The third term in the expansion of x26 can be calculated by applying the binomial theorem or by recognizing it as part of a polynomial expansion. If we are to consider the expansion of (a + b) to the power of 26, we need to determine the specific nature of the variables ‘a’ and ‘b’. … Read more
Finding the Maximum Volume of a Rectangular Box Inscribed in a Sphere To find the maximum volume of a rectangular box inscribed in a sphere, you can follow a mathematical approach involving calculus and geometry. Here’s a step-by-step guide to help you understand the process: 1. Understanding the Problem Consider a sphere of radius R. … Read more
To find the equation of the tangent plane to the surface determined by the equation: 7xy + yz + 4xz – 48 = 0 at the specified point (2, 2, 2), we can follow these steps: Determine the function: First, rewrite the equation of the surface in terms of a function: F(x, y, z) = … Read more
To find the greatest common factor (GCF) of the expressions 20×4 and 6×3, we follow a systematic approach involving both the numerical coefficients and the variable components. Step 1: Find the GCF of the numerical coefficients The numerical coefficients here are 20 and 6. We start by determining the factors of each number: Factors of … Read more
To determine the number of terms in the binomial expansion of an expression like (3x)^59, we first need to understand how binomial expansions work. The general binomial expansion for the binomial expression (a + b)^n has n + 1 terms. In our case, we are dealing with (3x + 0)^59, where 3x is a and … Read more
To determine which whole number is on the left of another on a number line, you must first understand how number lines work. A number line is a visual representation of numbers, where numbers increase as you move from left to right. This means that smaller numbers are found on the left side, while larger … Read more
To identify the horizontal asymptote of the function f(x) = (7x + 1) / (2x – 9), we need to analyze the behavior of the function as x approaches infinity (both positive and negative infinity). 1. **Understanding Horizontal Asymptotes**: Horizontal asymptotes describe the behavior of a function as the input values grow very large or … Read more
The function given is y = 2x + 9. To discover the sequence of y values generated by this function, we can substitute different whole number values for x. Let’s calculate the y values for the first few whole numbers: When x = 0: y = 2(0) + 9 = 0 + 9 = 9 … Read more
To solve the equation 2x + 15 = 6x + 9, we can follow these steps: Rearrange the equation: Start by moving all terms involving x to one side of the equation and the constant terms to the other side. We can do this by subtracting 2x from both sides: 2x + 15 – 2x … Read more
To find the equation of a line with a given slope and a point through which it passes, we can use the point-slope form of the equation of a line. The point-slope form is expressed as: y – y1 = m(x – x1) In this formula: m represents the slope of the line. (x1, y1) … Read more