Finding the Exponential Function To determine the exponential function that fits the given data points, we can start by analyzing the values of f(x) and x provided in the table: x = 3, f(x) = 64 x = 4, f(x) = 256 x = 5, f(x) = 1024 From this data, we observe that: 64 … Read more
In geometry, two angles are considered coterminal if they share the same terminal side when drawn in standard position. This means they can differ by any multiple of 360 degrees. To find an angle that is coterminal with 86 degrees, we can use the following formula: coterminal angle = original angle + (n * 360) … Read more
To find the exact length of arc ABC in circle E, we can use the formula for the length of an arc: Arc Length (L) = (θ / 360) * 2πr Where: L = length of the arc θ = the central angle in degrees (in this case, 324 degrees) r = radius of the … Read more
To solve the equation log₂(x) + log₂(x) = 6 + 4, we first need to simplify the equation. The left side of the equation, log₂(x) + log₂(x), can be combined. Since adding logarithms with the same base is equivalent to multiplying their arguments, we can rewrite it as: 2 * log₂(x) = 10 Now, we … Read more
To solve the inequality 24x – 3 ≥ -3 – 3x + 5x, we will first simplify the right side of the inequality. Let’s break it down step by step: Simplifying the right side: Combine the terms on the right side: -3 – 3x + 5x simplifies to -3 + 2x. Rewriting the inequality: Now … Read more
To solve the problem, we first need to understand the information provided by the inequalities and the values of m. We know that: If m ≤ 1, then the corresponding value is 105. If m ≤ 4, then the corresponding value is 115. This indicates that as the values of m increase, the corresponding values … Read more
To find the slope of the tangent line to the graph of y = ln(2x) at the point where x = 4, we need to differentiate the function and then evaluate the derivative at that particular value of x. Step 1: Differentiate the function First, let’s differentiate y = ln(2x). Using the chain rule, the … Read more
To find the second number in a sequence of 5 consecutive integers whose sum is 270, we can start by letting the first integer be represented by the variable x. The five consecutive integers can then be expressed as: x (1st integer) x + 1 (2nd integer) x + 2 (3rd integer) x + 3 … Read more
To write the equation of a circle, we use the standard form of the equation: (x – h)² + (y – k)² = r² Where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is given as (3, 8), so h = 3 … Read more
Sketching the Graph of f(x) = 5x + 4 The function f(x) = 5x + 4 is a linear function, where ‘5’ is the slope and ‘4’ is the y-intercept. To graph this function, follow these steps: Identify the y-intercept: The y-intercept occurs when x = 0. Plugging in this value gives us: f(0) = … Read more