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Write a system of equations with no solution or infinitely many solutions

For each positive I can think of, a counterbalancing negative also comes to mind. While the prose creates sharp, clear, atmospheric images, it is also burdened with numerous grammar and spelling errors.

The direction of time and the foundations of statistical mechanics The problem of the direction of time There is a long-standing tension between fundamental physical theories of microscopic phenomena and everyday human experience regarding the question of how the past is different from the future.

This tension will be treated below in its original, Newtonian version, but it persists in much the same form in the contexts of very different contemporary physical theories. Both absolute position and velocityfor example, play no dynamical role in Newtonian mechanics.

Perhaps surprisingly, neither does the direction of time. Consider a film that shows a baseball being thrown directly upward: Now imagine the same film run in reverse: Although the films obviously differ, they both depict a baseball that is accelerating constantly, at the rate of 32 feet per second per second, in the direction of the ground.

This is an absolutely general phenomenon. In any film of a classic physical process, the apparent velocity of a body at a given point when the film is run forward will be equal and opposite to the apparent velocity of the body at that point when the film is run in reverse.

However, the apparent acceleration of the body at any point when the film is run forward will be identical, both in magnitude and in direction, to the apparent acceleration of the body at that point when the film is run in reverse. Note that the mass of the body and the forces acting on it also will be the same at corresponding points in the film.

It is illuminating to consider various different ways in which this point may be formulated: However it is formulated, this conclusion is very much at odds with everyday experience.

Almost uniformly, natural physical processes—such as the melting of ice, the cooling of warm soup, or the breaking of glass—do not happen in reverse.

Thermodynamics A concise, powerful, and general account of the time asymmetry of ordinary physical processes was gradually pieced together in the course of the 19th-century development of the science of thermodynamics.

The sorts of physical systems in which obvious time asymmetries arise are invariably macroscopic ones; more particularly, they are systems consisting of enormous numbers of particles.

Because such systems apparently have distinctive properties, a number of investigators undertook to develop an autonomous science of such systems. As it happens, these investigators were primarily concerned with making improvements in the design of steam engine s, and so the system of paradigmatic interest for them, and the one that is still routinely appealed to in elementary discussions of thermodynamics, is a box of gas.

Consider what terms are appropriate for the description of something like a box of gas. The fullest possible such account would be a specification of the positions and velocities and internal properties of all of the particles that make up the gas and its box.

From that information, together with the Newtonian law of motion, the positions and velocities of all the particles at all other times could in principle be calculated, and, by means of those positions and velocities, everything about the history of the gas and the box could be represented.

But the calculations, of course, would be impossibly cumbersome. A simpler, more powerful, and more useful way of talking about such systems would make use of macroscopic notions like the size, shape, mass, and motion of the box as a whole and the temperaturepressure, and volume of the gas.

It is, after all, a lawlike fact that if the temperature of a box of gas is raised high enough, the box will explode, and if a box of gas is squeezed continuously from all sides, it will become harder to squeeze as it gets smaller.

Although these facts are deducible from Newtonian mechanics, it is possible to systematize them on their own—to produce a set of autonomous thermodynamic laws that directly relate the temperature, pressure, and volume of a gas to each other without any reference to the positions and velocities of the particles of which the gas consists.

The essential principles of this science are as follows. There is, first of all, a phenomenon called heat. Things get warmer by absorbing heat and cooler by relinquishing it.

Heat is something that can be transferred from one body to another. When a cool body is placed next to a warm one, the cool one warms up and the warm one cools down, and this is by virtue of the flow of heat from the warmer body to the cooler one.

The original thermodynamic investigators were able to establish, by means of straightforward experimentation and brilliant theoretical argument, that heat must be a form of energy.

There are two ways in which gases can exchange energy with their surroundings: The equation above, which expresses the law of the conservation of total energy, is referred to as the first law of thermodynamics.

The original investigators of thermodynamics identified a variable, which they called entropythat increases but never decreases in all of the ordinary physical processes that never occur in reverse. Entropy increases, for example, when heat spontaneously passes from warm soup to cool air, when smoke spontaneously spreads out in a room, when a chair sliding along a floor slows down because of frictionwhen paper yellows with age, when glass breaks, and when a battery runs down.

The second law of thermodynamics states that the total entropy of an isolated system the thermal energy per unit temperature that is unavailable for doing useful work can never decrease.

On the basis of these two laws, a comprehensive theory of the thermodynamic properties of macroscopic physical systems was derived. Once the laws were identified, however, the question of explaining or understanding them in terms of Newtonian mechanics naturally suggested itself.

It was in the course of attempts by Maxwell, J.1> Write a system of linear equations consisting of three equations in three unknowns with: a) no solution.

b) exactly one solution. c) infinitely many solutions. 2> Let a and b represent real numbers. Describe the possible solution sets of the (linear) equation ax = b (hint: the number of solutions depends upon a and b).

A student wants to prove that if equation 2 is kept unchanged and equation 1 is replaced with the sum of equation 1 and a multiple of equation 2, the solution to the new system of equations is the same as the solution to the original system of equations.

A system of linear equations can have a(n) _____ solution, no solution, or infinitely many solutions. Though nearly all courses are shown within English, many published projects as well as assessments could best admission paper proofreading services for mba To ensure that work experience in order to depend on the realization one of the most manages to graduate connected with Glendon's Intercontinental Experiments system possess .

A system of linear equations has no solutions, a unique solution or infinitely many solutions. Proof Here is a diagram that consolidates several of our theorems from this section, and which is of practical use when you analyze systems of equations.

JACL does a good job of imitating mainstream systems (especially Inform) in many ways, but in other crucial areas it falls critically short. the game did not meet the challenge of allowing me to use even this setup, because it did not allow alternate solutions to puzzles by using objects in unconventional ways.

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Solving Systems of Linear Equations; Row Reduction - HMC Calculus Tutorial