In vector mathematics, the component of vector a along the direction of vector b can be determined using the concept of projection. The projection of vector a onto vector b essentially tells us how much of a points in the direction of b. The formula for the projection of vector a onto vector b is … Read more
To solve for t in the equation 32t – 5 = 5t + 25, we will follow these steps: Isolate the variable terms on one side: First, we can move the 5t term from the right side to the left side. To do this, we subtract 5t from both sides: 32t – 5 – 5t … Read more
Geometric Shapes: Edges, Faces, and Vertices Understanding the fundamental properties of geometric shapes is essential for students and enthusiasts alike. Below, we outline the number of edges, faces, and vertices associated with each of the following shapes: 1. Cube Edges: 12 Faces: 6 Vertices: 8 2. Cuboid Edges: 12 Faces: 6 Vertices: 8 3. Cone … Read more
A parallelogram is a special type of quadrilateral where opposite angles are equal, and the sum of adjacent angles is supplementary, meaning they add up to 180 degrees. Given that one angle measures 80 degrees, we can determine the measures of the remaining angles as follows: The angle opposite to the 80-degree angle is equal … Read more
To find the two numbers, let’s define them first. Let x be the smaller number and since one number is three times the other, we can denote the larger number as 3x. According to the problem, the sum of these two numbers equals 36. We can set up the equation: x + 3x = 36 … Read more
To factor the polynomial expression x³ + 9x² + 5x + 45 by grouping, we can break it into two pairs of terms. Here’s a step-by-step guide: Group the terms: We first group the terms into two pairs: (x³ + 9x²) + (5x + 45) Factor out the common factors from each group: From the … Read more
To find the values of cos(8°) and tan(8°) given sin(8°), we can use some basic trigonometric identities and calculations. First, we know the Pythagorean identity which states: sin²(θ) + cos²(θ) = 1 Using this identity, we can rearrange it to find cos(8°): cos(θ) = √(1 – sin²(θ)) If sin(8°) is given as approximately 0.13917 (this … Read more
Dividing the Polynomial To divide the polynomial 2x² + 17x + 35 by x + 5, we can use polynomial long division. Here’s a step-by-step guide: Step 1: Set Up the Division Write the division in a long division format. We want to divide 2x² + 17x + 35 by x + 5. Step 2: … Read more
To factor the expression x³ + 3x², we first look for common factors in both terms. Both terms have x² as a common factor. We can factor x² out of the expression: x²(x + 3) Thus, the complete factorization of the expression x³ + 3x² is: x²(x + 3) This factorization tells us that if … Read more
To solve the equation 4x – 12 = 0, we need to isolate the variable x. Here are the steps: Add 12 to both sides: This gives us: 4x = 12 Divide both sides by 4: This simplifies to: x = 3 Since we find a single value of x (which is 3) that satisfies … Read more