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: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: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: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: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: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: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 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: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:A piecewise-defined function consists of two or more subfunctions while maintaining the rule that a function has only y-value for each x-value. Some mathematicians call the piecewise function a hybrid function. Merchants use piecewise functions in describing pricing schemes that give discounts for volume sales.
A:Learners can take calculus courses online through Massachusetts Institute of Technology, San Francisco State University, University of California in Berkeley or Brigham Young University. These courses range from introductory offerings to specific, advanced focuses.
A:A good application for vector analysis is the calculation of an airplane's flight path. This requires knowing the magnitude and direction of both the plane's thrust, as well as that of the prevailing winds acting on the plane.
A:A decimal number is written in expanded form by multiplying each individual number by the value of the decimal place that it occupies. Expanded form is rarely used, as both decimal form and mixed form are more convenient and practical forms of a non-whole number.
A:The term "roster method" refers to a technique in representing a set by directly listing all of its elements, which are separated by commas and enclosed by a pair of curly brackets. The roster method is also referred to as the "tabular form method."
A:The equation for the spring force is k = -F/x. This equation is derived from Hooke’s Law, which states that the force needed to extend or compress a spring a certain distance is proportional to that distance. The equation for Hooke’s Law is F=kx, where k is the spring constant.
A:A vector is a mathematical entity that has both magnitude and direction or is an element of a vector space. A vector is typically represented graphically by an arrow with its tip indicating the direction, while its length represents its magnitude. By denoting the origin end of the arrow with the letter O and the tip with the letter A, the vector can be represented algebraically as vector OA.
A:To make scones with Bisquick, combine the baking mix with sugar, butter, berries, eggs and milk, and bake the mixture for 15 minutes at 450 degrees Fahrenheit. Glaze the scones with lemon glaze before serving.
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:MyCalculus is a website that helps students solve integration and differentiation problems. When a user visits the MyCalculus site, he is redirected to Mathway. The platform provides math practice tools for several grades.
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.