Math 230 E Fall 2013 Homework 1 Solutions Drew Armstrong
... We wish to show that θ = 90◦ if and only if u · v = 0. First we will show that θ = 90◦ implies u · v = 0. Assume that θ = 90◦ . Then the Pythagorean Theorem implies that ku − vk2 = kuk2 + kvk2 , or kuk2 + kvk2 − ku − vk2 = 0. But the result of part (a) says that kuk2 + kvk2 − ku − vk2 = 2(u · v). Co ...
... We wish to show that θ = 90◦ if and only if u · v = 0. First we will show that θ = 90◦ implies u · v = 0. Assume that θ = 90◦ . Then the Pythagorean Theorem implies that ku − vk2 = kuk2 + kvk2 , or kuk2 + kvk2 − ku − vk2 = 0. But the result of part (a) says that kuk2 + kvk2 − ku − vk2 = 2(u · v). Co ...
TRIANGLES
... Similar Figures All congruent figures are similar but the similar figures need not be congruent. Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion). This again emphasises that two ...
... Similar Figures All congruent figures are similar but the similar figures need not be congruent. Two polygons of the same number of sides are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion). This again emphasises that two ...
ppt - ICTS
... Any quality function F depends only on those moments. To analyze the behavior of F, it is sufficient to study the evolution of the moments. ...
... Any quality function F depends only on those moments. To analyze the behavior of F, it is sufficient to study the evolution of the moments. ...
Lesson 3
... The Converse of the Pythagorean Theorem If a triangle has sides of lengths a, b, and c, and a2 b2 c2, then the triangle is a with hypotenuse of length c. ...
... The Converse of the Pythagorean Theorem If a triangle has sides of lengths a, b, and c, and a2 b2 c2, then the triangle is a with hypotenuse of length c. ...
msc_pre_phy_p2b1
... From the above equation it is clear that the cartesian components are not linear functions qj alone, but depend quadratically and linearly of components of generalised acceleration ...
... From the above equation it is clear that the cartesian components are not linear functions qj alone, but depend quadratically and linearly of components of generalised acceleration ...
Triangles
... Directions Print pages 1 & 2 (3 & 4 for the answer key) double sided. On my printer, I use the option to print double sided and to flip along the long edge. If you are printing single sided, and then photocopying, you will need to manually flip the pages. (I recommend making one copy, cut, and fold ...
... Directions Print pages 1 & 2 (3 & 4 for the answer key) double sided. On my printer, I use the option to print double sided and to flip along the long edge. If you are printing single sided, and then photocopying, you will need to manually flip the pages. (I recommend making one copy, cut, and fold ...
Noether's theorem
Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.