To find x when f(x) = 12 in the function f(x) = 2x + 8, we start by substituting 12 into the function. That means we set: 2x + 8 = 12 Next, we solve for x as follows: Subtract 8 from both sides: 2x + 8 – 8 = 12 – 8 2x = … Read more
Calculating the Area of a Regular Hexagon A regular hexagon is a six-sided polygon where all sides and angles are equal. To find the area of a regular hexagon, we can use the following formula: Area Formula Area = \\frac{3 \sqrt{3}}{2} s^2 where s represents the length of a side. Step-by-Step Calculation Given that the … Read more
To find the Maclaurin series for the function f(x) = (1 + x)-4, we can utilize the binomial series expansion. The binomial series allows us to express functions in the form of (1 + x)k, where k can be any real number. The general form of the binomial expansion is: (1 + x)k = ∑n=0∞ … Read more
To solve the problem, we first need to understand what it means for x to vary inversely with y. This means that the product of x and y is constant. Mathematically, we can express this as: x * y = k where k is a constant. Initially, we know that x = 4 when y … Read more
To find the present ages of Rahul and Haroon, we can start by using the ratio of their ages. Let the present ages of Rahul and Haroon be represented as: Rahul’s age = 5x Haroon’s age = 7x According to the problem, four years later, the sum of their ages will be 56 years: (5x … Read more
To find the sum of the summation of the expression 3i – 15 from i = 2 to i = 7, follow these steps: First, plug in the values for i from 2 to 7 into the expression 3i – 15. Next, compute the value for each i: For i = 2: 3(2) – 15 … Read more
Graphing the Function y = f(x) = 2x To graph the function y = f(x) = 2x for the range of x from 1 to 4, follow these steps: Step 1: Identify the Values of x We will be focusing on the values: x = 1, x = 2, x = 3, and x = … Read more
To find the zeros of the polynomial function f(x) = 6x³ + 31x² + 4x – 5, we need to determine the values of x for which f(x) = 0. The process of finding the zeros involves several steps: Identify the polynomial: The polynomial we are dealing with is a cubic polynomial. Use the Rational … Read more
To determine the range of the function y = 3x + 4 within the specified domain of 3 to 14, we need to evaluate the function at the endpoints of this domain. The first step is to calculate the value of y when x = 3: y = 3(3) + 4 = 9 + 4 … Read more
To express the compound inequality x < 4 or x > 5 in interval notation, we must break down each part of the inequality. 1. The inequality x < 4 means that all values of x less than 4 are included. In interval notation, this is represented as: (- ∞, 4) This indicates that the ... Read more