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To find the equation of the tangent line to the curve defined by y = √x at the given point (36, 6), follow these steps: Step 1: Differentiate the Function The first step is to find the derivative of the function, which gives us the slope of the tangent line. The function is: y = … Read more

The area of a trapezoid can be calculated using the formula: Area = (1/2) * (m + n) * k In this formula, ‘m’ and ‘n’ are the lengths of the two bases of the trapezoid, and ‘k’ is the height (or altitude). To solve for ‘m’, you’ll need to rearrange the formula. Here are … Read more

Multiplying fractions can seem tricky at first, especially when whole numbers and mixed numbers are involved. However, once you understand the process, it becomes a straightforward task! Step-by-Step Guide to Multiplying Fractions with Whole Numbers 1. **Understand the components**: A fraction consists of a numerator (top part) and a denominator (bottom part). A whole number … Read more

Yes, the difference between two rational numbers is always a rational number. To understand why, let’s first define what a rational number is. A rational number is any number that can be expressed as the quotient or fraction a/b, where a is an integer and b is a non-zero integer. For example, 1/2, -3/4, and … Read more

To Compute y and dy To find the values of y and dy using the formula y = 3x + 4x + 1, we first need to calculate y for each x value and then determine dy, which represents the change in y corresponding to a small change in x denoted by dx. The equation … Read more

To solve the system of equations given by x + 2y = 7 and x + 2y = 1, we need to analyze the equations more closely. First, we can observe that both equations have the same left-hand side, x + 2y. This means they represent two different situations for the same expression: From the … Read more

To find the altitude of a right triangle when you only have the length of the hypotenuse, you can follow a few mathematical steps. The process involves using the known relationships in a right triangle and applying the properties of triangles and geometry. Step-by-Step Guide Understand the Right Triangle: In a right triangle, the hypotenuse … Read more

To find the inverse of the function f(x) = 4x + 8, we need to follow a series of systematic steps. The goal is to express the input variable (x) in terms of the output variable (y). Step 1: Start by replacing f(x) with y: y = 4x + 8 Step 2: Next, we need … Read more

To find the value of x, you first need a mathematical equation or expression that includes x. Once you have the equation, you can follow these general steps: Step 1: Isolate the variable: Rearrange the equation to get all the x terms on one side and the constants on the other side. This often involves … Read more

Understanding the End Behavior of f(x) = x5 + 8×4 + 16×3 To analyze the end behavior of the polynomial function f(x) = x5 + 8×4 + 16×3, we need to examine what happens to the value of f(x) as x approaches both positive and negative infinity. General Rules for Polynomial Functions The end behavior … Read more