When is a Polynomial in One Variable in Standard Form?
A polynomial in one variable is said to be in standard form when it is expressed as a sum of terms, where each term is a product of a constant coefficient and a variable raised to a non-negative integer exponent. The standard form is typically written in descending order of the exponents of the variable. […]
How to Solve the Differential Equation 14 y” + y’ + 4y = x^2?
To solve the differential equation 14 y” + y’ + 4y = x^2 using the method of undetermined coefficients, we first need to determine the complementary solution and a particular solution. Step 1: Find the Complementary Solution (yc) The characteristic equation is derived from the homogeneous part of the differential equation: 14r2 + r + […]
Choose One of the Factors of x^6 1000
One of the factors of x6 1000 is 1000 itself. But to break it down further, we can factor 1000 as follows: 1000 = 103 10 can be factored further into 21 × 51 This means 1000 can be expressed as: 1000 = (2 × 5)3 = 23 × 53 So, in this case, you […]
The sum of three consecutive even numbers is 48. What is the smallest of these numbers?
To find the smallest of the three consecutive even numbers that sum up to 48, we can start by defining the numbers. Let’s say the smallest even number is represented as x. The next two consecutive even numbers would then be x + 2 and x + 4. Now, we can write the equation for […]
Let f(x) = x^2 + 3x + 7. Find f(3)
To find f(3), we need to substitute 3 into the function f(x) = x² + 3x + 7. So we have: f(3) = (3)² + 3(3) + 7 Calculating this step by step: 1. (3)² = 9 2. 3(3) = 9 Now, we add these results together: f(3) = 9 + 9 + 7 3. […]
Given that f(x) = 5x + 10 and g(x) = x + 3, solve for f(g(x)) when x = 1
To solve for f(g(x)) when x = 1, we first need to calculate g(1). We know g(x) = x + 3. Therefore, when we plug in 1: g(1) = 1 + 3 = 4. Now that we have g(1), we will use this result to find f(g(1)). Since g(1) = 4, we need to find […]
Find Sin if Cot 2 and Cos 0
To find sin given cot and cos values, we can use trigonometric identities. We know that: cot(θ) = 1/tan(θ) tan(θ) = sin(θ)/cos(θ) Now, if we have cot 2, it means: cot(2) = cos(2) / sin(2) From the problem, we need to find sin(2). However, we can also use the following identity: sin²(θ) + cos²(θ) = […]
What is the HCF of 399 and 437 by the Division Method?
To find the highest common factor (HCF) of 399 and 437 using the division method, we follow these steps: Divide the larger number by the smaller number. Here, we divide 437 by 399. Perform the division: 437 ÷ 399 = 1 with a remainder of 38 (since 437 – 399 = 38). Now, replace 437 […]
How do I simplify the expression x² + 15x + 365x + 60?
To simplify the expression x² + 15x + 365x + 60, we first need to combine the like terms. The terms 15x and 365x are both like terms as they both contain the variable x. We can add these terms together: 15x + 365x = 380x So now, our expression looks like this: x² + […]
What is the slope of the line that passes through the points (2, 5) and (1, 4)?
To find the slope of a line that passes through two points, you can use the formula: slope (m) = (y2 – y1) / (x2 – x1) Here, we can assign the points (2, 5) and (1, 4) as follows: (x1, y1) = (2, 5) (x2, y2) = (1, 4) Now substituting the values into […]