# Math

Q:

## What is the definition of "plane trigonometry"?

A:

"Plane trigonometry" is a branch of mathematics that focuses on the relationship between the sides and angles of a triangle. Plane trigonometry builds upon the basic concepts of Euclidean geometry, and it has applications in a variety of mathematical fields, from physics to advanced calculus.

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• ## Algebra

• #### Q:How do you simplify imaginary numbers?

A: Imaginary numbers are typically simplified in the same way that expressions with the variable x are simplified, with the exception of the expression i^2, which has a value equal to -1. For example, the expression 2i + 8i can be simplified by writing it first as (2 + 8) * i, with the final expression written as 10i.
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• #### Q:What are some things that come in groups of seven?

A: Some things that come in groups of seven include the days of the week, the books in the Harry Potter series, the notes in a typically major or minor scale, the games in the playoff series for Major League Baseball and the Pillars of the House of Wisdom in the Book of Proverbs. Other groups of seven include the number of heavens in Islam and the chakras in Hinduism.
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• #### Q:Who is the father of modern algebra?

A: The man known as "the father of modern algebraic notation" was French mathematician Francois Viète, according to the math department at Rutgers University. His substitution of letters to mark unspecified or unknown number quantities is recognized as the beginning step in the creation of the algebraic system.
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• #### Q:Where did algebra come from?

A: Algebra has been developed over thousands of years in several different countries. The earliest methods for solving mathematical problems with one or more unknown quantities come from ancient Egypt. The word "algebra" itself is derived from the title of Baghdad mathematician Al-Kwarizmi's 9th century book, "Hidab al-jabr wal-muqubala."
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• #### Q:What are some examples in which the Pythagorean theorem is used in real life?

A: The Pythagorean theorem is used often in construction, in engineering, in architecture, in design, in art and in aeronautics. The theorem states that, given a right triangle with sides a, b and c, where c represents the hypotenuse (or longest side), the sum of the square of the two sides (a squared plus b squared) is always equal to c squared.
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• #### Q:Why is math important in life?

A: Math is important in life because it is used to perform many different daily tasks, such as telling time, reading an odometer, counting change and to make strategic decisions in one's work life. Similarly, nearly every profession uses some form of math. For example, nurses, engineers, bank tellers, pharmacists and stock market analysts use math every day to perform their professional duties well.
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• ## Arithmetic

• #### Q:What does "median" mean in mathematics?

A: The median is the number that is in the middle in a list of sorted numbers. To find the median, the numbers must be sorted from lowest to highest.
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• #### Q:How do you change a fraction to a percent?

A: A fraction is converted to a percentage by first expressing the fraction with a denominator of 100, then writing the numerator with a percent sign behind it. Some fractions can be easily converted if basic ratio equivalents are known.
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• #### Q:How much money is in a roll of quarters?

A: In the United States, a roll of quarters is worth \$10. It includes 40 quarters.
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• #### Q:What is a "digit" in math?

A: "Digits" are the symbols or characters used to represent a number visually. A number like five contains one digit, whereas a number like 555 contains three digits. This is easily seen when they are written as numerals: 5 versus 555.
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• #### Q:What is the history of the square root in mathematics?

A: According to Saint Louis University, the ancient Egyptians created the square root and most likely used it for architecture, building pyramids and other daily activities that required math. Most of the present-day knowledge of Egyptian math comes from papyri written during the 12th dynasty.
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• #### Q:What are some facts about the abacus?

A: The abacus is a counting frame used since ancient times as a calculating device. The word abacus is derived from the Greek word "abax" meaning "flat surface."
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• ## Calculus

• #### 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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• #### 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 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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• #### 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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• #### 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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• #### 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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• ## Data Graphs

• #### Q:How is data turned into information?

A: According to the BBC, data is transformed into information after being imported into a database or spreadsheet. Information is defined as a collection of facts or data, whereas data is defined as information organized for analysis or used to reason.
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• #### Q:What is a segmented bar graph?

A: A segmented bar graph is similar to regular bar graph except the bars are made of different segments that are represented visually through colored sections. A segmented bar graph is sometimes known as a stacked bar graph, and it offers greater detail about data sets.
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• #### Q:Why are graphs important?

A: Graphs are beneficial because they summarize and display information in a manner that is easy for most people to comprehend. Graphs are used in many academic disciplines, including math, hard sciences and social sciences. They make appearances in corporate settings, serving as useful tools to convey financial information and facilitate data analysis.
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• #### Q:Why are points connected in a line graph but not in a bar graph?

A: A line graph is a graph that charts the relationship between two variables or a progression of a single quantity through time. Without the lines connecting points of data, it would be difficult to make sense of the data being presented if there was no overall trend between the dots. A bar graph, on the other hand, is meant to compare two or more statistics, such as population figures.