Obtaining Equations from Piecewise Function Graphs You may be asked to write a piecewise function, given a graph. To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph. Here are the graphs, with explanations on how to derive their piecewise equations:
What Is a Field? What Are Instants and Durations? A duration is a measure of elapsed time. It is a number with temporal units such as years or seconds. The second is the agreed upon standard unit for the measurement of duration [in the S.
In informal conversation, an instant is a very short duration. In physics, however, an instant is even shorter.
It is instantaneous; it has zero duration. There is another sense of the word "instant" which means, not duration, but a time, as when we say it happened at that instant. Midnight could be such an instant. It is assumed in physics that an event is always a linear continuum of the instants or times or moments that compose the event, but it is an interesting philosophical question to ask how physicists know it is a continuum.
Nobody could ever measure time that finely, even indirectly. A brief comment on the terms: Regarding time, there is no standard terminology about whether to say interval of time or period of time, although the latter is more popular.
The measure of a period of time is called a "duration" and it always needs a unit. The term "interval" in the phrase " spacetime interval " is a different kind of interval. What Is an Event? In ordinary discourse, an event is a happening lasting a finite duration during which some object changes its properties.
So, two events are the same if they are both events of the same object having the same property at the same time. A possible-worlds analysis of events might be the way to solve this problem of change. Physicists, instead, adopt the idealization that a basic event is a point event: No objects need to be involved.
The point event is specified relative to a reference frame. A physicist's event might be that an electron is there at that point in space at that point in time. A point event might involve multiple properties, such as the value not only of the electromagnetic field but also the mass.
Your trip to the supermarket to buy carrots is, in principle, analyzable as a collection of a great many point events. The point event is ontologically fundamental in the sense that an object is just a process which is composed of a, usually continuous, series of events.
A mathematical space is a collection of points, and the points need not represent real, physical space. Depending on the mathematical space, a point might represent anything, for example, an ordered-pair consisting of an item's sales price in dollars, and a salesperson's name.
These points would compose a two-dimensional space, but the points of a real space, that is, a physical space, can only be spatial locations, that is, places. For other philosophers it is unacceptable because it involves infinity, namely an infinitesimal size.To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph..
Here are the graphs, with explanations on how to derive their piecewise equations: Absolute Value as a Piecewise Function. Search the world's information, including webpages, images, videos and more.
Google has many special features to help you find exactly what you're looking for. Problem: Solution: Two students are bouncing-passing a ball between them. The first student bounces the ball from 6 feet high and it bounces 5 feet away from her.
The second student is 4 feet away from where the ball bounced.. Create an absolute value equation to represent the situation. Search the world's information, including webpages, images, videos and more. Google has many special features to help you find exactly what you're looking for.
For example, #|x|=-1# has no solution. The absolute value of a number is its distance away from zero. That number will always be positive, as you cannot be negative two feet away from something. So any absolute value equation set equal to a negative number is no solution. In this section we will discuss how to solve Euler’s differential equation, ax^2y'' + bxy' +cy = 0.
Note that while this does not involve a series solution it is included in the series solution chapter because it illustrates how to get a solution to at least one type of differential equation at a singular point.