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In two dimensions, 2x 1 + 2x 2 is the perimeter of a rectangle with sides of length x 1 and x 2. Similarly, 4 √ x 1 x 2 is the perimeter of a square with the same area, x 1 x 2, as that rectangle. Thus for n = 2 the AM–GM inequality states that a rectangle of a given area has the smallest perimeter if that rectangle is also a square.
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.
Originally, the Model 10 was sold to law enforcement only. The concept of this shotgun was quite interesting to many police agencies who adopted the Model 10 in the late 1960s and early 1970s; however, most of the agencies found many shortcomings, and ultimately ceased using the Model 10. The most common problem was the failure to cycle correctly.
Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.
In the same way, an extension K 2 of K 1 can be constructed, etc. The union of all these extensions is the algebraic closure of K , because any polynomial with coefficients in this new field has its coefficients in some K n with sufficiently large n , and then its roots are in K n +1 , and hence in the union itself.
The Model T engine was produced for replacement needs as well as stationary and marine applications until 1941, well after production of the Model T ended. The Fordson Model F tractor engine, that was designed about a decade later, was very similar to, but larger than, the Model T engine. [46]