Yes, every integer is indeed considered a rational number. To understand why, let’s start by defining what integers and rational numbers are. Integers are whole numbers that can be positive, negative, or zero. For example, -3, 0, and 7 are all integers. On the other hand, rational numbers are defined as numbers that can be … Read more
To prove that sin(πx) * sin(x) equals 0 for certain values of x, let’s first analyze the properties of the sine function and the specific conditions under which this product results in zero. The product of the sine functions sin(πx) and sin(x) will equal zero if either of the sine functions is zero. Therefore, we … Read more
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For the function f(x) = 3x^2, we can analyze it as follows: Understanding the Function: This function is a quadratic function, where 3 is the coefficient of x squared. Quadratics are polynomial functions characterized … Read more
The given sequence is: 5, 15, 6, 18, 7, 21, 8. To determine the next number in this sequence, let’s analyze the pattern: The first and second numbers are 5 and 15. Then the sequence alternates: 5 to 6 (increasing by 1), and 15 to 18 (increasing by 3). This pattern continues with 6 to … Read more
To evaluate the indefinite integral ∫ (cos(x) / x) dx using an infinite series, we can leverage the Taylor series expansion of the cosine function. The Taylor series expansion for cos(x) around 0 is given by: cos(x) = 1 – rac{x^2}{2!} + rac{x^4}{4!} – rac{x^6}{6!} + rac{x^8}{8!} – rac{x^{10}}{10!} + ext{…} Substituting this series into … Read more
To determine the value of a function at a specific point, such as when x = 2, you need to know the function itself. For instance, if you have a function defined as f(x) = 3x + 1, you can find the value at x = 2 by substituting 2 into the function. Here’s how … Read more
The length of segment BC can be determined from the given measurements, which are: 13.0 units 28.8 units 31.2 units 33.8 units To find the length of BC rounded to the nearest tenth, we first need to assess the requirements of the question. If the task is to choose one length from the provided values, … Read more
To solve the question "What is 30 divided by 10?", we simply need to perform the division operation. Dividing 30 by 10 is equivalent to asking how many times 10 fits into 30. When you divide 30 by 10, the calculation is as follows: 30 ÷ 10 = 3 This means that 10 goes into … Read more
To determine the angle between the hour and minute hands of a clock at 2 PM, we can follow a straightforward calculation method based on the positions of the hands. 1. **Position of the Hour Hand:**At 2 PM, the hour hand is pointing directly at the 2 on the clock. Each hour represents a 30-degree … Read more
To find an equivalent expression for the sum of 7a²b, 10a²b², and 14a²b³, we must first factor out any common terms shared by these expressions. Let’s analyze them one at a time: The first term is 7a²b. It consists of the factors 7, a², and b. The second term is 10a²b². Here we have factors … Read more