devyy To calculate the mean of a number sequence, you follow a straightforward process: Add all the numbers together: In this case, the sequence is 4, 2, 2, 2, 5, 15. So, you sum them up: 4 + 2 + 2 + 2 + 5 + 15 = 30 Count how many numbers are in the … Read more
To find the remainder when px2 + 7x + 3 is divided by x – 4, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by x – a, the remainder is f(a). In this case, we need to evaluate the polynomial at a = 4. This … Read more
To find the integral of sin(x)tan(x) dx, we first need to express tan(x) in terms of sine and cosine: tan(x) = rac{sin(x)}{cos(x)} This allows us to rewrite the integral as: ∫ sin(x)tan(x) dx = ∫ sin(x) * rac{sin(x)}{cos(x)} dx = ∫ rac{sin^2(x)}{cos(x)} dx Now, let’s denote this integral as: I = ∫ rac{sin^2(x)}{cos(x)} dx To … Read more
The Rational Root Theorem is a useful tool in algebra for identifying possible rational roots of polynomial equations. According to the theorem, if a polynomial function is of the form: f(x) = a_n x^n + a_(n-1) x^(n-1) + … + a_1 x + a_0 where: a_n is the leading coefficient, and a_0 is the constant … Read more
Understanding the Domain and Range of f(x) = 43√(81x) To determine the domain and range of the function f(x) = 43√(81x), we need to understand the constraints of the function based on its mathematical expression. Domain The domain of a function represents all possible input values (x-values) that can be used in the function without … Read more
Understanding the Equation Solution To find the solution for the equation f(x) = g(x), we need to determine the points where the graphs of these two functions intersect. This is where both functions hold the same value for the same input (x). Steps to Identify the Solution: Examine the Graph: Look closely at the graph … Read more
To find the linear factorization of the function f(x) = x4 – 9×2, we can start by recognizing that this is a polynomial function. The first step is to factor out the common term from both parts of the polynomial. 1. **Factor out the common term:** We can factor out x2 from the function: f(x) … Read more
When you roll two six-sided dice, there are a total of 36 different outcomes. This is because each die has 6 faces, and when they are rolled together, the combinations can be calculated as: 6 results from the first die × 6 results from the second die = 36 total outcomes. To find the chances … Read more
To find the equation of the line that passes through the point (2, 3) and is perpendicular to the line given by the equation 2x + 3y = 6, we need to follow a series of steps: Step 1: Determine the Slope of the Given Line First, we need to rewrite the line equation in … Read more
To solve the given expression 1 + tan²(a) + 1 + cot²(a) + 1 + tan(a) + 1 + cot²(a) tan²(a), we’ll first rewrite it in a clearer format: Let tan²(a) = x, so cot²(a) = 1/tan²(a) = 1/x. Now, substituting these in: The expression becomes: 4 + x + 1/x + tan(a) + 1/x … Read more