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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
A parabolic segment is the region bounded by a parabola and line. To find the area of a parabolic segment, Archimedes considers a certain inscribed triangle. The base of this triangle is the given chord of the parabola, and the third vertex is the point on the parabola such that the tangent to the parabola at that point is parallel to the chord.
giving the basic form of Brahmagupta's formula. It follows from the latter equation that the area of a cyclic quadrilateral is the maximum possible area for any quadrilateral with the given side lengths. A related formula, which was proved by Coolidge, also gives the area of a general convex
The area of a triangle can be demonstrated, for example by means of the congruence of triangles, as half of the area of a parallelogram that has the same base length and height. A graphic derivation of the formula T = h 2 b {\displaystyle T={\frac {h}{2}}b} that avoids the usual procedure of doubling the area of the triangle and then halving it.
Overview of particular steps and tools used when solving plane triangles The standard method of solving the problem is to use fundamental relations. Law of cosines a 2 = b 2 + c 2 − 2 b c cos α b 2 = a 2 + c 2 − 2 a c cos β c 2 = a 2 + b 2 − 2 a b cos γ {\displaystyle {\begin{aligned}a^{2}&=b^{2}+c^{2}-2bc\cos \alpha \\b^{2 ...
The quadrants may be named or numbered in various ways, but the quadrant where all coordinates are positive is usually called the first quadrant. If the coordinates of a point are ( x , y ) , then its distances from the X -axis and from the Y -axis are | y | and | x |, respectively; where | · | denotes the absolute value of a number.
The expression reads "All Science Teachers Crazy" and proceeding counterclockwise from the upper right quadrant, we see that "All" functions are positive in quadrant I, "Science" (for sine) is positive in quadrant II, "Teachers" (for tangent) is positive in quadrant III, and "Crazy" (for cosine) is positive in quadrant IV.
The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not be confused with the mass moment of inertia.