Finding the intersection is something that comes up a lot in math. To do this you need to set the expressions equal and solve for x. Then you can determine y by filling in the x you found.
The variance of a probability distribution is a measure to quantify the spread of a distribution. If the variance is low, all outcomes are close to the mean, while distributions with a high variance have outcomes that could be far away from the mean.
The mean is the most important measure of probability distributions. It tells a lot about the likelihood that certain events will happen.
If you were asked to add together all of the numbers from 1 to 100, what would you do? Would you go through each number, adding to your total as you went or is there a quicker way? Find out in this article.
A right triangle is a triangle in which one angle is right, meaning it is exactly 90°. For these triangles, it is possible to calculate the other angles using goniometric functions as the sine, cosine and tangent.
The limit of a function describes how the function behaves in the neighborhood of some value. Often, it is interesting to look at the limit for x to infinity. This describes what happens when you would follow the line of the graph of the function until "the end".
Finding the minimum or maximum of a function is very important in mathematics. It can help you finding the optimal solution to a problem. Often you want some quantity to be maximal, such as profits or capacity. Also minima can be very useful, for example, when looking at a cost function.
Finding the derivative is something that comes up a lot in maths, but what is it actually? The derivative tells you what the slope of the function is in a certain point. The derivative of a function can be calculated using the definition, but mostly it is done by using standard rules.
In this article, you can learn how to use the power-reducing formulas in simplifying and evaluating trigonometric functions of different powers.
The theorem of Pythagoras is well known, showing the relationship between the areas of squares on the sides of right-angled triangles. However, it may not be realised that the theorem can also be used to show relationships between shapes other than squares.
In this article, you can learn the concept of the Same-Side Interior Angles Theorem in Geometry through solving various examples provided. The article also includes the Converse of the Same-Side Interior Angles Theorem and its proof.
Linear equations pop up everywhere and solving them is one of the most basic tools in mathematics.
Learn to use Descartes' Rule of Signs in determining the number of positive and negative zeros of a polynomial equation. This article is a full guide that defines Descartes' Rule of Signs, the procedure on how to use it, and detailed examples and solutions.
This article is a full guide in solving problems involving the use of the factor theorem. It includes the definition, proof, examples and solutions about the factor theorem.
This article is a full guide to solving problems on 30-60-90 triangles. It includes pattern formulas and rules necessary to understand the concept of 30-60-90 triangles. There are also examples provided to show the step-by-step procedure on how to solve certain kinds of problems.
Bayes' Law is an important tool to calculate conditional probabilities, such as the probability that A happens given B happened. It has many applications, but is often interpreted incorrectly.
Complex numbers are an extension of the real numbers that allow us to calculate the square root of negative numbers. All numbers can be represented as a complex number, and we can do all kinds of computations with them.
A look at what fractals are and three of the most popular examples: the middle third Cantor Set, the Koch curve, and the Sierpinski triangle.
The tangent line of a function in a point is a straight line that has the same slope as the function has in that point.
Finding the roots of a function is a very important operation in maths. For quadratic functions, there are a couple of ways to easily find the roots by hand.
A Nash equilibrium is a situation in a mathematical game in which none of the players would want to change their strategy without the other players changing theirs. A Nash equilibrium can occur in non-cooperative games only.
If you have a room full of people, how many handshakes are required before everybody has shaken hands with everybody else exactly once?
How many squares of all different sizes are there on a chessboard? Instead of counting them up, we can calculate the answer with a formula.
A look at Bertrand's Paradox, where a seemingly simple probability question yields some very differing results.
Learn how to compute for the surface area and volume of truncated solids. This article covers concepts, formulas, problems, and solutions about truncated cylinders and prisms.
Learn how to calculate the surface area and volume of the frustums of the right circular cone and pyramid. This article talks about the concepts and formulas needed in solving for the surface area and volume of frustums of solids.
A number of stories surround the puzzle known as Tower of Hanoi, Tower of Brahma and Lucas' Tower. Over the years, the puzzle has provided challenge to people in all walks of life, including mathematicians, computer programmers and strategists.
Learn how to approximate the area of irregularly shaped curve figures using Simpson’s 1/3 Rule. This article covers concepts, problems, and solutions about how to use Simpson’s 1/3 Rule in area approximation.
Learn how to graph a circle given the general form and standard form. Familiarize with converting general form to standard form equation of a circle and know the formulas necessary in solving problems about circles.
Learn how to solve problems involving Quadrilaterals in Plane Geometry. It contains formulas, calculator techniques, descriptions, and properties needed in order to interpret and solve Quadrilateral problems.