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Laws of motion 6

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

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Chebyshev polynomials of the 2nd Kind
Given an integer _n_ ≥ 0, generate the _n_-th <http://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev polynomial of the...

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Chebyshev polynomials of the 1st Kind
Given an integer _n_ ≥ 0, generate the _n_-th <http://en.wikipedia.org/wiki/Chebyshev_polynomials Chebyshev polynomial of the...

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Rosenbrock's Banana Function and its derivatives
Write a function to return the value of <http://en.wikipedia.org/wiki/Rosenbrock_function Rosenbrock's two-dimensional banana fu...

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Generalized Laguerre polynomials
Given an integer _n_ ≥ 0 and a scalar _a_, generate the _n_-th <http://en.wikipedia.org/wiki/Laguerre_polynomials#Generalized...

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Geometry: Find Circle given 3 Non-Colinear Points
*This Challenge is to determine the center and radius of a circle given three non-colinear points.* *Input:* Points *Outpu...

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Lambert's W
Matlab cody does not support lambertw. Try to create a lambert's w function yourself. Lambert's W is the function that solves...

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Kepler's Equation
Solve <http://en.wikipedia.org/wiki/Kepler's_equation Kepler's Equation>. Note that the solution is rounded down to 5 decima...

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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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Find the sines of an isosceles triangle when given its area and height
Find the sines of an isosceles triangle when given its area and height. For example, when A=60 and h=5, the result is [0.3752...

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solid of revolution
Given an real polynomial P and two real numbers a,b with 0<=a<=b. Calculate the volume of the solid of revolution made by rota...

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distance to a straight line (2D) given any 2 distinct points on this straight line
Given 2 points P1,P2 on a straight line and a 3rd point, determine the distance of the 3rd point to the straight line. Your answ...

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Radiation Heat Transfer — View Factors (3)
View factors (aka configuration factors) are utilized in some radiation heat transfer models to estimate heat transfer rates bet...

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Radiation Heat Transfer — View Factors (2)
View factors (aka configuration factors) are utilized in some radiation heat transfer models to estimate heat transfer rates bet...

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Radiation Heat Transfer — View Factors (1)
View factors (aka configuration factors) are utilized in some radiation heat transfer models to estimate heat transfer rates bet...

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rectangle in circle
In the figure below, the rectangle at the corner measures a cm x b cm. What is the radius of the circle in cm? <<http://www....

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Edges of a n-dimensional Hypercube
Return the number of edges on an <http://en.wikipedia.org/wiki/Hypercube _n_-dimensional hypercube> (with an integer n ≥ 0). ...

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Right and wrong
Given a vector of lengths [a b c], determines whether a triangle with those sides lengths is a right triangle: <http://en.wikipe...

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Spherical radius given four points
Determine the radius of a sphere provided four non-coplanar points on the surface of the sphere. pts = [x1 y1 z1; x...

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Great Circle Distance
Find shortest between two points on a ball given their azimuthal and polar angles (in degrees) as well as the radius of the sphe...

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Vector parallel to plane?
Given the coefficients of the equation which defines a plane as follows: ax+by+cz=d, return a boolean indicating whether the 2n...

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Parallel vectors
Return true or false depending on whether 2 vectors are parallel or not. Vectors can be 2 or 3 dimensional. The origin is not c...

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Volume difference between Ellipsoid and Sphere
Given an ellipsoid of semi principal axis (a,b,c) find the volume of the difference between this ellipsoid and the sphere with...

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Circumscribed circles
Given the lengths of the 3 sides of a triangle, output the radius of the circumscribed circle. Example: [3 4 5] -> 2.5

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Similar Triangles - find the height of the tree
Given the height, h1, of a power pole, shorter than a tree, a given distance, x2 away, please find h2, height of the tree. Pleas...

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What is the distance from point P(x,y) to the line Ax + By + C = 0?
Given a point, P(x,y), find the distance from this point to a linear line. INPUTS: x, y, A, B, C OUTPUTS: d, the distance ...

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Is the Point in a Circle?
Check whether a point or multiple points is/are in a circle centered at point (x0, y0) with radius r. Points = [x, y]; c...

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Angle between two vectors
You have two vectors , determine the angle between these two vectors For example: u = [0 0 1]; v = [1 0 0]; The a...

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Volume of a Parallelepiped
Calculate the volume of a Parallelepiped given the vectors for three edges that meet at one vertex. A cube is a special case ...

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