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Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, people are given:
The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
This equation allows the relative density to be calculated from the change in displacement, the known density of the reference liquid, and the known properties of the hydrometer. If Δ x is small then, as a first-order approximation of the geometric series equation ( 4 ) can be written as: R D n e w / r e f ≈ 1 + A Δ x m ρ r e f ...
Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square.Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, d n, between points. [1]
These equations taken together are as powerful and complete as Maxwell's equations. Moreover, the problem has been reduced somewhat, as the electric and magnetic fields together had six components to solve for. [1] In the potential formulation, there are only four components: the electric potential and the three components of the vector potential.
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