To find the distance between a point and a line in analytical geometry, you can use the formula: distance = |ax + by + c| / √(a^2 + b^2) where a, b, and c are constants that represent the coefficients of the equation of the line in the form of ax + by + c…
The section formula is a formula used in analytical geometry to find the coordinates of a point that divides a line segment into two parts in a given ratio. Let A(x1, y1) and B(x2, y2) be two points in a coordinate plane, and let M(x, y) be a point on the line segment AB that…
In analytical geometry, the distance between two points in a plane is given by the distance formula: d = sqrt((x2 – x1)^2 + (y2 – y1)^2) where (x1, y1) and (x2, y2) are the coordinates of the two points and d is the distance between them. To use the formula, simply substitute the values of…
Inverse trigonometric functions are functions that return the angle whose trigonometric ratio is a given value. Here are the principal value only of inverse trigonometric functions and their elementary properties: It is important to note that inverse trigonometric functions are not always unique, as they depend on the quadrant in which the angle lies. For…
Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions can be defined in terms of the sides of a right triangle as follows: In addition to these three functions,…
The mean of a random variable is also known as its expected value. It is a measure of the central tendency of the distribution of the random variable. The expected value of a discrete random variable X with possible values x1, x2, …, xn and corresponding probabilities P(X = x1), P(X = x2), …, P(X…
Standard deviation and variance are measures of variability that provide information about how spread out a dataset is. The standard deviation is the square root of the variance, and it measures the average deviation of each data point from the mean. In general, the larger the standard deviation or variance, the more spread out the…
Mean deviation is a measure of variability that describes the average difference between the values in a dataset and their mean. It is also known as mean absolute deviation (MAD). The formula for calculating the mean deviation is: Mean Deviation = (Σ |xi – x̄|) / n where: Σ represents the sum of the absolute…
Sure! Probability and statistics are two interconnected fields of mathematics that deal with the analysis and interpretation of data. A fundamental aspect of both of these fields is the concept of measures of central tendency and measures of dispersion. Measures of central tendency refer to the summary statistics that describe the most typical or representative…
The determinant of a square matrix of order up to three can be calculated as follows: For a 1×1 matrix: The determinant of a 1×1 matrix is simply the value of the only element in the matrix. For a 2×2 matrix: The determinant of a 2×2 matrix is calculated as follows: |a b| |c d|…
