To find the equation of the line in point-slope form that passes through the points (0, 6) and (1, 3), we first need to determine the slope of the line. The slope (m) can be calculated using the slope formula: m = (y2 – y1) / (x2 – x1) Here, we can assign: (x1, y1) … Read more
The binomial series is a powerful mathematical tool used to represent the expansion of expressions of the form (a + b)n, where ‘a’ and ‘b’ are real numbers and ‘n’ is a non-negative integer or any real number. This series provides a way to express the sums of the powers of these terms and is … Read more
To factor the polynomial 4×4 + 20×2 + 3×2 + 15 by grouping, we can follow these steps: First, let’s rearrange the polynomial to group the terms effectively: (4×4 + 20×2) + (3×2 + 15) Next, factor out the common factors in each group: In the first group (4×4 + 20×2), we can factor out … Read more
When rolling two six-sided dice, the probability of getting a specific sum can be calculated by considering the total possible outcomes and the successful outcomes that yield the desired sum. In this case, we want to find the probability of rolling a total of 4. First, let’s determine the total number of outcomes when rolling … Read more
To find the fourth term in the expansion of the binomial expression (2x + 5)5, we can use the Binomial Theorem. The Binomial Theorem states that: (a + b)n = from k = 0 to n C(n, k) an-k bk, where C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k!(n-k)!). … Read more
To determine the value of x in the equation 4x + 8y = 40 when y = 8, we can start by substituting the value of y into the equation. Given: Equation: 4x + 8y = 40 Value of y: 8 Substituting y with 8: 4x + 8(8) = 40 This simplifies to: 4x + … Read more
To solve the equation sin(3x) * cos(2x) = 0, we can use the fact that the product of two functions is zero if at least one of the functions is zero. This means we need to set each function to zero: Step 1: Solve sin(3x) = 0 We know that the sine function equals zero … Read more
To find the product of the two functions, f(x) and g(x), we begin with their definitions: f(x) = 27x^5 + 33x^4 + 21x^3 g(x) = 3x^2 The product of the functions, denoted as (f * g)(x), can be computed by multiplying each term in f(x) by the entire function g(x). Let’s perform the multiplication step-by-step: … Read more
To find the perimeter of an equilateral triangle when the height is given, we can follow a series of steps. Let’s break it down. 1. **Understanding the Relationship Between Height and Side Length**: In an equilateral triangle, the height can be related to the side length using the formula: Height (h) = (√3 / 2) … Read more