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To calculate the arc length (s) of a circle, we can use the formula: s = r × θ Where: s = arc length r = radius of the circle θ = central angle in radians In this case, you have: r = 6 cm θ = 8π/5 radians Now, we can plug the values … Read more

To solve the system of equations given by 3x + 4y = 85 and 6x + 7y = 20, we can use either the substitution method or the elimination method. For this explanation, we will use the elimination method to find the values of x and y. Step 1: Set Up the Equations The equations … Read more

The product of the square roots of 23, 2, and 18 can be evaluated using the properties of square roots and multiplication. To find the product, we can first express it as follows: Square Root Product: √23 * √2 * √18 Using the property that the square root of a product is equal to the … Read more

Finding the Center and Radius of the Circle To find the center and radius of the circle from the given equation, we need to rewrite the equation in the standard form of a circle, which is: (x – h)² + (y – k)² = r² where (h, k) is the center of the circle and … Read more

To solve this problem, let’s define the ages of Harvey and Jane using algebraic expressions. Let J represent Jane’s age. Since Harvey is three times as old as Jane, we can express Harvey’s age as 3J. According to the information provided in the question, we know that the sum of their ages is 48 years. … Read more

To find a particular solution for the equation y = 2y + 6 by inspection, we start by simplifying the equation. Rearranging it gives: y – 2y = 6 Which simplifies to: -y = 6 From this, we can multiply both sides by -1 to isolate y: y = -6 Thus, y = -6 is … Read more

To simplify the expression cot(x) * sin(x) * sin(cos(x)), we need to break down the components of the expression step by step. 1. **Identify the components**: The expression consists of three parts: cot(x), sin(x), and sin(cos(x)). 2. **Understand cotangent**: Recall that the cotangent function is the reciprocal of the tangent function. Hence, we can express … Read more

To determine whether a number is divisible by 4 or 8 using divisibility tests, we can follow specific rules that apply to these numbers: Divisibility by 4 A number is divisible by 4 if the last two digits of the number form a number that is divisible by 4. Here’s how we can apply this … Read more

If a function f is continuous on the entire real line (often denoted as f: ℝ → ℝ), there are several important observations we can make about its graph: No Breaks or Jumps: Since f is continuous, its graph does not have any breaks, jumps, or holes. This means that you can draw the graph … Read more

Step-by-Step Solution to the Expression Let’s take a closer look at the expression: 2x³ + 4 + 6x² + 11x + 10 + 2x. The first step in solving this is to combine like terms. 1. Identify and Arrange Like Terms In polynomial expressions, we can group the terms based on their degrees: Degree 3: … Read more