To simplify the expression cot(x) * sin(x) * sin(pi/2 – x) * cos(x), we can follow these steps: Recall Definitions: Start by recalling that: cot(x) = cos(x) / sin(x) sin(pi/2 – x) = cos(x) (This is a fundamental identity for sine and cosine.) Substituting the Identities: Replace sin(pi/2 – x) in the expression: cot(x) * … Read more
Finding the Vertex of a Quadratic Function The vertex of a quadratic function in the standard form f(x) = ax² + bx + c can be found using the formula: x-coordinate of the vertex: x = -b / (2a) In the given function f(x) = x² + 6x + 13, we can identify: a = … Read more
To find the sum of the number 0743 using powers of 10, we first need to interpret each digit’s value according to its place in the number. The number 0743 can be broken down as follows: The digit 0
Calculating the Volume of the Iron Block The first step in solving the problem is to determine the volume of the solid iron cuboidal block. The volume (V) of a cuboid is calculated using the formula: V = Length × Width × Height Given the dimensions of the block: Length = 44 m Width = … Read more
The premium for a life insurance policy can vary significantly based on several factors, including the applicant’s age, gender, health status, lifestyle choices, and the insurance company’s underwriting criteria. In this case, we are focusing on a 48-year-old female looking to purchase a straight life insurance policy with a face value of $220,000. Insurance companies … Read more
To find the value of p in a binomial distribution where the mean (μ) is given, we can use the formula for the mean in a binomial distribution. The mean of a binomial distribution can be calculated using the formula: μ = n * p Where: μ is the mean of the distribution. n is … Read more
Calculating the Range and Interquartile Range To compute the range and the interquartile range (IQR) of a data set, follow these steps: Step 1: Organize the Data First, arrange the data values in ascending order. For your data set: 10, 12, 16, 17, 20 Step 2: Calculate the Range The range is the difference between … Read more
To solve the equation 4×2 + 3x + 9 = 2x + 1 using the quadratic formula, we first need to rearrange the equation into standard quadratic form, which is ax2 + bx + c = 0. 1. Start by moving all terms to one side of the equation: 4×2 + 3x + 9 – … Read more
To calculate the sum of the finite arithmetic sequence defined by the expression 4n + 10 for values of n ranging from 1 to 18, we first need to derive the terms of this sequence for each integer value of n within that range. 1. **Calculate the terms:** We substitute values of n from 1 … Read more
Understanding the Right Triangle In a right triangle, we have three sides: the opposite side, the adjacent side, and the hypotenuse. To find the length of side AB, we first need to understand the relationship between the tangent function and the sides of the triangle. The Tangent Function The tangent of an angle in a … Read more