To find the cosine of the angle (let’s call it θ) when given sin(θ) = 513 and tan(θ) = 0, we need to analyze the information provided. Firstly, the tangent of an angle is defined as the ratio of the sine to the cosine: tan(θ) = sin(θ) / cos(θ) If tan(θ) = 0, this implies: … Read more
To find the difference of the polynomials 4m, 5, 6m, 7, and 2n, we first need to clearly define what it means to find the difference of polynomials. In algebra, the difference of two polynomials is obtained by subtracting them. However, in this case, we want to find the combined difference of multiple terms. Let’s … Read more
To find the sum of the first 7 terms of the geometric sequence that starts with 4, 24, and 144, we first need to determine the common ratio of the sequence. The common ratio (r) can be found by dividing the second term (24) by the first term (4): r = 24 / 4 = … Read more
The expression x3 + 8 describes a mathematical function, specifically a polynomial function. To better understand its properties, we can break this down. This expression can be rewritten as: x3 + 23 Recognizing this as a sum of cubes allows us to apply the sum of cubes formula, which states: a3 + b3 = (a … Read more
To find the exact value of arctan(sin(p/2)), we first need to evaluate sin(p/2). The angle p/2 (or π/2 in radians) corresponds to 90 degrees. The sine of 90 degrees is one of the fundamental values in trigonometry, which is: sin(π/2) = 1 Now, substituting this back into our original expression: arctan(sin(π/2)) = arctan(1) The arctan … Read more
To express the expression sin(1/x) * cos(1/y) in terms of x and y only, we need to utilize some basic transformations and mathematical concepts related to trigonometric functions. 1. **Understanding the Terms**: The function sin(1/x) represents the sine of the angle 1/x, and cos(1/y) represents the cosine of the angle 1/y. 2. **Using Taylor Series … Read more
The average rate of change of a function over a specific interval can be calculated using the formula: Average Rate of Change = \( \frac{f(b) – f(a)}{b – a} \) where: \( a \) is the starting point of the interval, \( b \) is the ending point of the interval, \( f(a) \) and … Read more
To solve the equation 2x² + 12x + 32 by completing the square, the first step is to simplify the equation by dividing all terms by the leading coefficient (which is 2 in this case). This allows us to work with a simpler quadratic equation. Here’s how to do it: Start with the original equation: … Read more
To solve the problem, we need to find the value of u in relation to v. Given that: u = 6v v = 1 We can substitute the value of v into the equation for u. Let’s perform the substitution: u = 6 * v = 6 * 1 = 6 Thus, when v is … Read more
To find the Highest Common Factor (HCF) of 18 and 48 using the division method, you can follow these steps: Divide the larger number by the smaller number: Start with the two numbers, which are 48 and 18. Divide 48 by 18. Calculate the quotient and remainder: When you divide, you calculate: 48 ÷ 18 … Read more