HSC EV Higher Mathematics 2nd Paper 9th Chapter Note

HSC EV Higher Mathematics 2nd Paper 9th Chapter Note. The motion of Particles in a Plane. Galileo was quoted above pointing out with some detectable pride that none before him had realized that the curved path followed by a missile or projectile is a parabola. He had arrived at his conclusion by realizing that a body undergoing ballistic motion executes, quite independently, the motion of a freely falling body in the vertical direction and inertial motion in the horizontal direction. These considerations, and terms such as ballistic and projectile, apply to a body that, once launched, is acted upon by no force other than Earth’s gravity.

HSC EV Higher Mathematics 2nd Paper 9th Chapter Note. The motion of Particles in a Plane

HSC EV Higher Mathematics 2nd Paper 9th Chapter Note

HSC EV Higher Mathematics 2nd Paper 9th Chapter Note

HSC EV Higher Mathematics 2nd Paper 9th Chapter Note

This article describes a particle in planar motion when observed from non-inertial reference frames. The most famous examples of planar motion are related to the motion of two spheres that are gravitationally attracted to one another, and the generalization of this problem to planetary motion. See centrifugal force, two-body problem, orbit and Kepler’s laws of planetary motion. Those problems fall in the general field of analytical dynamics, the determination of orbits from given laws of force. This article is focused more on the kinematical issues surrounding planar motion, that is, determination of the forces necessary to result in a certain trajectory given the particle trajectory.

The complex number system can be defined as the algebraic extension of the ordinary real numbers by an imaginary number i. This means that complex numbers can be added, subtracted, and multiplied, as polynomials in the variable I, with the rule i2 = −1 imposed. Furthermore, complex numbers can also be divided by nonzero complex numbers. Overall, the complex number system is a field.

Most importantly the complex numbers give rise to the fundamental theorem of algebra: every non-constant polynomial equation with complex coefficients has a complex solution. This property is true of the complex numbers, but not the reals. The 16th-century Italian mathematician Gerolamo Cardano is credited with introducing complex numbers in his attempts to find solutions to cubic equations.

Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and the determinant can be used to solve those equations, although more efficient techniques are actually used, some of which are determinant-revealing and consist of computationally effective ways of computing the determinant itself. The use of determinants in calculus includes the Jacobian determinant in the change of variables rule for integrals of functions of several variables. Determinants are also used to define the characteristic polynomial of a matrix, which is essential for eigenvalue problems in linear algebra. In analytic geometry, determinants express the signed n-dimensional volumes of n-dimensional paralleled.

\Sometimes, determinants are used merely as a compact notation for expressions that would otherwise be unwieldy to write down. When the entries of the matrix are taken from a field (like the real or complex numbers), it can be proven that any matrix has a unique inverse if and only if its determinant is nonzero. Various other theorems can be proved as well, including that the determinant of a product of matrices is always equal to the product of determinants; and, the determinant of a Hermitian matrix is always real.

Is actually a polynomial because it’s possible to simplify this to 3x + 1 –which of course satisfies the requirements of a polynomial. (Remember the definition states that the expression ‘can’ be expressed using addition, subtraction, multiplication. So, if it’s possible to simplify an expression into a form that uses only those operations and whose exponents are all positive integers…then you do indeed have a polynomial equation)

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English Version HSC Higher Math Note