Rewriting the Equation in General Form To rewrite the equation 2x + 4y + 2 + 3y + 5 in general form, we will simplify it first and then rearrange it into the standard form of a linear equation, which is: Ax + By + C = 0, where A, B, and C are constants. … Read more
To find the equation of the line tangent to the graph of the equation x² + 3xy – 10 = 0 at the point (1, 3), we need to follow these steps: Differentiate the equation implicitly: Since the equation is not solved for y, we will use implicit differentiation. Starting with the equation: x² + … Read more
To find the solutions for the quadratic equation x² + 2x + 3 = 0, we can graph it by converting it into a system of equations. A helpful approach is to express the equation in terms of y: Equation 1: To represent the quadratic function, we can write: y = x² + 2x + … Read more
The standard equation of a parabola with a vertical axis of symmetry is generally expressed in the form: (x – h)² = 4p(y – k) Where: (h, k) is the vertex of the parabola, p is the distance from the vertex to the focus (and also from the vertex to the directrix). Given that the … Read more
To find the height of the oblique cylinder, we can use the formula for the volume of a cylinder: Volume (V) = πr²h Where: V = volume of the cylinder r = radius of the base of the cylinder h = height of the cylinder Given: Diameter of the cylinder = 14 units Volume = … Read more
The sequence defined by the formula 3n + 3 can be expressed by substituting the values of n starting from 1. Let’s derive the first 10 terms: For n = 1: 3(1) + 3 = 6 For n = 2: 3(2) + 3 = 9 For n = 3: 3(3) + 3 = 12 For … Read more
The end behavior of a polynomial function is determined primarily by its leading term, which is the term with the highest degree. In this case, the function given is: f(x) = 2×7 – 8×6 + 3×5 + 3 Here, the leading term is 2×7, which can be broken down into two key components: the coefficient … Read more
Understanding the Problem: We start with the polynomial function f(x) = x³ + 4x² + 20x + 48. We know that one of its roots is x = 6. This means that when we substitute 6 into the polynomial, f(6) should equal 0. Using the Remainder Theorem: The Remainder Theorem states that if a polynomial … Read more
To find the equation of a line given a specific slope and a point, we can use the point-slope form of the equation of a line, which is: y – y1 = m(x – x1) In this formula: m is the slope of the line. (x1, y1) is a point on the line. We are … Read more
To solve the equation x6 + 6×3 + 5 = 0 using factoring, we can start by recognizing that this polynomial can be simplified through substitution. Let y = x3. Then, the equation transforms into: y2 + 6y + 5 = 0 This is now a quadratic equation in terms of y. We can factor … Read more