To simplify the expression 3/x² divided by 1/x³, we first need to understand the mathematical operation involved: The expression can be rewritten using division: 3/x² ÷ 1/x³ Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the division as multiplication: 3/x² × x³/1 Now, we multiply the numerators … Read more
When a ball is dropped from a height of 10 feet, it starts its journey towards the ground due to the force of gravity. Upon reaching the ground, it compresses slightly and then rebounds. However, it doesn’t return to its original height; instead, it bounces back to a fraction of the height from which it … Read more
To find the vertex, focus, directrix, and focal width of the parabola defined by the equation x = 10y, we need to start by rewriting the equation in standard form. The equation x = 10y can be rearranged to y = (1/10)x, which represents a parabola that opens to the right. 1. Vertex The vertex … Read more
Solving the Equation x² + 12x + 5 = 0 by Completing the Square To solve the quadratic equation x² + 12x + 5 = 0 using the completing the square method, follow these steps: Step 1: Move the constant to the other side Start by isolating the x terms. Subtract 5 from both sides: … Read more
To solve the division problem 8x³ ÷ 6x ÷ 2x ÷ 1, the first step is to break down the expression into simpler parts. Starting with 8x³, we will divide it by 6x. Here’s how you can approach the first step: Divide the coefficients: 8 ÷ 6 simplifies to 4/3 or approximately 1.33. Next, divide … Read more
To find out how many feet of yarn you can buy for $0.52 at Ben’s General Store where the yarn costs $0.04 per foot, you can use the following calculation: First, you need to divide the total amount of money you have ($0.52) by the price per foot of yarn ($0.04). The calculation looks like … Read more
To determine the points at which the graph of the function f(x) = x² – 8 has a horizontal tangent line, we need to follow these steps: Find the Derivative: The first step is to find the derivative of the function, which gives us the slope of the tangent line at any given point. For … Read more
To determine whether the function f(x) = x^4 + x^3 is an even function, we need to check the defining property of even functions. An even function is one that satisfies the condition: f(-x) = f(x) for all x in the domain of f. This means that if we replace x with -x in the … Read more
To calculate the rate of interest earned on your investment, you can use the formula for the rate of return: Rate of Return ( ) = rac{(Ending Value – Initial Value)}{Initial Value} imes 100 In this case: Initial Value = $1800 Ending Value = $1924.62 Now, plug in the values: Rate of Return = rac{(1924.62 … Read more
The statement that the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B is false. Let’s break down why this is the case by examining the formulas for the lateral surface areas of both shapes. The lateral surface area of a cone is given by the formula: … Read more