To calculate the length of the curve defined by the equation y = 4×3 – 2x over the interval [0, 1], we need to use the formula for the arc length of a function given by: L = ∫ab √(1 + (dy/dx)2) dx 1. **Find the derivative of y**: The first step is to find … Read more
To find the zeros of the quadratic function f(x) = 9x² + 54x + 19, we can use the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a) In this equation, a, b, and c are the coefficients from the standard form of a quadratic equation, which is ax² + bx + c … Read more
Finding the least common multiple (LCM) of polynomials involves identifying the highest degree of each variable present in the polynomials and the highest coefficients. Let’s break it down step by step for the given polynomials: 9×2, 2x, and 3×2. Step 1: Identify the Polynomials The polynomials we are working with are: 9×2 2x 3×2 Step … Read more
To determine the height of a square pyramid, you can use the formula for the volume of a pyramid: Volume = (1/3) × Base Area × Height For a square pyramid, the base area can be calculated as follows: Base Area = Base Length × Base Length Given that the base length is 4 feet, … Read more
To sum the polynomials 6x³ + 8x + 5 and 3x³ + 6x², we need to combine like terms. Here’s how to do it: First, list out the two polynomials: First polynomial: 6x³ + 8x + 5 Second polynomial: 3x³ + 6x² Now, combine all the terms: 6x³ + 3x³ (for the x³ terms) 6x² … Read more
To determine the value of ‘a’ in the given polynomials, we first need to clarify the two expressions: 2x³ + ax² + 3x + 5 and x³ + x² + 4x + a. Next, we need to analyze these polynomials based on common properties such as degree, leading coefficients, or specific conditions like equality at … Read more
To find the two-digit number based on the given conditions, let’s denote the two-digit number as 10a + b, where a is the tens digit and b is the units digit. 1. The first condition states that the sum of the number and the number obtained by reversing its digits equals 165. So we have: … Read more
Calculating a percentage of a number is a straightforward process. To find a percentage, you’ll need to follow these simple steps: Identify the Number: First, determine the number you want to find the percentage of. For example, let’s say you want to calculate 20% of 50. Convert the Percentage to a Decimal: Convert the percentage … Read more
To simplify the expression 6x² + 3 + 5x³ + 4x³ + 2x² + 8, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. Let’s break down the expression: Terms with x³: 5x³ and 4x³ Terms with x²: 6x² and 2x² Constant terms: 3 … Read more
To evaluate the expression 9 + 2 – 8 + 5 – 2 + 2, we need to perform the arithmetic operations according to the order of operations, which is addition and subtraction in this case. Let’s break it down step by step: Start with the first two numbers: 9 + 2 = 11. Now, … Read more