Close-packed structures are arrangements of atoms or ions in a solid that result in the highest possible packing density. The two most common close-packed structures are the cubic close-packed (CCP) structure and the hexagonal close-packed (HCP) structure. In the CCP structure, also known as the face-centered cubic (FCC) structure, each atom or ion is surrounded…
Let $f(x)$ and $g(x)$ be two functions, and let $c$ be a real number. The sum of the two functions $f(x)$ and $g(x)$ is defined by $(f+g)(x) = f(x) + g(x)$ for all $x$ in the domain of both functions. To determine if the sum of $f(x)$ and $g(x)$ is continuous at $c$, we need…
The angle between two lines can be found using the slope of each line. If the slopes of the lines are m1 and m2, then the angle between the lines is given by the formula: θ = arctan(|(m1 – m2)/(1 + m1*m2)|) where arctan is the inverse tangent function. Note that the absolute value is…
A matrix is said to be symmetric if it is equal to its transpose. That is, for an n x n matrix A, A is symmetric if A^T = A. A matrix is said to be skew-symmetric if it is equal to the negative of its transpose. That is, for an n x n matrix…
