To find the value of 4p2 when p is equal to 8, we can follow these steps: First, substitute the value of p into the equation: 4p2. This gives us: 4 * (82). Calculate the exponent: 82 = 64. Now, substitute back into the equation: 4 * 64. Finally, multiply to get the result: 4 … Read more
To determine the values of x at which the function f(x) = x^4 – 8x^2 has a relative minimum, we begin by finding the derivative of the function. The first derivative, f'(x), gives us the critical points where the function can potentially have relative minima or maxima. Let’s calculate the derivative: f'(x) = 4x^3 – … Read more
The function f(x) = x6 is a polynomial function, and understanding its domain and range is essential for analyzing its behavior. Domain: The domain of a function refers to all the possible input values (x-values) that can be used in the function. For polynomial functions like f(x) = x6, there are no restrictions on the … Read more
To determine the number of boys in the class, we start with the total number of students and subtract the number of girls. Here’s a step-by-step breakdown: Total number of students: 35 Number of girls: 25 Now, to find the number of boys, we simply perform the following calculation: Number of boys: Total students – … Read more
To find the value of \( \tan(8) \), we can use the relationship between the trigonometric functions. We know that: \( \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} \) \( \sec(\theta) = \frac{1}{\cos(\theta)} \) From the given information, we have: \( \sec(8) = \frac{\sqrt{26}}{5} \) \( \sin(8) = 0 \) First, we can find \( \cos(8) \): \( \sec(8) … Read more
To determine the number of sides of the polygon, we can use the properties of interior angles in polygons. First, we need to recall the formula for the sum of interior angles of a polygon with n sides, which is: Sum of Interior Angles = (n – 2) × 180° In this case, we know … Read more
Synthetic division is a simplified method of dividing a polynomial by a linear binomial of the form (x – c). In this case, you want to divide the polynomial x4 + x + 1 using synthetic division. To demonstrate this, let’s assume you want to divide it by (x – r), where r is a … Read more
To find the solutions of the equation 4x² + 7x – 3 = 24, we first rearrange the equation to set it to zero: 1. Subtract 24 from both sides: 4x² + 7x – 3 – 24 = 0 2. Simplifying this gives: 4x² + 7x – 27 = 0 Now we have a quadratic … Read more
To simplify the expression 5 + 3i + 2i, follow these steps: Identify the real and imaginary parts: In this expression, 5 is the real part, and 3i and 2i are the imaginary parts. Add the imaginary parts together: Combine 3i and 2i to get 5i. Combine the real part with the summed imaginary part: … Read more
Understanding how to find the slope of a graph can give you valuable insights into a runner’s speed, particularly when measuring it in minutes per mile. Here’s a step-by-step guide to help you interpret the graph effectively: 1. Identify the Axes First, look at the graph’s axes. Typically, on a graph representing speed: X-axis: This … Read more