devyy To find the solution set of the equation 18 + 3n + 2n + 20 + 4n = 0, we will first simplify the left side of the equation. 1. **Combine like terms**: The terms involving n are 3n + 2n + 4n. If we add these together, we get: 3n + 2n + 4n … Read more
To solve the equation 6x = 1296, we first need to express both sides as powers of the same base. Let’s start with 1296. We can find the prime factorization of 1296. By dividing 1296 by 6: 1296 ÷ 6 = 216 216 ÷ 6 = 36 36 ÷ 6 = 6 6 ÷ 6 … Read more
To prove that the perpendicular drawn at the point of contact of a tangent to a circle passes through the center, we can follow a step-by-step geometric proof using basic properties of a circle. Definitions: Let O be the center of the circle. Let T be the point where the tangent touches the circle. Let … Read more
The question at hand asks for the value that is equivalent to the square root of the cube root of 5. Let’s break this down into simpler parts for better understanding. First, we need to find the cube root of 5. The cube root is the number that, when multiplied by itself three times (or … Read more
A topological space is a fundamental concept in the field of mathematics, specifically in topology. It provides a framework for discussing continuity, convergence, and the properties of space without necessarily relying on the concept of distance. To define a topological space, we start with a set, say X, and a collection of subsets of X, … Read more
To find the exact length of the curve defined by the equation y = 5 + 2×3 from x = 0 to x = 1, we employ the arc length formula. The arc length L of a curve y = f(x) between two points a and b is given by: L = ∫ab √(1 + … Read more
To find the equation of a line that passes through a specific point and has a given slope, we can use the point-slope form of the equation of a line. The point-slope form is represented as: y – y1 = m(x – x1) where: (x1, y1) is a point on the line, m is the … Read more
To find the linear approximation of the function f(x, y, z) = x² + y² + z² at the point (3, 2, 6), we first need to calculate the value of the function and the partial derivatives at that point. Step 1: Evaluate the function at (3, 2, 6) Plugging in the values, we get: … Read more
To determine a polynomial with the specified roots, we start by recalling that if a number is a root of a polynomial, then the polynomial can be expressed as a product involving that root. In this case, the roots given are √5 (repeated root) and 3. The general form for a polynomial derived from its … Read more
To find the probability of the complement of an event, we can use a simple formula. The complement of an event E, denoted as E’, represents all outcomes that are not contained in event E. The formula to compute the probability of the complement is: P(E’) = 1 – P(E) Given that the probability of … Read more