The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...

The representative heuristic describes a biased way of thinking, in which you unintentionally stereotype someone or something. For example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the opposite direction as compared to inductive reasoning, which means that it uses a general principle or law to predict specific results. From those general principles, a scientist can deduce and predict the specific results that would be valid as long as the general principles are valid.
For example, a researcher can deduce specific predictions...

In a spring-mass-damper system, the second-order differential equation describes the dynamic behavior of the system. When transformed into the Laplace domain under zero initial conditions, this equation can be effectively analyzed and manipulated. The transformation into the Laplace domain converts differential equations into algebraic equations, simplifying the process of isolating the output.

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in degrees to which the conclusions are credible. As such, inductive arguments can be weak or strong, rather than valid or invalid, and conclusions can be used to formulate testable, falsifiable hypotheses.
Inductive reasoning is common in descriptive science. A life scientist makes observations and records them. This data can be qualitative or...