To find the 31st term of the given sequence (9, 15, 21), we first need to analyze the pattern of the sequence. 1. **Identify the Pattern:** Let’s look at the differences between the consecutive terms: The difference between the 1st term (9) and the 2nd term (15) is 15 – 9 = 6. The difference … Read more
To calculate the present value (PV) of a future amount of money, we use the formula: PV = FV / (1 + r)^n Where: PV = Present Value FV = Future Value ($1,000 in this case) r = Discount rate (as a decimal) n = Number of years until the money is received (5 years … Read more
To find the value of f(13), we first need to evaluate the function f(x) defined as: f(x) = 3x + 1 Now, let’s compute f(13): f(13) = 3(13) + 1 Calculating this gives us: f(13) = 39 + 1 = 40 Therefore, the value of f(13) is: 40 Next, since it’s stated that f(1) is … Read more
The Leaning Tower of Pisa is a fascinating architectural marvel, and calculating its volume can give us insight into its impressive structure. To find the volume of the tower, we will use the formula for the volume of a cylinder. The formula is: Volume = π × r² × h π (Pi) is approximately 3.14159. … Read more
To find the general solution of the differential equation given by y dx + 6xy^8 dy = 0, we will follow a systematic approach. First, let’s rewrite the equation in a more manageable form: y dx + 6xy^8 dy = 0 This can be rearranged into the standard differential form: y dx = -6xy^8 dy … Read more
To find an ordered pair (x, y) that satisfies both inequalities: y < x + 1: This means that for any value of x, y must be less than one unit above x. y < x + 3: Similarly, y must be less than three units above x. Start by rewriting the inequalities for clarity: ... Read more
To solve the equation \( \frac{5}{x} + 8 = \frac{3}{x} \), we start by eliminating the fractions. First, we can multiply both sides of the equation by \( x \) (assuming \( x \neq 0 \)) to simplify our work: Step 1: Multiply through by \( x \) x(\frac{5}{x} + 8) = x(\frac{3}{x}) This simplifies … Read more
To delve into this question, we first need to understand what a power set is. The power set of a set is the collection of all possible subsets of that set, including the empty set and the set itself. For instance, if we have a set A = {1, 2}, its power set, denoted as … Read more
Writing numbers in words can make the information more accessible and engaging. Let’s break down each number one by one. 1. 12000: This number is expressed in words as twelve thousand. It’s a round number, making it straightforward to say and write. 2. 1212: This number is translated to words as one thousand two hundred … Read more