To find the area of a sector of a circle, you can use the formula: Area = (θ / 360) × π × r² Where: θ is the angle of the sector in degrees r is the radius of the circle In this case: r = 8 inches θ = 45 degrees Now, plug these … Read more
The series 2, 4, 8, 16, 32 is a sequence of numbers where each term is obtained by multiplying the previous term by 2. This is known as a geometric progression, and in this case, the first term (a) is 2, and the common ratio (r) is also 2. Let’s break it down: The first … Read more
To create a polynomial equation of degree 3 with the specified roots of 2 and an imaginary number, we need to remember a couple of important principles about polynomials and their roots. 1. **Understanding Roots**: Since the coefficients of the polynomial are usually assumed to be real, complex roots come in conjugate pairs. So, if … Read more
The binomial theorem provides a powerful way to expand expressions of the form (a + b)n. Although we are specifically looking to expand x13, we can think of this expression in the context of the binomial theorem by letting a = x and b = 0 since we want to express x13 as a binomial. … Read more
To solve this problem, we first need to determine how much work is involved in the job and how many men are required based on the time available. 1. **Calculate the total work**: The total amount of work done can be represented in terms of man-days. If 6 men can complete the job in 14 … Read more
To find a positive angle less than 2π that is coterminal with the angle 11π/3, we first need to understand the concept of coterminal angles. Coterminal angles are angles that share the same terminal side when drawn in standard position, which means they differ by a multiple of 2π. The process for finding a coterminal … Read more
To find the value of ‘b’ corresponding to the values in ‘a’, we first need to understand the sequences provided. The sequence ‘a’ consists of the numbers 3, 6, 9, 12, which represents a pattern that increments by 3. On the other hand, the sequence ‘b’ includes the numbers 2, 4, 6, 8, 10, 12, … Read more
To find the exact solution to the system of equations given by y = 6075x and y = 4x + 1, we can set the equations equal to each other since they both describe the variable y. 1. Start by substituting 6075x for y in the second equation: 6075x = 4x + 1 2. Next, … Read more
To find the equation of the tangent line to the curve y = sec(x) at the given point, we will follow these steps: Determine the point of tangency: You are given the point (2, sec(2)). First, calculate the y-coordinate at x = 2: y = sec(2) = 1 / cos(2) Differentiate the function: To find … Read more
To solve the equation 1/3 * 2x = 8 – 4, we will follow these steps: Simplify the equation: First, let’s simplify the right side of the equation: 8 – 4 = 4 So the equation now reads: 1/3 * 2x = 4 Eliminate the fraction: To eliminate the fraction on the left side, multiply … Read more