1. A

    Help : Deriving an inequality related to Lucas Sequence

    Hi, I am studying a paper by Yann Bugeaud (click here), on page 13 there is an inequality (16) as given below- $\Lambda:=\left|\left(\frac{\alpha(\gamma-\delta)}{\gamma(\alpha-\beta)}\right)\left(\frac{\gamma^{s}}{\alpha^{r}}\right)^{-d}-1\right| \ll \alpha^{-\eta r d}$ which is obtained from...
  2. J

    Deriving Ito process with a drift from geometric Brownian motion.

    Please help me solve this question. Thank you. Let the Geometric Brownian motion be: ∆S/S=µ∆t + σϵsqrt(∆t) ∆S = change in stock price (s) µ = expected rate of return σ = volatility of shock ϵ has standard normal N(0,1) distribution σϵsqrt(∆t) = stochastic companion...
  3. 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...
  4. M

    How to find the rotation vector by deriving the final vector with respect to the disp

    My understanding of a rotation of a vector can be done by using a 2D rotation matrix as shown below, $R(\theta )=\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \\\end{bmatrix}$. This rotates column vectors by means of the following matrix multiplication...
  5. A

    Help with deriving formula

    Can you help to derive a formula that can calculate b2, b3, b4 where T = a1(b1) + a2(b2) + a3(b3) + a4(b4) a1=a2=a3=a4=0.25 b1+b2+b3+b4=1 b1<b2<b3<b4 b1 = x1 T = y For example, one solution is b1=16%, b2=26%, b3=46% for Y = 2 and x1=12% 2 = 0.25(12%) + 0.25(16%) + 0.25(26%) +...
  6. B

    Deriving Functions Problem

    Suppose that g is a real valued, differentiable function whose derivative g' satisfies the inequality |g'(x)|less than or equal to M for all x in R. Show that if epsilon is greater than 0 is small enough, then the real valued function f defined by f(x)=x+epsilon*g(x) is one to one and onto...
  7. J

    Deriving y=W[x] (Lambert W (Omega) Function / Product Logarithm)

    Given the function: y=W[x] Where W[x] is the Lambert W (Omega) Function, also known as the Product Logarithm, how might I find the derivative, y'? For example, I know that: y'=d/dx[W[x]] But that's not very helpful. What is the proper way to write that in terms of y'?
  8. F

    Problem deriving radius from volume

    Having a bit of trouble with this question. 'The volume of a cylinder is 53 m3. If the height is five times the radius R, find the length of R to 3 sig. fig.'
  9. M

    Deriving Equation for Intersecting Cylinders Surface Area

    I'm really struggling in trying to find an equation to describe this part it terms of surface area (material useage). Variables, as seen in the picture, are d1, d2, d3, and (a) angle. L1 is not a variable and neither is branch length, both can be calculated from the previous noted variables. Any...
  10. X

    Deriving Equations for Laws of Motion

    Guys I am trying to teach myself calculus, and I have stumbled across these manuals my dad had and there are a few problem series that I need help with. Any suggestions or direction to help outside the forum is appreciated. 1) Suppose a body "A" does not begin at rest, but instead starts with...
  11. I

    Deriving the equation for an arbitrary curve

    I have the curve in this attachment (the red line) and I'd like to determine an equation for it so I can duplicate it in a program. Any idea how I might go about doing that? Thanks.
  12. J

    Deriving an equation for a function of two variables for a simulation

    Hi, I am having difficulty deriving an equation for a simulation for a moving laser on a test piece. The problem is: I have three different variables, Heat flux (h), time (t) and displacement in the y coordinate. The y axis ranges from y=0 to d, where d is the length of the test piece...
  13. C

    deriving the cdf of the unconditional time to trial purchase

    The problem is that time until first event is distributed exponential with rate parameter lambda, and the time until second event is distributed exponential with rate parameter mu. How do i derive the cdf of the "unconditional time to the second event"?
  14. Mr Davis 97

    Deriving the formula for summing a sequence of squares

    If we have the sequence 1^{2}, 2^{2}, 3^{2}, 4^{2},\cdots n^{2}, how do we derive \sum_{k = 1}^{n}k^{2} for any positive integer n?
  15. M

    deriving a line's equation

    I am attempting to find the equation of a 'perpendicular bisector'. So let's assume I have calculated the gradient and a point on the line correctly, they are: (-1,1) with a gradient of -5 I now ought to be able to find the equation of the line [ax + by +c = 0]: y - y1 = m(x - x1) y...
  16. A

    generating expressions instead of deriving solutions

    generating expressions instead of deriving solutions All possible expressions could be generated and each one tried out as a possible solution of a given problem. Once in a while we would find it to be an actual solution. This process of generating expressions as mere combinations of symbols...
  17. H

    deriving equations

    hi, "The rate of decay in time of the electric current ' i ' in the LR circuit is proportional to the current with the coefficient of proportionality R/L" The differential equation derived from the above statement is; di/dt = -Ri/L im trying to solve it in the general form for i, (that is...
  18. Z

    Problem with deriving oblique projection eq

    Hi, Can some body plz guide me how the values of xp and yp in case of oblique parallel projection is equal to: xp= x + L cos (phi) yp= y + L sin (phi) This is mentioned in slide 50 of following link: I also found that oblique...
  19. B

    deriving hyperbolic function

    g(x) = b/(x -m) + n x = 1 axis of symmetry The graph pass point A(3;4)
  20. Y

    deriving number

    Wonder you know how to derive the figure below Column a and b number and column c is different of a and b Column d is ratio of a and b Is it possible to derive XXX using 1.030092744 1.061587913 (column d) and second row 45.41 (Column c) WITHOUT using first row a and b 785.25 762.31 ...