devyy To raise five to the second power, you would use the exponentiation operator, often represented by the caret symbol (^). This operator takes a base number, in this case, five, and raises it to the power indicated, which is two here. Mathematically, this is expressed as: 5 ^ 2 When you calculate this, you are … Read more
Finding the Maximum or Minimum Value of the Quadratic Function To find the maximum or minimum value of the quadratic function y = 2x² + 4x + 7, we can use the method of completing the square. Completing the square not only allows us to rewrite the function in a vertex form but also helps … Read more
To complete the square for the quadratic equation x² + 3x = 6, we need to transform the left-hand side into a perfect square trinomial. Here are the steps to determine what number should be added: Start with the quadratic expression on the left side: x² + 3x 2. To complete the square, we need … Read more
To find the solution set for the given system of equations, we need to solve the two equations simultaneously. The equations given are: Equation 1: 2y = x + 3 Equation 2: 5y = x + 7 We can start by manipulating these equations to express ‘y’ in terms of ‘x’. Step 1: Rearranging Equation … Read more
To solve the equation x² + 2x – 6 = 2x + 3, we first simplify the equation. We can start by eliminating the 2x from both sides: x² + 2x – 6 – 2x = 3 This simplifies to: x² – 6 = 3 Next, we can move the 3 from the right side … Read more
To find the product of the functions f(x) and g(x), we start by defining these functions more clearly: f(x) = log2(3x + 9) g(x) = log2(x + 3) The product of these two functions, denoted as f(x) * g(x), can be expressed as follows: f(x) * g(x) = log2(3x + 9) * log2(x + 3) … Read more
To find the volume of a cube, we use the formula: Volume (V) = s3 where s is the side length of the cube. In this case, the side length s is given as: s = 3x + 2y Now, to calculate the volume, we need to cube the side length: V = (3x + … Read more
To determine how many times greater the area of circle C is compared to circle D, we first need to understand the relationship between the diameters and the areas of the circles. Let’s define the diameter of circle D as d. This means the diameter of circle C, which is stated to be 3 times … Read more
To solve the given system of equations, we have the following equations: 1. 2x + y + z = 3 2. 2x + 2y + 3z = 2 3. 3x + 3y + z = 4 Let’s solve the system step by step: Step 1: Simplify the equations The first equation remains as it is: … Read more
Finding the Volume Under a Paraboloid Using Polar Coordinates To find the volume of the solid that lies beneath the paraboloid given by the equation z = 8 – 2x² – 2y² and above the xy-plane, we can simplify our calculations by switching to polar coordinates. This method helps to handle circular symmetry efficiently. Step … Read more