Integrating a constant expression, such as 3, with respect to x is a straightforward process in calculus. When you perform integration, you are essentially finding the area under the curve of the function you are integrating. Here, our function is a constant. The integration of a constant c with respect to x can be described … Read more
To find the exact value of sin 225°, we can utilize the half-angle formula. The half-angle formula for sine is given by: sin(θ/2) = ±√((1 – cos θ) / 2) Now, 225 degrees is half of 450 degrees, so we can set: θ = 450° Next, we will find the cosine of 450 degrees. Since … Read more
To factor the polynomial x² + 9x – 20, we need to find two numbers that multiply to the constant term (-20) and add to the linear coefficient (9). First, let’s identify the necessary components: Constant term: -20 Linear coefficient: 9 We need to find two numbers that satisfy the following equations: Product: m * … Read more
To arrange the numbers 12, 56, 27, and 42 from least to greatest, we will compare each number and position them accordingly. 1. Start by listing the numbers: 12, 56, 27, 42. 2. The smallest number here is 12. 3. Next, we compare 56, 27, and 42. The next smallest number is 27. 4. Now … Read more
Converting an improper fraction (where the numerator is greater than or equal to the denominator) into a proper fraction (where the numerator is less than the denominator) involves a simple process of division and requires a bit of understanding of fractions. Here’s how to do it step by step: Identify the Fraction: Start with your … Read more
To determine what type of polygon has an interior angle of 135 degrees, we can use the formula for finding the measure of an interior angle of a regular polygon. The formula is: Interior Angle = (n – 2) * 180° / n Here, n represents the number of sides in the polygon. We can … Read more
To find the solution to the equation x3 = 27, we need to isolate x. Here’s how we can do it step by step: First, we want to eliminate the cube on x. To do this, we can take the cube root of both sides of the equation: x = √[3]{27} Now we calculate the … Read more
To convert an angle from radians to degrees, you can use the conversion factor that relates the two units. Specifically, 1 radian is equal to 180/π degrees. Thus, to perform the conversion, you multiply the number of radians by this conversion factor. Here’s the formula you can use: Degrees = Radians × (180/π) For example, … Read more
To solve the quadratic equation 3×2 + 42x + 3 = 0, we can either use the quadratic formula or factorization. In this case, it may be easier to apply the quadratic formula, which is: x = (-b ± √(b² – 4ac)) / (2a) For the equation given: a = 3 b = 42 c … Read more
The tangent function, denoted as tan(x), is classified as an odd function. This classification is based on its mathematical properties and the symmetry of its graph. To understand this, we can consider the definition of an odd function. A function f(x) is called odd if it satisfies the condition: f(-x) = -f(x) For the tangent … Read more