devyy

Verifying the Identity: 4 csc²(2x) = 2 csc²(x) tan(x) To verify the identity 4 csc²(2x) = 2 csc²(x) tan(x), we need to manipulate one side of the equation to show that it matches the other side. We can start by rewriting both sides using trigonometric identities. Understanding the Functions First, let’s recall the definitions of … Read more

To solve the expression 3b + 2 – 25 when b is equal to 7, we can follow these steps: First, we substitute the value of b into the expression: 3 * 7 + 2 – 25 Next, we perform the multiplication: 21 + 2 – 25 Now, we add 21 + 2: 23 – … Read more

To find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) of the numbers 18 and 45, we can start by using prime factorization. Prime Factorization First, let’s break each number down into its prime factors: 18: The prime factors of 18 are 2 and 3. Specifically, 18 can be expressed as: 18 = … Read more

To determine the slope of a line that is perpendicular to another line, we first need to find the slope of the given line. The equation provided is: 3y + 4x – 2 = 0 Let’s rearrange this equation into the slope-intercept form, which is y = mx + b, where m represents the slope. … Read more

To evaluate the indefinite integral of sin(t) * cos(t) with respect to t, we can approach it by using a substitution method or applying a trigonometric identity. One effective method is to utilize the identity: sin(t) * cos(t) = 1/2 * sin(2t) Using this identity, we can rewrite the integral: ∫ sin(t) * cos(t) dt … Read more

To determine the value of n in the equation represented by the square root of 16 divided by 43 times 4n, let’s break down the expression step by step. First, we need to calculate the square root of 16. The square root of 16 is: √16 = 4 Next, we take this value and divide … Read more

To find the factors of the polynomial q³ + q² + 2q + 2, we can start by attempting polynomial factorization. One effective method is to apply the technique of grouping. 1. **Grouping Terms**: Begin by grouping the terms in pairs: (q³ + q²) + (2q + 2) 2. **Factoring Out Common Factors**: Now, factor … Read more

To find the foci of the ellipse given by the equation 25x² + 16y² = 400, we first need to rewrite it in the standard form of an ellipse equation. The general form of an ellipse centered at the origin is: Ellipse equation: (x²/a²) + (y²/b²) = 1 From the given equation, we can simplify … Read more

To convert the Cartesian equation x² + y² = 6cx into polar coordinates, we need to use the relationships between Cartesian and polar coordinates: x = r cos(θ) y = r sin(θ) x² + y² = r² Substituting x and y in terms of r and θ into the original equation: x² + y² = … Read more

To simplify the expression cube root of x squared multiplied by the third root of x squared, we can use the properties of exponents and radicals. Start with the expression: √(x²) * ∛(x²) We can express these roots in terms of exponents: √(x²) = x²^(1/3) = x^(2/3) And for the third root: ∛(x²) = x²^(1/3) … Read more