coefficients, the coefficients would be dependent on the one independent variable 'x' say. For example, consider the following ODE: q(x)= A(y) ...
12. ### A Maclaurin expansion of arccos(-z) using only non-negative coefficients

I am trying to express the function $f(z) = \arccos(-z), \lvert z \lvert \leqslant 1$ with a Maclaurin expansion using only non-negative coefficients in a compact form as $$f(z) = \sum_{n=0}^\infty a_nz^n, a_n\geqslant0 \;\;\;(1)$$ From trigonometric identities and...
13. ### Identity with binomial coefficients

I have to show that \sum \limits_{n=m}^\infty \binom{n}{m} x^{n-m} = \frac{1}{(1-x)^{m+1}} for m \geq 0 and \forall x \in \mathbb{C} with \|x\| <1 . If I compute the left side I get \sum \limits_{n=m}^\infty \binom{n}{m} x^{n-m} =...
14. ### Factorials, central binomial coefficients and number factorization

Hi, I have this problem: It's very well know that if I have a number N = p*q, with p<q I can find the divisors of N in this way: I calculate sqrt(N)! and surely p is a divisor of sqrt(N)! but q is not, so I can do an euclidean algorithm between sqrt(N)! and N and I find p. What if...
15. ### Central binomial coefficients and factorials

Hi, if I have a central binomial coefficient, that is, (2n)!/(n!*n!) how can I find n! ? In general, is it possible to find a factorial from a central binomial coefficient? Thank you olmoelisa
16. ### Quadratic with odd coefficients

Have no clue where to start a thread - but I ended up here where I can actually write something so i'm gonna just post my question I need help with! Thanks and please respond. Suppose that a quadratic P(x) has all odd coefficients. Prove that P(x) = 0 has no rational roots. Polynomial: is not...
17. ### Hey, need help finding series coefficients

The details in the pic. Thanks in advance for all
18. ### Partition coefficients and mass balance calculations

Dear all, So, imagine we have a planet before the core being formed. I want to calculate the amount of X (in this case sulfur) that will partition in the core of a planet. For example, we have 1000 ppm of S in the whole planet (before the core being formed). I know the partition coefficient...
19. ### partial fractions equating coefficients

Question is - express (x^2+1)^2/(x^2-1)^3 in partial fractions We get (A/x+1)+(B/x-1)+(C/(x+1)^2)+(D/(x-1)^2)+(E/(x+1)^3)+(F/(x-1)^3 to give (x^2+1)^2=(A(x+1)^2*(x-1)^3)+(B(x+1)^3*(x-1)^2)+(C(x+1)*(x-1)^3)+(D(x+1)^3*(x-1))+(E(x-1)^3)+(F(x+1)^3) Letting x=1 & x=-1 gives us E=-1/2 & F=1/2 And...
20. ### Interpretation of regression coefficients

Hi, I have problem with interpretation of regression coefficients. My regression function is: y = a + b1*x + b2*x^2 How can I interpret b1 and b2 ?? Its a relationship between monetary aggregate M2 (X) and GDP (Y). There are coefficients: y = 588,63 + 0,6312*x - 0,000005*x^2...