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 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 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 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: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 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 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 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: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:The derivative of the square root of x is one-half times one divided by the square root of x. The square root of x is equal to x to the power of one-half.
A:The indefinite integral of sqrt(x^2y^2) with respect to x is x^2y/2 + c, assuming that x and y are independent variables. The definite integral of this function between x = a and x = b is b^2y/2 - a^2y/2.
A:The integral of arcsin is x times the inverse sine of x, plus the square root of one minus x squared, plus a constant expressed as C. Using mathematical notation, it can be expressed as the integral of arcsin x dx = x arcsin x + [sqrt](1-x^2) + C.
A:The derivative of e^(3x) is equal to three times e to the power of three x. In mathematical terms, the equation can be expressed as d/dx e^(3x) = 3e^(3x).
A:The phrase "pi r squared" refers to the mathematical formula used to determine the area of a circle. Normally, the equation is written as "pi * r2," or "Π * r2.
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: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:Using known properties of logarithms, one can expand a complex logarithmic expression into a series of simpler expressions. Logarithmic expressions are abbreviated with log and may involve combinations of multiplication, division and exponents.
A:The difficulty of differential equations depends on the particular problem. Since a differential equation can be any equation which contain derivatives, either ordinary or partial, the difficulty in solving an equation depends on the particular equation or type of equation.
A:The opposite of an inverse relationship is a direct relationship. Two or more physical quantities may have an inverse relationship or a direct relationship. Temperature and pressure have a direct relationship, whereas volume and pressure have an inverse relationship.
A:The formula for calculating true position is true position tolerance = 2 x SQRT(XVAR2 + YVAR2). In this instance, SQRT refers to a square root, XVAR refers to the amount of deviation from the basic dimension found in the X-axis, and YVAR refers to the amount of deviation from the basic dimension found in the Y-axis.