To express the complex number given by the expression 3cos(60°) + i sin(60°) in the form a + bi, we need to evaluate the trigonometric functions involved in the expression. First, let’s determine the values of the cosine and sine functions for 60 degrees: cos(60°) = 1/2 sin(60°) = √3/2 Now we can substitute these … Read more
To find the roots of the polynomial function with one factor being x – 7, we can apply the Remainder Theorem. According to this theorem, when we divide a polynomial by a linear factor of the form x – c, the remainder of this division is simply the value of the polynomial evaluated at c. … Read more
The integral of sec³(x) can be evaluated using integration techniques in calculus. It can be found by using a standard integration formula. Here’s how to compute it step by step: Integral of Sec³(x) To find the integral of sec³(x), we can use the following integral formula: ∫ sec³(x) dx = rac{1}{2} sec(x) tan(x) + rac{1}{2} … Read more
To find the equation of the line in point-slope form that passes through the points (0, 2) and (1, 5), we first need to determine the slope of the line. The slope (m) can be calculated using the formula: m = (y2 – y1) / (x2 – x1) In our case: (x1, y1) = (0, … Read more
To integrate the expression x – sin(x) divided by 1 – cos(x), we start with the integral: $$\int \frac{x – \sin{x}}{1 – \cos{x}} dx$$ This integral can be tackled through substitution or integration techniques. Let’s break it down: First, recognize the integral splits into two parts: $$\int \frac{x}{1 – \cos{x}} dx$$ $$\int \frac{-\sin{x}}{1 – \cos{x}} … Read more
The area of a regular hexagon can be calculated using a specific formula. For a hexagon where each side measures s, the area A is given by: A = rac{3 ext{√3}}{2}s^2 In this case, the side length s is 8 cm. Plugging this value into the formula: A = rac{3 ext{√3}}{2} imes (8)^2 Calculating that … Read more
To find the equation of the tangent line to the graph at the given point, we follow these steps: Identify the function: The function is given by y = 32 – 4x^2 + 5x + 6. Find the derivative: The derivative of the function, y’, will give us the slope of the tangent line. We … Read more
To find the area under the standard normal curve between the z-scores of 1.5 and 2.5, you can use the cumulative distribution function (CDF) for the standard normal distribution, which is often represented as Z or Φ(z). Here’s a step-by-step guide to perform the calculation: Find the CDF values: You’ll need to find the cumulative … Read more
To evaluate the expression (32 ÷ 5 × 24 ÷ 6) ÷ 3, we will follow the order of operations step by step. 1. **Start with the division and multiplication:** First, we divide 32 by 5: 32 ÷ 5 = 6.4 2. **Next, multiply the result by 24:** 6.4 × 24 = 153.6 3. **Then, … Read more
To solve for cdx, we start with the given equations: cx = 4×2 dx = x2 + 5x Next, we will find the expression for cdx by multiplying c and d together: cdx = c * dx Now, let’s substitute c from the first equation into this: From cx = 4×2, we can express c … Read more