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 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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  • 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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  • 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 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 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 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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  • 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 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 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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  • Q: What is taught in the Math 180 UIC class?

    A: University of Illinois at Chicago's Math 180 class covers Calculus I. The course is a requirement to earn a Bachelor of Science degree in mathematics, the teaching of mathematics or mathematics and computer science. It is also required for minor degrees in mathematics or mathematics and computer science.
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  • What are expanding logarithms?

    Q: What are expanding logarithms?

    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.
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  • Q: How can you get expert-level help on math topics?

    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.
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  • Q: How did Isaac Newton invent calculus?

    A: Calculus was developed independently by both Isaac Newton and Gottfried Leibniz during the later part of the 1600s. For Newton, calculus was primarily a tool he needed for explaining the motion of the planets. It would be difficult to say precisely how he developed his ideas because he was secretive about his methods, but it certainly grew out of his understanding of the laws of motion and acceleration.
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  • What is a linear function?

    Q: What is a linear function?

    A: A linear function is a function whose graph is a line in the plane. The characteristic property of these functions is that when the value of the input variable is changed, the change in the output is a constant multiple of the change in the input variable.
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  • Q: In what way is precalculus used in the real world?

    A: Precalculus is used in various fields like chemistry, biology and economics in the real world. It is used to make mathematical models or calculations for getting an optimal answer.
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  • Q: How do you use a GPA converter to covert a percentage into a 4.0 grade point average?

    A: To convert percentage grades into a 4.0 grade point average scale using a GPA converter, input your percentage grades. Then input either the number of credits or the weight of the class. Run the calculator.
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  • What is the vector equation of a line?

    Q: What is the vector equation of a line?

    A: The vector equation of a line is r = a + tb. In this equation, "a" represents the vector position of some point that lies on the line, "b" represents a vector that gives the direction of the line, "r" represents the vector of any general point on the line and "t" represents how much of "b" is needed to get from "a" to the position vector.
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  • What is the planar projection?

    Q: What is the planar projection?

    A: A planar projection is simply a map projection that hypothetically projects the Earth onto a tangent or secant plane; while any point on the planet can be used, a planar projection will generally take one of the poles as the point from which its projection is done.
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  • Q: Who created pi?

    A: According to History Today, William Jones created pi in 1706. This mathematics teacher used the symbol to refer to the constant ratio of any circle's circumference to its diameter.
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  • Q: How do you find the slope with two points?

    A: To find the slope of a line, you need the ratio of the change in y to the change in x. Even if there is no equation, you can still derive the slope by comparing two points on the line. After doing this, you can extrapolate the intercepts.
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