1. Chemist116

    How do I find a constant in an oscillation as given by a sphere in motion?

    The problem is as follows: The acceleration of an oscillating sphere is defined by the equation $a=-ks$. Find the value of $k$ such as $v=10\,\frac{cm}{s}$ when $s=0$ and $s=5$ when $v=0$. The given alternatives in my book are as follows: $\begin{array}{ll} 1.&15\\ 2.&20\\ 3.&10\\...
  2. tahirimanov19

    Euler-Mascheroni constant

    Is there a way to find the (approximate) value of $\gamma$ only with pen and paper? (No software, no simulation.)
  3. I

    Constant function

    Hello all, What are the extreme values of the function f(x)=C where C is a real constant? All the best, Integrator
  4. shunya

    The mathematical constant e (Euler's constant)

    The mathematical constant e (2.7182818...) is given by the formula: e = limit of (1 + 1/x)^x as x approaches infinity. I used the graphing tool Desmos and graphed the function y = (1 + 1/x)^x and saw the following results: 1. Horizontal asymptote at y = e 2. vertical asymptote at x =...
  5. T

    Deriving the constant acceleration formulas using functional notation.

    Hi, So I was trying to develop a more in-depth understanding of the constant acceleration equations, especially v^2 = u^2+2as. I found a video showing the derivation of this formula: JnFykw00HvE His logic goes like this. 1: Acceleration is the derivative of velocity w.r.t. time. a = dv/dt...
  6. E

    Inequality with integrals

    Let "k" be a constant on [1/4;1]. Prove that exists:
  7. S

    Show that A and B are constant

    Any help with that if you have some free time ? Show that A and B are constant A = sin6(x) + cos6(x) + 3sin2(x).cos2(x) B= 2sin4(x) - cos4(x) - 2sin2(x)
  8. S

    Constant angle protractor?

    Is there a protractor/compass that keeps a constant angle where one arm automatically moves the other arm? Say the protractor is closed at a 0 degree angle, you move one arm and the arm follows exactly opposite to it on the other side?
  9. S

    The biggest constant

    What is the biggest constant [except the radius of the universe or diameter of it]? Thanks for the responders...
  10. W

    Constant solution

    I want to find constant solutions of the differential equation $\frac{dy}{dx}=\frac{y^3}{x^2}-2\frac{y}{x}$. I set $y=c$, where $c$ is a constant. Then $\frac{dy}{dx}=0$ and the differential equation becomes $0=\frac{c^3}{x^2}-2\frac{c}{x}$ $\frac{c}{x}(\frac{c^2}{x}-2)=0$ $c/x=0$ or...
  11. D

    e (mathematical constant)

    Is this a proper expression of the Euler's number?
  12. D

    Constant C in differential equation

    Hi guys, $$\int {}\frac{1}{ky}dy =\int dx \rightarrow \frac{1}{k}\ln \left | y \right |=x+C$$ Why is C only on the right side and not on the left side? Thanks in advance
  13. idontknow

    Constant pi

    \pi is an irrational ratio \frac{P}{d}=\pi=3,14... Does there exist any more accurate rational ratio than \pi ? (can it be showed)
  14. L

    Linear Differential equation with constant coefficient

    A solution of $(D^2+1)^3y=\sin x$ is A) \sum_{n=1}^{3} (c_nx^{n-1}\sin x+d_nx^{n-1}\cos x) for some c_n, d_n \in R, 1 \leq n \leq 3. B) \sum_{n=1}^{3} (c_n \sin^n x+d_n \cos^n x) for some c_n, d_n \in R, 1 \leq n \leq 3. C) \sum_{n=1}^{3} (c_n \sin n x+d_n \cos n x) for some c_n, d_n \in R, 1...
  15. S

    Constant of the Integral as a derivative?

    Hey, I was solving this integral on a website: ∫ sin(x)cos(x)dx And I got two answers. One of them was this one: ½sin^(2)x + c and the other one was this one: -½cos^(2)x + c But on the site it shows this solution: -½cos^(2)x + c' where the constant is a derivative. I plugged the...
  16. S

    Multiplying f(x) with constant and x with constant is same thing?

    I am confused between multiplying whole function by constant and multiplying constant with its input. If let say there is a function defined as: $$F(x) = |x|$$ I can also write it like this in piecewise manner: $$ f(x) = \left\{ \begin{array}{lll} x & \quad x > 0...
  17. Z

    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...
  18. B

    Twin Prime counting function & Euler constant

    Hi everyone! I am new to the forum. In my spare time, I've been trying to find a way to count twin primes under any given x. I know there is a method that exists that utilizes the Twin Prime Constant. Anyways, I found the distribution of twin primes to be related to the Euler-Mascheroni...
  19. A

    unknown irrational constant

    approximate value : 0.3870390470848429822823913196442811150500998690060248818618095564586669754193505496422679380718579227......
  20. W

    Mimicking RC time constant

    I have a signal which is sampled every 0.2 seconds and decided I wanted to apply a simple filter to the data. I could have simply applied a nice 4 point moving average, but I wanted to go 'cheaper'. I figured if I took 3/4 of the current value and added 1/4 of the next value to come in, I'd...