Linear equation

The fundamental theorem of Calculus: The fundamental theorem of calculus asserts the interrelated properties of integration and differentiation. It says that a function when differentiated, can be brought back by integrating (anti-derivative) or a function when integrated, can be brought back by differentiation. First theorem: Let f be a function that is integrable on [a,x] for each x in [a,b], then let c be such that a≤c≤b and define a new function A as follows, A(x)=∫_c^x▒f(x)dt, if a≤x≤b.…

Freezing and crystallization are linked in that both processes involve initial nucleation followed by crystallization. Sonication is thought to enhance both the nucleation rate and rate of crystal growth in a saturated or supercooled medium by producing a large number of nucleation sites in the medium throughout the ultrasonic exposure. Two main theories which explained the mechanism of nucleation are Hickling theory and molecular segregation theory. Among two theories Hickling is most commonly…

civilizations. One source of these estimates is the Drake equation, created by Frank Drake of SETI, in which the number of civilizations capable of communication is derived…

The amount of time required for a chemical reaction to come to completion can vary tremendously depending on the reaction (Addison-Wesley, 2002). The speed at which any reaction proceeds can be defined as a reaction rate (J. Laidler, 2015). The rate of reaction can only be obtained experimentally, in order to yield a rate law. By conducting this experiment, it has the potential to harvest useful information regarding the understanding of rates of reaction. Understanding the rate of reactions is…

clock turns hours to days and days to years, details begin to protrude, warping the facade of childhood stories to their true state, presenting anything but a happy ending. Such stories are presented as Popular Mechanics by Raymond Carver, The Cold Equations by Tom Godwin, and This Year’s Class Picture by Dan Simmons, these three tales strive to entertain and warn about the choices and consequences of life and how it is not always what is desired. These three authors all portray characters as…

It is believed that at higher potential foils can be overheated and deformed, which can quench the reaction propagation. The quenched reaction front with deformation will be explained in more detail in the next section. The reaction front speed of 1Ti/2Al reactive foil is nearly constant for different potentials. The high conductivity of this foil type and moderate diffusion distance of atomic mixing exhibit nearly constant reaction velocity. With increasing activation potentials, the reaction…

Discussion As a result of the calculations made above, considering the overall; CH3COCH3 (aq) + I2 (aq) + HCl (aq)  CH3COCH2I (aq) + HI (aq) the rate law for this reaction is, Rate = k[CH_3 COCH_3 ]^m [I_2 ]^n [HCl]^p. As supported in question 3 part A, the reaction orders m, n and p for acetone, iodine and HCL, respectively were 1, 0, 1. Resulting in an overall reaction order of 2. Manipulations were based on the usage of initial concentrations to calculation the rate constant for the…

Kinetic can be defined as a study of the speeds or the rates of chemical reactions. The factors that could affect the rates of the reactions are physical state, reaction temperature, catalysts, pressure, concentration of solution, and reaction time. The change of the speed of the reaction can be predicted based on the different reaction conditions. Kinetic study is important because it can describe information about the reaction mechanism. The concentration has affected the frequency which the…

Chadwick, J. 1958. The Decipherment of Linear B, Cambridge, Cambridge University Press. In this article, Chadwick’s discussion is two-fold: I. Interpretation of the Linear B tablet founded in Crete. II. When the Minoan script of Linear A became extinct. As suggested in this article, Evans hypothesises the script of Linear B was a modified form of the Minoan script Linear A. Thus, this article deduces that the decipherment of Linear B is the most important piece of archaeological evidence for…

Regression-Discontinuity Design. A powerful, alternative design for causal inference that is underutilized in the health and intervention sciences is the regression discontinuity (RD) design (Thistlewaite & Campbell, 1960). In its simplest form, the RD design involves the use of a screening measure of some form that is continuous and given to all persons. A cut point or criterion is set, which determines whether individuals are assigned to an intervention condition or a comparison condition. The…