The antiderivative, or indefinite integral, of a function is essentially the reverse of taking the derivative. To find the antiderivative of the function 1/x², we can rewrite it using negative exponents: -1/x^2 = x^{-2}. Now, we will apply the power rule for integration. The power rule for integration states that for any real number n … Read more
16:05 is a time expressed in a 24-hour clock format, which means 16 hours and 5 minutes since midnight. In the 12-hour clock system, this would convert to 4:05 PM. The 24-hour format is commonly used in many parts of the world, especially in military, aviation, and train scheduling contexts, where avoiding confusion over AM … Read more
To find the length of a line segment in a two-dimensional space, you can use the distance formula derived from the Pythagorean theorem. The formula is as follows: Distance = √((x2 – x1)² + (y2 – y1)²) Here’s a step-by-step guide on how to calculate the length of a line segment: Identify the Endpoints: Determine … Read more
The value of i squared, written mathematically as i², is a fundamental concept in complex numbers. In mathematics, i represents the imaginary unit, which is defined as the square root of -1. Therefore, when we calculate i², we can express this as: i² = √(-1) × √(-1) When we multiply the two square roots, we … Read more
Counting to a quadrillion is a monumental task that, while theoretically simple, would take an extraordinarily long time. To understand the duration of this endeavor, let’s break down the numbers and the time involved. A quadrillion is equal to 1,000 trillion or 1 followed by 15 zeros: 1,000,000,000,000,000. If we consider an average person counting … Read more
To determine the probability of drawing a red face card from a standard deck of playing cards, we first need to understand the composition of the deck and what constitutes a red face card. A standard deck consists of 52 cards, which are divided into four suits: hearts, diamonds, clubs, and spades. Of these suits, … Read more
To factor the quadratic expression x² + 2x – 3, you’ll want to follow these steps: Identify the coefficients: In the expression x² + 2x – 3, the coefficients are as follows: A (the coefficient of x²) = 1 B (the coefficient of x) = 2 C (the constant term) = -3 Find two numbers … Read more
To convert the fraction 1/15 into a decimal, you’ll need to divide the numerator (1) by the denominator (15). Here’s how to do that: Perform the division: 1 ÷ 15. When you divide 1 by 15, you start by determining how many times 15 fits into 1. Since 15 is larger than 1, it fits … Read more
To integrate the function 1 + sin(x), we will proceed step by step. The integral we need to solve is: ∫ (1 + sin(x)) dx This integral can be split into two separate integrals: ∫ 1 dx + ∫ sin(x) dx Now, let’s solve each part: 1. Integrating 1: The integral of 1 with respect … Read more
To find the sum of the multiples of 4 from 16 to 100, we start by identifying the first and last multiples of 4 within that range. The first multiple of 4 in this range is 16, and the last multiple of 4 before reaching 100 is 100 itself, as 100 is also a multiple … Read more