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1 Litre of Tears
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Alternative Titles: One Litre of Tears | １リットルの涙 | A 15-year-old Ikeuchi
Aya was an ordinary girl, the daughter of a family who works at a tofu
shop, and a...
Introduction to Algebra: Common Terms Explained
Reading Math resources for Algebra is as wise as practicing writing – the more you practice, the more you improve your problem solving skills. But first, it’s important to define top Algebra terms to get a better understanding of how things work.
Expressions are mathematical terms or sums or differences of mathematical terms that may use variables, or numbers, or both. Examples of expressions are: 4, x, 2 + 5, 2xy + 3, 2 + 6x (6 – 2), z + 3x (8 – z).
Variables are symbols that represent a number. Typically, we use letters such as x, t, or n for variables. For example, X stands for one side of a right triangle. It’s helpful to use a letter that represents the variable it stands for.
Examples:
Let x be the number of cars in a parking lot, let n be the time it takes for a car to travel from point A to point B.
Equations are a statement expressing the equality of two numbers. We use equations to relate numbers and variables. Many problems in Algebra may be written down as equations easily with little practice, and there are simple rules to simplify equations.
Introduction to Conics Sections
In this lesson in our Math resources series, we discuss conics formulas or sections. Conic sections are plane curves obtained by intersecting the planes in a cone. The ancient Greeks revered these curves and, in fact, were written extensively by both Appolonius and Euclid. Today, conics formulas remain highly important because of their many diverse applications in modern mathematics.
Although the layman might conjure up an image of a figure with a round base and pointed top, a mathematician’s idea of a cone is a surface that is obtained in a very precise way.
How a cone is formed
Imagine a vertical and another line intersecting it at an angle f (phi). The vertical line is called the axis and the intersecting line is the generator. The angle f (phi) created between the two lines is called the “vertex angle”.
Now, use your imagination and imagine grasping the axis between forefinger and thumb on either side of the intersection point with a generator, and start twirling it. The resulting surface is called a “cone”.
While conic formulas are visually appealing, their definitions for the conic sections tell students little about their uses and property. Thus, one should strive to master their “plane geometry” definitions, as well.
Category:
Conic Sections,
Conics Formulas
Complex Numbers Problems and Solutions
This is one in a series of Math resources you’ll find in this site. In this article, we hope to clear up common complex numbers problems. They aren’t called complex for no reason but, as with all other math problems, these have solutions.
What are complex numbers?
First, it’s best to be cleared about complex numbers. Not too long ago, mathematicians of all time devised a complete number system that includes both real and imaginary. Numbers in this system are called complex numbers. These numbers is composed of all sums a + bi where a and b are real numbers and i is imaginary.
Real numbers belong to the complex number system because a = a + Oi.
I acts as would any other variable, such as:
Ex.
Problem: 7i + 9i
Solution: combine like terms.
16i
Like real numbers, complex numbers may be equal, as in the example: a + bi = c + di, where a and c and b and d must be equal.
Ex.
Find the values of x and y in 3x + yi = 5x + 1 + 2i
Solution: From the above definition for complex numbers equality, group the real numbers equal and do the same for the complex numbers to get the answer.
3x = 5x + 1 yi = 2i
-2x = 1 y = 2
X = -(1/2)
Both examples show how to approach complex numbers problems.
