A Pythagorean triple is a set of three positive integers, (a, b, c), such that a right triangle can be formed with the legs a and b and the hypotenuse c. The most common Pythagorean triples are (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25).
A:A Riemann sum is a method of approximating the area under the curve of a function. It adds together a series of values taken at different points of that function and multiplies them by the intervals between points. The midpoint Riemann sum uses the x-value in the middle of each of the intervals.
A:The definition of a limit in calculus is the value that a function gets close to but never surpasses as the input changes. Limits are one of the most important aspects of calculus, and they are used to determine continuity and the values of functions in a graphical sense.
A:The abbreviations "sin," "cos," "tan," "csc," "sec" and "cot" stand for the six trigonometric functions: sine, cosine, tangent, cosecant, secant and cotangent. Each function represents a particular relationship between the measure of one of the angles and the ratio between two sides of a right triangle.
A:According to class notes from Bunker Hill Community College, calculus is often used in medicine in the field of pharmacology to determine the best dosage of a drug that is administered and its rate of dissolving. Usually, the drug is slowly dissolved in the stomach.
A:The class midpoint, or class mark, is calculated by adding the lower and upper limits of the class and dividing by two. The class midpoint is sometimes used as a representation of the entire class.
A:One thousand millimeters is equal to 1 meter. The meter is the standard unit of length in the International System of Units, also known as the metric system. "Metre" is the standard spelling for all English-speaking countries except the United States. "Meter" is the accepted U.S. spelling.
A:To calculate bulk density, simply weigh the sample and divide its mass by its volume. Bulk density is commonly used when referring to solid mixtures like soil. Just like particle density, bulk density is also measured in mass per volume.
A:A nonlinear function in math creates a graph that is not a straight line, according to Columbia University. Three nonlinear functions commonly used in business applications include exponential functions, parabolic functions and demand functions. Quadratic functions are common nonlinear equations that form parabolas on a two-dimensional graph.
A:A Pythagorean triple is a set of three positive integers, (a, b, c), such that a right triangle can be formed with the legs a and b and the hypotenuse c. The most common Pythagorean triples are (3, 4, 5), (5, 12, 13), (8, 15, 17) and (7, 24, 25).
A:A few examples of how logarithms are used in the real world include measuring the magnitude of earthquakes or the intensity of sound and determining acidity. A logarithm explains how many times a number is multiplied to a power to reach another number. It is expressed as loge(x) and is commonly written as ln(x).
A:A person can consider a differential equation by determining an initial condition, as a differential equation is an equation that gives the derivative of an unknown function in terms of the function and the independent variable. A differential equation is considered differently depending on whether it is ordinary or partial and linear or non-linear.
A:A planar projection is simply a map projection that hypothetically projects the Earth onto a tangent or secant plane; while any point on the planet can be used, a planar projection will generally take one of the poles as the point from which its projection is done.
A:The derivative of cosh(x) with respect to x is sinh(x). One can verify this result using the definitions cosh(x) = (e^x + e^(-x))/2 and sinh(x) = (e^x - e^(-x))/2.
A:The manipulated variable in an experiment is the independent variable; it is not affected by the experiment's other variables. HowStuffWorks explains that it is the variable the experimenter controls. When there are control and experimental groups, the manipulated variable is the treatment supplied to the experimental group and denied the control group.
A:In mechanical engineering, mathematics is important because it is required to solve problems, to analyze mathematical relations and in using the laws of nature, which are mathematical expressions. A person who earns a degree in mechanical engineering will be primarily grounded in technical matters using their knowledge of physics, chemistry and mathematics to think creatively and analytically.
A:The antiderivative of the tangent of x equals the negative natural log of the absolute value of the cosine of x, plus a constant. In mathematical terms, the antiderivative can be expressed as = - ln |cos(x)| + C.
A:According to the University of Oregon, calculus is important because "it provides a systematic way for the exact calculation of many areas, volumes and quantities that were beyond the methods of the early Greeks." Calculus is concerned with the rates of change of continuous functions as their arguments change.
A:The coefficient of area expansion is a factor that relates change in a material’s external area to temperature. Materials generally expand as they are heated, causing their overall surface area to increase. The extent of this area increase for each degree on a temperature scale is the area expansion coefficient.
A:Printable worksheets, online games and online practice exercises are some effective ways for second graders to practice regrouping. Hands-on activities, such as regrouping with counters or base-ten blocks, pretend shopping and recording sports scores also provide students with engaging opportunities to sharpen their regrouping skills.
A:People use minimum and maximum values when proving limits of epsilon, because epsilon is a range around a limit point. To have a limit, one has to approach that limit from both the negative and positive directions.
A:Three ways to calculate a dividend payout ratio are by using net income, a retention ratio or a per-share basis. These figures all show how dividends paid out to stockholders relate to the reported net income of a company.