The reflection of a point across a line involves finding a corresponding point that resides on the opposite side of the line at an equal distance. In this case, we are reflecting the point (2, 4) across the line y = 1. To find the reflected point: Determine the distance from the point to the … Read more
To find the equation of a sine curve, we can use the general formula for the sine function: y = A * sin(B(x – C)) + D Where: A is the amplitude of the sine wave, which determines its maximum height. B affects the period of the wave, which is the distance over which the … Read more
To find the value of x in the equation cos(x) = sin(20x), we can start by utilizing the identity that relates sine and cosine: sin(A) = cos(90° – A). This allows us to rewrite the equation as follows: cos(x) = cos(90° – 20x) This implies two scenarios due to the properties of cosine: … Read more
To solve this problem, we need to start with the concept of a tangent line. The tangent line to a function at a certain point gives us both the value of the function at that point and its slope. We know that the tangent line to the function y = f(x) at the point (4, … Read more
To find the real zeros of the polynomial f(x) = x³ + 4x² + 9x + 36, we need to determine the values of x for which f(x) = 0. The first step is to look for rational roots using the Rational Root Theorem, which suggests that any possible rational root, in this case, would … Read more
To find the ratio of boys to girls in the school, we need to express the numbers of boys and girls as a fraction and then simplify it. We have: Number of boys: 675 Number of girls: 525 So the ratio of boys to girls is: Ratio = Number of Boys : Number of Girls … Read more
Mass and weight are two fundamental concepts in physics that are often used interchangeably in everyday language, but they represent different properties. To clarify how they are related, let’s dive into their definitions and provide a practical example. Understanding Mass and Weight: Mass is a measure of the amount of matter in an object, and … Read more
To determine the equation of a line depicted in a graph, you typically follow these steps: Identify Two Points on the Line: Look for two clear points that the line passes through. The coordinates of these points are typically in the format (x_1, y_1) and (x_2, y_2). Calculate the Slope (m): The slope of the … Read more
To address the question of what property justifies the statement that if 3x > 4 and 3x > 10, then 3x must also be greater than 6, we need to explore the properties of inequalities. The key concept here is the Transitive Property of Inequality. This property states that if a > b and b … Read more
To differentiate the function sin²(x) cos(x), we will use the product rule as well as the chain rule. The product rule states that if you have two functions, u(x) and v(x), the derivative of their product is given by: (u v)’ = u’ v + u v’ In our case, let: u = sin²(x) v … Read more