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Medium 9781616514235

Geometry on the Coordinate Plane

Michael Buckley Saddleback Educational Publishing PDF



Plotting Points on a Coordinate Plane

A point on a coordinate plane is defined by its x- and y-coordinates. The location of a point is given by an ordered pair.

Sign of




Ordered Pair




(x, y)



(x-coordinate, y-coordinate)

Rules for Plotting Points on a Coordinate Plane

1. Move right or left from the y-axis the number of units of the x-coordinate.

2. Move up or down from the x-axis the number of units of the y-coordinate.



Graph the following point: (–3, 4).


Step 1 Move right or left from the y-axis the

number of units of the x-coordinate.

Step 2 Move up or down from the x-axis the

number of units of the y-coordinate.



Move left from the y-axis 3 units.

Move up from the x-axis 4 units.




Graph the following points.

1. (2, –3)




Move right or left from the y-axis the number of units of the x-coordinate.

Move up or down from the x-axis the number of units of the y-coordinate.


Move the y-axis


Move the x-axis


from units.

2. (−5, 0)

3. (5, 3)



4. (0, 4)

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Medium 9781449320232

Conditional Compilation

Greg Shackles O'Reilly Media ePub

One technique you may have seen if youve done other cross-platform development is conditional compilation. With this method, you can tell the compiler to either include or exclude blocks of code based on compilation symbols that describe the target environment. For example, most .NET projects will define a symbol named DEBUG when the project is built in the debug configuration but not in the release configuration. If you have logging code that you only want included in debug builds, you can wrap it in a conditional expression using that symbol (see Example3-8). When the code is parsed for compilation, any code blocks surrounded by unsatisfied conditions are stripped out, and the file is compiled as if they were never there in the first place.

Example3-8.Using the DEBUG compiler symbol

Keep in mind that overuse of this pattern can quickly lead to code that is very difficult to read and maintain. If you find yourself using a lot of conditional compilation, its very likely that the abstraction pattern might be a better route to go down. That said, it can be a very handy tool when you need to make minor adjustments in a shared file based on the target environment.

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Medium 9780253339362

Appendix B: Dance Rhythms in Bach’s Larger Works

Little, Meredith Indiana University Press ePub

Note: This list contains the authors’ selection of pieces by Bach which use dance rhythms; all works mentioned in chapters 14 and 15 are included.



Sacred Vocal:

Sacred Vocal:



Sacred Vocal:

Sacred Vocal:



Sacred Vocal:

Sacred Vocal:



Sacred Vocal:



Sacred Vocal:

Sacred Vocal:

French Gigue-like


Sacred Vocal:

Sacred Vocal:



Sacred Vocal:



Giga I–like



Giga II–like

Note: Many of these pieces are not discussed in chapter 15.








Fughetto super “Dies sind die heiligen zehn Gebot” for organ, CLU III

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Medium 9780596101640

Hack #13. Use One Variable to Predict Another

Bruce Frey O'Reilly Media ePub

Simple linear regression is a powerful tool for measuring something you cannot see or for predicting the outcome of events that have not happened yet. With some help from our special friend statistics, you can make a precise guess of how someone will score on one variable by looking at performance on another.

Many professionals, both in and outside of the social sciences, often need to predict how a person will perform on some task or score on some variable, but they cannot measure the critical variable directly. This is a common need when making admission decisions into college, for example. Admissions officers want to predict college performance (perhaps grade point average or years until completion). However, because the prospective student has not actually gone to college yet, admissions officers must use whatever information they can get now to guess what the future holds.

Schools often use scores on standardized college admissions tests as an indicator of future performance. Let's imagine that a small college decides to use scores on the American College Test (ACT) as a predictor of college grade point average (GPA) at the end of students' first years. The admissions office goes back through a few years of records and gathers the ACT scores and freshman GPAs for a couple hundred students. They discover, to their delight, that there is a moderate relationship between these two variables: a correlation coefficient of .55.

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Medium 9781601323163

Quantum-Identity Equivalents of the Orthomodularity Law in Quantum Logic: Part 4

Hamid R. Arabnia, George A. Gravvanis, George Jandieri, Ashu M. G. Solo, and Fernando G. Tinetti CSREA Press PDF


Int'l Conf. Foundations of Computer Science | FCS'14 |

Quantum-Identity Equivalents of the

Orthomodularity Law in Quantum Logic: Part 4

Jack K. Horner

P. O. Box 266

Los Alamos, New Mexico 87544 USA

FCS 2014


The optimization of quantum computing circuitry and compilers at some level must be expressed in terms of quantum-mechanical behaviors and operations. In much the same way that the structure of conventional propositional (Boolean) logic (BL) is the logic of the description of the behavior of classical physical systems and is isomorphic to a Boolean algebra (BA), so also the algebra, C(H), of closed linear subspaces of (equivalently, the system of linear operators on (observables in)) a Hilbert space is a logic of the descriptions of the behavior of quantum mechanical systems and is a model of an ortholattice (OL). An

OL can thus be thought of as a kind of “quantum logic” (QL). C(H) is also a model of an orthomodular lattice, which is an OL conjoined with the orthomodularity axiom (OMA). The rationalization of the OMA as a claim proper to physics has proven problematic, motivating the question of whether the OMA and its equivalents are required in an adequate characterization of QL. Here I provide an automated deduction of two quantum- identity-based equivalents of the OMA. The proofs may be novel.

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