Finding the Solution to the System of Equations To solve the system of equations given by y = x + 10 and 2x + y = 4, we can use the substitution method. This involves substituting one equation into the other to find the values of x and y. Let’s break this down step-by-step: Step … Read more
To determine the factors of the polynomial f(x) = 7x³ + 22x² + 67x + 10, we can employ several methods such as factoring by grouping, synthetic division, or utilizing the Rational Root Theorem alongside polynomial division. Step-by-step factorization: 1. Identify possible rational roots: The Rational Root Theorem states that any rational root, expressed in … Read more
Calculating the Surface Area of a Square Prism To find the surface area of a square prism, we need to consider both the lateral surface area and the areas of the two square bases. Here’s how we can break it down step by step: Step 1: Understand the dimensions In this case, the square base … Read more
The degree of a polynomial is determined by the highest sum of the exponents of its variables in each term of the polynomial. In this case, we have the polynomial 4xy + 11y + 3. Let’s break it down term by term: For the first term, 4xy: The exponent of x is 1 and the … Read more
Finding the General Solution of the Differential Equation To find the general solution of the differential equation given by dy/dx = y * e^(2x) we can use the method of separation of variables. Here’s a step-by-step approach: Step 1: Separate the Variables We start by rewriting the equation to isolate y and x on opposite … Read more
In geometry, when a triangle is inscribed within a circle, it means that all the vertices of the triangle touch the circumference of the circle. In this case, we have triangle GJK inscribed in circle L, where the line segment GJ represents a diameter of the circle. Because GJ is a diameter of circle L, … Read more
To solve the quadratic equation 3×2 + 2x + 7 = 0, we can apply the quadratic formula, which is given by: x = (-b ± √(b2 – 4ac)) / (2a) In this equation: a = 3 b = 2 c = 7 Firstly, we will calculate the discriminant (the value under the square root … Read more
To find the equation of the tangent line to the curve y = sec(x) at the point (p/3, 2), we need to follow several steps: Find the derivative of the function: The derivative of y = sec(x) can be calculated using the chain rule. The derivative is given by: dy/dx = sec(x) * tan(x) Evaluate … Read more
To solve the equation log2(x) + 4 = 416, we first need to isolate the logarithmic term. We can do this by subtracting 4 from both sides of the equation: log2(x) = 416 – 4 This simplifies to: log2(x) = 412 Next, we will convert this logarithmic equation into its exponential form. Recall that if … Read more