devyy To analyze the symmetry of the equation given in polar coordinates as r = 9 sin(78), we need to explore the properties of such equations regarding their symmetry about the axes and the origin. Symmetry About the X-Axis A graph is symmetric about the x-axis if replacing y with -y results in the same equation. … Read more
Finding the Slant Height of a Figure The slant height is a crucial measurement, particularly in geometry when dealing with conical shapes, pyramids, or right triangular prisms. It represents the distance measured along the lateral surface from a point on the base to the apex (the top point) of the figure. Here’s how to find … Read more
A uniform probability density function (PDF) is characterized by a constant height across its range. Unlike other distributions where probabilities may vary, the uniform PDF maintains a steady value from the minimum to the maximum bounds of the random variable it represents. This constancy is what makes the uniform distribution unique. To better understand how … Read more
To find the composition of the functions f(x) = 5x + 4 and g(x) = 6x + 7, we need to determine what f(g(x)) looks like. This means we’ll substitute the entire function g(x) into the function f(x). Here’s a step-by-step breakdown: Start with g(x): g(x) = 6x + 7 Now substitute g(x) into f(x): … Read more
To find two numbers where the sum is 18 and the difference is 4, we can set up a couple of equations based on the information provided. Let’s denote the two numbers as x and y. We can express the conditions given in the problem as: Equation 1 (Sum): x + y = 18 Equation … Read more
Solving the Equation To solve the equation 2x + 5 = 2, we will start by isolating x. Here are the steps: Subtract 5 from both sides of the equation: 2x + 5 – 5 = 2 – 5 This simplifies to: 2x = -3 Next, divide both sides by 2: x = -3 / … Read more
The order in numerical expressions is crucial for accurately interpreting and solving mathematical problems. It helps to establish a consistent method for calculation and ensures that everyone arrives at the same result when faced with the same expression. In mathematics, the order of operations is a standard set of rules that dictates the sequence in … Read more
To determine the probability that a randomly selected positive two-digit integer exhibits specific characteristics, we first need to identify the total range of positive two-digit integers. The two-digit integers range from 10 to 99. This gives us: Lowest two-digit integer: 10 Highest two-digit integer: 99 Now, let’s calculate the total count of two-digit integers: Total … Read more
To determine the potential roots of the polynomial function p(x) = x^4 + 22x^2 + 16x + 12, we can use the Rational Root Theorem, which suggests that any rational root, in the form of a fraction p/q, where p is a factor of the constant term and q is a factor of the leading … Read more
To find the area of a 30-degree sector of a circle with a total area of 96π m², we first need to understand how to calculate the area of a sector based on the angle it encompasses. The formula to find the area of a sector is: Area of Sector = (θ / 360) × … Read more