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: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: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: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: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: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 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:The most common use for calculus is to predict the way in which a graph grows. The process uses two derivatives of differential calculus to make accurate estimations in regard to where specific points on graphs end up as well as what their shapes look like.
A:One calculus project idea is figuring out the center of mass of an irregular piece of Plexiglas. Students choose a piece of Plexiglas and use coordinate paper to determine its boundaries. They use that information to determine the centroid of the region, proving it by balancing the Plexiglas on a pencil stuck in sand. Students turn in drawings and examples of the work they used to arrive at the answer.
A:In the real world, calculus is used to build search engines and weather models, to study epidemiology and to construct buildings and bridges. Algorithms derived from calculus also allow searches to be conducted on social media sites like Facebook and Twitter.
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:Calculus problems come in many shapes and sizes, not all of which can be solved online (or at all). If your problem is purely computational, the Wolfram Alpha website is often helpful in computing things like integrals or derivatives, or solving certain differential equations.
A:The integral of sin 2x is -(1/2) X cos(2x) + C, where C represents a constant. The integral can be found using the substitution technique of integration, which reverses the method for finding a derivative using the chain rule.
A:Logarthims of the same base can be added together by multiplying their arguments and then performing the logarithm on the product. For example, assuming log means log base 10 as it does on a calculator: log(x) + log(y) = log(x * y)
A:For Dummies does not publish a book called "Calculus 3 for Dummies" as of 2014. Similar titles available from the For Dummies brand include "Calculus II for Dummies" and "Differential Equations for Dummies." Research & Education Association publishes "The Essentials of Calculus III," and W.H. Freeman & Company publishes "How to Ace the Rest of Calculus: The Streetwise Guide."