Calculus

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).

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  • How is calculus used in medicine?

    Q: How is calculus used in medicine?

    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.
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  • How do you calculate bulk density?

    Q: How do you calculate bulk density?

    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.
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  • How is the class midpoint calculated?

    Q: How is the class midpoint calculated?

    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.
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  • What is the precise definition of a limit in calculus?

    Q: What is the precise definition of a limit in calculus?

    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.
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  • How many millimeters equal 1 meter?

    Q: How many millimeters equal 1 meter?

    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.
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  • What is a nonlinear function in math?

    Q: What is a nonlinear function in math?

    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.
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  • How do you calculate the midpoint Riemann sum?

    Q: How do you calculate the midpoint Riemann sum?

    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.
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  • How are logarithms used in the world?

    Q: How are logarithms used in the world?

    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).
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  • What are the meanings of "sin", "cos", "tan", "csc", "sec" and "cot"?

    Q: What are the meanings of "sin", "cos", "tan", "csc", "sec" and "cot"?

    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.
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  • What are some common Pythagorean triples?

    Q: What are some common Pythagorean triples?

    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).
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  • How do you find the interval of convergence?

    Q: How do you find the interval of convergence?

    A: Interval of convergence in a power series is the set of all values of a particular variable, usually x, for which the series converges. To determine the interval of convergence, the ratio test must be conducted, and the radius of convergence calculated.
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  • What is an application of vector analysis?

    Q: What is an application of vector analysis?

    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.
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  • What are orthogonal vectors?

    Q: What are orthogonal vectors?

    A: Orthogonal vectors, also known as perpendicular vectors, are a type of vectors whose dot product or scaler is zero. However, if their cross product is zero, the vectors are said to be parallel.
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  • Q: How hard is precalculus compared to college algebra?

    A: Precalculus generally uses algebraic concepts taught in college-level algebra, but if there is a strong understanding of algebraic problems, precalculus may not be difficult. Both forms of mathematics courses involve a significant number of new concepts and whether a person finds one course more difficult than the other depends on the person's strengths as a mathematician.
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  • Q: What is the definition of "sine?"

    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.
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  • Q: What is the Lagrange remainder?

    A: The Lagrange remainder is a term that estimates the size of the error introduced by a partial sum of the Taylor series when it is used to compute an approximated value for the original function. The Lagrange remainder for the Taylor series is a tool not only for estimating errors but for giving a precise difference between the polynomial and the original function approximated by the polynomial.
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  • What is a manipulated variable?

    Q: What is a manipulated variable?

    A: The manipulated variable in an experiment is the independent variable; it is not affected by the experiment's other variables. HowStuffWorks explains that it is the variable the experimenter controls. When there are control and experimental groups, the manipulated variable is the treatment supplied to the experimental group and denied the control group.
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  • Q: What is integral cos 2?

    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).
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  • Q: What are some calculus project ideas?

    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.
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  • Q: What is the average rate of change in calculus?

    A: The average rate of change in calculus refers to the slope of a secant line that connects two points. In calculus, this equation often involves functions, as opposed to simple points on a graph, as is common in algebraic problems related to the rate of change.
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  • What is the first octant?

    Q: What is the first octant?

    A: In the context of solid three-dimensional geometry, the first octant is the portion under an xyz-axis where all three variables are positive values. Under a Euclidean three-dimensional coordinate system, the first octant is one of the eight divisions determined by the signs of coordinates.
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