To calculate the total area of the four walls of a room when the length, breadth, and height are in the ratio of 3:2:1, follow these steps: 1. **Define Variables**: Let the height of the room be represented as h. Based on the ratio: Length (l): 3h Breadth (b): 2h Height (h): h 2. **Calculate … Read more
To begin with, let’s determine the highest common factor (HCF) of the numbers 65 and 117. First, we’ll find the prime factorization of both numbers: 65 can be factored into: 5 × 13. 117 can be factored into: 3 × 39 or equivalently 3 × 3 × 13. From the factorizations above, we see that … Read more
Understanding the Center of Gravity The center of gravity (CG) is a crucial concept in physics and engineering, providing insight into how weight is distributed in an object. In different shapes, the CG varies based on symmetry, dimensions, and mass distribution. Let’s explore how to find the CG in a scalene triangle and a cylinder. … Read more
To solve for b2 in the formula A = 1/2 * h * (b1 + b2), where you know the values of A, h, and b1, you can follow these steps: Substitute the known values into the formula. The values provided are: A = 16, h = 4, and b1 = 3. The formula becomes: … Read more
To solve the equation 5x + 5 = 2x + 4, we follow these steps: Step 1: Start by simplifying the equation by getting all terms containing x on one side and constant terms on the other side. Subtract 2x from both sides: 5x – 2x + 5 = 4 This simplifies to: 3x + … Read more
To find the remainder when the polynomial x³ + 4x² + 12x + 9 is divided by x², we can use polynomial long division or simply substitute the variable to evaluate the polynomial’s remainder directly. Since we’re dividing by x², the remainder will be a polynomial of degree less than 2. This means we can … Read more
The given differential equation is: dy/dx = y * e7x To solve this first-order linear differential equation, we can use the technique of separation of variables. The main idea is to rearrange the equation in a way that allows us to separate variables y and x. 1. **Rearranging the equation**: We can separate the variables: … Read more
To find the 24th term of the sequence 3, 8, 13, 18, we first need to identify the pattern or rule that generates this sequence. We can observe that the difference between consecutive terms is consistent. Let’s break it down: 8 – 3 = 5 13 – 8 = 5 18 – 13 = 5 … Read more
To determine the constant of variation k in the direct variation equation of the form y = kx, we need to use the coordinates provided. Given the point (3, 2), we can interpret this as x = 3 and y = 2. We can substitute these values into the equation: y = kx This leads … Read more
To find the quotient of the expression 3×4 divided by 4×2 divided by 8x divided by 1 divided by x divided by 2, we need to break down this operation step by step. 1. **First Step**: Start with the first part of the expression, which is 3×4 divided by 4×2. The division can be expressed … Read more