devyy Finding the Roots of the Polynomial To find the roots of the polynomial equation g(x) = x^2 + 3x + 4x^2 + 4x + 29, we first rewrite the equation in standard form. 1. **Combine Like Terms**: The first step is to combine the like terms in the equation: Combining the terms gives us: x^2 … Read more
The sum of the interior angles of any convex polygon can be calculated using the formula: Sum of interior angles = (n – 2) * 180° Here, n represents the number of sides of the polygon. In the case of a convex 10-sided polygon, we plug in n = 10: Sum of interior angles = … Read more
The number 815,642,120 can be expressed in words using the international numbering system as follows: Eight hundred fifteen million, six hundred forty-two thousand, one hundred twenty. To break it down further: Eight hundred fifteen million: This part represents the first three digits (815) combined with the million place. Six hundred forty-two thousand: The next three … Read more
To find the rate of change of the area of a circle when its circumference is increasing, we can use the relationships between circumference, radius, and area. Step 1: Understand the relationship The circumference C of a circle is given by the formula: C = 2πr where r is the radius. The area A of … Read more
To find the equations of the lines that are parallel to the line given by the equation y = 3x + 5, we first need to understand the characteristics of parallel lines in geometry. Parallel lines have the same slope but different y-intercepts. The equation of the line is expressed in the slope-intercept form, which … Read more
To find the Highest Common Factor (HCF) of 1008 and 1080 using the prime factorization method, we will follow these steps: Prime Factorization of 1008: Divide 1008 by the smallest prime number, which is 2. 1008 ÷ 2 = 504 Continue dividing by 2: 504 ÷ 2 = 252 Again: 252 ÷ 2 = 126 … Read more
To prove the identity xa * xb + 1 = ab * xb + xc + 1 = bc * xc + xa + 1 = ca + 1, we need to analyze each part of the equation step-by-step. Let’s break it down systematically. 1. **Understanding Variables**: In this context, let’s define the variables: xa, … Read more
To find the angles of a triangle when the measures are in an extended ratio such as 3:4:8, you can follow these steps: 1. **Understand the Extended Ratio**: The ratio 3:4:8 means that we can represent the angles of the triangle as 3x, 4x, and 8x, where x is a common multiplier. 2. **Use the … Read more
To find the arc length function for the curve given by y = 2x^{3/2} between the points P(0, 36) and (4, 32), we begin with the formula for arc length: L = ∫_a^b ext{√(1 + (dy/dx)²) dx} where dy/dx is the derivative of the function with respect to x, and [a, b] are the limits … Read more