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To determine the number of variable terms in the expression 3x³y + 5x² + 4y + z + 9, we first need to identify what constitutes a variable term. A variable term is a term that includes at least one variable, as opposed to a constant term, which contains only numerical values. In our expression, … Read more

Finding the x and y intercepts of an equation is a fundamental skill in algebra, and it provides valuable insights into the behavior of functions. Let’s break it down step by step: Understanding Intercepts The x-intercept is the point where the graph of the equation crosses the x-axis. At this point, the value of y … Read more

To find the fifth roots of the complex number represented by 32cos(3π) + isin(3π), we first need to express this number in polar form. The given complex number can be written as: z = r(cos(θ) + isin(θ)) Here, r is the modulus (magnitude) of the complex number and θ is the argument (angle). 1. **Calculate … Read more

To find the value of f(3), we first need to understand the function f(x) which is defined as: f(x) = 2x + 3 Now, to calculate f(3), we will substitute the value of x with 3: f(3) = 2(3) + 3 When we carry out the multiplication: f(3) = 6 + 3 Now, we add … Read more

To translate the problem into an algebraic equation, let’s define the unknown number as x. According to the question, we need to consider two parts: Eight times a number: This can be expressed as 8x. The sum of eight times a number and seven: We write this as 8x + 7. The next part of … Read more

To divide the expression 3x² + 11x + 4 by x⁴, we start by reorganizing the division: The expression can be rewritten in quotient form: (3x² + 11x + 4) ÷ x⁴ Now, let’s break this down step by step: Each term in the polynomial will be divided by x⁴. We divide 3x² by x⁴: … Read more

Solving the Quadratic Equation: x² + 2x – 7 = 0 To solve the quadratic equation x² + 2x – 7 = 0, we can use the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In our equation, we can identify the coefficients as follows: a = 1 … Read more

The integral of the function eax cos(bx) can be solved using integration by parts or through the method of complex numbers. However, one of the most effective ways to address this integral is by recognizing it as a standard form. To evaluate the integral, we can express it as: I = ∫ eax cos(bx) dx … Read more

To find the sets a and b based on the relations provided, we need to analyze the definitions given: a b = {1, 5, 7, 8}: This indicates the set that results from the operation or relationship between sets a and b. b a = {2, 10}: This represents the reverse operation or relationship. a … Read more

To clarify the expression f(x) = 1 x, we interpret it as f(x) = 1 imes x. In this case, it means that the function f evaluates to the value of x when multiplied by 1. Since multiplying any number by 1 yields the same number, we can conclude that: f(x) = 1 imes x … Read more