Similar Triangles
... INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 P.M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of th ...
... INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 P.M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of th ...
Theorem list for these sections.
... • Way to compare between two triangles - side opposite wider angle is longer side, and vice versa. • Extends scalene inequality (which only allows comparisons within one triangle, instead of between two triangles). • I don’t think we’ve worked with this explicitly, but it’s pretty self evident (you’ ...
... • Way to compare between two triangles - side opposite wider angle is longer side, and vice versa. • Extends scalene inequality (which only allows comparisons within one triangle, instead of between two triangles). • I don’t think we’ve worked with this explicitly, but it’s pretty self evident (you’ ...
The Addition Theorem for Spherical Harmonics and Monopole
... The key point is to observe that the angular momentum operators in both cases satisfy the same SU(2) algebra. The only difference is that, for ordinary angular momentum operators L, they satisfy ^r:L = 0, where ^r is the radial unit vector. For the monopole angular momentum operators J, we have the ...
... The key point is to observe that the angular momentum operators in both cases satisfy the same SU(2) algebra. The only difference is that, for ordinary angular momentum operators L, they satisfy ^r:L = 0, where ^r is the radial unit vector. For the monopole angular momentum operators J, we have the ...
QFT II
... To get the right result for (Dirac) fermion fields as quantum operators with anti-commutation relation the classical fields (plugged in the path integral) have to anti-commute, too. So we need the notion of anti-commuting numbers.First consider a finite # of d.o.f. by ψ A (t, x) → ψi (t) These ψi (t ...
... To get the right result for (Dirac) fermion fields as quantum operators with anti-commutation relation the classical fields (plugged in the path integral) have to anti-commute, too. So we need the notion of anti-commuting numbers.First consider a finite # of d.o.f. by ψ A (t, x) → ψi (t) These ψi (t ...
Midterm Exam Topics and Problems
... Know how to graph coordinate pairs Know how to use the distance formula and the midpoint formula 1-9 Perimeter, Area Know how to calculate the perimeter and area of basic geometric shapes- square, rectangle, triangle. ...
... Know how to graph coordinate pairs Know how to use the distance formula and the midpoint formula 1-9 Perimeter, Area Know how to calculate the perimeter and area of basic geometric shapes- square, rectangle, triangle. ...
geometry – first semester exam review
... Use the diagram to the right to determine which lines, if any, must be parallel given the information below. a. 10 = 2 _________________________ b. 11 = 13 __________________________ c. 5 + 12 =180 _________________________ d. 1 = 3 _______________________________ ...
... Use the diagram to the right to determine which lines, if any, must be parallel given the information below. a. 10 = 2 _________________________ b. 11 = 13 __________________________ c. 5 + 12 =180 _________________________ d. 1 = 3 _______________________________ ...
Geometry - 7.5
... Corollary 2: The acute angles of a right triangle are complementary. Corollary 3: Each angle of an equilateral triangle is 60°. Theorem 21: An exterior angle of a triangle is equal to the sum of the remote interior angles. Theorem 22: The AAS Theorem – If two angles and the side opposite one of the ...
... Corollary 2: The acute angles of a right triangle are complementary. Corollary 3: Each angle of an equilateral triangle is 60°. Theorem 21: An exterior angle of a triangle is equal to the sum of the remote interior angles. Theorem 22: The AAS Theorem – If two angles and the side opposite one of the ...
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.