Understanding the Quotient of Polynomials To find the quotient of the polynomial expression x³ + 3x² + 3x + 2 divided by x² + x + 1, we will use polynomial long division. Step 1: Set Up the Division We want to divide: x³ + 3x² + 3x + 2 ÷ x² + x + … Read more
To solve the problem, we need to understand the concept of direct variation. When we say that y varies directly as x, we can express this relationship mathematically as: y = kx where k is a constant of variation. From the problem, we have the following two scenarios: 1. When x = n, y = … Read more
To determine how many triangles can be formed with one angle measuring 95 degrees and another angle being obtuse, let’s start by breaking down the properties of angles in a triangle. In any triangle, the sum of the interior angles must always equal 180 degrees. This means that if you already have one angle of … Read more
To find the other five trigonometric ratios (cosine, tangent, cosecant, secant, and cotangent) from the information given about angle 8, follow these steps: 1. **Understanding Sine**: The sine of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, if … Read more
To calculate the total cost of a pair of jeans that costs $50.00 with a sales tax of 7.5%, you can follow these steps: Convert the sales tax percentage to a decimal: The sales tax rate of 7.5% can be converted to a decimal by dividing by 100. So, 7.5% becomes 0.075. Calculate the sales … Read more
To solve the initial value problem using the Laplace transform, we can follow these steps: Initial Problem Statement: We are given the equation: y” + 5y’ + e4t = 0 Taking the Laplace Transform: Let Y(s) be the Laplace transform of y(t). The Laplace transform of derivatives is as follows: L{y’} = sY(s) – y(0) … Read more
To find the roots of the polynomial equation x3 + x2 + x – 18 = 0, we can utilize several methods, including synthetic division, the Rational Root Theorem, or numerical approaches if necessary. Firstly, it’s good to start with the Rational Root Theorem, which suggests that any rational solution (root) of the polynomial equation, … Read more
To determine how many years ago Sindhu was three times as old as Smita, we can set up the equation based on their current ages. Currently, Sindhu is 40 years old and Smita is 20 years old. Let’s denote the number of years ago we need to find as x. At that time, Sindhu’s age … Read more
Finding the Product 1938 99 To find the product represented by the numbers 1938 and 99, we first need to understand what is meant by ‘product’ in this context. In mathematics, the product is the result of multiplying two numbers. Thus, the product of 1938 and 99 can be determined using basic multiplication. Steps to … Read more