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: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 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: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: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 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 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 polynomial function is any function that contains more than one monomial, with non-negative exponents, and only contains addition, subtraction, multiplication or division operations. A monomial is a single term consisting of a coefficient and variable, even if the coefficient is one or the variable is 0 and isn't written explicitly.
A:A monotonic sequence is a mathematical term that refers to a function that preserves a given order between ordered sets. For a sequence to qualify as being monotonic, it must always decrease or increase progressively.
A:The integral of cosine squared is equal to x/2 + (1/4)sin(2x) + C, where C is a constant. The integral can be solved by using the half-angle identity of the cosine squared function, where cos2(x) = 1/2 + (1/2)cos(2x).
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:To calculate the discriminant of a quadratic equation, put the equation in standard form. Substitute the coefficients from the equation into the formula b^2-4ac. The value of the discriminant indicates what kind of solutions that particular quadratic equation possesses.
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: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 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.
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: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: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.