Find the First Six Terms of the Sequence: a1 = 4, an = an-1 + 8
To find the first six terms of the sequence defined by the initial term a1 = 4 and the recurrence relation an = an-1 + 8, we can start calculating each term step by step. a1: Given, a1 = 4 a2: Using the recurrence relation, a2 = a1 + 8 = 4 + 8 = […]
How to Write a Mixed Number as an Improper Fraction
Writing a mixed number as an improper fraction is a straightforward process. A mixed number consists of a whole number and a proper fraction. To convert it to an improper fraction, follow these steps: Multiply the whole number by the denominator: Take the whole number part of the mixed number and multiply it by the […]
What is the other number if the LCM of two numbers is 48, their HCF is 8, and one number is 16?
To find the other number when we know the LCM (Least Common Multiple), HCF (Highest Common Factor), and one of the numbers, we can use the relationship between these three values. The formula that connects them is: LCM × HCF = Number1 × Number2 In this scenario, we know: LCM = 48 HCF = 8 […]
What is the remainder when 3x³ + 2x² + 4x + 3 is divided by x² + 3x + 3?
To find the remainder when dividing the polynomial 3x³ + 2x² + 4x + 3 by x² + 3x + 3, we can use polynomial long division or synthetic division. First, we divide 3x³ by x², which gives 3x. We then multiply 3x by the entire divisor x² + 3x + 3: 3x * (x² […]
Which of the following is an even function: f(x) = x^12, f(x) = 8x, f(x) = x^2 + x, f(x) = 7?
To determine which of the functions is even, we need to use the definition of an even function. A function f(x) is considered even if for every x in its domain, f(-x) = f(x). 1. **f(x) = x^12**: Calculating f(-x): f(-x) = (-x)^12 = x^12. Since f(-x) = f(x), this function is even. 2. **f(x) […]
What is the smallest positive value for x where y sin 2x reaches its maximum?
The function y = sin(2x) reaches its maximum value when the sine function itself is at its maximum. The sine function achieves its maximum value of 1 at angles of the form: θ = π/2 + 2kπ, where k is any integer. For our function, we need to find when: 2x = π/2 + 2kπ […]
How would you write the name of a segment different from naming a line?
When naming a segment, you typically use the notation that highlights the end points of the segment. For example, if you have a line segment with endpoints A and B, you would denote it as AB or segment AB. This indicates that it is specifically a segment and not just any line. In contrast, when […]
In a 30-60-90 Triangle, What is the Length of the Hypotenuse When the Shorter Leg is 8 m?
In a 30-60-90 triangle, the lengths of the sides are in a specific ratio: 1 : √3 : 2. Here, the shorter leg (opposite the 30-degree angle) corresponds to the ‘1’ in the ratio. Given that the shorter leg is 8 m, we can use this ratio to find the length of the hypotenuse. The […]
What is the value of x in the equation 8x + 2y = 48 when y = 4?
To find the value of x in the equation 8x + 2y = 48 when y = 4, we start by substituting the value of y into the equation. 1. Substitute y with 4: 8x + 2(4) = 48 2. Simplifying this gives us: 8x + 8 = 48 3. Next, we need to isolate […]
Find the remainder when x³ – 2 is divided by x – 1
To find the remainder when dividing a polynomial by a linear term, we can use the Remainder Theorem. The theorem states that the remainder of the division of a polynomial f(x) by the linear polynomial x – c is f(c). In this case, our polynomial is f(x) = x³ – 2 and we are dividing […]