The relative maximum and minimum points of a function can be found by analyzing its critical points. A critical point occurs when the first derivative of the function is zero or undefined. Let’s go through the steps to find the critical points of the function f(x) = 2x³ + x² + 11x. Step 1: Find … Read more
To find the number of onto functions (surjective functions) from set A to set B, we can use the concept from combinatorial mathematics involving Stirling numbers of the second kind and inclusion-exclusion principle. Assuming that set A has m elements and set B has n elements, where m >= n, the formula for the number … Read more
To solve the problem of finding the probability of rolling exactly one ‘3’ when a fair 6-sided die is rolled three times, we can apply the binomial probability formula. The situation can be modeled as a binomial experiment, where: ‘n’ (the number of trials) = 3 rolls of the die ‘k’ (the number of successes … Read more
To graph a line with a given slope and a specific point, you can follow a simple process. In this case, the slope (m) is 7, and the point through which the line passes is (2, 9). Step 1: Understand the Slope The slope of a line measures how steep the line is, calculated as … Read more
To find the value of x, we first need to remember that for any regular polygon, the measure of each exterior angle can be calculated using the formula: Exterior Angle = 360° / n where n is the number of sides of the polygon. In our case, since we are dealing with a regular decagon, … Read more
To find the coordinates of the point that is equidistant from points A (2, 3) and C (5, 6), we can utilize the geometric concept of the midpoint of the line segment connecting these two points. The coordinates of the midpoint (M) can be calculated using the following formula: M = ((x1 + x2) / … Read more
To solve the system of equations 2x + 5y = 3 and x + 3y = 1, we can use either the substitution method or the elimination method. Here, we’ll use the elimination method for clarity. Step 1: Align the equations We start with the given equations: Equation 1: 2x + 5y = 3 Equation … Read more
To find the radius of the circle represented by the equation x² + y² – 8x – 6y – 21 = 0, we first need to rewrite this equation in standard form. The standard form of a circle’s equation is: (x – h)² + (y – k)² = r² where (h, k) is the center … Read more
Understanding Number Names in Different Numbering Systems When you come across the numbers 236749 and 48670002, it’s interesting to see how they are represented in both the Indian and international numbering systems. 1. Number: 236749 Indian Numbering System: Two Lakh Thirty Six Thousand Seven Hundred Forty Nine International Numbering System: Two Hundred Thirty Six Thousand … Read more