To determine the coefficient of the variable in the expression 4 + 3x + 7 + 6, we first need to understand what a coefficient is. A coefficient is a numerical factor that multiplies a variable. In this case, the variable is x. Now, let’s simplify the expression: 4 + 3x + 7 + 6 … Read more
To find the expected value E[x^2] given that E[x^5] is known and the variance V[x] is equal to 6 (which also equals E[x^2] minus E[x] squared), we can proceed stepwise. 1. **Understanding Variance (V[x])**: Variance is defined as: V[x] = E[x^2] – (E[x])^2 Given V[x] = 6, we can express this as: E[x^2] = V[x] … Read more
To simplify the expression 7 + 3i² + i, we need to understand the value of i. In mathematics, i is defined as the imaginary unit, and it is equal to the square root of -1. When simplifying the expression, we will substitute i² with -1 since i² = -1. Let’s break down the expression … Read more
To solve the problem, we need to set up a couple of equations based on the information provided. Let’s denote the two numbers as: x = the smaller number y = the larger number According to the problem: The sum of the two numbers is 70: x + y = 70 One number is four … Read more
To compute y and dy for the given expression y = 3x + x^2 + 3x + 0.6, we first simplify the equation: Combine like terms: y = 6x + x^2 + 0.6. Next, we need to substitute the provided values of x and dx. For this example, let’s assume: x = 1 dx = … Read more
To solve the equation 4sin²(x) – 4sin(x) + 1 = 0 in the interval [0, 2π], we will first treat it as a quadratic equation in terms of sin(x). Let us substitute y = sin(x). The equation then becomes: 4y² – 4y + 1 = 0 This can be solved using the quadratic formula: y … Read more
To determine the number of points of intersection between the parabola given by the equation y = x² and the circle centered at (0, 1) with a radius of 3, we’ll start by writing the equation of the circle. The standard form of a circle’s equation is given by: (x – h)² + (y – … Read more
To solve this problem, we first need to define some key terms and relationships between the numbers involved. We know: The HCF of the two numbers is 33. The LCM of the two numbers is 264. The first number (let’s call it A) divided by 2 yields a quotient of 33. The relationship between two … Read more
To find the derivative of the inverse function, we first need to clarify a few concepts regarding inverse functions and derivatives. Let’s denote the function as f(x) = x^(1/3). To find the derivative of the inverse function, we can utilize the relationship between a function and its inverse, given by the formula: (f-1(y))’ = 1 … Read more
To find the greatest common factor (GCF) of the expressions 4k, 18k^4, and 12, we first need to determine the factors of each term. Step 1: Factor Each Term 4k: The factors are 4 and k, which can be broken down to 2 × 2 and includes the variable k. 18k^4: The factors are 18 … Read more