To find the equation of a plane that passes through three points in three-dimensional space, we can follow a systematic approach. Let’s denote the three given points as: Point A: (2, 1, 2) Point B: (3, 8, 6) Point C: (2, 3, 1) The general equation of a plane can be expressed as: A(x – … Read more
To find the possible values of z in the quadratic equation z² + 4z + 4 = 0, we can first try factoring the equation. The expression z² + 4z + 4 can be factored as: (z + 2)(z + 2) = 0 Thus, we can rewrite the equation as: (z + 2)² = 0 … Read more
To determine how many solutions the equation 6x + 12 = 18 has, we first need to rearrange the equation to isolate the variable x. Start by subtracting 12 from both sides of the equation: 6x + 12 – 12 = 18 – 12 This simplifies to: 6x = 6 Next, divide both sides by … Read more
To factor the function f(x) = x4 – 64×2, we can start by noting that it has a common factor of x2. First, we can factor out x2 from the expression: f(x) = x2(x2 – 64) Next, we see that the remaining quadratic, x2 – 64, is a difference of squares, which can be factored … Read more
To calculate the distance a car can travel, you can use the formula: Distance = Speed × Time. In this case, the speed of the car is 60 km/h and the time is 12 hours. So, if we plug in the numbers: Distance = 60 km/h × 12 hours = 720 kilometers This means that … Read more
To find the x-intercept of the line represented by the equation 2x + 12y = 18, we need to determine the point at which the line crosses the x-axis. The x-intercept occurs when the value of y is equal to zero. Here are the steps to find the x-intercept: Start with the equation: 2x + … Read more
To solve the differential equation cos(x) dy/dx + sin(x) y = 1, we first rewrite it in a standard form. We start by rearranging the terms. The given equation can be rewritten as: dy/dx + (sin(x)/cos(x)) y = 1/cos(x) This is a first-order linear ordinary differential equation (ODE) of the form: dy/dx + P(x) y … Read more
To find the first 10 partial sums of the series given by: \( S = \sum_{n=1}^{\infty} \frac{16}{3^n} \) We can start by recognizing that this is a geometric series, where a (the first term) is \( \frac{16}{3} \) and the common ratio r is \( \frac{1}{3} \). The formula for the n-th partial sum of … Read more
The line of symmetry for a parabola can be found using the formula: x = -b / (2a) In the given equation, y = x² + 10x + 25, we can identify the coefficients: a = 1 (the coefficient of x²) b = 10 (the coefficient of x) c = 25 (the constant term) Now, … Read more
To find the value of f(4) using the function f(x) = sec(x), we first need to understand what the secant function represents in mathematics. The secant function is the reciprocal of the cosine function, which means: sec(x) = 1/cos(x) Now, to find f(4), we will substitute x = 4 into the function: f(4) = sec(4) … Read more