devyy The given sequence is 11, 8, 5, 2. To define it recursively, we need to establish the first term and the rule for generating subsequent terms. Recursive Definition: Base Case: The first term of the sequence is defined as: a(1) = 11 Recursive Case: For all integers n > 1, each term can be defined … Read more
The base of a triangle is one of its sides, typically chosen as the side upon which the triangle stands. In most cases, when we talk about the base, we refer to the horizontal side at the bottom of the triangle, although this can vary depending on the triangle’s orientation and the specific context in … Read more
Understanding the Square Root Function The square root function in question is f(x) = √(1 + x). To differentiate this function, we’ll use the rules of calculus, specifically the chain rule. Step-by-Step Differentiation Identify the outer and inner functions: In this case, the outer function is the square root, and the inner function is g(x) … Read more
Determining whether a year is a leap year involves a few simple rules based on the calendar system we use. A leap year has 366 days instead of the usual 365, with the extra day added to February, making it 29 days long instead of 28. Here’s how to tell if a year is a … Read more
A byte is a fundamental unit of digital data that consists of 8 bits. Each bit can have a value of either 0 or 1, which gives us a total of 28 = 256 unique combinations of bits. The values that can be represented range from 0 to 255. This means the highest decimal value … Read more
Yes, it is true that a force is a vector quantity characterized by both magnitude and direction. In physics, a vector is a quantity that has a specific direction along with a certain size or amount. This means that when we describe a force, we not only indicate how strong that force is (its magnitude) … Read more
The yard is a unit of length commonly used in the United States and the United Kingdom, and it is defined as equal to 3 feet. Therefore, if you’re looking to convert yards into feet, you can use the simple equation: 1 yard = 3 feet This means that for every yard you measure, you … Read more
Writing the number 12,012 in words can be simplified by breaking it down into its component parts. The number consists of two main elements: the thousands and the units. First, let’s identify the number itself: 12,000 represents twelve thousand 12 represents twelve Now, when you combine these together, you would write the number 12,012 as: … Read more
When we raise any non-zero number to the power of 0, the result is always 1. This mathematical rule applies universally regardless of the base number used. In this case, when we calculate 60, we apply this rule: Base: 6 Exponent: 0 According to the rule, 60 = 1. This concept can often be surprising … Read more
The expression “10 to the 10th power”, commonly written as 1010, represents a mathematical operation known as exponentiation. In this case, the number 10 is known as the base, and the exponent (or power) is 10. This means that you multiply the base (10) by itself a total of 10 times. In simpler terms: 1010 … Read more