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.
A:We will probably never know who discovered pi, or that the ratio of the circumference of a circle to its diameter is a constant. The search for that constant, also known as pi, goes back nearly 4,000 years, to the Egyptians and Babylonians.
A:While people struggle with math for many reasons, one of the most common is that math is a sequential subject and missing one concept along the way leaves the student in a growing state of confusion. A child who struggles with basic arithmetic doesn't have the foundation for algebra or advanced math classes. Other math-haters struggle to connect math to real life or suffer from a learning disability with numbers.
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.
A:Some mathematical problems that feature pi are the area of a circle, a circle's circumference, arc length and the different surface area and volume formulas for a cone, sphere and cylinder. In mathematics, the ratio between a circle's circumference and diameter is given as pi.
A:Calculate the sum of an arithmetic sequence with the formula (n/2)(2a + (n-1)d). The sum is represented by the Greek letter sigma, while the variable a is the first value of the sequence, d is the difference between values in the sequence, and n is the number of terms in the series.
A:A factor is a number or expression that divides another number or expression evenly without a remainder. For instance, two, four, five and 10 are factors of 20 because 20 can be divided by all those smaller numbers an exact number of times. Prime numbers are positive integers greater than one that have exactly two factors. A composite number has more than two factors.
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.
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: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 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: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: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 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: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.
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.
A:The primary advantage of using a graph or chart in a presentation is that they help the audience to visualize the point of the presentation. Graphs emphasize the main point, make the data more convincing, provide a compact way of presenting information and help audiences stay engaged. Disadvantages of graphs include being time consuming to construct and costly to produce. They also require technology that some may lack.
A:Graphs of various types provide convenient visual representations of scientific data that would otherwise be presented in intimidating blocks of text or a series of numbers. Graphs represent statistics such as changes over time, comparisons, or parts of a whole. Graphs can be used to make date more accessible to both scientists and laypersons.
A:To make a tally chart, single lines are drawn next to one another until reaching five, where the fifth line crosses the four other lines diagonally. This is a simple charting method that can be used quickly for surveys or other needs.
A:A pie graph is an effective visual tool used for showing how something breaks into parts. A pie graph is essentially a circle sliced into 100 pieces. Each category or part represented in the pie graph is given a piece of the pie to represent the percentage that it comprises of the whole.