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Laws of motion 5

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Laws of motion 3

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Distance of the centroids of the balls
Given *n* balls of radius *r* and the vector *p (nx3)* with all position *(x,y,z)* of the balls, return the symmetric matrix *A ...

3 years 前

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A disk is placed in a rectangular room with dimensions a and b in a point with coordinates x0 and y0. The disk is given a startu...

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Mechanical Advantage of a Gear Train
Calculate the mechanical advantage of a gear train. The mechanical advantage of a gear couple is given by MA = T_o/T_i where ...

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Energy of an object
Calculate the total mechanical energy of an object. Total Energy= Potential energy + Kinetic energy P.E.=m*g*h K.E.=1/2...

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Combined Ages 1 - Symmetric, n = 3
You have probably seen the common riddle wherein combined ages are provided and you must determine the individual ages. For exam...

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Draw a '1' in a zero matrix!

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Damping of Servomotors with Tachometer Feedback
In Control Engineering, servomotors with tachometer feedback can be modeled by the second order system K / [J*s^2 + (B + K*K...

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Linear system of equations
Solve the system of equations in three variables.

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Laguerre polynomials
Given an integer _n_ ≥ 0, generate the _n_-th <http://en.wikipedia.org/wiki/Laguerre_polynomials Laguerre polynomial>. *Ex...

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Write a function that evaluates the derivative of a function in a given point using the well-know formula of the difference quot...

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Make a diamond
Given n, odd number > 1, return n by n matrix consist of "null" and "*" characters arranged like a diamond. No toolbox funct...

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Sum of series I
What is the sum of the following sequence: Σ(2k-1) for k=1...n for different n?

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Sum of series II
What is the sum of the following sequence: Σ(2k-1)^2 for k=1...n for different n?

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Sum of series III
What is the sum of the following sequence: Σ(2k-1)^3 for k=1...n for different n?

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Sum of series IV
What is the sum of the following sequence: Σ(-1)^(k+1) (2k-1)^2 for k=1...n for different n?

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Sum of series VI
What is the sum of the following sequence: Σk⋅k! for k=1...n for different n?

3 years 前