devyy The function given is f(x) = x4 + 12. To find the inverse of this function, we need to follow a series of steps. Replace f(x) with y: Start by rewriting the function as: y = x4 + 12 Switch x and y: To find the inverse, we exchange the roles of x and y: … Read more
To find the Highest Common Factor (HCF) and the Least Common Multiple (LCM) of the numbers 396 and 1080 using prime factorization, follow these steps: Step 1: Prime Factorization First, we need to determine the prime factors of each number. Prime Factorization of 396: 1. Start with the smallest prime number, which is 2: 396 … Read more
To find a polynomial with specific roots, we can construct it using the fact that if a number r is a root, then the factor (x – r) is part of the polynomial. In this case, the given roots are: 5 4i -4i Starting with the root 5, the corresponding factor is: (x – 5) … Read more
To find the equation of the tangent line to the curve at the given point (2, 6), we need to follow these steps: Calculate the derivative of the function: The function is given as: y = x³ + 2x + 2 The derivative of this function, which represents the slope of the tangent line at … Read more
To find the GCF (Greatest Common Factor) of the polynomial terms 33×3 and 18×6, we will follow these steps: Identify the coefficients of the terms. The coefficients are the numerical parts, which are 33 and 18. Find the GCF of the numerical coefficients: The factors of 33 are 1, 3, 11, and 33. The factors … Read more
To find the absolute maximum and minimum values of the function f(x, y) = xy² on the given domain defined by the constraints x > 0, y > 0, and x² + y² ≤ 3, follow these steps: Understanding the Domain: The inequalities x > 0 and y > 0 indicate that we are only … Read more
To find the value of y at the point where x = 0 in the equation xy = 3ey, we start by substituting x = 0 into the equation. When we substitute x with 0, the equation becomes: 0 * y = 3e * y Multiplying 0 by any value of y still results in … Read more
The equation of the parabola given is y = 112x². This is a standard form of a parabola that opens upwards. To find the focus and directrix, we first need to rewrite the equation in the standard form of a parabola. The standard form for a parabola that opens upwards is: y = 4p(x – … Read more
To find the values of f(1) and f(2) using the function f(x) = 2x³ + 3x² + 7, we will substitute the values of x into the function. First, let’s calculate f(1): Substituting x = 1 into the function: f(1) = 2(1)³ + 3(1)² + 7 Calculating further: f(1) = 2(1) + 3(1) + 7 … Read more
To determine the approximate value of z for a 72 percent level of confidence in the context of statistics, we begin by understanding what this confidence level represents. A confidence level of 72% means that we are willing to accept a 28% chance of being incorrect in our estimate of a proportion. In statistical terms, … Read more