Express the complex number in trigonometric form 6 + 6i
To express the complex number 6 + 6i in trigonometric form, we first need to find its modulus and argument. 1. **Modulus**: The modulus of a complex number a + bi is given by the formula: r = √(a² + b²). For our complex number, a = 6 and b = 6. So, we calculate: […]
What is the difference between the polynomials 8r^6s^3, 9r^5s^4, 3r^4s^5, 2r^4s^5, 5r^3s^6, and 4r^5s^4?
The difference between the polynomials 8r6s3, 9r5s4, 3r4s5, 2r4s5, 5r3s6, and 4r5s4 involves identifying the unique terms, organizing them, and understanding their coefficients and exponents. To find the difference between these polynomials, we need to first combine like terms. In this case, we can group the terms based on their expressions involving ‘r’ and ‘s’: […]
What is the simplified base for the function f(x) = 23272x?
The simplified base of the function f(x) = 23272x is 23272. In this expression, 23272 is a constant multiplier for the variable x. In mathematical terms, this means that 23272 is the base coefficient that scales the value of x. If you were to evaluate this function for different values of x, the output would […]
What is the equation of the quadratic graph with a focus of (4, 3) and a directrix of y = 13?
The equation of a quadratic graph can be derived from its focus and directrix. In this case, the focus is at the point (4, 3), and the directrix is the line y = 13. To find the equation, we first recognize that the vertex of the parabola lies midway between the focus and the directrix. […]
What is the domain of the following relation: (3, 5), (8, 6), (2, 1), (8, 6)?
The domain of a relation consists of all the first elements (or inputs) from each ordered pair in that relation. In this case, the relation provided is: (3, 5) (8, 6) (2, 1) (8, 6) To determine the domain, we extract the first elements from each pair: 3 from the pair (3, 5) 8 from […]
Is the value pi/12 a solution for the equation 4 cos(24x) = 3? True or False?
False. To determine if pi/12 is a solution for the equation 4 cos(24x) = 3, we start by substituting x with pi/12: Step 1: Substitute x = pi/12 into the equation: 4 cos(24 * (pi/12)) = 4 cos(2pi) = 4 * 1 = 4. Step 2: Compare the result with 3: 4 ≠ 3. Since […]
Find the value of y for a given value of x if y varies directly with x.
To solve this problem, we need to establish the relationship between y and x based on the information given. When we say that y varies directly with x, it means that there is a constant of proportionality (k) such that: y = k * x We know from the problem that when x is 84, […]
What is the derivative of tan(2x)?
To find the derivative of tan(2x), we will use the chain rule. The chain rule states that if you have a composite function, the derivative can be found by multiplying the derivative of the outer function by the derivative of the inner function. First, let’s identify our functions: the outer function is tan(u), where u […]
How to Solve the Expression: Find a b 2a 3b a and a b a i 4j 3k b 4i j 5k?
To solve the expression, we need to analyze and simplify the terms. Let’s break it down: Identify terms: The expression contains variables and coefficients such as a, b, j, k, and numbers like 2, 3, 4, and 5. Group similar terms: Begin by rearranging the terms based on their variables. For example, we can group […]
Lines DE and AB intersect at point C. What is the value of x: 12, 25, 38, or 52?
To determine the value of x where lines DE and AB intersect at point C, we need to analyze the given options in relation to the geometric properties of intersecting lines. When two lines intersect, the angles formed at the intersection can provide us with clues about the value of x. In typical problems involving […]