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: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: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 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: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: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 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 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: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: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:Precalculus with limits is a high school math course that covers topics in algebra, geometry and trigonometry and prepares students to study calculus. Students often take this course as juniors or seniors in high school.
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:Find the equation for the tangent line to a curve by finding the derivative of the equation for the curve, then using that equation to find the slope of the tangent line at a given point. Finding the equation for the tangent line requires a knowledge of calculus and the formula for the slope.
A:Ratios are figured with addition and subtraction and represent a comparison between numbers or a group of numbers. They are often represented as fractions and can be simplified as such using division.
A:The fundamental theorem for line integrals states that if a line integral passes through a gradient field, it can be evaluated by evaluating the endpoints of the curve in the initial scalar field. If a smooth curve C exists and a function with a gradient vector is continuous on curve C, then the line integral can be calculated using the fundamental theorem of calculus for single integrals.
A:In math, the sine of an angle is defined as the length of the side of a right triangle opposite the acute angle divided by the length of the hypotenuse. The lengths of these sides can be determined through the Pythagorean Theorem.
A:The x intercepts of a parabola equation are the values of x for which y is equal to zero. These are the points at which the line of the parabola intercepts the x-axis.
A:Single variable calculus covers derivative and integral functions that contain one variable. Functions that contain two or more variables are a part of multivariable calculus.
A:The mean absolute deviation formula is Σ|x - μ| / N. The symbol Σ is used to denote the sum of a series of numbers, while μ represents the mean, x represents each value and N represents the total number of values. The formula takes the absolute value of the difference between a value and the mean and divides it by the number of values.
A:The most direct way to get expert-level help on math topics is to ask an expert - a professor, researcher, or strong student. Asking experts individually is not very efficient, so asking an expert-level question on a dedicated website, such as Math.StackExchange.com, usually yields quicker results.