Finding the area of an irregular shape can seem daunting, but there are several effective methods to tackle it. Here’s a detailed breakdown of how to calculate the area of an irregular shape: 1. Divide and Conquer One of the most straightforward strategies is to divide the irregular shape into simpler geometric shapes, such as … Read more
To find the height of a triangle when you know the area and the length of the base, you can use the formula for the area of a triangle. The area (A) of a triangle can be calculated using the formula: A = (base * height) / 2 In this case, you have: Area (A) … Read more
To determine the interval over which the function f(g(x)) is negative, we first need to analyze the behaviors of both f and g. 1. **Understanding the Functions**: Begin by examining the function g(x). Identify its range and any important points (like intercepts or asymptotes). This will help you understand what output values g(x) can take … Read more
To calculate the total price of the camera including sales tax, you’ll first need to determine the amount of sales tax that will be added to the original price of the camera. Here’s how to do it step by step: Calculate the Sales Tax: To find the sales tax amount, multiply the original price of … Read more
The range of a relation is defined as the set of all second elements of the ordered pairs in that relation. In your case, the relation consists of the following pairs: (3, 2), (1, 2), (1, 4), and (1, 2). To find the range, we need to extract the second elements from each ordered pair: … Read more
To find the equation of a line that passes through the point (10, 3) and is perpendicular to the line described by the equation y = 5x + 7, we first need to determine the slope of the original line. The given line has a slope of 5. Two lines are said to be perpendicular … Read more
To evaluate the integral ∫ (log(x) / (x^2 – 1)) dx, we can use substitution and integration techniques. Step 1: Understanding the Integral The integral we are considering is: ∫ (log(x) / (x^2 – 1)) dx Where log(x) is the natural logarithm of x. Note that the term (x^2 – 1) can be factored to … Read more
To convert 80 percent into a fraction, we start by understanding what 'percent' means. The term "percent" refers to a ratio per hundred. Therefore, 80 percent can be written as: 80% = 80/100 Now, we can simplify this fraction. To do that, we need to find the greatest common divisor (GCD) of the numbers in … Read more
To find the first six terms of the sequence defined by a1 = 8 and the recurrence relation an = 5an-1, we will start by calculating each term using the previous term. a1 = 8 To find a2, we use the formula: a2 = 5a1 a2 = 5 * 8 = 40 a3: a3 = … Read more
To find the sum of the given expressions, we need to first combine like terms. The expressions provided are: 3x² 5x 8 5x² 13x 5 Let’s group the like terms together: Quadratic terms (x²): 3x² and 5x² Linear terms (x): 5x and 13x Constant terms: 8 and 5 Now, calculate the sum for each group: … Read more